CRE Form 2 Best Notes {Updated and Free)

FORM TWO

GOD MEETS US IN JESUS CHRIST

  1. LUKE’S GOSPEL

INTRODUCTION

Matthew, Mark, Luke and John record the life of Jesus Christ and his ministry in the four Gospel books.

We shall trace the life, and ministry of Jesus Christ as written by St Luke to Theophilus. St Luke was amedical doctor.

 

TOPIC ONE: OLD TESTAMENT PROPHESIES ABOUT THE MESSIAH

Introduction: Read 2 Samuel 7:13, Isaiah 7:10-16

Messiah

Meaning: The word Messiah is from a Hebrew word meshiach, which means the anointed: thus a

Messiah is one called, anointed and appointed by God to serve Him.

Prophecy:

A prophecy refers to a prediction of what will happen in future.

Messianic Prophecies: These are those predictions that were made by the prophets to describe thecoming of a righteous King who will rule Israel according to God’s will.

 The origin of the Messianic prophecies in the Bible starts with prophet Nathan’s prophecy to KingDavid.

 

NOTE:

The Roman ruled the Israelites before the birth of Jesus. They hated the Roman leadership and longedfor somebody of their own to lead them into victory over the Roman rule.

The prophet of Israel (the Old Testament) communicated a message that God would send a messiah tobring all people into a lasting relationship with Him. The prophets who were sent had different ideasabout the Messiah. Their ideas about the Messiah were different from the Jewish expectations –whereby they hoped for political King to lead them into victory over the Roman rule. But the prophetswere talking about a religious one – to free them from sin.

 

Topic Outcomes By the end of this topic, you should be able to:

  1. a) Explain the Old Testament prophecies about the coming of the Messiah.
  2. b) Relate the concept of the Messiah in the Old and New testaments.
  3. c) Explain the link between the Old and the New Testament
  4. d) Discuss the role of John the Baptist.

 

LESSON ONE. OLD TESTAMENT PROPHESIES ABOUT THE COMING OF THE MESSIAH.

Learning Outcomes: By the end of this lesson, you should be able to describe prophesies of Nathan,Isaiah, Jeremiah, Psalmist prophecy (David) and Micah concerning the Messiah

(i) NATHAN’S PROPHECY (2 Samuel 7:3 – 17) and (Psalms 89: 20 – 38).

David proposed to build God a house. Nathan, the prophet was given a message (an oracle) for David. Inthis prophecy, God told Nathan to tell King David that:

 God would ensure that the Kingdom of David would last forever.

 an heir from David’s lineage would rule

 David’s heir shall build a house for God’s name. God would establish the throne of his Kingdomforever.

 David heir shall be God’s son and God shall be his father.

 David house and Kingdom shall be established forever.

David died. But God’s mercy shall not depart from the heir of David. Hence the promise that the

Kingdom of David shall last forever refer to the messiah who was to come. David is an ancestor ofChrist.

 

(ii) ISAIAH’S PROPHECY – Isaiah 7: 10 – 16; 9: 1- 7; 61:1 –2; and 63.

In these readings, Isaiah prophesied that the Messiah would be:

 Born of a virgin

 A boy, born of a virgin and called ‘Emmanuel’ that is ” God with us”

 A Wonderful, Counselor, Mighty God, The everlasting Father, and the Prince of Peace.

 The Spirit of God inside him

 Anointed of God

 Sent to preach the good news to the poor, to bring liberty to the captives, proclaim the year of favour7from God.

 Isaiah also prophesied that the Messiah would be the suffering servant (Isaiah 53)

 

CHARACTERISTICS OF THE SUFFERING SERVANT – ISAIAH 53

 He would bear the sins of human kind

 He was oppressed, afflicted, despised, rejected of men

 He bore suffering and disgrace submissively

 He was mocked and spat on and wounded

 He was innocent of sin and yet treated as a criminal.

 He was pierced and wounded in the sides

 He was crucified with thieves and made intercession for the sinners

 He was buried in a rich man’s tomb.

 

iii. JEREMIAH’S PROPHECY- JEREMIAH 23: 5 – 6.

God promised to rise up a (branch) who shall:

 Choose as King, a righteous descendant of David

 Prosper

 Rule wisely, do what is right, and just in the world

 Execute justice on the earth

 Ensure that Judah and Israel are safe and live in peace.

 Be called ‘the God our righteousness” – “The Lord our salvation’

What does the term a ‘righteous branch ‘means?

 

  1. MICAH’S PROPHESY, (MICAH 5: 1 – 5).

Micah prophesied that:

 The Messianic King shall come from Bethlehem

 He shall lead with authority

 He will bring peace

 

 

  1. v. THE PSALMIST PROPHECY (Psalm 41:9 and 110:1 –2).

David spoke of

 Betrayal by a close friend

 Messiah is referred to as ‘ the Lord’

 The messiah shall rule/reign in the midst of enemies.

Summary

Nathan, Isaiah, Jeremiah, Psalmist prophecy (David) and Micah prophesied of a Messiah to come. The

Jews expected a Messiah who would be a political leader, a victorious ruler and a King. They expected a

Messiah:

 Who would lead his people into a time of great national power and prosperity;

 In whose reign, there shall be no illness, no sorrow, no injustice,

 In whose reign, there shall be no fear

 In whose reign, land shall be filled with joy and peace

 Who shall rule forever.

 

Revision questions

1) Describe the prophecy of Jeremiah concerning the Messiah

2) What does the term Messiah mean?

3) Highlight the Jewish expectations of the Messiah in the Old Testament?

4) Did Jesus Christ fulfill the O.T. prophecies concerning the Messiah? How?

5) Which prophets in the Old Testament prophesied about the expected Messiah?

 

LESSON TWO. THE CONCEPT OF THE MESSIAH IN THE NEW TESTAMENT

Learning Outcomes. By the end of this lesson, you should be able to explain the concept of the Messiahin the New Testament

The concept of messiah is found in Luke 1:26 – 38; 2:1-23; 23:1 – 35; 24:50 – 51. The writer of Luke’sGospel makes it clear that Jesus fulfilled the Old Testament prophecies concerning the coming of theMessiah. How did He do this? Well Jesus fulfilled the Old Testament prophecies because;

 Jesus was born from the lineage of David (Mathew 1)

 Angle Gabriel said the child to be born shall rule forever (Luke 1:32) Nathan’s prophecy

 Jesus was born of Mary a Virgin, as pre told by Isaiah 7:14

 Messiah is called Emmanuel, Isaiah’s prophecy. Mathew 1:18 – 25

 Jesus was born in Bethlehem – Micah’s prophecy

 The Messiah would be a ‘Son of David’ – Nathan, and Jeremiah prophesies. Jesus was referred to as a‘Son of David’ (Luke 18:38)

 Jesus would bring salvation said by Simeon during dedication of Jesus. Luke 2:29 – 32. This was afulfillment of Isaiah’s prophecy.

 Jesus referred to himself as the Messiah by reading the scroll. Isaiah 61:1 – 2.and Luke 4: 18 – 19

 Isaiah prophesied that the Messiah would perform miracles. Jesus performed many miracles.

 The prophecy of the suffering servant (Isaiah 53) was fulfilled through the passion, death andcrucifixion of Jesus Christ.

 We see Jesus betrayed by one of his disciples – friend, fulfilling the Psalmist prophecy.

Note that the Jews in the New Testament expected a messiah who would deliver them from the rule ofthe Romans. Jews expected Jesus to be a political leader or king. However, Peter called him ‘the Christ ofGod’ (Luke 9:20). Matthew called him King of the Jews in chapter (2 verse 2). Hence, Jesus came as aSpiritual Leader and King, and not as a political Leader / King.

 

Self-Assessment Questions

  1. What does the name Emmanuel mean?
  2. Explain the concept of the Messiah in the New Testament?

 

LESSON THREE. ANNUNCIATION OF THE BIRTH OF JOHN THE BAPTIST

Introduction

The parents of John the Baptist were Zechariah and his wife Elizabeth. Zechariah’s name meant ‘God hasremembered’. Elizabeth’s name meant ‘God has sworn’.

 

Learning outcomeBy the end of this lesson, you should be able to describe the annunciation of thebirth of John the Baptist and Jesus.

 

John the Baptist

  1. The Annunciation – Read – Luke 1:5 – 25.

Zechariah was a priest. He and his wife Elizabeth were old, good and righteous people of God. But theydid not have a child. They were barren. But God gave them a child, John the Baptist. His birth wasannounced to his father, Zechariah, when he was in the temple offering incense. An Angel appeared toZechariah and told him that his prayers had been heard. His wife Elizabeth will bear a son. The angel saidthe child would be called John, which means that ‘God is gracious’. The child

 will be set aside to serve God.

 will be filled with the Holy Spirit

 

As an adult, John

  • Will be a Nazarite. He should neither cut his hair nor drink wine.
  • Shall turn many hearts of people to the Lord their God.
  • shall also turn the hearts of the fathers to their children

Zachariah expressed unbelief to these words. Angel Gabriel told him that he shall be dumb until thefulfillment of the God’s words.

The Birth, Circumcision and Naming Of John the Baptist

Elizabeth brought forth a son. This brought great joy to her and Zachariah. The cousins, and neighboursof Elizabeth wanted the Child to be named Zechariah after the father. But Elizabeth insisted on thename John. When Zechariah was asked to name the child, he wrote down the name John. On the 8thday, the child was named John as the angel had said. John was circumcised on the 8th day according tothe Jewish traditions.

After naming his Child John, the mouth of Zechariah opened immediately and he started to speak. Hesang a song – referred to as Benedictus in Luke 1:67 – 79. As he sung the Benedictus, Zechariahprophesied that God has:

 Raised up a horn of salvation on the house of David

 Remembered his covenant with Abraham

 

Zechariah said this about his Child John:

 He shall be the prophet of the most high

 The child/John shall prepare the way of the lord by

(i) Calling men to forgiveness

(ii) Showing men the light of salvation

(iii) Guiding people into peace.

 

LESSON FOUR. THE ROLE OF JOHN THE BAPTIST

The role of John the Baptist is found in Isaiah 40: 3 – 5, Malachi 3:1, 4:5 – 6, and

Luke 7: 20 – 35.

Learning Outcomes. By the end of this lesson, you should be able to describe the role of John the Baptistin the Gospel.

John the Baptist had an important role to play according to the Angel who announced his coming birth.

His role was to: .

  • Be a Prophet with qualities of Elijah (see Malachi 3:1, 4:5)
  • Announce the good news to come just like Elijah did.
  • Be the link between the Old Testament and New Testament
  • Prepare the way for the Lord.
  • Announce the coming of God’s reign that was near.
  • Preach a baptism of repentance
  • Baptize with water
  • Introduce people, and his disciples to the Messiah – Jesus Christ.
  • Fulfill the Prophecy of Elijah that a messenger was sent before the coming of the Messiah.

John theBaptist was likened to Elijah.

 

Topic review questions

  1. Outline the qualities of John as described by angel Gabriel to Zechariah
  2. Why was John referred to as the second Elijah?
  3. What lessons do Christians learn from annunciation of the birth of John the Baptist?
  4. Describe the birth of John the Baptist

 

TOPIC TWO: THE INFANCY AND EARLY LIFE OF JESUS – LUKE 1:26 – 38

Learning Outcomes: By the end of this lesson, you should:

  1. Explain events leading to the birth of Jesus
  2. Describe the meeting between Mary and Elizabeth
  3. Describe the birth of Jesus
  4. Explain the dedication of JESUS
  5. Describe Jesus at the Temple

 

  1. Angel Gabriel announces the birth of Jesus. Angel Gabriel said that Mary would conceive and bear achild. Angel Gabriel called Mary ‘the highly favored one’. Mary was an ordinary virgin girl in Galileeengaged to marry Joseph, a descendant of David. The Angel said that Mary will bear

(i) A Son

(ii) CalledJesus (which means God serves.

(iii) The child shall be great

(iv) He shall be called the son of the highest.

(v) He shall be given the throne of his father David

(vi) He shall reign forever

(vii) His kingdom will neverend.

 

Read again and explain what angel Gabriel said concerning the child to be born to Mary?

  1. Mary visits Elizabeth. Luke 1:39-56

Angel Gabriel had told Mary that her cousin Elizabeth was also going to have a child. Mary went to visither. The child in Elizabeth’s womb leaped when Mary greeted Elizabeth. The Holy Spirit revealed toElizabeth that Mary is the mother of her Lord, the Messiah. Mary answered Elizabeth by singing thehymn “The Protector” in Psalm 121:3, The Love of God. Psalm 103:17, 98:3.

 

The Magnificent In this hymn Mary says:

Her soul magnifies the Lord.

The Lord has regarded the poor and those of low estate.

God’s mercy is on them that fear him from generation to generation.

God humbles the proud and mighty, and exalts those of low estate (the lowly)

God has filled the hungry and sent the rich away empty

Through the magnificent, Mary, expresses her joy, gratitude and favour given to her and the world.

  1. The birth of Jesus Christ. Luke.2: 1 – 20

The birth of Jesus took place in Bethlehem, in Judea, during the reign of Augustus Caesar, a RomanEmperor. During that time, Rome was conducting a census of the people / citizens for the purpose ofcollecting taxes. The census was ordered by the emperor to determine payment of taxes. The methodthat Rome was using was counting. Joseph, of the house of David went to his hometown, calledBethlehem; for the census. Jesus was born during this time. He was wrapped in swaddling clothes andlaid in a manger because there was no accommodation in Bethlehem.

The first people to receive the news that a Savior was born were the shepherds. An angel announcedthe birth of the Savior, Christ the lord, to the shepherds. The shepherds went to Bethlehem and saw thechild Jesus. They spread the word concerning what had been told them about the child.

 

How was the annunciation of the birth of Jesus extraordinary?

  1. The dedication of JESUS – LUKE.2: 22 – 38

Like John the Baptist, Jesus was circumcised, and named on the 8th day. He was named Jesus whichmeans ‘the savior’ or Yahweh or save’s. Mary and Joseph observed the Jewish customs according to theLaw of Moses. For her purification and dedication of the child Jesus, Mary brought a pair of turtledovesas an offering. The first born males were dedicated to God as Holy. Simeon took the child up in his armsfor dedication and said that:

“The child is set for the fall and rising of many in Israel. A Sword will pierce Mary’s soul on account of thechild.” Prophet Anna also came to the temple and prophesied that the child shall bring deliverance.

 

 

  1. Jesus at the Temple Luke 2:42 – 52

The parents of Jesus Mary and Joseph went to Jerusalem every year for the feast of the Passover. WhenJesus was 12, he accompanied them to Jerusalem. After the feast the parents went home withoutrealizing that their child, Jesus was not with them. But while on the way, they realized he was notamongst them.

They returned to Jerusalem, and looked for him for 3 days. They found him sitting in the temple;listening and asking teacher’s questions. All those who were in the temple were astonished by hiswisdom and intelligence. It is in the temple that Jesus is revealed, first as a true son of his people andalso as light and salvation for all people. On being questioned by Mary and Joseph, Jesus answered thus:

”Didn’t you know I had to be in my Father’s house, about my Father’s business?” This was an echo ofMalachi 3:1 “the Lord whom you seek will suddenly come to his temple”.

 

Answer these questions

1 Trace occasions when angels appeared to people in the New Testament

2 How did Jesus follow the customs and traditions of the Jewish people?

 

Answers

  1. Occasions when angels appeared to people in the New Testament

(a) Angel appeared to Zechariah to announce birth of John the Baptist

(b) Angel appeared to Mary to announce the birth of Jesus Christ

(c) Angels appeared to the shepherds on the night Jesus was born

(d) Angel appeared to Joseph in a dream warning him to flee to Egypt with the child and Mary

 

  1. How Jesus followed the customs and traditions of the Jewish people

(i) He was named on the 8th day

(ii) He was circumcised on the 8th day

(iii) His parents took him to the temple for the annual cerebrations of the. Passover

(iv) He went to the synagogue

(v) In his dedication as a first male, his parents offered the sacrifices expected from them.

Topic Review Questions

  1. Explain events leading to the birth of Jesus
  2. Describe the meeting between Mary and Elizabeth
  3. Describe the birth of Jesus
  4. Explain the dedication of JESUS
  5. Describe Jesus at the Temple

 

TOPIC THREE: THE GALILEAN MINISTRY – LUKE 3-8

John the Baptist and Jesus Christ

Learning Outcomes: By the end of this topic, you should:

  1. a) Explain the teachings of John the Baptist
  2. b) Describe the baptism and temptation of Jesus and its relevance to Christians today.
  3. c) Give reasons as to why Jesus was rejected at Nazareth
  4. d) Describe the first miracles of Jesus at Capernaum

 

 

LESSON ONE. THE PREACHING OF JOHN THE BAPTIST (Luke3: 1 – 20)

John the Baptist preached about

  1. Baptism of repentance for the forgiveness of sins. Baptism means to dip in water’. Repentance means‘change of heart/mind, turning around. Baptism was a symbol of repentance, which means a totalchange heart/mind, a confession of sins). Baptism of water was a preparation of the baptism of fire andHoly Spirit by Jesus.
  2. He warned people of God’s coming Judgment. The religious leaders stressed outward observance ofthe law rather than inner righteousness. John the Baptist told them to bear fruits worthy of repentance.He told them to live righteous lives and not as hypocrites (brood of vipers). Religious leaders alsoassumed that since they were descendants of Abraham, God would not punish them. He warned themthat God could raise descendants of Abraham from stones.
  3. He announced the coming of the Messiah as Judge. John the Baptist became famous that somethought he is the promised messiah. He however pointed to a messiah who will not baptize with waterbut with the Holy Ghost and fire (Jesus Christ).
  4. He preached on social justice. He taught, emphasized, advised:
  • That those who have should share with those who do not have
  • The need for fairness and honesty for example tax collectors not to collect more than what wasrequired.
  • That soldiers should not to abuse their power by accusing others falsely, robbing. They were told tobe content with their wages.
  1. He condemned King Herod’s immoral behavior. King Herod had married Herodians – his ownbrother’s wife. Herod imprisoned John the Baptist and this led to his death (Luke 3 v.22)

 

 

 

What does the term social justice mean?

Find the answer in (d).

Summary of the teachings of John the Baptist

  • He taught on repentance and forgiveness of sins.
  • He warned people of God’s coming judgment.
  • He announced the coming of the messiah who would be judge.
  • He preached on social justice. Those who have should share with the poor.
  • He emphasized the need for fairness and honesty.
  • He warned against abuse of power by those in power and authority.
  • He condemned taking of bribes, corruption and over taxation.
  • He condemned sexual immorality (adultery).

 

Relevance of the teachings of John the Baptist to Christians today

The teachings challenge Christians to be fair, honest, and just in their dealings with other people.

Christians should avoid being hypocritical to one another.

Christians need to know that God will judgethem for their wrongdoing. Hence Christian should repent their sins sincerely and seek forgiveness.

Christians should warn non-believers of the coming judgment. They should preach against evils withoutfear; and avoid corruption, and sexual immorality. Christians should live together in harmony. Baptismwas important to Christians.

Group Activity: Read Luke and find out how John the Baptist was killed, why and by whom

LESSON TWO. THE BAPTISM OF JESUS AND ITS RELEVANCE TODAY

Learning Outcomes: By the end of this lesson, you should be able to:

  1. Describe the baptism of Jesus Christ
  2. Give reasons why Jesus was baptized
  3. State relevance or the importance of the baptism of Jesus to Christians

 

  1. The baptism of Jesus Christ (Luke 3: 21 – 22)

When Jesus was around 30 years of age, He went to be baptized by John the Baptist. Jesus was the last to be baptized. Although he did not need to repent as He did not sin ; He nevertheless was baptized even though He was without sin.

When he was baptized, the heaven opened and the Holy Ghost descended on Him in the form of a dove. At the same time, a voice from heaven said, “This is my beloved son, in whom I am well pleased”.

  1. Reasons why Jesus was baptized.

He was baptized because:

  1. Jesus wanted to show his approval of John’s Ministry of baptism
  2. Jesus accepted the work of redemption of human kind to be completed through suffering and death
  3. Jesus identified himself with the sinful humankind who needed redemption through baptism
  4. Jesus carried all the sins of humankind (baptized last)
  5. He wanted to carry sins of people/humankind upon himself in order to bring about reconciliation between people and God.
  6. God can confirm to the people that Jesus Christ was the messiah (Ps 2:7)
  7. It was an act of preparing those who were ready to receive the Messiah.
  8. Baptism was a way of fulfilling the Old Testament prophecy.
  9. Relevance or the Importance of the baptism of Jesus to Christians

 

  1. Christians practice baptism. They follow example of Jesus baptism. There are many forms of baptism such as full immersion in water, sprinkling of water on the forehead, partial immersion (head only) and passing under a flag.
  2. Christians teach importance of baptism. It qualifies a new convert to become a member of Christian fellowship.
  3. Through baptism, Christians receive the power of the Holy Ghost.
  4. Through baptism, Christians identify themselves with Jesus Christ and all that he stands for.
  5. Baptism unites Christians in the body of Christ.
  6. Baptism is a symbol of death and resurrection. In some denominations, the baptized are given new names of other Christians and Jews.
  7. Baptism signifies the forgiveness of sinsthrough baptism one is considered a child of God.
  8. Baptism is a form of preparation for the kingdom of God.
  9. Baptism is a sign of Christ’s forgiveness of sins.

Lesson Revision questions

  1. What is the relevance of john the Baptist teaching to Christians today?
  2. Give reasons why Jesus accepted to be baptized
  3. Describe the baptism of Jesus
  4. What is the significance of the baptism of Jesus to Christians today

 

LESSON THREE. TEMPTATIONS OF JESUS: RELEVANCE TO CHRISTIANS TODAY

Learning Outcomes. By the end of the lesson, you should

  1. Narrate temptations of Jesus
  2. State relevance of the temptations of Jesus to modern Christians
  3. State lessons that Christians can learn from temptations of Jesus

 

  1. The temptations of Jesus (Luke 4:1 – 13).

Jesus, full of the Holy Spirit returned from Jordan into the  desert. Like Elijah, Moses, He ate and drunk nothing for 40 days and nights. He was hungry after 40 days.

It is at this time of weakness when the devil tempted Him.

 

First temptation.

The devil told Jesus to proof that He was the Son of God by turning the stones to become bread. Jesus however replied that it is written man does not live on bread alone to sustain him but on everything that the Lord says (Deut 8:3). Satan was telling Jesus to use his Messianic power and Spirit to obtain material security for himself and his followers for selfish, materialistic purposes.

 

What can we learn from this temptation?

Jesus was not seeking to establish a material paradise on earth.

 

Second temptation.

The devil led Jesus up to a high place (High Mountain) and showed Him in an instant all the Kingdoms of the world. He told Him that he would give Him all their authority and splendor, if He bows and worships Satan. Jesus replied… it is written worship the Lord your God and serve him only. Do not worship other gods (Deut.6: 13-14). Satan wanted Jesus to use Godly power and influence. This was idolatry i.e. worshipping other gods.

 

What can we learn from this temptation?

Jesus did not come to seek a worldwide political military reign as many Jews expected Him to do.

 

Third Temptation.

The Devil led Jesus to Jerusalem and had Him stand on the highest point of the temple. He told Jesus to throw Himself down if He was the Son of God for it is written that the Lord will

command angels to guard him (Psalm 91:11 – 12). Jesus replied and said it is written, do not put the Lord your God to the test. Satan wanted Jesus to presume on God’s good care by jumping from the roof of the temple.

 

 

What can we learn from this temptation?

Jesus will not force belief in His Messiah ship through aspectacular sign.

Notice that the temptations came after Jesus’ Baptism, where he had solemnly accepted the opening of his public ministry and God confirmed it. Therefore the temptations were a testing of his loyalty to God’s chosen way of life.

 

  1. Relevance of Jesus temptations to Christians

Jesus, though without sin was tempted. His followers must expect to be tested in their faith. Christians learn that it is not sinful to be tempted. Since Jesus was tempted, he understands Christian’s difficulties when they are tempted. Jesus is always ready to help Christians to cope with temptations.

 

Why do you think Christians are tempted?

Through temptations and trials, Christian’s faith in God is strengthened. Christians learn to refer to the Bible for guidance when tempted. Jesus said that it is written… in reference to scripture. Christians should seek the Holy Spirit to give them strength to fight any form of trials and temptations.

Jesus, full of the Holy Spirit went to the wilderness and was tempted by the devil……………” In

temptation, God does provide a way out. Thus followers of Jesus Christ (Christians) should not be seekers of spectacular signs.

 

LESSON FOUR. REJECTION OF JESUS AT NAZARETH

Learning Outcomes. By the end of the lesson, you should

  1. Describe rejection of Jesus at Nazareth
  2. Suggest possible reasons for rejection

 

  1. Rejection of Jesus at Nazareth (Luke 4:14 – 30).

After the temptation, Jesus went to Galilee, His home district to begin his ministry. As a faithful Israelite, Jesus attended service in the synagogue every Sabbath day. During that time, it was customary for visiting Rabbis (Teachers of the law) to be given the honor of reading from the law or to address the congregation. When Jesus was given this opportunity, He opened the scroll and read from Isaiah 61: 1 – 3 …’The Sovereign Lord has filled me with his spirit. He has chosen me and sent me.’ Luke writes in 4 v 18 “ The Spirit of the Lord is upon me, because he has chosen me to bring good news to the poor”. On completion of the reading, Jesus told them that today this scripture has been fulfilled in their hearing.

From this reading Jesus referred to himself as the Messiah. The people of Nazareth in indignation wanted to kill Jesus by throwing him over a cliff.

 

  1. Possible Reasons for Rejection.

Jews of Nazareth rejected Jesus because one, they knew him as theson of Mary and Joseph. They did not know Him as the Son of God. Two, Jesus did not fit into the idea of a political King that the Jews were expecting. They were waiting for a King with an army and horses.

Three, Jesus preaching was seen as being against that of Pharisees, Scribes and Sadducees: the religious leaders at that time. Four, Jesus pointed out evils of religious leaders. Five, a leader is never accepted at home especially in a superior or senior position. Six, Jesus did not follow the general rules of the Mosaic Law. These were fasting, healing and working on the Sabbath day. Worse still Jesus associated Himself with Jewish outcasts such as sinners, and the sick.

 

 

Discussion question

  1. What are the possible reasons for rejection of Jesus at Nazareth?

Answers

(i) He was known by people as son of Mary and Joseph

(ii) He did not fit in the idea of a political king that Jews were expecting

(iii) Often times one is not accepted at home and at a senior position

(iv) He did not follow the general rules of the law of Moses

(v) He associated with sinners, and outcasts

 

LESSON FIVE. HEALING AT CAPERNAUM

Learning Outcomes. By the end of this lesson:

  1. Describe Jesus’ healing at Capernaum
  2. Explain healing of a man possessed with an evil spirit
  3. Describe Jesus healing of Simon’s mother – in law

 

  1. Jesus’ healing at Capernaum LK. 4:31 – 44

After his rejection in Nazareth and an attempt to throw him down a hill, Jesus went on to Capernaum. Here he cast out demons (Luke 4: 40 – 41). He was teaching people. He performed many miracles of healing. For example:

  1. Healing a man possessed by an evil spirit. A man was possessed by an unclean demon/spirit. He was in the synagogue. When he saw Jesus, the evil spirit shouted, “Ah! What do you want with us, Jesus of Nazareth? Have you come to destroy us? I know who you are, the Holy one of God” (Luke 4:34). Jesus replied, “Be silent and come out of him.” The Demon threw the man down and came out without doing any harm. The man was made whole.

 

  1. Jesus heals Simon’s mother – in law. After Jesus left the synagogue, he went to the house of Simon Peter’s mother in law. She had a fever, Jesus commanded the fever to leave and she was made whole immediately.

 

 

Which lessons do Christians learn from the healings at Capernaum

There are many lessons. These are that

1) Jesus is the son of God

2) Jesus came to establish the Kingdom of God and destroy the kingdom of Satan.

3) Jesus has power over evil spirits / demons.

4) Jesus came to save human beings from the slavery of sin

5) God cares for his people.

 

 

 

 

LESSON SIX. THE CALLING OF THE FIRST DISCIPLES Luke 5: 1 – 11

Introduction:

A disciple is a learner, a student or a follower. Learners followed a master so as to learn about religious matters. Disciples were followers of Christ.

 

 

 

Learning Outcomes.

By the end of the lesson, you should be able to describe the call of the first disciples. Rabbis. These were teachers of law. They had special schools where they taught law. In these schools, learning was by memorization and repetition what students heard from the rabbis.

The disciples of Jesus did not memorize. They learnt by observation. They were witnesses – and they spoke what they heard and described or explained what they saw.

 

Call of the first disciples

Jesus entered into Simon’s ship and started to teach people who were there. Later, He told Simon to “push off a little from the shore”. Jesus sat in the boat and taught the crowd. After speaking, he told Simon, and his partners James and John; “Push the boat out further to the deep water…and let down your nets for a catch of fish”. Simon told Jesus that they had toiled all night, and caught nothing. But if you say so, I will let down the nets. Simon obeyed. They let down the nets and caught a multitude of fish. They called for assistance from other fishermen. When Simon Peter saw this, he told Jesus “Go away from me, Lord! I am a sinful man!” Jesus said to Simon “Don’t be afraid, from now on you will be catching people”. On getting to the shore, Peter and his friends James and John sons of Zebedee forsook all and followed Jesus

Thus the first disciples of Jesus were Simon Peter; James and John.

 

Lessons from the call of the first disciples

1) God can choose anybody to serve him regardless of his or her social status.

2) God still calls people to serve him in various capacities as evangelists, pastors and others.

3) Those called should repent their sins as Peter did

4) Christians should trust in God – Simon Peter trusted Jesus and cast his nets even though they had caught no fish from the same spot.

5) God can intervene in people’s lives through miracles (miraculous catch of fish)

6) Christians should work together as a team. Fishermen worked together.

7) There is hope for those who follow Jesus. He told them ‘follow me and I will make you fishers of men’ God reveals himself to people in everyday activities as Jesus revealed himself to Simon Peter, and his friends James and John through fishing.

9) Christian’s vocation may require renunciation of family ties and occupations or a change of life.

10) Those called to serve God are expected to be humble

 

LESSON SEVEN. OPPOSITION IN GALILEE

Learning Outcomes. By the end of the lesson, you should

  1. Describe the Pharisees? Scribes?Sadducees.
  2. Identify the differences between the Pharisees and the Sadducees.
  3. Explain why Jesus faced opposition from Pharisees, Sadducees, and Scribes

Jesus ministry consisted of teaching, healing and doing many miracles. Because of this work, Jesus faced opposition from the Pharisees, Sadducees and Scribes. These were Jewish religious leaders.

  1. Opposition by Pharisees and Sadducees. Luke 5:12- 6:11

Why did Jewish religious leaders; the Pharisees? Scribes? Sadducees oppose Jesus? There were many reasons for Jewish opposition to Jesus. These were:

 

1) Jesus was becoming more famous than the religious leaders

2) His claim to forgive sins. This was reserved only for God.

3) His association with tax collectors / publicans and sinners. For example, Jesus ate with Levi.

4) His failure to observe the law of fasting. Jesus disciples did not fast like the disciples of the Pharisees and John the Baptist.

5) Doing what religious leaders regarded as unlawful things on the Sabbath day. For example,

  1. Eating on Sabbath with unwashed hands (disciples),
  2. Plucking corn on the Sabbath day
  3. Working. Jesus healed on the Sabbath day. This was considered as work, which was unlawful. Jesus healed a man with a paralyzed hand on the Sabbath day.
  4. Touching the unclean. Jesus reached out his hand and touched a leper and healed him. Religious leaders were not allowed to touch the unclean lepers.
  5. Associating with tax collectors who were regarded as sinners because they were corrupt. They

collected more tax than the required amount. Jesus was supposed not to associate with them or support them in any way.

 

Who were the Pharisees? These were

 Referred to as the ‘separated ones’

 Religious leaders who expected people to respect and honour them.

 Pious leaders and wanted everybody to recognize them.

 Rich Jews and looked at their riches as blessings from God.

 Called ones and thought of themselves as the ‘righteous’ ones.

 Popular to the poor who respected them.

 

Characteristics of Pharisees

  1. They believed in the Law of Moses and accepted the first five books of the Bible as God inspired. They insisted on strict observance of the law.
  2. They upheld and insisted on the observance of the oral traditions of the elders.
  3. They followed strictly 632 distinct rules and regulations broken down from the ten commandments
  4. They believed in the teachings of the prophets and other writings of the Old Testament.
  5. They passed religious traditions of the Jews from generation to generation and regarded this as a duty or obligation.
  6. They believed in the existence of angels and regarded them as intermediaries between God and human beings.
  7. They believed in the existence of demons and Satan
  8. They believed in and waited for the Messiah of God to come
  9. The believed in the resurrection of the dead
  10. The believed in the judgment of God at the end of time for all human kind
  11. They were strong nationalists and political leaders who resisted all foreign influences and power.

 

Who were the Scribes?

The word Scribe means ‘a writer. The work of a scribe was to rewrite by hand – new manuscripts of the

Jewish scriptures. The copied the word exactly as it was. The scribes were either Pharisees or Sadducees.

At the time of Jesus, majority of the Scribes were associated with the Pharisees. A scribe was also a ‘Rabbi’ – teacher. Some scribes managed schools called ‘Rabbinical Schools’. In these schools, Jewish male youth learnt the Mosaic Law from the age of 13 years. Scribes were represented in the Jewish religious council called the Sanhedrin. Sanhedrin was the Jewish Court of Justice, which tried those who committed religious sins.

 

Who were the Sadducees?

Sadducees were the wealthy people. They were an influential group. These were the majority in the Sanhedrin, the Jewish Court of Justice. The poor hated them. They were also members of the Jerusalem priesthood. The chief priests were mainly drawn from the Sadducees. They believed in the divine authority of the Law of Moses and the Pentateuch’s first five Books of the bible. They believed that Moses wrote the first 5 books of the Bible. They regarded all the other books in the Old Testament as not divinely inspired. Hence they rejected them. They rejected and did not believe in

(a) The resurrection of the dead

(b) Last judgment

(c) Coming of the Messiah

(d) Angels and demons and

(e) theoral traditions of the Pharisees.

They were enemies of the Pharisees particularly because of religious matters. However, they joined with the Pharisees and Scribes to oppose Jesus Christ.

 

LESSON EIGHT. THE SERMON ON THE PLAIN (Luke. 6:12–16, 27– 49)

Review

In the previous section, we learnt that Jesus chose His apostles. He came down the hill and stood on a level place. He gave a sermon to those present. This address is referred to as the sermon on the plain in Luke’s Gospel.

The people had come to hear Jesus’ word to receive healing and for Jesus to exercise unclean spirits from them. In the sermon, Jesus talked of the characteristics of the new community. All those who would listen to His word would be the “New Israel”.

 

Learning Outcomes. By the end of the lesson, you should be able to

(a) Name the12 disciples

(b) Summarize the teachings of Jesus on true discipleship

 

Analyse the teachings of Jesus on the plain (sermon on the plain)

Selection of 12 disciples (Luke. 6:12 – 16)

Jesus went into a mountain to pray. In the morning, he called his disciples. From them, he selected 12 disciples, whom he also called apostles. Apostle means one who is sent, a missionary. The 12 disciples were:

(1) Simon Peter

(2) Andrew

(3) James

(4) John

(5) Phillip

(6) Bartholomew

(7) Mathew (Levi)

(8)

Thomas

(9) James son of Alphaeus

(10) Simon who was called the Patriot

(11) Judas son of James and

(12) Judas Iscariot who became the traitor (Luke vs. 14-16)

 

Jesus teachings’ on true discipleship

Jesus taught that a follower or disciple of Christ should:

(a) Have unshakeable faith

(b) Be obedient to God’s word

(c) Be self-critical/analytical/self-searching

(d) Be kind, loyal, objective, fair, and generous

(e) Accept others without discrimination.

(f) Be a disciple and show concern for others.

 

The Sermon on the plain (Luke 6: 17 – 49)

The Sermon on the plain is a lecture or lesson that Jesus gave to “ a large number of his disciples and a large crowd of people who had come from Judea, Jerusalem, tyre, and Sidon. They came to listen to the sermon of Jesus and to be healed of diseases, evil sprits. The purpose of the sermon was to teach the crowd the meaning of following Christ. Jesus covered 6 beatitudes or topics in his sermon. These are.

1) Blessings and woes – beatitudes

(2) Love for enemies

(3) Judging others

(4) Giving to the needy

(5) A tree and its fruits

(6) Wise and foolish builders – hearing and doing the words of Jesus.

 

We shall now discuss each of these beatitudes in detail.

  1. Blessings and woes. Jesus taught that:

(i) Blessed are the poor for theirs is the Kingdom of God.

(ii) Blessed are the hungry for they shall be filled

(iii) Blessed are those who weep now for they shall laugh

(iv) Blessed are those who men shall hate, reject, reproach for the sake of Christ’s for their great reward is kept in heaven.

(v) Woe to those who are rich, for they have already received their reward.

(vi) Woe to those who are full for they shall go hungry

(vii) Woe to those who laugh now for they shall mourn and weep

(viii) Woe to those whom people speak well, for ancestors said the same about the false prophets.

Those who accept to be followers of Christ are promised blessings while those who reject Christ are to suffer in future.

 

  1. Love your enemies. Luke. 6: 27 – 36.

Love is often defined as a warm feeling / affection towards somebody or something. Jesus taught his followers to love their enemies and do well to those who hate you. Bless those who curse you. Pray for those who mistreat you. Do unto men as you expect them to do unto you. Lend also to your enemies.

Love your enemies and do good to them. Lend and expect nothing back. Be merciful.

From these teachings: true discipleship of Jesus Christ:

  1. a) Entails unconditional love even for enemies
  2. b) Doing good without expecting any returns
  3. c) Praying for those who mistreat us
  4. d) Showing love to our enemies by exhibiting God’s love in us.
  5. e) Is love; because those who love are children of the most high who is kind and merciful to the sinners.

 

(3) Judging others Luke. 6: 37– 42

Jesus taught his followers not to judge others lest they are also judged. They should not condemn others lest they are also condemned. He asked disciples to forgive others and they shall also be forgiven. True discipleship requires acknowledging one’s shortcomings and avoiding criticism of others.

(4) Giving to the needy.

A true disciple should share what they have with the needy. Those who share shall be rewarded. He also said that the blind couldn’t lead the blind. There is a master and a follower. The disciple is not above his master.

(5) A tree and its fruits.

A healthy tree bears good fruits. A poor tree bears poor fruit. Neither does a corrupt tree bring forth good fruits. A tree is known by its fruits. Followers of Christ are evident to others by their actions. They are not hypocritical or fault finding.

(6) Wise and foolish builders.

A wise builder digs a deep foundation on a rock. When floods come, the house is able to stand. A foolish builder builds his house upon the sand. Without a foundation, when floods come, the house falls and is ruined. Wise builders are those who hear the word of God and do what is required. Those who do not adhere to the teachings are the unwise builders. True discipleship entails obedience to the teachings of  Jesus Christ.

 

Relevance of the lessons of the Sermon on the Plain to Christian Life

Christians are urged to love even those that hate them. The challenges that followers of Christ encountered in the New Testament are not different from those that Christians experience today.

Christians should forgive others, share with the needy, avoid judging others, and follow the teachings of Christ.

Lesson Revision questions

  1. Give the main teaching of Jesus on the sermon on the plain
  2. What is the relevance of the (beatitudes) sermon on the plain to Christians today?

 

 

 

 

LESSON NINE. JESUS’ WORKS OF COMPASSION

In this lesson, Jesus’ works of compassion is discussed. These include the works of mercy for those in distress and pity for the suffering. Jesus’ mission lays its foundation in these works of compassion, because He came to establish the kingdom of God by conquering all forms of suffering caused by Satan.

Compassion is a feeling of empathy for other people’s sufferings. It’s being merciful, showing concern and affection for others.

 

Learning Outcomes. By the end of this lesson, you should be able to:

  1. a) Give examples of Jesus works of compassion
  2. b) Narrate Jesus works of compassion
  3. c) Give reasons why Jesus used parables
  4. d) Identify categories of the miracles of Jesus
  5. e) Give lessons learnt from each example in each category

 

  1. a. Examples of Jesus works of compassion. There are many examples of compassion
  2. i) Healing of the centurion’s servant (Luke 7:1 – 10)

Centurion is an officer in charge of 100 men. Jesus healed the servant of a Roman soldier and a Gentile. The Centurion showed love and concern for his servant. The centurion sent Jewish elders to Jesus with a request to heal his servant. The leaders said ‘this man deserves to have you do this, because he loves our nation and has built our synagogue’ (Luke 7:5). Jesus agreed and went with the elders. But before Jesus reached the centurion’s house, the centurion sent his friends to stop him from coming to his house. He said that he was not worthy to have Jesus under his roof. He said that he was a man of authority. Hence Jesus could give an order and the servant would be healed. On hearing this, Jesus declared to the crowd ‘I tell you, I have not found such great faith even in Israel’. When the men returned, they found the servant well.

 

Lessons Christians can learn from the healing of the centurion servant.

  1. Faith in God is important for healing to occur
  2. We should confess our faith in Jesus. The centurion declared his faith in Jesus by saying he believed that Jesus could heal his servant by his word.
  3. Christians should have compassion like Jesus. He took compassion on the servant and was ready to go and heal him.
  4. Salvation was not for Jews alone, but for all who believed in Jesus. Centurion was not a Jew but a gentile officer in the Roman army. But he had faith in Jesus healing.
  5. Christians should love each other regardless of their background or social status – the centurion loved his servant dearly.
  6. Christians should learn to relate well with all around them – the centurion related well with the Jewish elders and others.
  7. Jesus has power to heal any form of sickness.
  8. ii) The raising of the widows son – Luke 7:11 – 17.

A widow is a woman whose husband is dead. The widow was of the city of Nain. When Jesus neared the gates of the city, he saw the funeral procession of the widow’s son, the only son of his mother. Jesus had compassion on the widow and told her ‘ weepnot’. Jesus then touched the casket and said ‘young man I say unto you, arise’. The dead sat up and began to speak. All the people were filled with fear and glorified God, saying God has visited his people.

Lessons Christians learn from the raising of the widow’s son

1) Jesus has power over death

2) Jesus empathizes with the suffering

3) Acts of love should not be hindered by traditions – Jesus touched the casket even though Jewish traditions forbid it.

4) The Widow of Nain was a gentile. This is a sign that salvation was universal.

5) The crowd acknowledged Jesus’ lordship; Christians should acknowledge the lordship of Jesus.

What are the practices pertaining to the disposal of the dead in your culture? and community?

 

iii) Assurance to John the Baptist (Luke 7:20 – 30).

A question arose whether Jesus Christ was the Messiah. John the Baptist wanted to assure his disciples that Christ; was the expected messiah: and not him (John the Baptist). He sent his disciples to Jesus to ask “if you are the one he said was going to come, or if we should expect someone else?” (Vs. 20). Jesus told the disciples of John to go back and tell John of the miracles works they saw and heard. Jesus then gave a testimony of John the Baptist as a prophet, whose life and missions is beyond that of ordinary prophets. Jesus testified that John the Baptist; was the forerunner or messenger of Jesus Christ: as the prophets in the Old Testament had written. The Pharisees and the publicans (teaches of the law) however rejected the testimony about John the Baptist. They had refused to be baptized by John. Those baptized by John the Baptist, the tax collectors acknowledged the testimony of Jesus. Jesus rebuked the Pharisees and teachers of law for their hypocrisy.

In what ways were the Pharisees and teaches of law hypocritical?

 

  1. iv) The forgiveness of the sinful woman (Luke 7: 36 – 50)

Jesus was invited by one of the Pharisees called Simon to his house to dine with him. In that city, there was a sinful woman. She went to the house of Simon when she learnt that Jesus was in the Pharisees house. She brought with her an alabaster jar full of perfume. She stood behind Jesus. She was weeping and washing his feet with her fears. She then wiped the tears from the feet of Jesus with her hair, kissed his feet, and anointed them with oil (an alabaster box of ointment). When Simon, the host saw this he said within himself, ‘if this man was a prophet, he would know who this woman is who is touching him” a sinful woman. Jesus told Simon a parable of a man who forgave two people that owed him money one 500, the other 50. Jesus asked which of the two debtors would love him most. Simon said the one that was forgiven much, Jesus then told Simon that when he came to his house, Simon did not give him water for his feet; neither did he welcome Jesus with a kiss; nor provide him with olive oil. But the woman washed his feet with her tears, and wiped them with her hair. She also kissed his feet. Jesus told the people that her sins, being many are forgiven for she loved much. Jesus turned to the woman and told her ‘thy sins are forgiven’. ‘Thy faith has saved thee, go in peace’. The people who were eating with

Jesus murmured. Who was Jesus? He forgives sins.

 

Lessons from the forgiveness of the sinful woman

  1. The Jews believed that by associating with sinners, one becomes virtually defiled. Jesus however allowed the sinful woman to touch him.
  2. By her actions, the woman acknowledged that she was a sinner, and repented. This was in contrast tothe Pharisees who were self-righteous and therefore did not repent.
  3. The Woman’s great love for Jesus led to her being forgiven of her sins.
  4. Christians need to accept their sinful nature and seek forgiveness from God.
  5. Faith in Jesus is necessary.

Summary.

Jesus is accepted women to be his followers unlike the Jewish customs which viewed women as lesser than men. Other women that played a key role in the ministry of Jesus include Mary Magdalene, Joann Joanna and Susanna among many others.

 

Lesson Revision questions

  1. What role do women play in the church ministry?
  2. Narrate the story of the forgiveness of the sinful woman (Lk 7: 36, 8:3)
  3. What lessons do you learn from the above story?
  4. Describe the story of the raising of the widow’s son at Nain (Lk 7: 11-17)

Answers

Women play many roles in the church ministry. Some of these are:

(i) Carrying out duties of pastors, bishops, and deacons

(ii) Management. Some are heads of the women groups

(iii) Leading in church service

(iv) Participating as church ushers, choir singers, and youth leaders

(v) Attending church. Women are part of the congregations

 

LESSON TEN. JESUS TEACHING IN PARABLES (LK. 8: 4- 21)

Introduction

Jesus used parables to teach. A parable is a Greek word. It means comparing or ‘putting side by side’ in order to understand. A parable is defined as a short story or description, which teaches something or answers some questions. It is an allegory – an earthly story with a hidden or heavenly meaning.

 

  1. Use of parables.

Jesus used parables in his teachings in order to explain unfamiliar messages in a language that his hearers could understand. Other reasons were because Jesus wanted to:

1) Provoke critical thinking

2) Make the audience understand issues from a different point of view

3) Explain the nature of the kingdom of God by giving real life examples.

4) Explain the nature of God. The parables brought out the attributes of an invisible God. For example, the parable of the prodigal son who had been lost.

5) Attract the attention of his audiences so that they could listen and understand.

6) Make people understand how they should relate to one another. Read the parable of the good

Samaritan

7) Teach God’s love to mankind. The parable of the lost sheep, lost coin.

Separate / identify those who were sincere in seeking the kingdom of God from the onlookers.

9) Challenge the imagination of his hearers since entry to God’s kingdom was a personal decision.

10) Make an indirect attack on his opponents like the Pharisees, the scribes and the Sadducees.

11) Teach his disciples that they should be persistent and never be discouraged.

12) Make his teachings interesting and easy to understand.

  1. 1. The parable of the sower Lk 8:4 – 15

Jesus told this parable to the crowd that followed him. He said that a farmer went out to sow corn. He scattered seeds in the field. As he did so, some of them fell on the path, and they were trampled on and eaten by birds. Other seeds fell on the rock ground. When they germinated, they withered because they lacked moisture. Some seed fell among thorns bushes. They grew with bushes, which choked them as they grew. Some other seeds fell on fertile soil. They grew up in fertile soil and their yield was100 seed for each seed sown.

 

Meaning or interpretation of the parable

Jesus gave the meaning of the parable to his disciples. He said that the seed is the word of God.

  1. Seed that fell on the path represents people who hear the word of God, and then the devil comes and takes away the word from their hearts so that they do not believe. Such listeners are like the seeds that fell on the path. They hear the word but soon after the devil takes away the message to stop them from believing and being saved.

 

  1. Seed that fell on the rocky ground are people who receive the word with joy but it does not stay with them. They believe for a while but when faced with trials and temptations they stop believing and fall away.

 

  • Seed that fell on the thorny bushes stands for people who receive the word. However, they fail to follow their beliefs because of interference by life’s worries, riches and pressures of the world. They failto mature as believers.

 

  1. Seed that fell on the good soil are those people with a noble and good heart. They hear the word, andretain it in their hearts. Such people persevere and produce good harvest.

 

  1. The different types of soil in this parable refer to different kinds of Hearts of people.The farmer is Jesus, God or Preacher.

 

 

We learn that:

 One should not despair and

 It’s important to receive the word of God, practice it and persevere so as to bear fruits.

 

  1. The parable of a lamp under a bowl (Lk.8: 16 – 18).

Jesus taught that no one lights a lamp, then covers it with a bowl or hide it under a bed. When one lights a lamp, they put it on the lamp stand so as to illuminate a room and for people to see the light. For whatever is hidden or covered up shall be revealed. In this parable Jesus is the light. The disciples had a duty to pass on to others messages they had learnt from Jesus. They should not keep messages to themselves.

Interpretation.

From this parable of a lamp under a bowl, we learn that:

i A Christian has a duty to share the knowledge of God with others

ii One cannot be a Christian if this knowledge is hidden

iii Those who do not share may loose their beliefs.

  1. Jesus mother and brothers. Luke 8:19 – 21

The mother of Jesus and brothers came to see him. Someone told Jesus that they were there. He told the crowd. “My mother and brothers are those who hear the word of God and obey “. Accepters and believers are the members of the family of Jesus.

Lesson Revision Questions

  1. Give reasons why Jesus used parables
  2. Identify various methods used by Christians in spreading the gospel today
  3. Discuss the reasons why Jesus faced opposition fro the Jewish leaders.

 

LESSON ELEVEN: MIGHTY WORKS OF JESUS

Learning outcomes. By the end of this lesson

  1. Organise in categories miracles performed by Jesus
  2. Narrate each miracle
  3. Discuss the significance of the miracle and lessons to learn

Jesus continued to do miracles; and teach. His work is referred to as the mighty works of Jesus in various books. Miracles can be defined as acts of power whose purpose is to establish the kingdom of God.

 

Miracles can also mean extraordinary events that go against the laws of nature.

  1. a. Categories / types of miracles

Jesus performed four types of miracles. These were:

1) Nature miracles – miracles that dealt with nature e.g. calming of the storm

2) Raising of the dead e.g. Jairus daughter

3) Healing miracles – healing Simon’s mother in law of fever, healing of the woman with the flow of blood.

4) Exorcism miracles – casting out of evil spirits e.g. the Gerasene demonic

  1. i) The calming of the storm

One day, Jesus entered a boat with his disciples to go across Lake Galilee. As they sailed Jesus was asleep in the ship. Suddenly, there was a strong wind and the boat began to sink. The disciples woke him up saying, “ Master, we are about to die”. Jesus woke up and gave an order to the winds and the raging waters. They obeyed and there was calm. He then said to his disciples ‘where is your faith?’ Disciples were afraid and amazed and wondered, “Who is this man?” Winds and waves obey him.

This miracle teaches Christians to have faith and to depend on Jesus when they face raging temptations and persecutions. Jesus has power over nature.

 

 

 

  1. ii) Jesus Heals a Man with demons (Lk8: 26 – 39)

Jesus and his disciples sailed to Gerasa town across Lake Galilee. On arrival a man who had demons in him for a long time met Jesus. He lived naked in tombs, and wilderness. On seeing Jesus, he cried out, threw himself down at the feet of Jesus and shouted; “Jesus son of the Most High God! What do you want with me?” ” I beseech thee, torment me not’. Jesus had ordered the demons to go out of him.

Jesus asked him “what is your name?” He replied Legion or Mob. This was because the man had been possessed by many demons. The demons begged Jesus not to send them into the deep but to let themgo into some pigs (swine) that were feeding by. Jesus allowed them and the devils went out of the man,into the pigs. The herd ran down the cliff into the lake and drowned. The herders run to the city and spread the news. The multitude found the man sitting at the feet of Jesus clothed, and in his right mind.

The multitude asked Jesus to leave their country region. The healed man wanted to follow Jesus but Jesus declined and told him to go and tell others of the great things that God had done for him. The man went to town and told all “what Jesus had done for him”.

 

This miracle teaches Christians that:

  1. The mission of Jesus’ was universal.
  2. Jesus mission is to teach all the people irrespective of their race, tribe or geographical location. The demon man was healed in a Gentile area.
  3. Jesus has power over evil
  4. Powers of evil (demons) are real
  5. Human life is more valuable than man’s material things
  6. The demons – evil spirits identified Jesus as the Son of the most High
  7. Christians need to fight the power of evil

 

SAQ.

What were the causes of mental illness and spirit possession in traditional African society and in

modern society?

 

iii) Jairus daughter is raised. Lk.8: 40 – 42, 49 – 56

Jairus was an official in the local synagogue. He begged Jesus to come to his house and heal his only daughter who was 12 was dying.

 

  1. iv) Woman with the flow of blood is Healed (Lk. 8:43 – 48)

When Jesus was on route to Jairus house, great crowds followed him and pressed him on either side. Amongst them was a woman who had suffered from severe bleeding for 12 years. She consulted doctors and spent all her savings on physicians. But she was not cured. The society considered the woman unclean. It blamed her for her illness. She herself was embarrassed by her condition. This woman walked behind Jesus and she touched the hem of the garment of Jesus. Her bleeding stopped at once. Jesus asked, who touched me? Everyone denied it. Peter replied the multitude was around Jesus and it was difficult to know who had touched him. Jesus persisted someone touched him. The woman who had touched Jesus the woman came forward, and fell at his feet and confessed to all her sickness and explained why she touched Jesus and how she was healed at once. Jesus said to her “My daughter, your faith has made you well. Go in peace”.

 

Jairus daughter is raised. Lk.8: 40 – 42, 49 – 56

As Jesus was talking to her, Jairus was told that his little girl was dead. “Don’t bother the teacher anymore. Jesus told Jairus not to fear but to believe and she will be well. When he got to the house he went into the room with Peter, John and James and the parents of the girl. People around were weeping and wailing. But Jesus told them not to weep. She is not dead but asleep. They scorned and laughed at him for saying that she is asleep because they knew she was dead. Jesus took the girl by hand and calledout “Get up, my child” – ‘little girl arise’. She immediately got up and Jesus ordered the parent to give her food. He commanded them not to tell what had happened.

 

Teachings from these two miracles

The miracle of raising Jairus daughter teaches Christians that Jesus is compassionate and the author of life. He has power over death, resurrection and life.

In the miracle of healing the Woman with the flow of blood:

 

  1. Jesus made her healing public. This was probably because He wanted to acknowledge the woman’s faith in the public. Jesus made it clear that her faith made her whole.
  2. Jesus wanted to challenge the cultural practices that kept women in bandage and could notparticipate in public life.

Jesus made her healing public so that the community can receive her back and shall not isolate her again.

From this miracle of healing this woman, Christians learn that one; Jesus is the healer. He has power over all sicknesses even those without cure. Two, Christians should have faith in Jesus Christ.

 

Lesson Revision Questions

  1. Narrate the healing of the Gerasene demoniac Lk 8: 26-39
  2. What lessons can Christians learn fro the healing of the demoniac man above?
  3. What do the miracles of Jesus teach us about him?
  4. Compare the raising of Jairus daughter and the healing of the woman with the flow of blood

 

Answers.

A comparison of the raising of Jairus daughter and the healing of the woman with flow of blood

(i) Jairus daughter was 12 years old and the woman sick with the flow of blood had suffered for 12 years.

(ii) Jesus referred to both of them as daughter

(iii) Their situation – death and flow of blood did not have a cure

(iv) The public witnessed the miracle of the woman with the flow of blood.

(v) Jesus commanded Jairus to keep secret raising of his daughter

 

 

 

 

 

 

LESSON TWELVE. COMMISSIONING OF THE TWELVE DISCIPLES

Lk 9:1 – 10

Introduction.

Commission means to officially ask someone to do something.

Learning Outcomes: By the end of the lesson, you should be able to:

a Describe the commissioning of the twelve disciples.

b Explain the story of the feeding of the 5000

c Describe the transfiguration of Jesus

d Explain the teachings of Jesus on faith and humility.

 

  1. The commissioning of the twelve disciples

The twelve disciples or followers accompanied Jesus wherever he went. They were regarded as apostles. An apostle comes from a Greek word ‘Apostols’ which means ‘send out’ one who is sent or a ‘missionary’. The commissioning of the 12 disciples meant that they were given four main duties, power and authority to:

  1. a) Exorcise or cast out demons
  2. b) Cure diseases
  3. c) Heal the sick
  4. d) Preach the Kingdom of God and proclaim the arrival of God’s Instructions. They were told to:
  5. i) Take nothing for the journey
  6. ii) Initiate attack on the forces of evil

iii) Depend entirely on God to take care of them

  1. iv) Take no stick, no beggars’ bag, no food, no money and not even an extra shirt for their journey
  2. v) Whatever house they entered they were to stay there until they leave the town.
  3. vi) If they were not welcomed, they were to leave that town and shake the dust off their feet as a warning to that city or town.

With these instructions, the disciples left and travelled to all villages preaching the Good News and healing people everywhere. King Herod was perplexed by the work of the disciples and he desired to see Jesus.

 

  1. Feeding of the five thousand.Luke chapter 9. Verses 11-17)

After reading these verses, about feeding of the five thousand (5000) people we learn that

  1. Jesus is concerned about people’s physical needs
  2. Jesus demonstrated that he is the bread of life
  3. Jesus has divine power
  4. The Church has the duty of continuing to feed its followers both spiritually and physically.
  5. The feeding of the 5000 people points to the Messianic banquet
  6. Christians must learn to share whatever they have with one another
  7. From this miracle, Jesus expected his disciples to appreciate their responsibility. Their work was not only to preach and heal but also feed the hungry. Feeding was both physical and spiritual.

 

 

 

 

The personality of Jesus and his identity Lk. 9:18 – 27

When Jesus was alone with his disciples, he asked them who people say he is. The disciples told him that some say he is John the Baptist, others say he is Elijah and others say he is one of the old prophets who have risen again. Jesus asked them who they, disciples say he is. Peter replied that he is Christ of God.

Jesus then told them not to tell people who he is for he Son of man has first to suffer many things be rejected by the elders chief, priests and scribes, be killed and be raised the third day. Jesus announced to the disciples of his passion (great sufferings) Jesus is the Christ (anointed) of God – Messiah as well as the son of man. A divine nature and a human nature. Jesus went on ahead to tell his disciples that theyshould deny themselves (self – denial) take up their cross daily and be ready to lose their lives for Jesus. However, great is the reward for the faithful.

 

LESSON THRTEEN: THE TRANSFIGURATION (LK.9: 28 – 36)

Read. Luke chapter 9, verse 28 to 36. hen answer revision questions that follow.

A brief summary from the Bible

Transfiguration is change or transformation of form or appearance. Jesus was transformed in appearance when he took Peter, John and James to the mountain to pray. During the transfiguration, Moses and Elijah came down from heaven to talk with Jesus about his coming death in Jerusalem. Moses, Elijah and Jesus were in heavenly glory and glorious splendor. Peter, John and James were asleep. When they woke up, they saw Jesus’ glory. They also saw Elijah and Moses with Jesus. Peter suggested to Jesus that they build three tents for Jesus, Elijah and Moses. As he spoke a cloudovershadowed them. A voice from the cloud said ‘this is my son, whom I have chosen——– listen to him”. The cloud left and the disciples found themselves with Jesus. They kept what they saw and heard to themselves.

 

Significance and importance of transfiguration

  1. The voice from heaven confirmed that Jesus is the Christ of God, or the Messiah
  2. Moses represented the Old Testament law. Jesus came to fulfil the Law of Moses. It showed that

Jesus was not against the Law of Moses.

  1. Elijah represented the Old Testament Prophets. This meant that Jesus had fulfilled the Old Testament

prophecies. He is above the prophets.

  1. Jesus is above or greater than the law and the prophets.
  2. Transfiguration was a way of preparing the disciples for the death and resurrection of Jesus. Death is

not the end of life (Moses and Elijah appeared to confirm this)

  1. The transfiguration prepared and gave strength to Jesus for what lay ahead of him
  2. Dazzling appearance showed the glory of Jesus
  3. The transfiguration also shows the importance of encouraging each other.

5.0 Revision questions

  1. Explain the teachings of John the Baptist
  2. Describe the baptism and temptation of Jesus and its relevance to Christians today.
  3. Give reasons as to why Jesus was rejected at Nazareth
  4. Describe the first miracles of Jesus at Capernaum
  5. Narrate and dramatize the temptations of Jesus from the gospel according to St Luke,
  6. Identify five occasions when Jesus was tempted
  7. Explain ways in which Christians can be tempted today
  8. Outline ways in which Christians can overcome temptations in the contemporary world
  9. Identify lessons that Christians can learn from the temptations of Jesus?
  10. What is the role of the clergy in Kenya?
  11. How does the church participate in the upkeep of the clergy?
  12. Define and describe the transfiguration of Jesus

 

TOPIC FOUR: THE JOURNEY TO JERUSALEM – LUKE ch. 9-18

Introduction

As Jesus travelled to Jerusalem, He prepared His disciples for the life they were to lead after He leavesthem.

Learning Outcomes. By the end of the topic, you should be able to

a Identify duties and privileges and cost of a disciple.

b Describe the teachings of Jesus on prayer, hypocrisy, wealth and watchfulness’.

c Describe parables Jesus used to teach about prayer, hypocrisy, wealth and watchfulness.

 

LESSON ONE. DUTIES, PRIVILEGES AND COST OF DISCIPLESHIP

Lesson Outcomes. When you read this lesson, you should:

  1. Explain discipleship
  2. List duties given to disciples by Jesus Christ
  3. Explain relevance of Christian discipleship to modern Church

 

Jesus’ teaching on faith and humility

A brief summary from the Bible. Read (Luke 9: 37 – 50) for details. After the transfiguration, Jesus usedtwo incidents to teach his disciples about faith and humility. One incident was the healing of a boypossessed by an evil spirit (Luke 9: 37 –43). Jesus rebuked the unclean spirit out of the boy and the boywas healed. Jesus told His disciples that their lack of faith was the reason why they did not cure the boy.

Jesus informed his disciples that faith in him was important when carrying out his work.

 

Jesus’ teaching on His Work

The next question was ….. who is to work for Jesus? All Christians can work for Jesus even believers whoare gentiles. Read (Luke 9 vs. 49 – 50). Jesus told his disciples not to forbid others from carrying out hiswork for whoever is not against Him is for Him. This means that whoever had faith; even the Gentilescould carry out Jesus work.

 

Jesus’ teaching on His followers

Jesus was determined to go to Jerusalem. As He travelled, men volunteered to follow him wherever hewas going. Jesus replied that foxes have holes, birds of the air have nests but the Son of Man hasnowhere to lay his head. Jesus had no earthly home. His mission on earth was only for a time. A manrequested to follow Jesus but asked permission to bury his father. Jesus told him to let the dead burytheir dead. Disciples of Jesus have to leave their families in order to do His Work.

 

 

Mission of the 72 men. Read Luke 10:1 – 24

On the way to Jerusalem, Jesus sent out 72 disciples on a mission to promote the Gospel of the Kingdomof God through preaching and service. The 72 disciples were sent in 2s in order to encourage or helpeach other. The 72 were given instructions. Jesus told them that He has given them power over demons,serpents, scorpion. They have power over all the powers of Satan. When disciples returned, theyreported that demons obeyed them. In Luke 10 verse 20, Jesus asked the 72 to rejoice not becausedemons flee but because their names are written in heaven. Out of the many followers, Jesus chose 12apostles who learnt from Jesus and became His witnesses.

 

Jesus’ teaching on the greatest disciple

Read (Luke 9: 46- 48). The disciples asked themselves– who is the greatest amongst disciples amongstthe 12 disciples? In response Jesus took a child by His side and said to the disciples. Whoever welcomesthis child in my name, welcomes me, as well as the one who sent me. For the one who is least amongstyou shall be the greatest in Heaven. Lessons from this example. Jesus explained that His disciplesneeded values of humility and simplicity. These virtues were needed to carry out the work ofdiscipleship.

 

Teaching about Discipleship

  1. True followers of Jesus Christ must
  2. Be ready to detach themselves from families and material possessions.
  3. Be ready to face rejections because not all people will accept them or their message.
  4. Be ready to serve.
  5. Be ready to cater for people’s physical needs.
  6. Be self – less.
  7. Not be hypocrites and should accept hospitality whenever it is given.
  8. Be able to exercise self-evaluation.

 

  1. Duties of a disciple were:
  2. a) To preach the good news of salvation to other people and be ready to suffer for the sake of Christ.
  3. b) Obey God’s commandments and follow teachings of Jesus.
  4. c) To help the needy spiritually and with material needs.
  5. d) To teach others about the Kingdom of God.
  6. e) To heal the sick.
  7. f) To cast out demons.
  8. g) Be prepared to suffer for the sake of the gospel.
  9. h) Being loyal to Jesus and faithful to the gospel.
  10. i) Commitment and loyalty

 

  1. Privileges of a disciple
  2. a) One becomes a member of the Kingdom of God.
  3. b) They get an assurance of eternal life.
  4. c) They receive joy of winning other people to follow Jesus.
  5. d) They receive peace, and blessings of God.

How are these teachings relevant to modern church leaders and members?

Modern church leaders have a duty to continue preaching God’s word to all people. They should serveGod in several ministries such as visiting the sick, caring for orphans, the destitute, widows, widowers,and the aged. They should also be ready to suffer and even face rejection for the sake of the Christ.

Exercise

  1. What are the characteristics of a true follower of Christ?
  2. State the privileges of being a disciple of Jesus Christ
  3. Why did Jesus choose the 12 disciples?

 

LESSON TWO: A COMMITTED FOLLOWER OF CHRIST

Read Luke 10: 25-37, and Luke 11: 1-13

  1. The parable of the Good Samaritan

A teacher of law asked Jesus questions in order to tempt him. One was “ what must I do to receiveeternal life? (Read Luke 10: 25 to 28). Jesus replied with a question. What do the scriptures say? Hereplied and Jesus told him to do as the scripture say. . He asked another question. Who is my neighbour?(Luke 10 v 29). Jesus answered with the parable of the Good Samaritan. In this parable, the righteouspeople among the Jews, Levites and priests, did not help the injured man. A Samaritan whom Jewsconsidered unclean and sinners helped him. After narrating this parable Jesus asked the lawyer, who ofthe 3 travelers was a good neighbour? The lawyer said the Samaritan.

 

Lessons learnt from the parable of the Good Samaritan

In the above parable, Jesus stressed that a follower of Jesus should be:

(1) Committed

(2) Show love of God by loving people in need and their neighbours. A neighbour is anybody whorequires assistance or help regardless of race, ethnicity, creed, colour or gender. Jesus wants hisfollowers to show love and concern to all people regardless of their background. A neighbour useshis/her resources selflessly to help the needy. A neighbour is also compassionate, kind, and generous tothe needy.

 

Jesus Visit to Martha and Mary (Read Luke 10: 38 – 42)

Martha welcomed Jesus in her home where she lived with her sister Mary. While Martha prepared food,Mary sat at Jesus’ feet listening to his teaching. Martha complained. She was doing all the work whileMary sat listening to Jesus teaching. Jesus told Martha that Mary had made the right choice to listen toHis teaching.

 

Lessons we can learn from Jesus Visit to Martha and Mary

  1. A committed follower of Jesus is one who creates time to study and listen to God’s word.
  2. A follower of Christ should ensure that their commitment to God is not overshadowed by daily duties,worries and responsibilities.
  3. Jesus visit to Mary and Martha was also to teach disciples on the characteristics of a true disciple.

Revision exercise

  1. From the teachings of Jesus, on the parable of the good Samaritan; who do you think is a committedfollower of Jesus?

LESSON THREE. JESUS’ TEACHING ON PRAYER (Read Luke 11:1 – 13)

Prayer is communication with God. It is talking with God. People pray to God all the time. For example,people pray to God when:

  1. They are in problems and in happiness;
  2. Seeking healing and wealth,
  3. Giving thanks to God,
  4. Identifying the needs to be met, and asking for favors from God
  5. Repenting and confessing their sins
  6. Thanking God

There are many forms or types of prayers. These are:

  1. Intercessory prayer – Praying for the needs of others.
  2. Prayer for repentance – for forgiveness of sins.
  3. Thanksgiving prayer – giving thanks to God for what he has done.
  4. Worship prayer – prayers to worship God.
  5. Praise prayers – to praise God, Honor God.
  6. Supplication and petition prayer – whereby an individual makes their needs known to God and asksfor divine intervention.

Jesus prayed often during his life’s Ministry. The disciples asked him to show them how to pray. Jesusresponded by teaching them the Lords Prayer.

“Our Father who art in Heaven

Hallowed be thy name

Thy Kingdom come

Thy will be done on earth as

It is in heaven

Give us this day our daily bread

Forgive us our trespasses

As we forgive those who trespass against us

Lead us not into temptation

But deliver us from evil”

 

  1. a) Our Father who art in heaven – The disciples were told to address God as ‘Our father’. God is to beseen and addressed as a Father.
  2. b) Hallowed be thy name – The name of God should be respected and revered.
  3. c) Thy Kingdom come – In Prayer, Christians/disciples are to pray that the rulership of God reignamongst them.
  4. d) Thy will be done on earth as it is in heaven – Christians to obey the will of God.
  5. e) Give us this day our daily bread – Christians to pray for their needs.
  6. Forgive us our trespasses – we ask for forgiveness of our sins and those of others.
  7. Jesus taught that one should be persistent in prayer. If a man goes to his friend at midnight and asksfor bread to give to his visitor, the friend will open the door and give his friend all that he needs. This isbecause his friend was persistent in knocking on the door.

In conclusion, if prayers are to be effective, one must have faith and be persistent. Believe that God shallanswer prayers. A committed follower of Jesus should pray at all times. In prayer, one shouldacknowledge that God is the Father and that all prayers should be addressed to him. Two, one shouldhave faith that God answers prayers. Therefore we should be persistent in prayer.

 

Reasons why Christians should pray

 To honor God

 To request for favors

 To offer thanksgiving

 To confess their sins and seek for forgiveness of sins

 To seek God’s protection

 To intercede on behalf of others

 To strengthen their relationship with God

 

Revision exercise

  1. What did Jesus teach about prayer?
  2. What is the importance of prayer?

 

LESSON FOUR: USE OF GOD’S POWER TO OVERCOME EVIL. Read Luke 11:14 – 28

Learning outcomes. By the end of the lesson, you should be able to:

  1. Narrate Jesus teaching about demons
  2. Explain why the sign of Jonah was important
  3. Describe how God’s power overcomes evil

 

  1. Jesus and Beelzebub. (Read Luke 11: 14 to 28)

Jesus drove out a mute demon. The possessed man began to talk. The crowd said that Jesus was castingout demons using the power of Beelzebub (the price of demons). Beelzebul was an evil spirit. However

Jesus replied “Any country that divides itself into groups which fight each other will not last very long,and a family divided against itself will fall. Jesus said it is by the power of God that drives out demons.

 

Lessons learnt

  1. Satan cannot fight against himself therefore Jesus cannot be an agent of Beelzebub / Satan.
  2. Gods Kingdom and that of Satan were two separate Kingdoms and could not co exist.

iii. The destruction of Satan’s power meant that the Kingdom of God was in Israel and it was powerful.God’s power destroyed Satan’s kingdom. It is impossible to be neutral in the battle between Christ andSatan. One has to belong to either Christ or Satan.

  1. Jesus has power to drive out demons.
  2. Demons occupy people. They bring disabilities and diseases.

What makes people to be insane? Mentally sick

 

  1. The sign of Jonah. (Read Luke 11: 29 – 32)

After Jesus drove out the dumb spirit, Jews demanded performance of greater miracles. They wantedJesus to prove that he was their expected messiah. Jesus said that Jonah was a great miracle. But Jesuswas greater miracle than that of Jonah, and King Solomon. King Solomon was full of wisdom. He was sogreat that Queen of Sheba came to listen to his wisdom. Jesus like Jonah had brought a message ofjudgment. Jesus is greater than Jonah or Solomon. If Jews refuse to receive and listen to Jesus, theGentiles like Queen of Sheba, will bear testimony against the Jews and receive God’s salvation.

  1. The light of the body. Read Luke: 11: 33 – 36

Jesus taught that no one lights a lamp and hides it under a bowl. A lamp is placed where all can see itslight. He said that the human eye is the lamp or the light of the body. Jesus asked the listeners to makesure that “the light in you is not darkness” (vs. 35).

What is the main message in this story?

 

LESSON FIVE: JESUS TEACHING ON HYPOCRISY, WEALTH, WATCHFULNESS AND READINESS

Introduction

Hypocrisy is being dishonest and insincere or pretending to someone else or people. What did Jesusteach about hypocrisy?

Learning outcomes. After reading these verses in Luke:

  1. State what Jesus taught on hypocrisy
  2. Explain value of wealth
  3. Discuss how modern Christians can be watchful and ready for the coming of Jesus Christ

 

  1. Hypocrisy. Read Luke 12: 1- 12

A Pharisee invited Jesus to his house for a meal. When Jesus did not wash before eating the meal, thePharisee was surprised. Jesus told him “..you Pharisees clean the outside of your cup and plate, butinside you are full violence and evil”, greed and wickedness (vs. 39). Jesus condemned the Pharisees fortheir hypocrisy. They were concerned with outward appearances and traditions such as ceremonialwashing of cups, hands, and dishes but not the souls of people. They loved the outward show and publicrecognition. Pharisees tithed, “but neglected justice and love of God” (vs. 42). They imposed rules andregulations for people to follow, yet they themselves did not practice what they preached. They refusedto confess their sins but pointed out sins in others. They hinder others from entering the kingdom ofGod. They had failed to make people understand the true interpretation of the law. They were likeunmarked graves – dead to people yet the people trusted them. After this teaching, the Pharisees andthe teachers of the law began to oppose Jesus fiercely.

 

What do we learn from Jesus teachings? Followers of Jesus should be

  1. Sincere and upright (honest);

(2) obey God’s commands;

(3), live to please God but not other people;

(4) confess publicly their loyalty to God and

(5) love God without fear and (6) be dependent on the Holy

Spirit

  1. The Parable of the Rich Fool. (Read Luke 12:13 to 21).

Someone wanted justice. His brother had refused to share with him his father’s wealth. He wanted Jesusto order his brother to divide their father’s inheritance between him. In response, Jesus answered himwith the parable of the rich fool.

A rich man expected a good harvest of his crops. He thought he did not have storage for the crop heexpected to harvest. The man said to himself. i will demolish my granaries and stores, then build biggerones to store all my corn, and other goods. He expected to have enough food to last him a lifetime. Thenhe can enjoy his wealth; eating, drinking and making merry. But God told him that his life would bedemanded from him that same night. What will happen to his wealth, as he was not rich in God’s sight?

Lessons to learn

i Followers of Jesus should not put their trust in material wealth but in God

ii Life consists of food, other material wealth and trust in God

iii Whoever seeks God’s kingdom, will receive material blessings from God

iv Jesus did not condemn material possessions but rather the attitude towards material possessions.

v Jesus condemned attachment to material wealth instead of trust in God who controls our lives.

  1. Watchfulness, Readiness, and Instructions. (Read Luke 12: 35 – 59)

 

Jesus told his disciples to be:

i Watchful and ready for the return of the Son of Man i.e. Jesus.

ii Faithful servants so that when Jesus returns, he will find them ready and acting responsibly

iii Watchful of possible divisions in families

iv Royal to Christ

v Ready for the coming of the Son of Man. He will come at unexpected time; like a thief who comeswhen the owner of the house is not aware.

vi Observing things of the kingdom of God, which were present in the person of Jesus.

vii Like good servants, and watch over the affairs of the master.

viii Be decision makers and follow the teachings of Jesus without being watched.

Review questions

  1. In what ways were the Pharisees hypocritical?

 

LESSON SIX: THE KINGDOM OF GOD

Learning Outcomes. By the end of this topic, you should be able to

  1. Explain the teachings of Jesus about the kingdom of God
  2. Narrate the parables of
  3. The unfaithful fig tree
  4. The mustard seed
  5. Parable of the feast
  6. Parable of the great feast
  7. Parable of the lost sheep and the lost son

 

The Kingdom of God

Kingdom of God refers to rule of God, or God’s authority on people’s lives and the world He created. Thekingdom of God was present in Jesus. It is now and in the future reality. The teachings, and miracles ofJesus were a manifestation of the Kingdom of God. For anyone to enter God’s kingdom, one has torepent and ask for forgiveness. The Kingdom of God continues to grow and spread through the work ofthe Church. Those who accept the teachings of Jesus Christ about God’s Kingdom are members of theKingdom of God. Now to enter the Kingdom of God, one has to repent and not judge others.Read Luke 13:1-5. Luke has explained the kingdom of God and outlined who will enter it.

 

 

The Kingdom of God has unfruitful fig tree (Read Luke, 13: 6 – 9).

A farmer had a fig tree that wasunproductive for 3 years. He ordered the gardener to cut it down. The gardener requested for the figtree to be given another chance. He promised to dig around the fig tree and add fertilizer. If it bearsfruits well, it can survive, if it doesn’t bear fruit, then it should be cut down.

Lessons learnt from the parable

The unproductive fig tree represents followers of Jesus who are unproductive because they do notfollow the teachings of Jesus Christ. God gives people chances to repent just like the fig tree was given asecond chance to bear fruit. Jesus is the gardener who pleads for people before God. The followers ofJesus are expected to be fruitful.

 

What are the figs used for?

  1. Parable of the mustard seed. Read Luke, 13:18 – 19

Jesus likened the kingdom of God to a mustard seed, which is very small. When a mustard seed isplanted, it grows fast to become a big tree. It is difficult to control its growth. When mature, the fig treeattracts many birds, which feed on its seeds.

Lesson learnt from the parable.

The Kingdom of God

 Begins as a small seed and grows quietly and humbly

 Then it grows and spreads to all corners of the earth

 And It attracts many people

 

  1. Parable of the Yeast. Read Luke, 13: 20 – 21

The Kingdom of God is like yeast. Yeast makes dough rise and the bread big. The Kingdom of God growssecretly and slowly just like the dough rises without being noticed. It is only God who knows how akingdom grows. The Kingdom of God grows as a small unit that eventually grows, spreads and reachesout to many people in many nations.

 

  1. The narrow door. Read Luke, 13: 22 – 30

As Jesus was teaching in towns and villages, a person asked him whether a few people would be saved.Jesus replied that his followers should make every effort to go through the narrow door as it leads to theKingdom of God. The narrow door will not remain open forever.

Lesson learnt from the parable

 Those who wish to follow Jesus must repent immediately

 Entrance to God’s Kingdom is through repentance

 Everybody is invited to enter into the Kingdom of God.

 

  1. Jesus heals a crippled woman on the Sabbath. Luke, 13:10 – 12

Jesus was teaching in the synagogue on Sabbath. Jesus healed a woman who had an evil spirit, whichhad bent her back (Hunch back) for 18 years. Jesus saw her and told her “woman, you are free from yourillness!” She was made straight and immediately glorified God. The official of the synagogue wasannoyed that Jesus was healing on a Sabbath. He and others were hostile to Jesus for healing/workingon the Sabbath. Jesus told him, you hypocrite. You feed and look after your animals on the Sabbath day.Jesus emphasized that human life is more important than animal life or even observing the Sabbath.

 

 

Lessons learnt from the parable

Jesus came to set people free from the bondage of sickness and Satan. Jesus work of liberation iscontinuous. It has to be performed even on a Sabbath day because human life is more important thananimal life or even observing the Sabbath.

 

  1. Jesus’ Love for Jerusalem. (Read Luke13: 31 – 35)

As Jesus continued with his teachings, he reached Jerusalem. Pharisees informed him that Herodwanted to kill him. His response was ‘go and tell that fox ” I will continue healing the sick and casting outdemons. Jesus however, lamented over Jerusalem for rejecting God’s messengers. God would abandonJerusalem for rejecting Jesus. Jerusalem was the site of Jesus death. It would eventually acknowledgeJesus as the Messiah who brings salvation to Israel and to the rest of the world.

 

  1. Man with dropsy healed (Read Luke 14:1 – 6).

Jesus was invited to the house of the leading Pharisees for a meal on a Sabbath. A man with dropsy(swollen legs and arms) came to Jesus for healing. The Pharisees watched Jesus closely to see what hewould do. Jesus asked the Pharisees “ does our Law allow healing on the Sabbath or not?” They keptquiet. Jesus healed the man who then left. Jesus asked the Pharisees, would they save their son or an oxif it fell in a well on a Sabbath. They kept quiet.

 

  1. Humility and Hospitality. (Read Luke 14: 7 – 14)

Jesus was in the house of a leading Pharisees and observed that some of the invited guests werechoosing the best places to sit at the table. He taught the disciples how to be humble. He said, wheninvited for a meal; let the owner give you a seat of honor that is reserved for important and honorableguests. Read verse 11.

Jesus advised his host to invite the poor, cripples, and the blind who cannot invite you, as they havenothing to give back for generosity.

Lessons learnt from the parable

Jesus is teaching about humility and hospitality. Those who are humble shall be elevated. Those whoelevate themselves shall be humbled. Followers of Jesus should extend invitations to the poor and theunderprivileged in the society. The Kingdom of God belongs to the humble people.

 

  1. The parable of the Great Feast. Read Luke, 14: 15 – 24.

A man said to Jesus, “How happy are those who will sit down at the feast in the Kingdom of God” (verse15). In response Jesus told him that a man made a great feast and invited many friends and colleaguesto the feast. The invited guests failed to come and a servant was sent to inform them that the feast wasready. All the invited guests gave personal excuses explaining why they could not come.The master was angry and asked the servant to invite the poor, crippled, lame, the blind and anyonewilling to come to the feast.

 

Lessons learnt from the parable

God has invited all people to the great feast of the Kingdom of God. Those who honor his invitation willbe blessed. Those who reject the invitation will be excluded from the feast. Jesus explained that theKingdom of God is like a great feast open to all Jews and Gentiles.

To enter the Kingdom of God, one has to make a personal decision because following Jesus meanssacrificing activities that we consider important to us.

  1. The Cost of Being a Disciple

Read Luke 14: 25 – 33

True discipleship means loving Jesus more than ones family. This is a great sacrifice to detach oneselffrom the family. A disciple must be ready to suffer for the sake of following Jesus. Following Jesusrequires skills of careful thinking, planning and detailed preparations. Jesus compared true discipleshipto the planning required when building a tower or engaging in a military operation.

 

Lessons / teachings learnt from the parable

True discipleship means making great sacrifices, “none of you can be my disciple unless you give upeverything you have” (verse 33). Jesus disciples are expected to do careful planning before deciding tofollow him because they are required to love God more than anyone else even their relatives andfriends.

 

  1. The parable of the Lost Sheep

Read Luke, 15:1 – 7

Pharisees and teachers of law complained to Jesus because Jesus was teaching ordinary people such astax collectors, and outcasts considered sinners by them.

Jesus told the Pharisees and teachers of law the parable of the lost sheep. He told them that if ashepherd with 100 sheep lost one of them, what action would he take? Wouldn’t he leave the 99 sheepand go out to look for the lost sheep? And on finding it, wouldn’t the shepherd celebrate with friendsand neighbours? Jesus said that God celebrates if “over one sinner who repents than over 99respectable people who do not need to repent.”

 

Lessons / teachings learnt from the parable

iii God is a shepherd and takes care of all his people.

iv He does not want any of his people to be lost.

v God searches for those lost in sin until he finds them.

vi When one sinner repents, God is overjoyed and rejoices.

vii God is the good shepherd who has come to seek and save the lost.

 

  1. Parable of the Lost Coin.

Read Luke, 15: 8 – 10

If a woman losses one of her ten silver coins, she searches until she finds it. And if it is found, she invitesher friends and neighbours to celebrate.

 

Lessons learnt from the parable

God and the angels in heaven search make every effort to seek the lost sinner until they find them. Jesuslights the world, looking for sinners who are lost because they are precious in God’s sight.

  1. Parable of the Lost Son (prodigal son)

Read Luke 15:11 – 32

Jesus then told the story of a father who had two sons. The younger was given his share of inheritancehe had requested. He went to foreign lands and wasted his inheritance. He became poor and decided toreturn home and ask his father to forgive him and employ him as a servant.

His father kissed him and celebrated his return. The father announced to his guests that the son whowas lost is now found. – – The one who was dead is now live.

The elder son was angry and unhappy because his father had never held a celebration for him, in spite ofhis hard work and obedience.

His father told him “my son you are always here with me, and everything I have is yours”. We are justcelebrating the return of the lost son.

 

Lessons learnt from the parable

  1. A person dies spiritually if they sin
  2. God loves all people including sinners
  3. God is ready to forgive every sinner who repents
  4. There is no sin that God cannot give
  5. Jesus taught that both the righteous and unrighteous require God’s forgiveness
  6. There is joy and happiness in heaven when one sinner repents.
  7. Christians should confess their sins and acknowledge that Jesus saves repentant sinners
  8. God accepts unconditionally any sinner who comes back to him in repentance
  9. Confession of sins is a condition for entering the Kingdom of God.

 

A GREAT FEAST FOR ALL WHO ARE PREPARED Luke 14: 1 – 35

SAQ. What are the qualities of those who belong to the kingdom of God?

Answer. Qualities of people who belong to the Kingdom of God

Those who belong to the Kingdom of God:

  1. Obey God’s commandments
  2. Accept God’s rule in their lives

iii Show God’s love to others

iv Are ready to make sacrifices so as to be followers of Jesus

v Read God’s word and preach to others

vi Confess their sins and seek forgiveness of their sins through repentance.

Review questions

  1. Give an explanation of the term Kingdom of God
  2. What did Jesus teach about the kingdom of God?
  3. What lessons do Christians learn from the parables of the lost son?

Answer

  1. The term Kingdom of God means the role of God or God’s authority in people’s lives and the world.

 

LESSON SEVEN: TEACHINGS ON WEALTH AND POVERTY. LK 16:1 – 32

Learning Outcomes. By the end of the topic, you should be able to:

  1. a) Explain the teachings of Jesus on wealth, and poverty
  2. b) Narrate the teachings of Jesus on repentance

Introduction

While wealth is possession of material things such as money or occupation of a high social economicstatus, poverty is the opposite. It is lack of basic needs such as water, education, food, shelter, clothing,and health.

When teaching about wealth, Jesus taught using two parables. These were: (1) parable of the shrewdmanager (2) parable of the rich man and Lazarus

Parable of the shrewd manager

Read Luke, 16: 1 – 18

When the shrewd manager realized that his master was going to sack him due to his dishonesty, heasked the debtors to change the amounts they owed their master to smaller amounts. He did this tomake friends with a few people who would give him a place to stay after he was sacked. The masterpraised the shrewd manager and did not sack him. The shrewd manager is praised not because of hisdishonesty but because he acted promptly and with great presence of mind in a moment of crisis.

Jesus is encouraging his disciples and followers to make prompt (quick, appropriate, timely) decisions.

They should use wealth to serve God. It should not be allowed to take the place of God. Followers ofJesus should be honest in small and big things.

 

The Rich Man and Lazarus. Read Luke, 16: 19 – 31.

A rich man lived in luxury. At his gates was a poor man, called Lazarus whose body was covered by sores.The rich man did not feed Lazarus. He ate food remains together with the rich man’s dogs.

When rich man died, he went to hell. When Lazarus died, he went to heaven and sat at Abraham/sbosom. When in hell, the rich man was tormented while Lazarus was at peace.

Lessons to learn from this parable.

The rich isn’t condemned for being rich but because of his altitude towards Lazarus. He used his wealthfor self-gratification and not for service to the needy. The wealthy should realize that it is God who giveswealth and he should be given honor. Riches can hinder the wealthy from inheriting eternal life,especially if they put their trust in riches instead of God who is the source of all wealth and blessings.

Revision exercise

  1. From the parable of the rich fool what can Christians learn about the use of wealth?
  2. Narrate the parable of the shrewd manager

LESSON EIGHT. JESUS TEACHING ON FORGIVENESS

Read Luke 17: 1 – 4

Learning outcomes. By the end of this lesson, you shall explain the power of Christian faith. Sin. Read Luke 17: 1-4.

Jesus taught his disciples to forgive offenders who repent. Those who sin should seek forgiveness. If theyoffend 7 times in a day, forgive them 7 times. Followers of Jesus need faith to forgive others.

The power of faith. Read Luke, 17: 5 – 11.

Faith is defined as complete trust or confidence in God. It is absolute truthfulness and trust in everything that comes from God. The apostles asked Jesus to increase their faith. Followers of Jesus should have faith. Faith has no measure. Faith as big as a mustard seed can empower Christians to perform miracles that serve God. Faith is necessary. With faith, Christians can forgive others and be servants of God.

Disciples should have faith. Christians understand that they owe everything to God.

 

 

 

 

Jesus heals ten lepers. Read Luke, 17:11- 19

Jesus was on his way to Jerusalem when he met ten lepers. They requested Jesus to heal them.

Jesus told them to go and show themselves to the priests. On the way, they were healed. One of them, a Samaritan, returned to thank Jesus for healing him. The Samaritans and the Jews did not associate. Jesus told the Samaritan that his faith has made him whole. Faith is necessary for healing any disease.

Leprosy is a disease that leads to loss of fingers, toes and other parts of the body. It was a dreadful skin disease, which Jews feared. Lepers were isolated from other people. They lived dejected lives

 

The coming of the kingdom. Read Luke 17: 20 – 37

The Pharisee demanded to know when the kingdom of God would come. Jesus replied that the kingdom of God was within those who had accepted Jesus and his teachings. Those who wanted had received the kingdom. Faith is necessary to discover the power of God’s kingdom.

The coming of the son of man, i.e. Jesus will bring the kingdom to reality.

The coming of the son of man is also referred to as the day of the Lord, Day of Judgment. Read Luke, 21: 27- 28. Those who obey Jesus will be saved but those who reject him will be punished.

Lessons to learn. God expects Christians to have faith in him. Christians should have faith in Jesus so that they can inherit eternal life. Faith is needed to strengthen Christians. Faith is important in the life of a Christian until Jesus returns, i.e. the second coming.

 

Revision exercise

  1. What did Jesus teach on forgiveness

 

LESSON NINE. PERSISTENCE IN PRAYER, Read Luke, 18:1 – 14

Learning outcomes. By the end of this lesson, discuss the values of persistence in prayer

To teach about persistence in prayer, Jesus used two parables. These were the parables of: the widow and a corrupt judge and examples of prayer by a Pharisee and a tax collector.

  1. The widow and the unjust judge. Read Luke, 18: 1 – 9

Jesus had already taught the disciples how to pray. He now tells them that they ought to pray and not faint. He gives a parable to explain his point.

A widow went to a corrupt judge to have her adversaries judged. The judge was corrupt and ignored her. He however gave in to her demands since she was persistent and wearing him down. The judge helped her because of her persistence and courage.

 

Lessons learnt from the parable

Followers of Jesus should pray with courage and be persistent in prayer. God hears and answers prayers. Christians should pray without ceasing and with faith and trust that their prayers will be answered.

 

  1. Parable of the Pharisee, and tax collector, Read Luke, 18:9 – 14

A Pharisee and tax collector went to the temple to pray. The Pharisee offered a long prayer focusing on his achievements. The tax collector (publican) did not have much to say except asking for mercy, as he was a sinner. Followers of Jesus should acknowledge they are sinners and seek forgiveness. They should approach God in humility and avoid spiritual pride, and self-righteousness.

Revision exercise

  1. State the parable of the widow and the unjust judge

 

LESSON TEN. THE WAY TO SALVATION, Read Luke, 18: 15 – 19: 1 – 27.

Introduction: The word ‘salvation’ refers to the act of saving or being saved from sin. Those who have received salvation area assured of eternal life. To receive salvation a person must acknowledge that he is a sinner and repent their sins. In this way, they receive forgiveness and are reconciled to God.

Learning outcomes. By the end of this lesson, you should

  1. State the meaning of salvation
  2. Discuss characteristics of salvation
  3. Give examples of those who will enter the Kingdom of God.
  4. Explain how Jesus predicted his death

 

Introduction

Salvation means being saved from a life-threatening situation. In Christianity, salvation refers to the process of being delivered from sin and its consequences. Those who are saved are assured of eternal life.

Jesus taught about salvation using children to illustrate his message. This is what happened. Some people brought their children to Jesus so that he could bless them. The disciples scolded them. Jesus asked the children to come to him and he blessed them.

Jesus taught his disciples that they must be humble like children in order to enter the kingdom of God.

The road to salvation is by being simple, humble, and trusting like little children. The kingdom of God belongs to those who humble themselves like the little children.

 

The rich man. Read Luke, 18:18 – 30

The entry into the kingdom of God was further explained through the story of the rich man. The rich man came to Jesus wanting to know how he could inherit eternal life and be saved. Jesus reminded him of the importance of keeping the commandments. The young man responded that he had observed the commandments since he was young. Jesus told him there is one thing remaining to do; sell everything he has, and give it to the poor, and then follow Jesus.

The rich man was very sorrowful for he was very wealthy. Wealth can hinder the rich from receiving salvation. Jesus acknowledged the sacrifice made by his disciples. He emphasized that disciples shall receive salvation in the present and in life to come. Salvation is a gift from God. Salvation is received; by those who accept to follow Jesus. Trusting in wealth can be a hindrance to salvation. The rich may find it difficult to inherit eternal life. Jesus predicts his death, a 3rd time. Read Luke, 18: 31 – 34.

Jesus predicted his death a three times. First was after asking his disciples who they say he was. The second time was after transfiguration when his face was set towards Jerusalem. The third prediction shall be in Jerusalem (Luke 18:31-34). Jesus told the disciples that previous prophecies would be fulfilled in Jerusalem. His death was going to take place in Jerusalem according to the writings of the prophets. It was going to be a painful death. He shall be beaten, mocked, spit upon and put to death. But on the third day, he shall rise again.

The disciples did not understand what Jesus was telling them. Jesus had to die so that those whobelieved in him may receive eternal life. The death and resurrection of Jesus gives Christians hope of eternal life.

Jesus heals a blood beggar. Read Luke, 18: 35 – 43

As Jesus neared Jericho, a blind man sat by the roadside begging. When he heard the multitude pass by, he inquired what was going on and he was told that Jesus of Nazareth was passing by. He then cried out “Jesus, Son of David, have mercy on me”

The crowds rebuked him but he cried out louder to Jesus to have mercy on him. Jesus asked him what he wanted. He said he wanted to see. Jesus told him to receive his sight for his faith had made him whole. The beggar was joyful and he followed Jesus rejoicing.

Lessons learnt. Christians should have faith in Jesus. They should also be persistent and make specific requests.

 

LESSON THIRTEEN: JESUS AND ZACCHAEUS LK 19:1 – 9

Learning outcomes. By the end of this lesson,

  1. Narrate events leading to salvation of Zacchaeus
  2. Explain meanings of the story of the man who gave gold coins to his servants

Zacchaeus was short. His profession was a tax collector. He was rich. He wanted to be saved.

When Jesus was passing by Jericho, he wanted to see Jesus. He couldn’t because he was short. He ran and climbed a sycamore tree to see Jesus. When Jesus came to the place where Zacchaeus was, he looked up and said “Hurry down, Zacchaeus, because I must stay in your house today” (verse 5). Jesus then went with Zacchaeus to his house. When people saw this they grumbled, and murmured. They said that Jesus was going to a house of a sinner.

Jesus told them that salvation has come to the house of Zacchaeus, a son of Abraham … the Son of man came to seek and save the lost. There is no sin that God cannot forgive, even that of a tax collector. Zacchaeus told Jesus that he was going to give to the poor half of his wealth and whatever he took from any man and woman wrongfully, he will restore four times. From this salvation, we learn that the rich should share their wealth with the needy.

 

The Parable of the Gold Coins: Luke, 19: 11 – 27.

A certain nobleman went to a far country. Before he left he called his ten servants and gave each a gold coin (ten pounds in total). He told them to trade with the coins until he returns.

When he returned, he called the servants to report profits they had made. The first servant said that one-pound coin had made profit of 10 pounds (gold coins). He made the manager of ten cities. The second servant had traded and gained 5 pounds. He was made the manager of 5 cities. The third one had hidden the pound. He did not trade. He accused the master of being mean, and cruel. He returned the pound, which was given to the servant with 10 pounds.

Lessons to learn.

This parable was about the kingdom of God. God expects us to use opportunities he has given to us for his work. Each one of us shall account for the use of the abilities and skills that God gave to us –students, workers, and other professionals. To receive eternal life, Christians should repent and be obedient to God’s instructions.

Revision questions

  1. What did Jesus teach by using the example of little children?
  2. Give an account of how Jesus healed the blind beggar
  3. Explain the relevance of Jesus’ teachings on salvation to Christians

TOPIC FIVE: THE JERUSALEM MINISTRY. Luke, 19: 28 – 21: 38

Lesson Outcomes. By the end of this topic, you should:

  1. Describe the triumphant entry of Jesus into Jerusalem
  2. Narrate events in the cleansing of the temple
  3. Discuss Jesus’ teachings about eschatology

 

LESSON ONE: THE TRIUMPHANT ENTRY OF JESUS TO JERUSALEM LK. 19:28 – 40

Learning outcomes. By the end of this lesson, you should

  1. Explain why Jesus rode on a young colt into Jerusalem
  2. Discuss why Jesus wept over Jerusalem
  3. Describe what Jesus did when he went to the temple

 

  1. The triumphant approach to Jerusalem. Luke 19: 28- 40.

Jesus death had to happen in Jerusalem. Hence Jesus went to Jerusalem. He sent two disciples to a place where there was a colt (young donkey) that no person had ever ridden. They took it to Jesus. They threw their garments on the colt, and Jesus sat on it. As Jesus rode, people spread their clothes on the road. As Jesus neared Jerusalem, a “large crowd of his disciples began to” praise God (vs37). The crowd said ‘blessed be the king who comes in the name of the lord’.

The Pharisees told Jesus to rebuke the disciples. Jesus told them if the disciples kept quiet the stones would start shouting.

Jesus made his entry into Jerusalem in a royal (kingly) procession. He was Israel’s humble king who came with peace and not a political leader. He rode on a donkey – a symbol of peace. This was unlike the political kings who rode on the horses during that time.

 

  1. Jesus weeps over Jerusalem. Read, Luke 41- 44.

When Jesus was near Jerusalem he wept. He then foretold the coming destruction of Jerusalem due to its rejection of the messiah.

The rejoicing of his triumphant entry to Jerusalem turned to mourning as he foretold the destruction of Jerusalem by Romans in 70 A.D.

 

  1. Jesus goes to the temple. Read Luke 19:45 – 48.

Jesus went to Jerusalem temple and evicted traders. He told them that the house of God is a house of prayer not a den of thieves. Jeremiah spoke these same words during his temple sermon. The chief priests and scribes began planning how to kill Jesus.

 

 

 

LESSON TWO. PHARISEES, SCRIBES QUESTION JESUS. LUKE 20 1-47

Learning outcomes. By the end of the lesson you should be able to: –

  1. Describe the question about the authority of Jesus
  2. Describe the parable of the tenants in the vineyard
  3. Describe the question about paying taxes
  4. Describe the question about resurrection
  5. Describe Jesus’ teachings against the teachers of law
  6. Describe the parable of the widow’s offering
  7. The question about Jesus’ authority. Read Luke, 20:1 – 8.

The Jewish leaders wanted to know from Jesus by whose authority he was doing all the things he was doing. In response Jesus asked them “did John’s right to baptize come from God or from human beings?” (Vs4).

They discussed among themselves and decided not answer. Jesus told them “neither will I tell you”. In response to his authority being questioned he told a parable.

 

  1. The parable of the Tenants in the Vineyard.

Read the parable in Luke, 20: 9 – 18. The tenants refused to pay the owner of the vineyard his share of the harvest. They threw out the servants he sent to collect his share of the harvest. When he sent his son, they killed him so that they can own the vineyard. Jesus asked the people… “What will the owner of the vineyard do to the tenants?”

 

  1. The Question about paying taxes. Read Luke 20:19-28

Pharisees, and scribes (teachers of the law) and chief priests planned to arrest Jesus but they were afraid of the people. They sent spies to trick Jesus by asking this question -” …is it against our law for us to pay taxes to the Roman Empire, or not?

Jesus used the currency and told them “pay the Emperor Caesar what belongs to him and pay God what belongs to God.” (Verse 25)

This was a tricky question. Jesus here teachers people to obey the rules of the land and to obey God’s rules.

 

  1. The Question about Resurrection

The Sadducees who did not believe in resurrection tempted Jesus with another question. They wanted to know this. When resurrection comes, who shall be the husband to a woman who was married to the first brother and inherited as a widow by the other six brothers?

Jesus told them the men and women who shall be worthy of resurrection shall not marry. They shall be like angels and cannot die (verse 34 to 38)

  1. Jesus warns against the Teachers of the law

Jesus warned his disciples. Be careful and guard yourselves against teachers of the law, the scribes. They were hypocritical. They wore long robes, said long prayers, looked for positions of honor and exploited the widows.

  1. The Widow’s Offering. Luke, 21: 1- 4

When people were giving offerings in the temple, a widow gave “two little copper coins”. Jesus said the poor widow had given all she had. Likewise Christians should give to God not to be seen but from their hearts. It is not the quantity of the gift that matters but the attitude of the giver.

 

LESSON THREE: THE TEACHINGS OF JESUS ABOUT ESCHATOLOGY LK. 21: 5 – 38

Eschatology is from two Greek words, ‘eschatus’ and ‘logos’. Eschatus means end, Logos means study.

Eschatology means the study of the end times or in CRE the last days of Jesus. For biblical information, read Luke 21:5-38 and Mathew 24: 1 – 36 and Mark 13:1-31.

Learning outcomes. After this lesson, you should:

  1. Identify signs of end times
  2. State uses of the temple during the time of Jesus
  3. Discuss ways in which Christians can apply the parable of the fig tree
  4. State relevance of Jesus’ teachings on eschatology
  5. Signs of the end times. Jesus gave many signs that will inform Christians that end of the time has

come. These were to happen at different times. The signs were:

  1. a) Destruction of the temple of Jerusalem by invading armies which shall surrounded it
  2. b) Hatred of disciples and Christians because they were followers of Christ
  3. c) Rejection of disciples by families because they were followers of Christ
  4. d) Betrayal of the followers of Christ
  5. e) Prosecution and imprisonment of Christians.
  6. f) Many false messiahs. People would come claiming to be the Messiah, the Son God
  7. g) Wars as nation rise against nations
  8. h) Eruption of natural calamities such as plagues, earthquakes, famines, great fear among people.
  9. i) Disruption in the sky and seas. Fall of strange heavenly beings from the sky and rise of seas.
  10. j) Natural calamities such as earthquakes, plagues, famines bringing despair and distress in all nations
  11. k) The times shall be announced by signs in the stars, moon, sun and sea
  12. l) Appear of the ‘Son of man ‘ in power and glory at the end of times.

 

  1. Uses of the temple during the time of Jesus

During the time of Jesus, the temple was used for

(a) Child dedication

(b) Circumcision

(c) Purification

(d)Trading and business centre

(e) Worshiping and prayer

(f) a place for celebrating festivals such as the Passover and other major feasts

(g) a learning centre or school for religious purposes. For example disciples of the scribes learnt law in the temple.

The destruction of the temple symbolized the birth of Christianity. From that time Christians became the new temple of God.

 

  1. The parable of the fig tree Lk.21: 29 – 33

Jesus used the parable of the fig tree to explain more about the end times. Appearance of leaves in the fig tree and other trees inform us that summer will soon come. When Christians see signs of the end times, they should know that the kingdom of God is about to come. Jesus told disciples to be watchful, alert, and praying for strength to endure the coming tribulations. See the previous teachings on watchfulness and readiness. Christians are to watch out and be ready for the end times.

 

  1. Relevance of Jesus’ teachings on eschatology

These teachings assure and continue to tell Christians these messages from Jesus:

  1. a) There is life after death
  2. b) Christ will return to receive the faithful
  3. c) Christians are to be watchful, prayerful, and hopeful despite trials and tribulations
  4. d) Christians are assured of God’s protection from evil.
  5. e) Christians should prepare for the coming of Christ by leading a righteous life
  6. f) Do not lose hope
  7. g) Do not be pre occupied with the cares of this would for they never end
  8. h) Preach and spread the word of God
  9. i) Obey God’s commandment
  10. j) Help the needy

Revision questions

  1. Describe Jesus triumphant entry into Jerusalem according to Luke chapter 19:29- 30
  2. What does the manner of Jesus entry into Jerusalem reveal about the nature of his kingdom?
  3. What lessons can Christians learn from Jesus’ triumphant entry into Jerusalem
  4. State and explain why Jesus wept over Jerusalem
  5. Explain the cleansing of the temple
  6. Give reasons why Jesus cleansed the temple of Jerusalem
  7. What lessons can Christians learn from the cleansing of the temple?
  8. Explain Jesus’ conflict with the Jewish leaders
  9. Describe the parable of the tenants in the vineyard
  10. Explain the relevance of the parable of the of tenants in the vineyard
  11. Explain the question about paying taxes
  12. Explain the question about the resurrection
  13. What is eschatology?
  14. What will happen at the end of the world (eschatology) according to Jesus’ teaching in Luke’s gospel

21; 5-38

  1. How do Christians prepare for the second coming of Christ?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TOPIC SIX: THE PASSION, DEATH AND RESURRECTION OF JESUS

  1. 22 – 24

Passion is a strong feeling of love, hate or anger. Passion of Jesus is the great sufferings of Jesus, which was a deep emotional anguish.

Learning outcomes

By the end of this topic, you should be able to:

(a) Discuss the events of the Lord’s supper

(b) State relevance of the Lord’s supper to Christians today

(c) Describe the events that took place at mount Olives

(d) Describe the events that took place between the arrest and burial of Jesus

(e) Relate the relevance of the sufferings and death of Jesus to Christians today

(f) Explain the importance of resurrection of Jesus to Christians

(g) Describe the resurrection of Jesus – the evidence of his resurrection

(h) Narrate the ascension of Jesus

 

The plot against Jesus

The Jewish religious leaders were determined to ensure that Jesus was either arrested or killed (Lk.22: 1 – 6)

They were helped by Satan who entered into Judas Iscariot one of the twelve disciples of Jesus. Judas decided to betray Jesus. He communed with the Jewish leaders who agreed to pay him money to betray Jesus. He searched for a way to betray Jesus without knowledge of Jesus. He forgot who Jesus was.

Judas agreed to betray Jesus probably because:

  1. He belonged to the party of Zealots who wanted political changes
  2. He was probably frustrated by Jesus’ approach to the Kingdom of God which was establishing a peaceful spiritual kingdom
  3. He expected Jesus to establish a political kingdom
  4. He was greedy for money
  5. Satan entered him

 

LESSON ONE: THE LORDS SUPPERS/ THE LAST SUPPER. LK 22: 7 – 13

The last supper was the lost Passover meal that Jesus took before his arrest. Passover is celebrated in obedience to God’s command to Moses. It is a remembrance of Israel’s deliverance by God from slavery in Egypt.

  1. The Passover meal

Preparations for the Passover, Read Luke 22: 7 – 23.

Peter and John were sent by Jesus to go and prepare the Passover meal. They were to do so in a house in the city. They were taken to the house by, a man who was carrying a vessel of water. They were given a big furnished upper room upstairs. They prepared the Passover meal as instructed by Jesus.

Passover meal

During the meal with the 12 disciples / apostles Jesus told them that this was going to be his last meal with them before his death. He took a cup of wine gave thanks to God and said “Take this and share itamong yourselves. I tell you that from now on I will not drink this wine until the Kingdom of God

comes.” The cup of wine was his blood that he was going to shed for them. Wine therefore symbolized the blood of Jesus, shed for the purification of humankind and forgiveness of sins. This blood is the New Testament and covenant with Christians.

After drinking of wine, He “took a piece of bread, gave thanks to God “ and shared it and told them that the piece of bread represented his body which is “given for them”.

He presented his death as a sacrifice whose blood sealed the new covenant. His death replaced the sacrifices of the Old law, those of animals, which sealed the Sinai covenant. The new covenant will be for all people including Gentiles. This is to fulfill God’s promise of salvation for all people. Jesus and disciples ate Passover together so that henceforth Christians would eat the meal together in remembrance of Jesus. Passover was initially taken to remind them of the deliverance from Egypt. But during the last supper, Jesus gave the Passover a new meaning.

As they ate, Jesus foretold of his betrayal by one of his disciple.

 

SAQ.

  1. Which items were used to celebrate the Passover in the Old Testament?
  2. What items do modern Christians use to celebrate the Lord’s Supper?

 

Comparisons of the Lord’s Supper and the Passover

(a) The Passover commemorates the divine act of redemption of the Jews from their bondage in Egypt while the Last Supper commemorates the deliverance of human kind from sin.

 

(b) The Passover feast reminded the Israelites that they were free, redeemed people while the Lords Suppers is to remind Christians of their forgiveness of sins. The death of Jesus set Christians free from sins.

 

(c) Passover was followed by the Old covenant of Mount Sinai. The Lords suppers is a new covenant based on the death of Jesus for sins of humankind

 

(d) Passover (Old testament) was sealed by the blood of Lambs while New Covenant (Lords suppers) is sealed by the blood of Jesus on the cross.

 

(e) Items for celebrating in Passover (old testament) are different from the cup of wine and pieces of bread used by Jesus to celebrate his last supper with the disciples.

 

Relevance of the Lord’s Supper today

Christians celebrate the Lords supper. This celebration is called the Eucharist, the Lords suppers, or Lords meal. Christians celebrate it as an act of repentance; through which they receive assurance of forgiveness of their sins. The presence of Jesus becomes a reality when Christians share bread and wine.

Bread and wine are symbols of heavenly feast, which Christians will partake in God’s kingdom.

The Lords supper is also a sacrifice of praise and thanksgiving to God. It is a time for rededication to Christ and self-renewal. Through the celebration of the Lords supper, Christians anticipate the second coming of Jesus and the establishment of Gods Kingdom. It is also a time to remember the death and resurrection of Jesus and reflect on God’s love for humankind.

 

 

  1. The Argument about Greatness. Read Luke, 22: 24 – 30

 

A question arose among the disciples. They wanted to know who among them was the greatest. Jesus told them that they do not belong to the world system of authority given on the basis of wealth and fame.

The authority among the disciples will be determined on the basis of their service to others. The greatest is the servant. Jesus likened himself to a servant hence disciples are called to serve. By sharingin trials and sufferings of Jesus, the disciples will share in his ruling power over the new Israel.

Leadership in church should be understood in terms of service – being a servant of people. In the community of Christians, all people who are followers of Jesus are all equal.

 

SAQ. In your opinion, which are the signs of greatness in the world?

  1. Jesus Predicts Peters’ Denial. Read Luke, 22: 31 – 38

Jesus told peter that Satan had received permission to test or tempt all the disciples but Jesus had prayed for Peter’s faith not to fail. Jesus told Peter that he shall deny Jesus three times before the cock crows.

Jesus was telling his disciples that they will encounter hostility in their evangelism hence they should be prepared for suffering and opposition because of Him as Isaiah 53:12 says ‘he shared the fate of evil men.’ Jesus death was imminent inevitable. The disciples were expected to be strong

 

LESSON TWO: PRAYER, ARREST OF JESUS AND DENIAL BY PETER

Learning Outcomes. By the end of this lesson, you shall:

  1. Narrate the events that took place at Mount of Olives
  2. Describe the arrest of Jesus
  3. Discuss Peter’s denial of Jesus
  4. Describe the arrest of Jesus

 

  1. a. Prayer on the Mount of Olives. Read Luke. 22: 39 – 46

After celebrating the last supper, Jesus went to the Mount of Olives with his disciples to pray to resist temptation. Jesus went ahead of his disciples, knelt down and prayed.

Jesus left them to pray by himself. He said” Father if you will, take this cup of suffering away from me.

Not my will, however, but your will to be done” (42). An angel came to strengthen him. He prayed earnestly, in agony and turmoil great than the physical pain. He sweated great drops of blood.

After praying, Jesus found his disciples asleep “worn out by their grief” vs. 45). Jesus asked them to wake up and pray to avoid temptation.

Significance

The disciples fell asleep. This was a sign of moral and physical exhaustion. Jesus expressed inner struggle about the fulfillment of his messianic mission. He prayed for God’s help. Christians should always pray to avoid temptation and seek God’s help.

 

 

 

  1. b. Betrayal and arrest of Jesus. Read Luke, 22: 47 – 53

Jesus was arrested by: the chief priest, elders, officers of the temple guard, and a crowd of people as he talked to his disciples. He was taken to the house of the high priest. Judas had identified Jesus with a kiss. Jesus asked Judas” him “Judas, is it with a kiss that you betray the Son of man?”

Jewish religious leaders had come to arrest Jesus as they arrested other criminals. Jesus told his disciples not to resist his arrest. He rejected armed resistance refusing the role of a political messiah. Peter followed him from a distance.

 

 

  1. Peters Denies Jesus. Read Luke, 22: 54 – 65

After Jesus was arrested he was taken to the house of the High Priest. As Peter sat warming himself with

others, a maid identified Peter. She said, “This man too was with Jesus. Peter denied knowing Jesus

three times. After the third denial, the cock crowed just as Jesus predicted.

Jesus turned and looked at Peter who remembered the words of Jesus. “Peter went out and wept

bitterly” (Vs. 62). Weeping was a sign of repentance

 

LESSON THREE: THE TRIALS AND CRUCIFIXION OF JESUS

Lesson Outcomes.By the end of this lesson. You should

  1. Describe trials of Jesus by the various authorities
  2. Explain the importance of the judgement by Pilate
  3. Narrate events leading to crucifixion of Jesus
  4. Trials of Jesus by the various authorities
  5. Trial by the Sanhedrin Lk.22: 66 – 71

 

After being taken to the house of the High Priest, the next morning Jesus was taken to the Jewish

Religious council or court; called the Sanhedrin. They all asked him if he was the messiah. Jesus told they wouldn’t believe whatever he says. But “ the Son of Man will be seated on the right hand of Almighty God.” (Vs. 69). Jesus told them he was the Son of God. The Sanhedrin accused Jesus of blasphemy, a sin punishable by death.

 

  1. ii. Trial before Pilate. Read Luke 23: 1 – 5

The second court was the Roman court. The judge was Pilate, the Roman Governor. In this court the Sanhedrin accused Jesus of:

 Inciting people to revolt, and rebelling against Roman authority

 Forbidding people to pay taxes to the Emperor

 Claiming to be the king, a Messiah,

They could not accuse him of blasphemy before Pilate since this offence was not acceptable under the Roman law. Pilate asked Jesus if he was the king, Jesus replied, “ So you say”. (vs.3). Pilate found no fault with Jesus so he sent him to Herod.

 

iii. Trial by Herod. Read Luke, 23: 6 – 12

Herod was in Jerusalem. When Jesus was brought before him, he expected Jesus to perform miracles to impress him. He asked Jesus many questions and Jesus kept quiet. Herod and his soldiers mocked Jesus, and ridiculed him. They put on him royal clothes; then sent Jesus back to Pilate.

 

  1. Jesus is sentenced to Death. Read Luke 23: 13 – 25

Jesus was brought back to Pilate a second time. Pilate repeated that Jesus was not guilty (innocent) of any crime. Pilate offered to have Jesus beaten and then released.

The crowds, leaders and chief priests gave their judgment. “Kill him!” and release Barabbas, who was a rioter and a murderer. Pilate did not find Jesus guilty. But he did what they wanted. He released Barabbas and “ handed Jesus over for them to do as they wished” (vs. 25).

 

  1. v. The crucifixion of Jesus. Read Luke 22: 26-43

 

Jesus was led away to be crucified. Solders forced Simon of Cyrene to carry the cross for Jesus. Women followed Jesus and weeping. Jesus told them not to weep for Him but for themselves and their children.

Jesus was then crucified at a place called Golgotha (place of skull) or Calvary together with two male criminal; one on His right and the other on His Left. Jesus asked God to forgive them (persecutors) for they did not know what they were doing.

The Jewish leaders, said “He saved others; let him save himself if he is the Messiah whom God has chosen” (vs. 35); Solders mocked Jesus and said “Save yourself if you are the king of Jews” and one criminal hanged with Jesus mocked Jesus and told Him “Aren’t you the Messiah? Save yourself and me”.

The other thief rebuked him saying they deserved the punishment for their deeds but Jesus had done nothing. This thief repented and told Jesus, “Remember me, Jesus, when you come as King”. Jesus told him that he would be in paradise with Jesus on that day (vs. 42 – 43).

On top of the cross, Jews wrote, “This is the King of the Jews” (vs. 38).

 

LESSON FOUR: DEATH OF JESUS. Read Luke. 23: 44 – 50

Learning outcomes. By the end of this lesson,

  1. Describe the death of Jesus
  2. Narrate the burial of Jesus
  3. State relevance of the suffering and death of Jesus to Christian life today
  4. The death of Jesus. There was darkness from 12 o’clock until thee o’clock.

The veil/curtain of the temple tore into two. Jesus cried out with a loud voice “ Father, into thee hands I commit my spirit”. At this shout Jesus died.

The Roman centurion saw and praised God. He declared, “Certainly this was an innocent man”. The multitude that watched the crucifixion and death went home beating their breasts, a sign of repentance.

The women, who knew Jesus from Galilee, stood at a distance watching all these things.

 

  1. The burial of Jesus. Read Luke 23: 50 – 56.

Joseph from Arimathea, a town in Judea sought permission from Pilate to bury the body of Jesus. He was waiting for the coming of the Kingdom of God, a likely secret disciple of Jesus. He was a good and honorable man.

The body of Jesus was laid in a sepulchre (Tomb) where nobody had ever been laid. Jesus’ burial in Joseph’s tomb fulfilled Isaiah’s prophecy that the suffering servant of Yahweh was buried in a rich man’s tomb (Isaiah 53:9)

The Galilean women and Joseph saw where the body of Jesus was laid. They went home, and prepared spices to use to wash Jesus’ body. They rested on the Sabbath.

 

  1. Relevance of the suffering and death of Jesus Christ to Christian life today

Christians today should practice or do the following activities.

  1. Pray in times of sorrow, pain, trials and temptations.

iii They should not give up when rejected.

iv They should be aware of hypocrites and traitors amongst them.

v They should be willing to suffer for the sake of the Kingdom of God.

vi They should be ready to fight for a just cause

vii They should never condemn the innocent.

viii They should go through their suffering bravely.

ix They should know and accept suffering as a part of the Christian calling

x They should not be afraid of rejection by people l

xi They should be encouraged that Jesus suffered for them.

 

  1. d. In which ways can Christians prepare for their death?

Death is inevitable. Hence, Christians should at all times: live a holy life, repent sins, forgive those who have wronged them, make a will, accept death as inevitable, and read the word of God

 

LESSON FIVE: THE RESURRECTION OF JESUS. Read Luke 24: 1 – 53

  1. The Resurrection.

Resurrection refers to the event of Jesus rising from the dead

After the Sabbath day, on Sunday morning; Mary Magdalene, Mary the mother of James, Salome (Joanna) and other women, went to the tomb with the spices they has prepared. They found the entrance open. The stone covering the tomb was rolled away. The tomb was empty. The body of Jesus was not in the tomb.

Suddenly, two men, who were angels, appeared dresses in dazzling and shining clothes. They said “ Whyare you looking among the dead for one who is alive? He is not here; he has been raised. ”

The women went and told the 11 disciples, who did not believe them. Peter ran to the tomb and found it empty.

Women were the first to witness the resurrection of Jesus Christ. This is significant as they (women) were empowered to become witnesses of Christ as evangelists beyond the Jewish culture.

  1. Witnesses of the resurrection of Jesus

The disciples’ en route to Emmaus

Two disciples were traveling to Emmaus, which was 11 km from Jerusalem discussing Jesus suffering, death and the empty tomb. Jesus met them but their eyes were blinded and they did not recognize him.

The disciples explained to Jesus the events that had taken place and how they had hoped that Jesus would liberate Israel from the Roman rule.

Jesus explained to them the scriptures concerning the messiah. When they got to Emmaus, they invited him to dine with them for it was evening. When Jesus, “took the bread and said the blessings; then he broke the bread and gave it to them”, the disciples recognized Jesus but he vanished out of their sight

(vs. 30-31). They returned to Jerusalem and told the 11 disciples that Jesus has risen.

 

  1. Jesus appears to his Disciples. Read Luke 24: 36 – 49. As the two disciples explained the event that happened on the journey to Emmaus, Jesus came and said to them ‘Peace be with you’ (vs. 36). Disciples were terrified and frightened. He asked them to look and touch his hands, and feet. He was not a ghost.

He has flesh and bones unlike ghosts, which do not have.

He explained to the apostles his mission, which was prophesied by prophets, and written in the Law of Moses, and Psalms (v.44).

He commissioned the disciples to preach repentance and remission of sins and be his witnesses. He alsopromised to send them the promise of the father (Holy Spirit)

SAQ. What was the nature of the resurrected body of Jesus?

  1. The ascension of Jesus, Luke, 24: 50 – 53

From Jerusalem, Jesus took his disciples to Bethany, a town outside Jerusalem. He lifted his hands and blessed them. As he blessed them, he was lifted up and carried to heaven.

The disciples worshipped him and returned to Jerusalem with great joy. They continued to go to the temple to praise and give thanks to God.

The disciples were now confident about their mission and who Jesus was

 

  1. The importance of the resurrection of Jesus to Christian

Resurrection is the foundation of Christian faith. Christianity is based on the fact that Jesus resurrected and was taken up to heaven. Further to this:

  1. Resurrection proved that Jesus is the Son of God.
  2. Through resurrection, Christians have hope of eternal life
  3. Through resurrections, Christians are assured of a new life in Christ
  4. Sin and death were conquered by resurrection, giving hope of victory to Christians over death and sin.
  5. Resurrection is a fulfillment of the writings of the prophets. It fulfilled Old Testament prophesies by Moses, Elijah, Elisha and others.
  6. It is a proof that there is life after death.
  7. Through resurrection, man was reconciled to God.
  8. Jesus has power over death, over Satan and his Kingdom of darkness
  9. It led to the coming of the Holy Spirit.

 

Revision questions

  1. Give the different names used in reference to the lord’s supper by Christians in different churches
  2. Describe the institution of the lord’s supper

c, State the Christian teaching about the lord’s supper

  1. What is the meaning of the lord’s supper to Christians?
  2. Compare the Passover feast with the practice of the lord’s supper
  3. Describe the prayer on mount olives
  4. Describe the betrayal and arrest of Jesus
  5. State the reasons that made Judas Iscariot to betray Jesus
  6. Describe the trial of Jesus under the following headings:-

the council of Sanhedrin, the trial before Pilate, the trial before Herod and Pilate’s judgement.

  1. Why do you think Pilate agreed to have Jesus crucified?
  2. Identify and explain the lessons that Christians learn from the actions of Pilate during the trial of Jesus
  3. Actions taken by the Jewish leaders to ensure that Jesus was put to death
  4. Explain the crucifixion of Jesus
  5. Describe the death of Jesus
  6. The burial of Jesus
  7. Define the term resurrection
  8. Describe the four witnesses of the risen Christ
  9. Describe Jesus’ appearance to the disciples
  10. Describe the ascension of Jesus
  11. Give five evidences from the bible to show that Jesus rose from the dead
  12. Explain the significance of passion, death and the resurrection of Christ
  13. What is the significance of Jesus resurrection to Christians today
  14. Explain five importance of eulogy of death of the society.

Revision question and answers

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ebukanga TVC Kuccps Courses, Fees, Requirements, Duration & Career Opportunities

Ebukanga TVC Kuccps Courses, Fees, Requirements, Duration & Career Opportunities

EBUKANGA TECHNICAL AND VOCATIONAL COLLEGE

PROGRAMMES ON OFFER FOR 2023/2024 CYCLE

# PROGRAMME CODE PROGRAMME NAME INSTITUTION TYPE YEAR 1 – PROGRAMME COST 2022 CUTOFF 2021 CUTOFF 2020 CUTOFF
1 4100701 DIPLOMA IN AUTOMOTIVE ENGINEERING KSH 67,189
2 4100708 DIPLOMA IN MECHANICAL ENGINEERING KSH 67,189
3 4100746 DIPLOMA IN SUPPLY CHAIN MANAGEMENT KSH 67,189
4 4100755 DIPLOMA IN HUMAN RESOURCE MANAGEMENT KSH 67,189
5 4100758 DIPLOMA IN INFORMATION COMMUNICATION TECHNOLOGY KSH 67,189
6 4100774 CERTIFICATE IN BUILDING TECHNOLOGY KSH 67,189
7 4100775 CERTIFICATE IN SECRETARIAL STUDIES SINGLE AND GROUP KSH 67,189
8 4100831 CERTIFICATE IN ELECTRICAL AND ELECTRONIC ENGINEERING (POWER OPTION) KSH 67,189
9 4100876 DIPLOMA IN BUILDING TECHNOLOGY KSH 67,189
10 4100888 CERTIFICATE IN HUMAN RESOURCE MANAGEMENT KSH 67,189
11 4100889 CERTIFICATE IN INFORMATION COMMUNICATION TECHNOLOGY KSH 67,189
12 4100917 DIPLOMA IN ELECTRICAL & ELECTRONIC ENGINEERING (POWER OPTION) KSH 67,189
13 4100920 CERTIFICATE IN MECHANICAL ENGINEERING KSH 67,189
14 4100927 CRAFT CERTIFICATE IN AUTOMOTIVE ENGINEERING – OLD PROGRAMME KSH 67,189
15 4100935 ARTISAN IN PLUMBING – OLD PROGRAMME KSH 67,189
16 4100957 CRAFT CERTIFICATE IN SUPPLY CHAIN MANAGEMENT KSH 67,189
17 4100981 CRAFT CERTIFICATE IN WELDING AND FABRICATION KSH 67,189
18 4100A21 ARTISAN IN ELECTRICAL INSTALLATION KSH 67,189
19 4100A29 ARTISAN IN MOTOR VEHICLE MECHANICS KSH 67,189
20 4100A44 ARTISAN IN MASONRY KSH 67,189
21 4100B08 ARTISAN IN MECHANICAL ENGINEERING KSH 67,189
22 4100B15 ARTISAN WELDING AND FABRICATION KSH 67,189
23 4100C03 CRAFT CERTIFICATE IN AUTOMOTIVE ENGINEERING KSH 67,189

Kabete National Polytechnic kuccps admission letters portal login

Received a message from Kuccps that you have been selected to join the Kabete National Polytechnic? Well. Congratulations for the selection.

The next step is for you to download your Kuccps admission letter at the Kabete National Polytechnic kuccps admission letters portal login.

Your admission letter is an important document that shows proof of admission. It also enables you to prepare for your admission.

ADMISSION REQUIREMENTS

This offer is made on the basis of the statement of your qualifications as contained in the copies of certificates that you supplied along with your application for admission and is therefore subject to satisfactory verification by the Polytechnic. Any information found to be untrue will automatically lead to nullification of this offer.

In view of this, you MUST, on the reporting date, present the following;

 Two (2) Passport size photos,
 Two (2) copies of letter of offer of Admission,
 Originals and Copies of the following: (a) KCPE result slip, (b) KCSE result slip, (c) Birth certificate, (d) National ID card,
 Data Capture Form A (downloadable from mis.kabetepoly.ac.ke after completing your data submission)
 Duly signed Bond of Conduct (form B) , Medical Certificate of fitness (form C) (downloadable from mis.kabetepoly.ac.ke),
 Training requirements (Available on the mis.kabetepoly.ac.ke).

The offer is also subject to the following conditions:

i. Your undertaking to adhere to the Rules and Regulations, governing studentship of the Polytechnic
ii. Your acceptance to pay fees in accordance with the Polytechnic fee payment guidelines).
iii. Your promise to abide by the terms and conditions set out in the attached declaration for Admission and;
iv. Your execution of the attached Bond of conduct (downloadable from mis.kabetepoly.ac.ke)

FEE PAYMENT

Fees is payable in full on or before commencement of each Term. A Trainee shall be allowed to register only after paying full fees as per the new Government fee payment model available at www.hef.co.ke

You are thereafter required to download the Polytechnic’s Fee Structure (Available on the Dashboard) and make payments as per your need level and submit M-Pesa message/ payment receipt through www.mis.kabetepoly.ac.ke

CATERING AND ACCOMODATION

Limited Accommodations is available at the Polytechnic. Trainees are thus advised to confirm availability of hostel before paying the accommodation fee. The slots are only allocated upon
payment of full tuition fees and priority will be given to persons living with disability.

Allocation of Hostels to interested persons will be done during Registration on reporting day and will be based on first come first served.

The Polytechnic operates cafeteria system i.e. Pay as You Eat which has incorporated a cashless payment system using the equity bank smart card. This technology allows parents/guardians to top up the credit on their son’s/daughter’s cards using Mpesa or direct bank deposits.

We encourage you to purchase meals in the Polytechnic as they are safe and highly subsidized (Download Reporting and Orientation Program)

Welcome to Kabete National Polytechnic. Premier Polytechnic of Choice.

Continue reading:

Kuccps portal login

The KUCCPS Portal Guide – Simplified KUCCPS Application Guide

KUCCPS Portal, Website


Your Complete guide to Higher Education Courses:

Guide to KMTC Courses, requirements, contacts, fees, duration and how to apply

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Baraton University Courses, requirements, contacts, fees, duration, portals, website and how to apply

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University of Eldoret Courses, requirements, contacts, fees, duration, portals, website and how to apply

KCSE 2023 Exams: Latest News on Marking and Results Release

The Marking exercise for the 2023 Kenya Certificate of Secondary Education, KCSE, is ongoing. The marking exercise is carried out by Kenya National Examinations Council, Knec, invited examiners; who are usually Secondary school teachers.

The 2023 marking exercise is being done at centres in Nairobi City and its environs. Knec has announced an increment in the Coordination fees, transport and scripts marking fees. This will ensure that the marking exercise is smooth and may not be disrupted like in 2022.

After marking is done, results are expected by 22nd of this Month; before Christmas.

Also read: Knec Introduces New KCSE Grading System 2023 onwards

2023 KCSE candidates will be able to receive their results instantly by using any of the following methods:

One: Knec SMS Code.

Knec has unveiled a new SMS code for the KCSE results. Once results are out, the students can send their full KCSE 2023 index number to 40054.

Two: Using the Knec Portal.

KCSE 2023 results are also posted on the official Knec Portal. Login here to download results for all candidates.

Three: Visiting Former Secondary Schools.

KCSE 2023 candidates can at the same time visit their secondary schools to get results on the Master nominal roll and provisional KCSE result slips.

Keep it here for all the results analysis and ranking of students and schools.

TSC Minet Latest List of all Service Providers, Hospitals in Kilifi County: Their Contacts, Location and Services Offered

TSC Minet Latest List of all Service Providers, Hospitals in Kilifi County: Their Contacts, Location and Services Offered

Region County Sub-county Town Name of Service Provider Access Services
COAST KILIFI
COAST KILIFI BAMBA BAMBA BAMBA MATERNITY AND NURSING HOME DIRECT OP
COAST KILIFI MALINDI MALINDI BLISS GVS HEALTHCARE LTD MALINDI DIRECT OP/OPTICAL
COAST KILIFI KILIFI SOUTH MTWAPA BLISS GVS HEALTHCARE LTD MTWAPA DIRECT OP/DENTAL/OPTICAL
COAST KILIFI GANZE GANZE CHAMALO MEDICAL CLINIC DIRECT OP/MAT
COAST KILIFI KILIFI MARIAKANI MEPHI HEALTH SERVICES DIRECT IP/OP/MAT
COAST KILIFI KILIFI NORTH TEZO JAMBO JIPYA MEDICAL CENTRE AND MATERNITY DIRECT IP/OP/MAT
COAST KILIFI MALINDI MAGARINI KIJANAHERI MEDICAL CENTRE MAGARINI DIRECT OP
COAST KILIFI MALINDI MARAFA KIJANAHERI MEDICAL CENTRE MARAFA DIRECT OP
COAST KILIFI MALINDI MALINDI MERIDIAN HOSPITAL GALANA DIRECT IP/OP/MAT
COAST KILIFI KILIFI NORTH KILIFI STAR HOSPITAL DIRECT IP/OP
COAST KILIFI KALOLENI KALOLENI BOMBOLULU DIAGNOSTIC MEDICAL CENTRE DIRECT IP/OP/MAT

Bachelor of Business Administration Degree 2023-2024 Kuccps Cutoff Points, Clusters

Bachelor of Business Administration Degree 2023-2024 Kuccps Cutoff Points, Clusters

BACHELOR OF BUSINESS ADMINISTRATION WITH IT
# PROG CODE INSTITUTION NAME PROGRAMME NAME 2023-2024
1 1053153 JARAMOGI OGINGA ODINGA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
BACHELOR OF BUSINESS
ADMINISTRATION WITH IT
21.444
2 1063153 TECHNICAL UNIVERSITY OF MOMBASA BACHELOR IN BUSINESS ADMINISTRATION 21.444
3 1173153 DEDAN KIMATHI UNIVERSITY OF TECHNOLOGY BACHELOR OF BUSINESS ADMINISTRATION 21.444
4 1229153 MASENO UNIVERSITY BACHELOR OF BUSINESS
ADMINISTRATION ( WITH IT)
21.444
5 1240153 MERU UNIVERSITY OF SCIENCE AND TECHNOLOGY BACHELOR OF BUSINESS ADMINISTRATION 21.444
6 1060153 RIARA UNIVERSITY BACHELOR OF BUSINESS ADMINISTRATION 24.258
7 1077153 KENYA METHODIST UNIVERSITY BACHELOR IN BUSINESS
ADMINISTRATION
21.444
8 1090153 SCOTT CHRISTIAN UNIVERSITY BACHELOR IN BUSINESS ADMINISTRATION 21.444
9 1107153 ST PAULS UNIVERSITY BACHELOR IN BUSINESS ADMINISTRATION 21.444
10 1119153 AFRICA INTERNATIONAL UNIVERSITY BACHELOR IN BUSINESS
ADMINISTRATION
21.444
11 1181153 UNIVERSITY OF EASTERN AFRICA, BARATON BACHELOR IN BUSINESS ADMINISTRATION IN MARKETING 21.444
12 1196153 PRESBYTERIAN UNIVERSITY OF EAST
AFRICA
BACHELOR OF BUSINESS
ADMINISTRATION
21.444
13 1515153 TOM MBOYA UNIVERSITY BACHELOR OF BUSINESS ADMINISTRATION ( WITH IT) 21.444
14 1555153 KENYA ASSEMBLIES OF GOD EAST UNIVERSITY BACHELOR IN BUSINESS ADMINISTRATION 21.444

KCPE 2023 Top 100 Candidates Nationally

Here is a list of the KCPE 2023 top 100 candidates nationally.

Michael Warutere who topped the 2023 KCPE exams countrywide
Michael Warutere who topped the 2023 KCPE exams countrywide

Michael Warutere from Riara Group of Schools emerged top student in KCPE 2023 with 428 marks. He says he wants to go to Mang’u High School and eventually persue Software Engineering.

Emmaculate Washeke of Gilgil Hills Academy scored 427 marks in KCPE 2023

Emmaculate Washeke of Gilgil Hills Academy scored 427 marks in KCPE 2023; leading candidate in the country has 428 marks.

Debra Aluel from Ndima Kanini primary school in Nyeri scored 425

Debra Aluel from Ndima Kanini primary school in Nyeri scored 425 mark while number one nationwide got 428 mark

2023 KCPE Results Summary:

– 400 to 500 marks: 8,525 candidates

– 300 to 399 marks 352,782 candidates

– 200 to 299 marks: 658,278 candidates

– 100 to 199 marks:- 383,025 candidates

– 01 – 99 marks: 2,060 candidates

– Top candidate scored 428 marks

– 1,406,557 candidates sat for the 2023 KCPE examination.

– 9,354 candidates didn’t sit for the examination and will have a chance to do a special examination in January 2024.

– No candidate will repeat Class 8 as this year’s results will be the last of KCPE under the 8-4-4 system.

– 2023 KCPE marks the end of the 8-4-4 system. KPSEA system will be fully operational.

– Candidates can get their results by sending their index Number followed by initials ‘KCPE’ to SMS 40054.

KUCCPS Student Portal : Application Portal 2022

KUCCPS Student Portal : Application Portal Guide

KUCCPS Student Portal : KUCCPS Application Portal: KUCCPS Application Portal | KUCCPS Students Portal : KUCCPS Application Portal

The KUCCPS Students Portal : KUCCPS Application Portal  –  students.kuccps.net… Kenya Universities and Colleges Central Placement Service Portal | University of Nairobi Student Portal Login / Registration for the fresh and stale students.

Kenya Universities and Colleges Central Placement Service Student Portal, KUCCPS Student Portal , KUCCPS Principal Portal, KUCCPS Institution Portal, KUCCPS kuccps.net…. See Full Detail Below…

The Authority of the Kenya Universities and Colleges Central Placement Service (KUCCPS) has enabled the student portal. The Online Portal is created for formal and prospective students of a University to create an account or log in to perform certain academic actions at ease e.g. Application to an institution, checking the list of courses offered by institutions, Checking Admission Status and so much more.

KUCCPS Students Portal : KUCCPS Application Portal  –  students.kuccps.net

You may visit and Access the KUCCPS Students Portal, KUCCPS Principal Portal, KUCCPS Institution Portal, KUCCPS kuccps.net using a computer or mobile via the following links:

  • 1 KUCCPS Students Portal: http://students.kuccps.net/
  • 2 KUCCPS Student Login Portal: http://students.kuccps.net/login/
  • 3 KUCCPS Principal Portal: http://schools.kuccps.net/
  • 4 KUCCPS Institution Portal: http://institutions.kuccps.net/
  • 5 KUCCPS Official Website: http://www.kuccps.net/

KUCCPS Contact Details

ACK Gardens, 1st Ngong’ Avenue, Upperhill Nairobi

Telephone : 0723954927, 0734879662

Email : info@kuccps.ac.ke

Website: kuccps.ac.ke

P. O. Box 105166 – 00101

See Also:

1 Kenya Universities and Colleges Central Placement Admission Letters

2 Kenya Universities and Colleges Central Placement Courses

3 Kenya Universities and Colleges Central Placement Admission List

4 Kenya Universities and Colleges Central Placement Contacts

5 Kenya Universities and Colleges Central Placement Cluster Points

6 Kenya Universities and Colleges Central Placement Diploma Courses

7 Kenya Universities and Colleges Central Placement Intake

8 Kenya Universities and Colleges Central Placement Application Procedure

9 Kenya Universities and Colleges Central Placement Application Fee

10 Kenya Universities and Colleges Central Placement Bachelor Courses

11 Kenya Universities and Colleges Central Placement Cut Off Points

12 Kenya Universities and Colleges Central Placement Diploma Application

13 Kenya Universities and Colleges Central Placement Application Deadline

14 Kenya Universities and Colleges Central Placement Extension

15 Kenya Universities and Colleges Central Placement Huduma Centres

16 Kenya Universities and Colleges Central Placement eligibility

17 Kenya Universities and Colleges Central Placement Fee Structure

18 Kenya Universities and Colleges Central Placement First Revision For Candidates

Quick Links

1 Kenya Universities and Colleges Central Placement University First Revision of Courses

2 Kenya Universities and Colleges Central Placement Online Application Form Download

3 Kenya Universities and Colleges Central Placement Formula

4 Kenya Universities and Colleges Central Placement Government Sponsorship

5 Kenya Universities and Colleges Central Placement Helb Loan Application

6 Kenya Universities and Colleges Central Placement Inter University Transfer

7 Kenya Universities and Colleges Central Placement Institutions

8 Kenya Universities and Colleges Central Placement Intake Deadline

9 Kenya Universities and Colleges Central Placement Inter University Transfer Form

10 Kenya Universities and Colleges Central Placement January Intake

11 Kenya Universities and Colleges Central Placement May Intake

12 Kenya Universities and Colleges Central Placement Marketable Courses

13 Kenya Universities and Colleges Central Placement Mpesa Payment

14 Kenya Universities and Colleges Central Placement Online Application

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16 Kenya Universities and Colleges Central Placement Paybill Number

17 Kenya Universities and Colleges Central Placement Placement Deadline

18 Kenya Universities and Colleges Central Placement Late Application

19 Kenya Universities and Colleges Central Placement Admission Requirements

20 Kenya Universities and Colleges Central Placement Nursing Qualifications

21 Kenya Universities and Colleges Central Placement Registration Fee

How to remove your name from CRB blacklisting

Some times you may be frustrated when seeking for services only to find that you have been blocked due to listing with the Credit Reference Bureau, CRB. Listing with CRB is due to defaulted loan facilities that you may have taken with a financial institution. The listing with CRB should not worry you as it is reversible. You can access CRB services from Metropol website, Metropol Crystobol App or by simply using the USSD code; 433.

CRYSTOBOL REGISTRATION PROCESS.

In order to access the CRB services, first you must register by following the following simple steps: 1). Dial *433# from your registered Safaricom line. 2). Enter your National ID Number; It is mandatory that you use the same ID number that you registered with on M-pesa. 3). Enter the Agent Number; if you were referred by a Metropol Agent, enter their Metropol Agent Number. Otherwise, enter 0 (Zero) to proceed. 4). Confirmation of entered details; Confirm the entered details in order to complete the registration. 5). Payment; In order to complete the registration, you have to pay Sh100. To complete your registration, go to the M-pesa menu, select Payment Services (Lipa Na M-pesa) then select Paybill. Enter 220388 as the Business Number and your ID Number (Which you used to register) as the account number. Enter 100 as the amount. Then enter your M-peas PIN and click on send. 6). Successful message; If the payment is successful, you will receive an SMS confirming your registration, together with your Crystobol PIN and link to your free credit report. 7). How to download your Free Credit Report; Your Credit Report will enable you to know which institutions have made you to be listed on CRB. To download your free Credit Report, Remember to check your Metro score and your Credit Report regularly.  

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Form Three English Schemes of Work {Revised and Final}

ENGLISH FORM 3 SCHEMES OF WORK

TERM 1

WEEK LESSON TOPIC SUB – TOPIC OBJECTIVES LEARNING/TEACHING ACTIVITIES LEARNING/TEACHING RESOURCES REFERENCES REMARKS
1 1 LISTENING AND SPEAKING STRESS By the end of the lesson, the learner should be able to:

 

·        Stress the appropriate syllables in words

·        Appreciate the fact that stress contributes to meaning

Students reading words given in pairs

Change roles after first reading

 

·        Readers

·        Pictures

·        Secondary English Book 3 students book Page 1-2

·        Teachers Book page 1-2

·        English dictionary

 
  2 STUDY SKILLS Study reading By the end of the lesson, the learner should be able to:

-Choose the right place and time to study

-Develop techniques for concentration.

-Identify the main points as well as the supporting materials.

·        Writing

·        Discussion

·        Reading

·        Demonstration of sitting postures.

·        Chalkboard

·        posters

·        SecondaryEnglish Book 3 students book Page 2-3

·        Teachers guide page 2

 
  3/4 READING Comprehension

The Miracle of Adolescence

By the end of the lesson, the learner should be able to:

·        Read the passage silently

·        Answer questions on the passage correctly.

·        Show awareness of the changes that take place during adolescence.

Reading comprehension

 

·        Pre-reading active

·

·        ties

·        SecondaryEnglish Book 3 students book Page 3-5

·        Teachers guide page 2-4

 
  5/6 GRAMMAR Common ways of forming nouns By the end of the lesson, the learner should be able to:

·        Form nouns using common noun-forming suffixes

·        Use nouns bearing the relevant suffixes in sentences.

·        Discussing

 

·        Writing sentences

·        Dictionary ·        Secondary English Book 3 students book Page 5-8

·        Teachers guide page 4-6

 
  7/8 WRITING SUBSTITUTION IN WRITING By the end of the lesson, the learner should be able to:

·        Write neatly and legibly

·        Use a variety of sentence structures and vocabulary

·        Substitute words for others in order to eliminate clumsiness and repetition.

·        Discussing

·        Writing

Writing

 

·        Secondary English Book 3 students book Page 8

 

·        Teachers guide page 7-8

 
2 1/2 Intensive  reading  

THE PEARL By  John Steinbeck

 

 

 

 

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  3 LISTENING AND SPEAKING INTONATION By the end of the lesson, the learner should be able to:

·        Use rising intonation correctly

·        Use falling intonation correctly

·        Students to work in pairs read given sentences as statement and as questions chalkboard ·        Secondary English Book 3 students book Page 9-11

·        Teachers guide page 9

 
  4 STUDY SKILLS Techniques of pre-reading By the end of the lesson, the learner should be able to:

·        Survey reading materials

·        Formulate pre-reading questions

·        reading chalkboard ·        Secondary English Book 3 students book Page 11-12

·        Teachers guide page 10

 
  5/6 READING Comprehension

The bitter forbidden fruit

By the end of the lesson, the learner should be able to:

·        Read the passage silently

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Appreciate the need to abstain from pre-marital sex.

·        Reading comprehension

·        Writing

·        Discussion

·        Reading

·        Pre-reading activities ·        Secondary English Book 3 students book Page12-14

·        Teachers guide page 11-12

 
  7/8 GRAMMAR

 

Gender-sensitive language By the end of the lesson, the learner should be able to:

·        Recognize gender biased language

·        Use gender-sensitive language

 

·        Discussing

 

·        Writing sentences

·        Dictionary ·        Secondary English Book 3 students book Page 14-16

·        Teachers guide page 12-13

 
3 1/2 WRITING

 

Transitional words that add information By the end of the lesson, the learner should be able to:

·        Write neatly and legibly

·        Recognize transitional words used in adding information.

·        Use transitional words used in adding information

·        Writing

·        discussion

chalkboard ·        Secondary English Book 3 students book Page 16-17

·        Teachers guide page14-15

 
  3/4 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  5 LISTENING AND SPEAKING Rhythm By the end of the lesson, the learner should be able to:

·        Identify features of rhythm in a poem

·        Appreciate the importance of using rhythm in poetry.

·        Read a poem to bring out its rhythm.

·        Reciting poems

·        chanting

Chalkboard

Poems on manila

·        Secondary English Book 3 students book Page 18-20

·        Poems from East Africa

·        Demystifying poetry

 
  6 STUDY SKILLS Concentration techniques in reading By the end of the lesson, the learner should be able to:

·        Survey through learning material

·        Write pre-reading questions

·        Review the material just read.

·        reading chalkboard ·        Secondary English Book 3 students book Page 20-21

·        Teachers guide page 18

 
  7/8 READING Comprehension

Restoring Integrity in the public service

By the end of the lesson, the learner should be able to:

·        Appreciate the importance of integrity in the public service

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        Secondary English Book 3 students book Page 21-24

·        Teachers guide page 19

 
4 1/2 GRAMMAR Case in pronouns By the end of the lesson, the learner should be able to:

·        Identify pronouns in their various case forms.

·        Use pronouns correctly in the various case forms.

·        Discussing

 

·        Writing sentences

·        Dictionary

·        chalkboard

·        Secondary English Book 3 students book Page 24-27

·        Teachers guide page 21

 
  3/4 WRITING Transitional words that show contrast By the end of the lesson, the learner should be able to:

·        Write neatly and legibly

·        Identify transitional words that show contrast

·        Correctly use the transitional words that show contrast

·        Writing

·        discussion

Chalkboard ·        Secondary English Book 3 students book Page 28

·        Teachers guide page 24-25

 
  5/6 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  7 LISTENING AND SPEAKING Alliteration and assonance By the end of the lesson, the learner should be able to:

·        Identify alliteration in poetry

·        Identify assonance in poetry

·        Explain use of alliteration in poetry

·        Explain the use of assonance in poetry

·        Writing

·        Discussion

·        Reading

chalkboard ·        Secondary English Book 3 students book Page 29-31

·        Teachers guide page 26-28

 
  8 STUDY SKILLS Note-making By the end of the lesson, the learner should be able to:

·        Distinguish main points from illustrations

·        Organize the main points to make notes

·        Reading

·        Writing

chalkboard ·        Secondary English Book 3 students book Page 31-32

·        Teachers guide page 28

 
5 1/2 READING Comprehension

Women break from shackles of traditions

By the end of the lesson, the learner should be able to:

·        Appreciate the importance of gender equality

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        Secondary English Book 3 students book Page 32-34

·        Teachers guide page 29-31

 
  3/4 GRAMMAR demonstratives By the end of the lesson, the learner should be able to:

·        Recognize demonstrative words correctly

·        Use demonstrative words correctly

·        Mark agreement with demonstrative words correctly

·        Discussing

 

·        Writing sentences

·        Dictionary ·        Secondary English Book 3 students book Page 34-36

·        Teachers guide page 31

 
  5/6 WRITING Transitional words that show consequences, cause and effect By the end of the lesson, the learner should be able to:

·        Write neatly and legibly

·        Identify transitional words that show consequences, cause and effect.

·        Use transitional words that show consequences correctly.

·        Writing

·        discussion

chalkboard ·        Secondary English Book 3 students book Page 36-37

·        Teachers guide page33-35

 
  7/8 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
        · · · ·  
6 1 LISTENING AND SPEAKING Dilemma stories By the end of the lesson, the learner should be able to:

·

·        Writing

·        Discussion

·        Reading

chalkboard ·        Secondary English Book 3 students book Page

·        Teachers guide pa

 
  2 STUDY SKILLS Studying a poem through an analysis of diction By the end of the lesson, the learner should be able to:

·        Develop an interest in reading poetry

·        Distinguish among the different kinds of vocabulary available to poets.

·        Relate diction to the meaning of a poem.

·        Writing

·        Discussion

·        Reading

chalkboard ·        Secondary English Book 3 students book Page 40-41

·        Teachers guide pa

 
  3/4 READING Comprehension

Citizens role in good governance

By the end of the lesson, the learner should be able to:

·        Read the passage silently

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        Secondary English Book 3 students book Page  43-45

·        Teachers guide page 39-40

 
  5/6 GRAMMAR Transitive and intransitive verbs By the end of the lesson, the learner should be able to:

·        Distinguish between transitive and intransitive use of verbs.

·        Construct sentences using verbs transitively and intransitively

·        Discussing

 

·        Writing sentences

·        Dictionary ·        Secondary English Book 3 students book Page 45-48

·        Teachers guide page 4-6

 
  7/8 WRITING Use of the colon and the semi-colon, and writing reminders By the end of the lesson, the learner should be able to:

·        Write neatly and legibly

·        Demonstrate mastery in the use of the colon and the semicolon.

·        Write reminders.

·        Writing

·        discussion

chalkboard ·        Excelling in English Book 3 students book Page48-50

·        Teachers guide page 45-47

 
7

 

 

 

     
MID-TERM EXAMS
· · ·  
8        

 

 

 

 

 

·
MID-TERM BREAK
· ·  
9  

1/2

 

 

 

THE PEARL By  John Steinbeck

 

  By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  3 LISTENING AND SPEAKING Features of dilemma story By the end of the lesson, the learner should be able to:

·        Discuss the features of a dilemma story re-tell a dilemma story

·        Story-telling ·        chalkboard ·        Secondary English Book 3 students book Page 51-52

·        Teachers guide page 48-49

·        Oral literature

 
  4 STUDY SKILLS Appreciating a poem By the end of the lesson, the learner should be able to:

·        Identify the features of a poem systematically, analyze a poem.

·        Reciting poems

·        reading

·        Reading

·        Writing

·        Discussion

·        Secondary English Book 3 students book Page 51-52

·        Teachers guide page 48-49

·        Poems from East Africa

 
  5/6 READING Comprehension

HIV The Emotional Journey

By the end of the lesson, the learner should be able to:

·        Appreciate the emotional experiences of HIV infected persons.

·        Read the passage silently

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        Secondary English Book 3 students book Page 55-56

·        Teachers guide page 52-53

 
  7/8 GRAMMAR Infinitives By the end of the lesson, the learner should be able to:

·        Recognize infinitive uses of verbs

·        Construct sentences using both the to-infinitive and the ing-infinitive.

 

·        Discussing

 

·        Writing sentences

·        Dictionary ·        Secondary English Book 3 students book Page 56-58

·        Teachers guide page 54-55

 
10 1/2 WRITING The use of dash and parentheses, and writing personal journals By the end of the lesson, the learner should be able to:

·        Write neatly and legibly

·        Use the dash and parentheses correctly

·        Write personal journals.

·        Writing

·        discussion

Chalkboard

Sample journals

·        Secondary English Book 3 students book Page 58-60

·        Teachers guide page 56-57

 
  3/4 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  5 LISTENING AND SPEAKING Aetiological narratives By the end of the lesson, the learner should be able to:

·        Listen and respond to information on etiological narrative.

·        Explain what an etiological story is.

·        Writing

·        Discussion

·        Reading

chalkboard ·        Secondary English Book 3 students book Page 61-63

·        Teachers guide page 59

 
  6 STUDY SKILLS Critical reading: looking for evidence By the end of the lesson, the learner should be able to:

Read critically by identifying evidence

Read critically by evaluating evidence.

·        Writing

·        Discussion

·        Reading

·        Reading

·        Writing

·        Discussion

·        Secondary English Book 3 students book Page 63-64

·        Teachers guide page 60

 
  7/8 READING Comprehension

“Our rights and responsibilities”

By the end of the lesson, the learner should be able to:

·        Appreciate their rights

·        Appreciate their responsibilities

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 64-66

·        Teachers guide page 62

 
11 1/2 GRAMMAR Phrasal verbs and idiomatic expressions By the end of the lesson, the learner should be able to:

·        Recognize phrasal verbs and idiomatic expressions

·        Use phrasal verbs and idiomatic expressions correctly

·        Appreciate the expressive value of this forms

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 66-69

·        Teachers guide page 63-64

 
  3/4 WRITING Thank you and congratulatory messages By the end of the lesson, the learner should be able to:

·        Write neatly and legibly

·        Write thank you messages

·        Write congratulatory messages

·        Writing

·        discussion

Chalkboard

Sample messages of thanks

·        SecondaryEnglish Book 3 students book Page 69-70

·        Teachers guide page 66-67

 
  5/5 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·         Reading aloud ·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  7 LISTENING AND SPEAKING Features of aetiological narratives By the end of the lesson, the learner should be able to:

·        Role-play in etiological narratives

·        Identify features of etiological narratives

·        speaking Chalkboard ·        SecondaryEnglish Book 3 students book Page 71-73

·        Teachers guide page 68-69

 
  8 STUDY SKILLS Recognize tone and attitude By the end of the lesson, the learner should be able to:

·        Recognize and describe tone and attitude in a piece of writing

·        reciting Chalkboard ·        SecondaryEnglish Book 3 students book Page 73-74

·        Teachers guide page 70-71

 
12 1/2 READING Comprehension

A slip not a Fall

By the end of the lesson, the learner should be able to:

·        Appreciate the value of education.

·        Answer questions on the passage correctly.

·        Learn and use new vocabulary.

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 74-76

·        Teachers guide page 72-73

 
  3/4 GRAMMAR Participles By the end of the lesson, the learner should be able to:

·        Recognize participles

·        Distinguish between verbal and adjectival participles

·        Use participles

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 76-80

·        Teachers guide page 74-76

 
  5/6 WRITING Messages of condolences By the end of the lesson, the learner should be able to:

·        Write neatly and legibly

·        Appreciate the need to empathize with others.

·        Write messages of condolences

·        Writing

·        discussion

Chalkboard

Sample condolence messages

·        SecondaryEnglish Book 3 students book Page80-81

·        Teachers guide page76-77

 
  7/8 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
13 1 LISTENING AND SPEAKING Giving and receiving instructions By the end of the lesson, the learner should be able to:

·

·        Writing

·        Discussion

·        Reading

Chalkboard ·        SecondaryEnglish Book 3 students book Page 82-83

·        Teachers guide page 79

 
  2 STUDY SKILLS Distinguish facts from opinions By the end of the lesson, the learner should be able to:

·        Develop a critical attitude as they read or listen.

·        Distinguish between a fact and an opinion

·        Writing

·        Discussion

·        Reading

Chalkboard ·        SecondaryEnglish Book 3 students book Page 83-84

·        Teachers guide pag81-82

 
  3/4 READING Comprehension

The Great Revelation

By the end of the lesson, the learner should be able to:

·        Appreciate the need  to pay attention to our spiritual needs.

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 84-86

·        Teachers guide page 82-83

 
  5/6 GRAMMAR Quantifiers: few, a few, little and a little. By the end of the lesson, the learner should be able to:

·        Use the quantifiers few, a few, little and a little.

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page86-88

·        Teachers guide page 84-85

 
  7/8 WRITING Imaginative compositions By the end of the lesson, the learner should be able to:

·        Write neatly and legibly

·        Identify the features of an imaginative composition

·        Demonstrate the ability to create suspense in a story

·        Writing

·        discussion

chalkboard ·        SecondaryEnglish Book 3 students book Page 88-89

·        Teachers guide page 86-87

 
  7/8 INTENSIVE READING

 

THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
 

 

 

 

 

 

 

 

 

 

 

 

   
END OF TERM EXAMS

&

CLOSING

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        ·
TERM TWO 2019
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1 1 LISTENING AND SPEAKING Debating By the end of the lesson, the learner should be able to:

·        Appreciate the importance of developing debating skills

·        Participate in a debate and observe the conventions of debating

·        discussion Chalkboard

Picture on students book 3

·        SecondaryEnglish Book 3 students book Page 91-92

·        Teachers guide page 89

 
  2 STUDY SKILLS Reading aloud: interpretive reading By the end of the lesson, the learner should be able to:

·        Explain the meaning of interpretative reading

·        Practice reading poems and passages interpretively

·        Reading

·

Chalkboard

Written speeches

·        SecondaryEnglish Book 3 students book Page 93-95

·        Teachers guide page 92

 
  3/4 READING Comprehension

Global Warming

By the end of the lesson, the learner should be able to:

·        Read the passage silently

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 96-98

·        Teachers guide page 94-96

 
  5/6 GRAMMAR Attributive and predicative use of adjectives By the end of the lesson, the learner should be able to:

·        Distinguish between attributive and predicative use of adjectives

·        Use adjectives attributively and predicatively in their own writing

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 98-100

·        Teachers guide pg 96-98

·

 
  7/8 WRITING Telegrams By the end of the lesson, the learner should be able to:

·        Write neatly and legibly

·        Identify main features of telegram

·        Compose an effective telegram message

·        Writing

·        discussion

Chalkboard ·        SecondaryEnglish Book 3 students book Page 100

·        Teachers guide page 99-100

 
2 1/2 POETRY POETRY Discuss poetic features in a poem ·        Writing

·        Discussion

·        Reading

  ·        Understanding Poetry by Ezekiel Alembi  
  3/4 INSTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  5 LISTENING AND SPEAKING Giving directions By the end of the lesson, the learner should be able to:

·        Appreciate the importance of clear and correct directions

·        Give clear and correct directions.

·           Discussion Chalkboard

Sketch map

·        SecondaryEnglish Book 3 students book Page 101

·        Teachers guide page  101

 
  6 STUDY SKILLS Handling context questions By the end of the lesson, the learner should be able to:

·        Place an extract in its context

·        Answer context questions correctly

·        reading Chalkboard

Excerpts from novels

 

·        SecondaryEnglish Book 3 students book Page  101-103

·        Teachers guide page 103-105

 
  7/8 READING Comprehension

The grand deception

By the end of the lesson, the learner should be able to:

·        Read the passage silently

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 104-106

·        Teachers guide page 105-107

 
3 1/2 GRAMMAR Formation of adverbs By the end of the lesson, the learner should be able to:

·        Recognize adverbs

·        Form and use adverbs in sentences

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 106-108

·        Teachers guide page 108-109

 
  3/4 WRITING Letters of application By the end of the lesson, the learner should be able to:

·        Identify features of a good application letter

·        Write a good a[application letter

·        Writing

·        discussion

Chalkboard

Sample letters

·        SecondaryEnglish Book 3 students book Page108-110

·        Teachers guide page 109-110

 
  5/6 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  7 LISTENING AND SPEAKING Non-verbal cues in communication By the end of the lesson, the learner should be able to:

·        Appreciate the need to dress properly

·        Recognize aspects of appropriate dressing and grooming and how these are related to communication

·        Writing

·        Discussion

·        Reading

Chalkboard

Newspaper cuttings on grooming

·        SecondaryEnglish Book 3 students book Page 111

·        Teachers guide page 111

 
  8 STUDY SKILLS Character and characterization in literary works

 

By the end of the lesson, the learner should be able to:

·        Identify  the different ways in which authors reveal their characters

·        Describe a character correctly

·        Writing

·        Discussion

·        Reading

chalkboard ·        SecondaryEnglish Book 3 students book Page 111-113

·        Teachers guide page 112-113

 
4 1/2 READING Comprehension

Why monkeys live on trees

By the end of the lesson, the learner should be able to:

·        Identify etiological narratives

·        Describe characters in aetiological narratives

·        Answer questions on the passage correctly.

·        Learn and use new vocabulary

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 114-116

·        Teachers guide page 114-116

 
  3/4 GRAMMAR Functions of adverbs By the end of the lesson, the learner should be able to:

·        Recognize the functions of adverbs

·        Use adverbs correctly

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 117-118

·        Teachers guide page 116-119

 
  5/6 WRITING Writing reports By the end of the lesson, the learner should be able to:

·        Write a report

·        Appreciate the importance of writing reports

·        Explain the different parts of a report

·        Writing

·        discussion

Chalkboard

Sample report

·        SecondaryEnglish Book 3 students book Page118-119

·        Teachers guide page 119-120

 
  7/8 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
5 1 LISTENING AND SPEAKING Hot-seating By the end of the lesson, the learner should be able to:

-Define hot-seating and set up hot-seating sessions

-individually impersonate a main character in a play, a novel or short story

Prepare to field questions about their character and role

·        Speaking

·        Discussion

chalkboard ·        SecondaryEnglish Book 3 students book Page 120-121

·        Teachers guide page 121-122

 
  2 STUDY SKILLS How to read the short story By the end of the lesson, the learner should be able to analyze and appreciate  :

·        The plot of a short story

·        The characters in a short story

·        The style of a short story

·        The point of view of a short story

·        The themes and experience of a short story

·        Writing

·        Discussion

·        Reading

Chalkboard

A chart

·        SecondaryEnglish Book 3 students book Page 122-124

·        Teachers guide page 122-123

 
  3/4 READING Comprehension

A precious Gift

By the end of the lesson, the learner should be able to:

·        Read the passage silently

·        Appreciate the need not to discriminate against HIV infected people

·        Appreciate the need to empathize with HIV infected people

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities

·        Posters with HIV/AIDS information

·        SecondaryEnglish Book 3 students book Page 125

·        Teachers guide page 123-125

 
  5/6 GRAMMAR Differences among prepositions, conjunctions and adverb participles By the end of the lesson, the learner should be able to:

·        Correctly distinguish among prepositions, conjunctions and adverb participles

·        Use prepositions, conjunctions and adverb participles correctly.

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 126-128

·        Teachers guide page 125-128

 
  7/8 WRITING Synopsis of a short story By the end of the lesson, the learner should be able to:

·        Define synopsis

·        Write a synopsis of a short story

·        Write neatly and legibly

 

·        Writing

·        discussion

Chalkboard ·        SecondaryEnglish Book 3 students book Page 128-130

·        Teachers guide page 128-129

 
6 1 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  2

 

LISTENING AND SPEAKING How to speak in public By the end of the lesson, the learner should be able to:

·        Develop strategies in managing stage fright

·        Stand before an audience

·        Face an audience

·        Use gestures appropriately

·        Deliver an effective public speech

·        Writing

·        Discussion

·        Reading

chalkboard ·        SecondaryEnglish Book 3 students book Page 131-132

·        Teachers guide page 130-132

 
    STUDY SKILLS How to participate in group discussions By the end of the lesson, the learner should be able to:

·        Organize themselves for a group discussion

·        Prepare for group discussions

·        Participate in group discussions

·        Writing

·        Discussion

·        Reading

chalkboard ·        SecondaryEnglish Book 3 students book Page 132-134

·        Teachers guide page 132-133

 
  3/4 READING Comprehension

Ozone

By the end of the lesson, the learner should be able to:

·        Appreciate the danger posed by the depletion of the ozone layer

·        Read the passage silently

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading

·        Pre-reading activities

 

· ·        SecondaryEnglish Book 3 students book Page 134-136

·        Teachers guide page 134-135

 
  5/6 GRAMMAR Correlative conjunctions By the end of the lesson, the learner should be able to:

·        Recognize correlative conjunctions

·        Use correlative conjunctions correctly

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 136-138

·        Teachers guide page 135-137

 
  7/8 WRITING Speech By the end of the lesson, the learner should be able to:

·        Develop an outline for a speech

·        Choose an appropriate way of introducing a speech

·        Do an appropriate build-up of a speech

·        Choose an appropriate way of concluding a speech

·        Write neatly and legibly

 

·        Writing

·        discussion

Chalkboard

sample

·        SecondaryEnglish Book 3 students book Page 138-139

·        Teachers guide page 137-138

 
7 1 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  2 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  3

 

LISTENING AND SPEAKING Discussion based on a dilemma story By the end of the lesson, the learner should be able to:

·        develop awareness of discussion etiquette

·        Participate in a discussion effective

·           discussion chalkboard ·        SecondaryEnglish Book 3 students book Page 140

·        Teachers guide page 139

 
  4 STUDY SKILLS Improving one’s Vocabulary By the end of the lesson, the learner should be able to:

·        Appreciate the need to continually build their vocabulary

·        Identify ways of figuring out the meaning of a new word

·        Acquire and use new words

·        Reading chalkboard ·        SecondaryEnglish Book 3 students book Page 140-142

·        Teachers guide page 140

·        A good English dictionary

 
  5/6 READING Comprehension

The return

By the end of the lesson, the learner should be able to:

·        Appreciate the resilience of the human spirit

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 143-144

·        Teachers guide page 142-144

 
  7/8 GRAMMAR Prepositional phrases By the end of the lesson, the learner should be able to:

·        Identify prepositional phrases

·        Identify the functions of pp.

·

MIDTERM EXAMS

Use prepositional phrases correctly.

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page

·        Teachers guide page

 
 

8

 

 

        · · ·  
 

9

 

 

 

   
MIDTERM BREAK
  · · ·  
10 1/2 WRITING Argumentative essays By the end of the lesson, the learner should be able to:

·        Appreciate the importance of supporting one’s argument with sufficient evidence.

·        Master the components of an argumentative composition.

·        Write neatly and legibly

 

·        Writing

·        discussion

Chalkboard

sample

·        SecondaryEnglish Book 3 students book Page 147

·        Teachers guide page

 
  3/4 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  5

 

LISTENING AND SPEAKING Role playing By the end of the lesson, the learner should be able to:

·        Role play an interview

·        Play an interviewer’s role in gathering information

·        discussion chalkboard ·        SecondaryEnglish Book 3 students book Page 148-149

·        Teachers guide page 148-149

 
  6 STUDY SKILLS Reading newspapers and magazines By the end of the lesson, the learner should be able to:

·        Demonstrate familiarity with different sections of a newspaper and magazine.

·        Read the different sections of a newspaper or magazine effectively.

·        Scanning

·        skimming

chalkboard ·        SecondaryEnglish Book 3 students book Page 149-150

·        Teachers guide page 150

·        Newspapers and magazines

 
  7/8 READING Comprehension

Diet in HIV/AIDS Management

By the end of the lesson, the learner should be able to:

·        Appreciate the importance of diet in HIV/AIDs management

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 150-152

·        Teachers guide page 151-152

 
11 1/2 GRAMMAR Adjective Phrases By the end of the lesson, the learner should be able to:

·        Recognize adjective phrases

·        Use adjective phrases in sentences correctly.

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 152-154

·        Teachers guide page 152-155

 
  3/4 WRITING Notification of Meetings By the end of the lesson, the learner should be able to:

·        Appreciate the importance of sending our notices of meetings

·        Write a notice for a meeting

·        Write neatly and legibly

·        Writing

·        discussion

Chalkboard

sample

·        SecondaryEnglish Book 3 students book Page 154-155

·        Teachers guide page 155

 
  5/6 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
  7

 

LISTENING AND SPEAKING Retelling an Aetiological Story By the end of the lesson, the learner should be able to:

·        Use voice/tone variation in storytelling

·        Use gestures in storytelling

·        Use facial expressions in storytelling

·           Narration

 

chalkboard ·        SecondaryEnglish Book 3 students book Page 156-157

·        Teachers guide page 156-157

 
  8 STUDY SKILLS Note-making in preparation for summary writing By the end of the lesson, the learner should be able to:

·        Identify the main points in a text

·        Present the points in note form.

·        Writing chalkboard ·        SecondaryEnglish Book 3 students book Page 157-159

·        Teachers guide page 157-158

 
12 1/2 READING Comprehension

Akoko’s Quest for Justice

By the end of the lesson, the learner should be able to:

·        Appreciate Akoko’s and by extension women’s quest for justice.

·        Answer questions on the passage correctly.

·        Learn and use new vocabulary.

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 159-161

·        Teachers guide page 158-159

 
  3/4 GRAMMAR Conditional clauses By the end of the lesson, the learner should be able to:

·        Recognize conditional clauses.

·        Use conditional clauses correctly

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 161-163

·        Teachers guide page 161-163

 
  5/6 WRITING Creative story By the end of the lesson, the learner should be able to:

·        Identify and explain the elements of a creative story.

·        Write a creative story.

·        Write neatly and legibly

·        Writing

·        discussion

Chalkboard

sample

·        SecondaryEnglish Book 3 students book Page 163-164

·        Teachers guide page 163-164

 
  7/8 INTENSIVE READING THE PEARL By  John Steinbeck

 

By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the novel

·        Discuss the character traits, themes and style in the novel

·        Write notes based on the novel

·        Reading set text

·        Discussing the background of The Pearl

·        Discussing the character traits, themes and style in THE PEARL

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        The Pearl by John Steinback

·        Teacher’s guidebook

 
13 1

 

LISTENING AND SPEAKING Retelling a dilemma story By the end of the lesson, the learner should be able to:

·        Listen actively to a reading of a story.

·        Identify the dilemma in the story

·        Retell the story in their own words

·         narration chalkboard ·        SecondaryEnglish Book 3 students book Page 165-167

·        Teachers guide page 165

 
  2 STUDY SKILLS summary By the end of the lesson, the learner should be able to:

·        Pick out the main points in a given passage

·        Summarize the passage by reducing it to about a third of its length

·        Write this condensed version in connected paragraphs

·        Critical reading

·        writing

chalkboard ·        SecondaryEnglish Book 3 students book Page 167-169

·        Teachers guide page 166-168

 
  3/4 READING Comprehension

The technology of iris scan

By the end of the lesson, the learner should be able to:

·        Explain how the technology of iris scan is used to identify people

·        Appreciate the merits and demerits  of the technology

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 169-171

·        Teachers guide page 168

 
  5/6 GRAMMAR Adjectival Clauses By the end of the lesson, the learner should be able to:

·        Recognize adjectival clauses

·        Use adjectival clauses in sentences correctly

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 171-172

·        Teachers guide page 169-170

 
  7/8 WRITING The Agenda of a Meeting By the end of the lesson, the learner should be able to:

·        Identify the features of an agenda for a meeting

·        Write neatly and legibly

·        Prepare an agenda for a meeting.

·        Writing

·        discussion

Chalkboard

sample agendum

·        SecondaryEnglish Book 3 students book Page 172-173

·        Teachers guide page 172

 
 

 

END OF TERM EXAMS & CLOSING
      ·   ·  
 

 

 

 

   
TERM THREE 2019
  · · ·  
1 1 INTENSIVE READING A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

·        Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S HOUSE

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  2   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  3   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  4   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  5

 

LISTENING AND SPEAKING Using your voice effectively By the end of the lesson, the learner should be able to:

·        Project their voices as they speak and read

·        Articulate words distinctly

·         speaking chalkboard ·        SecondaryEnglish Book 3 students book Page 174-175

·        Teachers guide page 173

 
  6 STUDY SKILLS How to write a book review By the end of the lesson, the learner should be able to:

·        Appreciate the nature and functions of book reviews

·        Discussion

·        writing

chalkboard

sample review

·        SecondaryEnglish Book 3 students book Page 176-177

·        Teachers guide page 174

 
  78 READING Comprehension

Medical Innovations

By the end of the lesson, the learner should be able to:

·        Develop awareness in genetic engineering

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 177-179

·        Teachers guide page 175

 
2 1/2 GRAMMAR Noun Clauses By the end of the lesson, the learner should be able to:

·        Identify noun clauses

·        Use noun clauses in sentences correctly

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 179-180

·        Teachers guide page 176-178

 
  3/4 WRITING Minutes By the end of the lesson, the learner should be able to:

·        Write neatly and legibly

·        Develop the skill of writing minutes

·        Write minutes

·        Writing

·        discussion

Chalkboard

Sample minutes

·        SecondaryEnglish Book 3 students book Page 180-183

·        Teachers guide page 178-179

 
  3 INTENSIVE READING A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

·        Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  4   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  5   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  6   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  7

 

LISTENING AND SPEAKING Delivering a Speech and Listening Actively By the end of the lesson, the learner should be able to:

·        Listen carefully to a variety of information

·        Listen actively to the famous “I Have a Dream” speech by Martin Luther king Jr.

·        Read the speech interpretively

·        Deliver the speech effectively

·        Describe the different parts of the speech

·           Reading -Chalkboard

-Collected speeches

·        SecondaryEnglish Book 3 students book Page 184-188

·        Teachers guide page 180

 
  8 STUDY SKILLS Understanding Exam Language By the end of the lesson, the learner should be able to:

·        Interpret exam instructions more accurately

·        Analyse  exam questions correctly

·        Writing

·        Discussion

·        Reading

chalkboard ·        SecondaryEnglish Book 3 students book Page 188-189

·        Teachers guide page 182

 
3 1/2 READING Comprehension

Governance

By the end of the lesson, the learner should be a

ble to:

·        Identify the general features of good governance

·        Answer questions on the passage correctly.

·        Learn and use new vocabulary

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 189-191

·        Teachers guide page 184-185

 
  3/4 GRAMMAR Compound-complex sentences By the end of the lesson, the learner should be able to:

·        Identify a compound-complex sentence

·        Use compound complex sentences correctly

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 191-193

·        Teachers guide page 186-187

 
  5/6 WRITING The Argumentative Essay By the end of the lesson, the learner should be able to:

·        Identify an argumentative essay in their reading

·        Describe the structure of an argumentative essay

·        Appreciate the style of an argumentative essay.

·        Write neatly and legibly

 

·        Writing

·        Discussion

Chalkboard

sample

·        SecondaryEnglish Book 3 students book Page 193-194

·        Teachers guide page 187-188

 
  7 INTENSIVE READING A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

·        Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  8   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
4 1   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  2   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  3

 

LISTENING AND SPEAKING Non-verbal Cues in Listening By the end of the lesson, the learner should be able to:

·        Interpret non-verbal cues correctly

·        Use non-verbal cues in active listening

·           Speaking chalkboard ·        SecondaryEnglish Book 3 students book Page 195

·        Teachers guide page 189

 
  4 STUDY SKILLS Time Management in exams By the end of the lesson, the learner should be able to:

·        Appreciate the need of time management in exams

·        Manage time in examinations effectively

·        Discussion chalkboard ·        SecondaryEnglish Book 3 students book Page 194-197

·        Teachers guide page 190

 
  5/6 READING Comprehension

Yes Sir, I’m  Fine

By the end of the lesson, the learner should be able to:

·        See the need to condemn exploitation in the society

·        Answer questions on the passage correctly.

·        Infer meaning of the new words used

·        Reading comprehension

·

·        Pre-reading activities ·        SecondaryEnglish Book 3 students book Page 197-199

·        Teachers guide page 191-193

 
  7/8 GRAMMAR Direct and Indirect Speech By the end of the lesson, the learner should be able to:

·        Distinguish between direct and indirect speech

·        Use direct speech correctly

·        Use indirect speech correctly

·        Discussing

 

·        Writing sentences

·        Dictionary ·        SecondaryEnglish Book 3 students book Page 199-203

·        Teachers guide page 193-195

 
5

 

 

 

     
MIDTERM EXAMS
· · ·  
6 1/2 WRITING Writing a Play By the end of the lesson, the learner should be able to:

·        Identify the features of a play

·        Write neatly and legibly

·        Write a skit

·        Writing

·        discussion

Chalkboard

sample

·        SecondaryEnglish Book 3 students book Page 203-204

·        Teachers guide page 195-196

 
  3/4 INTENSIVE READING A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

 

 

 

 

 

 

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  5/6   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  7/8   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
7 1/2   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  3/4   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  5/6   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  7/8   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
8 1/2   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  3/4   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  5/6   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By

·        Teacher’s guidebook Henrik Ibsen

 
  7/8   A DOLL’S HOUSE By Henrik Ibsen By the end of the lesson, the learner should be able to:

·        Read the text

·        Discuss he background of the play

·        Discuss the character traits, themes and style in the play

Write notes based on the play

·        Reading set text

·        Discussing the background of A Doll’s House

·        Discussing the character traits, themes and style in A DOLL’S

·        Setbooks Analysis DVDs

·        Sample context and essay questions and answers

·        A DOLL’S HOUSE By Henrik Ibsen

·        Teacher’s guidebook

 
9

 

 

 

 

 

 

 

 

 

 

 

 

 

     
END OF YEAR EXAMS

&

CLOSING

· · ·  

 

SIMPLIFIED FORM 2 HISTORY LESSON NOTES

HISTORY AND GOVERNMENT

FORM 2

SIMPLIFIED NOTES

New Syllabus

CHAPTER 1

Trade

Trade is the exchange of goods or services for money or other commodities for mutual benefits. It is basically the buying and selling of goods.

Trade originated during the New Stone Age. During this period, man began a settled lifestyle. He became specialised in various activities such as weaving, pottery and livestock keeping. This specialisation made some people to produce certain items which others did not produce. The need of satisfying various essential material needs therefore led to emergence of trade.

 

Methods of Trade

 

Barter trade and currency trade are the two existing forms of trade in the world.

 

Barter trade.

Barter trade is the oldest method of trade in the world. It existed even during the Old Testament time. Barter trade exists even today. This occurs when people exchange goods for other goods. In this case no established medium of exchange is used. In certain occasions, services are exchanged for goods. The goods may also be exchanged for services.

Barter system was very popular before the introduction of money. For instance a cow could be exchanged for a number of goats. A basket of millet could be exchanged for a basket of maize or beans.

The people of ancient Ghana exchanged their gold with the people of North Africa for salt.

This form of trade did not succeed very well where there was language barrier. Barter trade exists even today. In Kenya, certain commodities e.g. agricultural products are exchanged for machinery and oil.

 

Advantages of barter trade were:

  1. There was direct exchange of goods or services for goods.
  2. It encouraged people who were exchanging goods for goods to get involved in actual production of the items. This kept the communities busy.
  3. Barter trade enabled people who had no goods for exchange to acquire goods they wanted by merely rendering services to those who had.
  4. It enabled people to acquire the goods they did not produce themselves.

 

Disadvantages of barter trade were:

 

  1. Barter trade was not very convenient because sometimes people could not acquire the commodities they intended to exchange their goods for. For example one may have intended to exchange a bag of maize with a bag of millet just to find that there was no millet in the market.
  2. The method was tiresome because all those who wanted to exchange goods had to carry those goods to the market sometimes for long distances.
  3. Since in normal trade there is a buyer and a seller, it became difficult to specify who the buyer or seller was because both were just exchanging items and there was no specific buyer or seller.
  4. It was difficult to transport bulky goods to the market.
  5. It was difficult to value goods being exchanged to ensure that the deal was fair for both parties exchanging items.
  6. Barter trade was not very successful where the people exchanging goods had no common language to ease communication.
  7. It was not easy to exchange certain items such as a bull or a donkey because if the other party did not have sufficient goods for exchange, a bull or a donkey could not be split into smaller units to match with the goods available.

 

The Currency trade

This method of trade involves the use of money as a medium of exchange. The medium of exchange must be acceptable and convenient to people.

Money may be used to purchase commodities or to pay for services. Money is also used a measure of value. Today, people value their property in terms of money. Objects which have ever been used as money before the introduction of modern currencies are cowrie shells, iron bars, bronze, salt, gold and silver.

 

The major world currencies are:

 

  1. i) US Dollar
  2. German Deutsche Mark
  • British Sterling Pound
  1. French Franc
  2. Canadian Dollar
  3. Mexican Peso
  • Japanese Yen
  • European Union Euro

 

Advantages of currency trade are

  1. It is easy to carry money when going to buy items because it is not heavy.
  2. Money can be split into smaller units which enables people to purchase any quantity of goods in the market.
  3. Items are valued easily in terms of Shillings, Dollars, Yen, Pound Sterling, etc. This makes the buyer to have an idea of the value of various items in advance.
  4. Currency trade brings about clear definitions of the terms buyer or seller. In this case the buyer is the one who gives out money to acquire goods while the seller is the one who gives out goods to acquire money.
  5. When one receives money for goods delivered or sold, he can save it in banks or store it without fear of any damage such as decay for a long time.

 

Disadvantages of currency as a medium of exchange are

 

  1. i) Currency can easily loose value (purchasing power) as it happened in Uganda during the era of President Idi Amin.
  2. If there are no goods available for buying, money becomes useless. Many a times people have starved almost to death during famine due to shortage of food to buy with the money they have.
  • Use of currency in business has encouraged robbery, pickpocketting and many other forms of crime.

 

Types of trade

There are three types of trade namely: local trade, regional trade and international trade.

 

Local Trade

Local trade is the exchange of goods within the same community at the village level. It may also involve the neighbouring communities or people who share a common boundary.

People who conducted local trade established markets on the community boundaries or in a central place where people from a number of villages met to exchange goods. People exchanged goods they had for the things they did not have. This type of trade exists in Kenya even today where local county councils have established markets in certain trading centres. Local trade covers a small area.

 

          The origin of local trade

Local trade originated from the time early man began a settled lifestyle. It was facilitated by the need to acquire what one did not have from those who had. The environmental differences also contributed the emergence of this type of trade.

 

          The development of local trade

Local trade developed as human population increased. The increase in population led to demand for various items such as food, clothing, pots and ornaments. Some people became specialised in making iron tools, others in making items such as pots, baskets and bark-cloth while others became pastoralists and kept cattle, sheep and goats.

The blacksmith obtained meat from the pastoralists and grains from the cultivators. The pastoralists needed knives and spears from the blacksmiths. The cultivators needed iron hoes; knives for harvesting; millet, sorghum and axes for clearing fields for cultivation. The demand for goods therefore encouraged local trade to develop and markets were established where people met to buy and sell things.

 

          The organisation of local trade

People established markets at the most convenient places for all. They set market days when they would meet to exchange goods. At the beginning, the form of trade was mainly barter. Later there was introduction of money (currency) which acted as a medium of exchange.

During this trade, people transported their commodities on their heads and backs. Some communities such as the Maasai used donkeys to carry their goods to the markets while the Somali and the Boran used camels.

People who traded were provided with security by local leaders.

Some established local merchants bought the items and resold them to other traders far away beyond the local boundaries. For example ivory was sometimes bought from the local markets in Samburu and Baringo and then transported to the coast where it was bought and shipped to Asia.

 

          The impact of the local trade

Local trade led to intermarriages between people of different villages and people of neighbouring communities.

It contributed to the unity of family members who constituted a community. This is because the interaction of people in the markets united them. Local trade enabled people to acquire what they did not have from those who had.

It laid the basis for other types of trade such as the regional and the international trade because some of the goods sold at regional and international levels were bought from local markets by the traders and eventually sold far away from the sources.

Local trade enabled some people such as Chief Kivoi of Ukambani to acquire skills in trade thereafter becoming experienced long distance traders. Where members of one community traded with members of another community there was development of languages through word borrowing as well as cultural exchange.

In this case members of each community would borrow some cultural practices which became known to them as they interacted in the markets.

 

 

Regional Trade

Regional trade is the exchange of goods within a specified part of a continent or region. It can be trade between different communities in a region who are living apart.

This trade involves a bigger geographical area than the one covered by local trade. It also involves more traders. An example of regional trade is the Trans-Saharan trade.

 

          The origin of the Trans-Saharan trade

It is not known exactly the time this trade started but it was going on between 1000AD and 1500AD. The people of West Africa and those from North Africa exchanged goods from very early times even before the Sahara dried up into a desert. The desert trade was later revolutionised by the introduction of the camel in the first century AD.

 

          The development of the Trans-Saharan trade

The Trans-Saharan trade began developing after the introduction of the camel which replaced the use of oxen and horses which were used by traders before the Sahara turned into a desert.

The people involved in this trade were the local inhabitants of West Africa such as the people of ancient Ghana, Mali and Songhai. There were also desert communities like the Tuaregs, the Berbers and the Arabs from North Africa. Later Europeans and Jewish traders who had settled along the North African coast became engaged in this lucrative trade.

The people of West Africa (Western Sudan) sold Gold, ivory, slaves, gum, ostrich feathers, colanuts and hides and skins to the people of North Africa and in return obtained horses, silk cloth, beads, cotton cloth, spices, mirrors, needles, dried fruits and salt from the North African traders. The salt sold was obtained from Targhaza, Taodeni and Ghadames while the gold brought for sale was obtained from Wangara, Bure and Budu mines.

The main trade routes were that which connected Fez and Sijilmasa in Morocco with Audaghost in West Africa and passed through Targhaza. The other started from Tunis in Tunisia through Ghadames, Ghat and Agades in the Sahara desert to Hausaland. Another one ran from Sijilmasa through Tuat, Gao and reached Timbuktu. The other one started from Tripoli and went past Fezzan to Bornu via Bilma. There were several other minor ones which made the trade routes to resemble a cobweb. All these routes touched the salt mines in the desert as salt was a commodity of trade very much needed by the people of western Sudan.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Some Trans-Saharan trade routes and sources of goods

The Trans-Saharan trade developed due to the following reasons:

  1. The trade commodities which the traders from both sides demanded were available.
  2. The trade goods themselves were in great demand. For instance the people of West Africa demanded salt while the people of North Africa demanded gold.
  3. The West African rulers provided the traders with security.
  4. The desert Tuaregs guided traders; provided them with water, food and accommodation; showed traders direction; acted as interpreters; provided traders with security while crossing the desert and cared for the oasis where traders obtained water.
  5. There were established trade routes in the desert which provided considerable transport and communication services to traders.
  6. There were enterprising professional merchants who conducted trade across the desert.
  7. There were means of transport provided by use of camels, horses and donkeys.
  8. There was sufficient capital to finance trade.
  9. The local trade which existed in North Africa and West Africa laid the basis for the Trans-Saharan trade.

 

The development of the Trans-Saharan trade was hampered by some of the obstacles traders encountered as they conducted their business across the desert. Some of these obstacles were:

  1. Traders lost direction in the desert.
  2. They were attacked by desert robbers. This occurred when the Tuaregs changed their role of guides to that of robbers.
  3. vggbThe traders were affected by numerous sandstorms which blocked the routes they followed.

 

  1. The trades were also affected by weather variations because sometimes it became too hot and at other times too cold.

 

  1. The distance traders travelled across the desert was too long and scaring.

 

  1. Traders were sometimes in danger of attacks by dangerous desert creatures such as snakes and scorpions.

 

  1. There was communication barrier due to lack of a common language. This made it necessary for traders to use the Tuaregs as their guides and interpreters but later they became unreliable when they began stealing goods from traders.

 

  1. There was lack of adequate basic needs such as food and water especially in the desert.

 

iii)      The organisation of the Trans-Saharan trade

The Trans-Saharan trade was conducted by the people of western Sudan and the people of North Africa. The traders from North Africa crossed the Sahara desert by use of camels. The traders travelled in large caravans some with about 1000 camels and hundreds of people for security reasons.

The Tuaregs and Berbers were recruited to act as guides (takshifs) to the traders. These guides provided the traders with security. It took about three months to cross the desert. For this reason the traders had stopping places at the oases where they bought food and water for themselves and for their camels. It is the Tuaregs who maintained the oasis and acted as interpreters. When the traders reached western Sudan, they sometimes gave their goods to the local agents on credit. The form of trade was mainly barter.

The rulers of West Africa controlled the trade and provided security to traders. In return the traders paid taxes to the rulers. The main items of trade included gold, salt, horses, hides and skins, beads and cloth. When the time to travel back to North Africa reached, the North Africa traders employed people to be left trading on their behalf. The merchants stored goods in specific gathering points which acted as distribution centres. They mainly travelled one way in a year.

 

The problems the Trans-Saharan traders encountered

The Trans-Saharan traders faced a lot of problems as they carried out their business. The traders travelled long distances across the Sahara desert. Their journeys were tiresome and they had insufficient food and water. Sometimes the trade goods became exhausted.

The traders were frequently interrupted by hostile desert communities who wanted to steal their goods and by dangerous sandstorms which blocked their way. Traders lost direction and they were sometimes attacked by dangerous desert creatures. There were frequent shifts of trade routes. Traders were sometimes robed by desert dwellers.

 

The impact of the Trans-Saharan trade

The Trans-Saharan trade had several consequences:

 

  1. The trade led to development of urbanisation for example towns such as Gao, Timbuktu and Jenne.

 

  1. The trade led to the decline of empires such as ancient Ghana and Mali while others such as Songhai emerged.

 

  1. Islamic religion and culture were introduced.

 

  1. Intermarriages between North Africans and West Africans were promoted.

 

  1. The Trans-Saharan trade led to a class of wealthy merchants who participated in the trade.

 

  1. New cultures were introduced such as eating habits and new styles of dressing.

 

  1. The trade led to the introduction of foreign architectural designs in West Africa.

 

  1. The Trans-Saharan trade contributed to the establishment and development of diplomatic ties between West Africa and North Africa.

 

  1. There was growth of agricultural production as a result of the introduction of new crops.

 

  1. The sharia laws were introduced in the administration of West Africa.

 

  1. The trade exposed Africa to the outside world.

 

  1. The trade led to the development of communication between North and West Africa.

 

 

The decline of the Trans-Saharan trade

The Trans-Saharan trade began to decline in the 15th century and disintegrated completely in the 19th century following colonisation of West Africa by the Europeans. The factors which contributed to its decline were as follows:

 

  1. a) The gold mines in western Sudan got exhausted. This discouraged traders from coming to West Africa because the main trading commodity was not available.

 

  1. b) The Morrocans invaded West Africa in the 16th This undermined the trade because it created anarchy and insecurity in the region. The Morrocans wanted to capture this prosperous trade.
  2. c) The political instability in West Africa together with the decline of empires such as Mali and Songhai increased anarchy and insecurity in the region.

 

  1. d) West Africa was invaded by the Almoravids and the Tuaregs. This further increased insecurity along the major trade routes.

 

  1. e) The Tuaregs who guided the traders changed their roles from that of guides to that of robbers.

 

  1. f) The emergence of the Trans-Atlantic trade attracted the West African traders who were formerly involved in the Trans-Saharan trade. This led to reduction of the volume of goods and traders who participated in the Trans-Saharan trade.

 

  1. g) The Turks invaded North Africa creating insecurity along the caravan routes.

 

  1. h) The colonisation of West Africa by the Europeans reduced regional links and encouraged European exploitation of West African resources therefore undermining the Trans-Saharan trade.

 

  1. i) The British anti-slave trade pressure and eventual abolition of slave trade led to decline of the Trans-Saharan trade.

 

  1. j) Rivalry between caravans and the stiff competition of the traders sometimes resulted to wars which scared traders.

 

  1. Moroccan ports along the Mediterranean Sea were invaded by the Spanish and Portuguese soldiers in the late 15th century and early 16th This disrupted trade.

 

  1. European merchants began penetrating into the interior of West Africa for trade. They diverted the flow of goods such that goods were later taken to the West African coastal town such as Port Elmina and Accra.

 

International Trade

 

International trade refers to trade between nations. In modern international trade, nations within the same continent are included. The international trade of the period before the mid 20th century which is our main concern involved nations particularly those in different continents and which were not part of one geographical region.

This ancient international trade developed as a result of the improvement in water transport. This was achieved mainly through the construction of strong ships and acquisition of better knowledge of navigation which enabled sailors to explore and acquire knowledge about foreign lands overseas. An example of the international trade was the Trans-Atlantic trade.

 

The Trans-Atlantic trade

 

  1. i) Origin

The Trans-Atlantic trade began after the Portuguese explored the West African coast in the 15th century and after the Spanish sailor, Christopher Columbus sailed to Americas.

In the 16th century the Americas became colonised by the Portuguese and the Spanish. These two nations began to open up and develop their acquired territories through mining and establishment of sugar plantations. Attempts to use the Red Indians as labourers eventually failed. There was need to import Africans to supply labour in the mines and sugar plantations. This attempt marked the beginning of the Trans-Atlantic slave trade. The increased demand for sugar, tobacco and cotton in the European countries led to the establishment and growth of more and more plantations in Americas. A lot of labourers were therefore needed to work in the growing plantations.

Africans were more suited to plantation farming because they were handy and could work effectively in hot climates. They were used to tropical diseases and could survive longer. The Africans were also used to physical strains and hardships. All these made Africans to be regarded as the most potential suppliers of labour in the American plantations.

 

 

 

iii)      The development of Trans-Atlantic trade

The first African slaves were the twenty people who were captured and taken to Henry the Navigator in 1442. By 1510 a large number of African slaves from Guinea were exported by the Portuguese to the Spanish colonies. Later slaves were transported directly form Guinea coast to the West Indies.

At first the Portuguese were the leading slave exporters. In the 17th century, the Dutch took the leading role as more Europeans settled in Americas and increased the demand for slave labour.

The French and the British involved themselves in this lucrative trade. The British captured the leading role from the Dutch and they dominated the Trans-Atlantic slave trade in the 18th century.

The increased demand for precious stones, sugar, cotton and tobacco in the European markets and the demand for fire arms, cloth, alcoholics, tobacco, utensils, glassware ornaments, sugar, sweets and iron bars in West Africa accelerated trade.

 

The Trans-Atlantic trade developed and grew rapidly due to the following factors:

 

  1. The commodities which were required by the Africans as well as the Europeans and Americans, were available in the three continents that took part in trade.

 

  1. The goods were also in great demand in the continents especially during the industrial revolution.

 

  1. The West African coast had natural harbours where ships anchored.

 

  1. The West African rulers provided foreign traders with security.

 

  1. There existed enterprising merchants in America, Europe and West Africa who engaged in trade.

 

  1. The steamships provided efficient transport and communication means between the three continents.

 

  1. The acquisition of new knowledge of navigation enabled sailors to sail across the deep and stormy seas and oceans.

 

  1. The decline of the Trans-Saharan trade enabled a big volume of goods to be taken to the West African coastal markets.

 

iii)      The organisation of Trans-Atlantic trade

 

The Trans-Atlantic trade was well organised inform of a triangle which connected Europe, Africa and America. It involved European traders, African middlemen and American plantation owners.

Ships loaded with European manufactured goods such as fire arms, cloth, wines and spirits, cigarettes, iron bars, utensils, glassware, ornaments and sweets left Europe and anchored along the West African coast. Slaves captured in the interior of West Africa were marched along the coast. There were established places where the slaves were kept while awaiting shipment.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The ships from Europe were unloaded and the European manufactured goods exchanged for slaves, colanuts, precious stones, hides and skins. The ships were once more loaded with the West African commodities which were shipped across the Atlantic ocean to Americas.

In Americas, the slaves were sold through auction. The ships were then filled with indigo, cotton, tobacco, rum, sugar, rice, timber and the precious stones like gold and silver. They were then shipped to European markets.

 

How the slaves were obtained during the Trans-Atlantic trade

  1. Raids were conducted for capturing slaves.

 

  1. Free men were kidnapped and thereafter sold as slaves.
  2. Two communities conducted wars and the one which was defeated had is people captured as slaves.

 

  1. Leaders sold criminals and even some of their innocent subjects.

 

  1. Slaves were battered with other commodities African traders required.

 

  1. Children and women were enticed with sweets and thereafter captured.

 

  1. The weaker states were forced to pay tributes imposed on them by use of slaves.

 

  1. The people who failed to pay debts were captured and sold as compensation. Alternatively, they surrendered a family member to be sold instead.

 

The impact of the Trans-Atlantic trade

  1. The Trans-Atlantic slave trade caused immense pain and suffering to innocent Africans who were captured, chained, beaten and forced to walk long distances to the West Africa coast.

 

  1. The trade caused an incalculable number of deaths especially during inter community wars, raids and during shipment. The death tool is estimated to be about 20 million.

 

  1. There was a decline in the local industries because the able bodied people were sold away leading to loss of labour and because of sale of cheap manufactured goods.

 

  1. There were changes in the role of chiefs who instead of protecting their people sold them as slaves.

 

  1. There was intensification of warfare in a bid to capture slaves. This resulted to division among and within communities which caused bitterness and disunity of the Africans. The wars between communities were accelerated by the acquisition of firearms.

 

  1. A class of slave merchants emerged in West Africa. Examples of the slave merchants were Jaja of Opobo and Nana of Isekri. The two were very powerful and wealthy.

 

  1. Some states such as Asante, Benin, Oyo and Dahomey rose to power and expanded due to the great wealth obtained from trade.

 

  1. The Trans-Atlantic trade led to expansion of urban centres along the West African coast where commodities were exchanged. Such towns were Whydah, Accra, Porto Novo and Badgry.

 

  1. To some extent some parts of West Africa where raids were conducted became depopulated. This contributed in retarding economic development in those areas.

 

  1. The European traders intermarried with the people of the West African coast giving rise to halfcaste (mulato).

 

  1. Africans developed a taste of the European goods.

 

  1. Some weaker kingdoms such as Ketu declined due to constant raids conducted by stronger states such as Dahomey.

 

  1. The Trans-Atlantic trade contributed to the decline of the Trans-Saharan trade because the goods flowing Northwards across the Sahara desert got reduced and instead were taken to the West African coastal markets.

 

  1. Some powerful rulers such as King Geso of Dahomey emerged as a result of the introduction of fire-arms.

 

  1. The trade encouraged slave raids which destroyed property. Houses and crops for instance were burnt into ashes during slave raids.

 

  1. The Trans-Atlantic trade led to the development of agricultural plantations in the Americas.

 

  1. The trade gave rise to people of African descent in Americas. These are referred to as American Negroes.

 

  1. The final blow as a result of this trade was that West Africa was colonised and therefore came under European control.

 

The decline of the Trans-Atlantic trade

The Trans-Atlantic trade declined in the 19th century because of a number of factors. The industrial revolution in USA led to use of machines to work in the farms. Slave labour was no longer necessary.

There emerged the humanitarian movement and the Christian Missionaries in Britain who considered slave trade and slavery as unjust and inhuman. A typical example of humanitarians was Sir William Wilberforce who presented the issue of slave trade and slavery to the British parliament. Dr. Livingstone also advocated slave trade to be abolished.

Some economists and scholars were of the feeling that free labour was more paying and productive than slave labour. Some of them argued that mass migration of the Africans should be discouraged to ensure retention of the markets for the European manufactured goods. The decline of plantation economy in America and the Carribeans reduced the demand for slaves for use in the farms. Also the slaves in the Carribeans and America resisted because they wanted to be left free from being enslaved.

Lastly, some Europeans felt that it was necessary to retain Africans in their motherland so that they could produce raw materials needed in the European industries. In order to achieve this, it was necessary to abolish the Trans-Atlantic slave trade which was draining Africa of its labour force.

 

 

Review Questions

 

  1. a) Define the following:
  2. i) Barter trade
  3. ii) Currency trade

iii)      Local trade

  1. iv) Regional trade
  2. v) International trade
  3. b) Explain the advantages of using currency over barter trade.

 

  1. a) Explain the origin and  organisation of local trade.
  2. b) Discuss the factors which contributed to the development of the

Trans-Saharan trade.

 

3        a)       Describe the role of Takshifs during the Trans-Saharan trade.

  1. b) Give five trade routes traders followed during the Trans-Saharan trade.

4        a)       what problems did the traders encountered during Trans-Saharan

trade?

 

  1. Discuss the effects of the Trans-Saharan trade on the people of western Sudan.

 

5        a)       What factors contributed to the development of the Trans-Atlantic

trade.

 

  1. b) Explain the impact of the Trans-Atlantic trade under the following headings.
  2. i) Social impact
  3. ii) Economic impact

iii)      Political impact

 

6        Why did the Trans-Atlantic trade decline in the 19th century?

 

 

Students’ Activities

 

  • Visit the nearest shopping centre and find out the problems the traders encounter as they carry out their business.

 

  • Draw relevant maps indicating the trade routes during the Trans-Atlantic trade and Trans- Saharan trade.

 

  • Demonstrate the methods used to obtain slaves and the way they were finally transported to the market along the West Africa Coast and sold.

 

 

 

 

CHAPTER 2

 

 

Development of Transport and Communication

 

Transport is the movement of people and goods from one place to another. Communication is the transmission of information in form of news, messages and ideas over some distances. It includes sending and receiving of information.

The early forms of transport included land transport, water transport, human transport and animal transport. Human transport involved carrying goods from one place to another on one’s back, head and shoulders. Animals were also used to carry goods and people on their backs from one place to the other.

The earliest forms of communication were smoke signals, drum beats, messengers, horn blowing and written messages on scrolls and stone tablets.

 

 

Traditional Forms of Transport

 

  1. a) Land transport

This form of transport involved movement of people and goods on land. They either walked or they were transported by use of tamed animals which pulled carts and wagons.

Land transport developed mainly because of the invention of the wheel. The invention of the wheel made transport easier because at first it was used to move war chariots and carts which carried agricultural produce. This also encouraged the development of trade and wars. The invention of the wheel therefore eased transportation of bulky loads and speeded transportation of people to various destinations. It also facilitated travel over long distances within a limited period of time. Wheeled vehicles were pulled by horses, donkey and oxen. The invention of the wheel was followed by the development of roads.

 

  1. b) Human transport

Human transport involved carrying of goods from one place to the other on the backs, shoulders and heads. Sometimes people used shoulder poles to transport goods. The slave traders in East Africa captured slaves and forced them to carry ivory from the interior to the East African coast.

Human transport exists even today. It is common to see Kenyan women carrying firewood, coffee, picked tea and cattle feed either on their heads or back.

 

 

 

 

 

 

 

 

 

 

Porters

 

 

  1. c) Animal Transport

After man domesticated animals, he learnt that some could be used to transport goods from one place to the other. These animals carried loads on their backs and they also pulled wheeled vehicles such as carts and wagons.

The beasts of burden such as camels, oxen, horses and donkeys were also referred to as pack animals. Donkeys were commonly used in Kenya by the Maasai and the Kamba to fetch water. In many other places, donkeys carried trade goods to the markets. Oxen transported people and goods from one place to the other. They were also used for ploughing.

 

 

 

 

 

 

 

 

 

 

Oxen drawn carts

 

Horses were used to transport soldiers during war times. The soldiers sometimes fought on horseback. Horses also pulled chariots which transported soldiers to battle fields.

A camel was a very efficient beast of burden in the desert because it could stay for a long time without water or food. This is because it has a store of fat in its hump. Camels were used to transport goods during the Trans-Saharan trade.

 

Other animals which are used for transport are elephants, water buffaloes, dogs and Llamas.

 

  1. d) Water transport

Water transport began due to the need to cross rivers and lakes to look for food on the other side.

Man’s first boat like vessel was made of a tree trunk. It was later improved by hollowing it to make a dug-out canoe.

Man also discovered that he could make rafts with animal skins or from bundles of reeds tied together. The canoes and rafts were used to move across the shallow waters.

The Phoenicians, the Egyptians and the Greeks made the earliest ships many years before the birth of Christ. These ships were used in seas and oceans. The Arabs made dhows that were driven by wind.

 

 

 

 

 

 

 

 

A dhow

Development of modern means of Transport

 

Modern means of transport involves road transport, railway transport, water transport, air transport and space exploration by use of rockets.

 

Road transport

 

The Romans were the first to introduce good quality roads which were of very high standards. This occurred before the birth of Christ. Roman roads survived for hundreds of years because they were well drained and durable. These roads were used by carts chariots and wagons which were pulled by horses, donkeys and oxen.

In the 17th and 18th century, British engineers began constructing better roads and bridges. Some of these engineers were George Wade, John Macadam and Thomas Telford. These engineers brought about the construction of high quality roads that were durable and well drained.

By the close of the 19th century various modes of modern transport such as bicycles and motor vehicles had been invented and were in use especially in Europe. The invention of the pneumatic tyres by Dunlop to replace the solid ones and the invention of steam power engines revolutionised land transport. Etienne Lenoir from France invented the first internal combustion engine.

A German citizen, Nicholas Otto, invented the four-stroke compression engine. Later in 1883 Gottliep Daimler of Germany came up with an efficient and portable petrol engine which he used to make the first motorcycle and later petrol driven car which was the first ever made.

Others who joined in the league of manufacturing vehicles were Karl Benz of Germany and Henry Ford of USA who founded Ford motor company in USA and began manufacturing cars for sale.

The vehicle industry since then has been greatly improved. Vehicles that move at very high speed have been introduced. This has resulted to many accidents. As a result of this, in January 2004, Kenya government took the following measures to reduce the increasing number of accidents on the Kenyan

Roads and to make travel comfortable and enjoyable:

 

 

 

 

 

 

 

 

 

Modern cars

 

  1. i) All motor vehicles were to be fitted with seat belts.
  2. All public service vehicles were to be fitted with speed governors and were to move at a speed not exceeding 80 kilometres per hour.
  • The carrying capacity of public service vehicles was reduced.
  1. Drivers and conductors of public service vehicles were to be permanently employed.
  2. Drivers and conductors of public service vehicles were to be issued with uniforms and badges and photographs for identification.
  3. Drivers and conductors of public service vehicles were required to have certificates of good conduct.

 

There are millions of motor vehicles in the world today. The number is still increasing each day because they are manufactured in thousands each day in the world.

 

 

Railway transport

The idea of making railway lines came earlier than the invention of the locomotive engines. For instance the Germans used wooden rails for their trucks. The trucks were pulled by horses and donkeys. Later iron rails replaced the wooden rails.

The first steam engine that could be mounted on a truck was made by Richard Trevithick but it was slow and heavy. It was George Stephenson, a coal miner in England who came up with the best and powerful steam locomotive which was called the Rocket. Later diesel and electric engines were designed. A German called Rudolh Diesel designed a diesel engine. The Siemens brothers designed the electric locomotives in Britain.

After these inventions the railway transport spread to other parts of the world. The European colonialists developed the railway transport in Africa in the 19th century and 20th century.

 

Water transport

The first sailing ships were propelled by wind. These ships were made of wood. When steam power was discovered, ships began being propelled by steam engines.

 

 

 

 

 

 

 

 

A ship of the 17th century

 

A Scottish engineer known as William Symington built a steamship which was driven by a paddle wheel. An American called Robert Fulton built a steamship called Clermont that was used to carry passengers between Albany and New York. Some years later, internal combustion engines were invented. Since then oil replaced the power from coal in driving engines.

From 1881 iron and steel ships began replacing wooden ships. From 1840s, fast moving ships were developed when propellers or screws replaced paddle wheels. Between 1953 and 1962, the Americans were able to make war ships called submarines which used nuclear power.

The ships of today are propelled by very powerful engines and are resistant to strong waves.

 

Air transport

The first person to fly used a balloon. The use of balloons was followed by the introduction of airships that carried passengers within the first half of the 20th century. The airships used hydrogen gas that caused accidents because it was highly flammable. The Wright brothers made the first aeroplane that used a petrol engine. Their findings helped to develop aeroplanes that were used in the First World War.

Further improvements of engines brought about the development of jet planes that carry many passengers and travel at supersonic speed.

 

An aeroplane

 

Space Exploration

The first satellite was launched into orbit round the earth by the Soviet Union in 1957. The USA also sent satellites into orbit round the earth in 1961. Yuri Gagarin from Soviet Union became the first man in space.

The USA sent the first man, Neil Armstrong, to the moon in 1969. Since then a number of countries have engaged themselves in space exploration. The USA for example have a programme called Space Shuttle which helps to promote space exploration.

 

 

Impact of modern means of transport

 

The development of modern means of transport has positive and negative impact in the world.

 

Positive impact

The development of water transport, railway transport, road transport and air transport has improved trade between nations because it has quickened movement of business people and urgent documents and messages relating to trade.

Goods are quickly and easily transported from one place to another. Job opportunities have been created in the transport sector. For example people have taken careers such as driving, mechanics, engineering and piloting.

Industries for manufacturing engines, spare parts and other accessories have been established. Air transport has encouraged international co-operation and facilitated quicker and easier movement of perishable items such as fruits and meat. It has also enabled pests such as locusts to be sprayed from the air. It has enabled countries to conduct student exchange programmes.

Air transport has encouraged space exploration by use of satellites. Geologists have used aeroplanes to explore and map oil pools. Geographers have used aeroplanes when conducting aerial survey.

Water transport has provided cheaper means of bulky goods across seas and oceans for example the transportation of crude oil, machinery, agricultural products and chemical fertilizers. It has also promoted the fishing industry.

In addition railway transport encouraged settlers to settle in the colonies acquired by their mother countries. It also encouraged migration of people to other places and enhanced colonisation. Railway transport encouraged urbanisation on railway junctions. It encouraged mining and farming as it opened up remote areas during the colonial rule in Africa.

Road transport has helped to link communities leading to rapid cultural interaction. Road transport has also enabled many countries to have effective administration through quick transportation of administrators and police to the areas they are needed.

 

Negative impact

Modern means of transport have encouraged pollution of environment. Trains and vehicles emit fumes while aeroplanes produce a lot of noise. When ships carrying oil or mercury wreck, they contaminate the ocean waters and cause destruction of marine life.

Modern means of transport have led to loss of life of many people due to accidents. Plane and vehicle hijacking has increased. There is piracy in seas and oceans. International terrorism has been encouraged through air transport. Modern transport has encouraged wars because ships, vehicles, trains and aeroplanes transport soldiers and weapons during wars.

 

 

Traditional forms of communication

 

The traditional forms of communication involve smoke signals, drum beats, messengers, horn blowing and written messages on scrolls and stone tablets. Communities used these forms of communication to make their members informed of what was happening and what was expected of them. The messages were sent quickly and easily over considerable distances.

The traditional forms of communication alerted people of impending dangers in times of war. For instance warriors used them in times of crisis to inform others of the approaching enemies. Lastly they enabled relatives who were living apart to keep in touch with each other.

 

Smoke signals

Fire was lit in the areas that were visible for example on hills. The smoke produced was used to convey certain information. The smoke signals reached people very fast. It was a convenient method because firewood was readily available and therefore making it easy to make fire.

The method was disadvantageous in the sense that smoke signals could not be sent at night because smoke could not be visible. Smoke signals could not be used during cloudy and foggy weather.

For the message to reach, people had to be on lookout. It was not possible to use this method to communicate with people who were blind. It was difficult to make fire during the rainy season on hilltops. Strong winds also hampered lighting of fire. Sometimes the receiver could wrongly interpret the message signalled. The message was also never recorded or stored for future reference. Confidential messages could not be transmitted without being revealed to people.

 

Drum beats

Many communities used drum beats as means of communication. People made special drums for communicating. The drums were made in such a way that they produced different sounds. Messages were conveyed through the sounds. The Buganda people used drums for communicating. The Ibos of Nigeria used talking drums to communicate matters concerning deaths and festivals. Sounds from drums were heard by people who were several kilometres away.

This method was advantageous because messages were sent quickly. Sending the messages was not tiresome. People knew the meaning of the sounds produced by the drums so communication was easy.

The method however had some disadvantages. The drums could not be heard by people who were separated by hills because of echoes. Sometimes people could interpret the sounds wrongly.

Drumbeats required specialists to send accurate sounds for accurate interpretations. Deaf people could not communicate using the method.

 

Messengers

Messengers were people who were sent to deliver messages by word of mouth. They travelled on foot for some distances before they conveyed the messages to other messengers who also conveyed the messages to others. This continued until the message reached the recipient. These organised groups of messengers were known as runners. The messengers relayed the information and sometimes brought the feedback. They made people of a community to keep in touch with one another and to be aware of what was happening. Messengers informed rulers of the approaching enemies.

The disadvantages of this method were as follows:

The messengers sometimes gave wrong information in case they forgot the message. Sometimes the message could be distorted. Messengers were at times attacked by wild animals and killed. This resulted to the failure to deliver messages.

Sometimes messengers delayed the information in cases of sickness or an accident. Messengers delivered limited ranges of messages because of the problems of memory. The information relayed could not be easily kept confidential.

The relay method was tiresome because one had to run for considerable distances.

 

Horn blowing

Horn blowing was a method which was widely used among the African communities to send important messages. Sometimes horn blowing was used to call people for urgent meetings. It gathered warriors together in times of war. Special horns were blown to call hunters together especially among the Ameru people of Kenya.

Horns were also blown to alert people about important ceremonies such as circumcision among the Chuka people who are part of the Meru communities. Use of this method was advantageous in the sense that horn blowing could be used successfully at any time of both day and night except when it was raining heavily accompanied by thunderstorms because people could not hear.

Horns relayed specific messages and could be used in all seasons. They spread messages very fast without delay. Horns were obtained from domesticated animals such as cows and goats and from wild animals such as antelopes and gazelles.

The disadvantage of this method is that people who were specialised in blowing horns to produce meaningful sounds were required. Sometimes the messages could be wrongly interpreted if the horns were not accurately blown.

People who were deaf could not get the message. People could not use the method to communicate with others if they were separated from them by mountain ranges and hills. This is because the hills acted as a barrier and reflected the sound back.

 

Written messages on scrolls and stones tablets

A scroll was a roll of paper which was rolled round a piece of wood for writing on. Scrolls were used in Egypt, Greece, China and Japan.

Before the introduction of papers, the Egyptians used several sheets of papyrus to make a long sheet, which was known as a Scroll. They wrote messages on the scrolls. Part of the Old Testament Bible was written on scroll.

Stones were also shaped and messages written on them. These were called stone tablets. The Ten Commandments in the Bible were at first written on stone tablets. These stone tablets are sometimes called clay tablets. Writing was done on wet clay which later dried and left permanent marks. In Mesopotamia this type of writing was called cuneiform.

 

 

 

Developments in modern means of communication

 

The modern means of communication are Telephones, Televisions, Radios, Telegraphs, Electronic mails, Facsimile transreceivers, Telex, Pager, Internet as well as the print media which includes newspapers, magazines, journals and periodicals. All these send messages over long distances. They also keep people informed of what is happening and enable them to keep in touch with one another.

 

Telephone

The first telephone was invented in 1875 by Alexander Graham Bell. It enabled speech to be transmitted along wire. The following year it became possible to send the first telephone messages after Thomas Edison made improvements on the initial model.

At one end speech sound was converted into electric vibrations while at the other end the vibrations were converted into original speech. The telephone provides a very quick means of communication that enables the caller to get immediate feedback. Today, the telephone is competing stiffly with mobile phones.

 

 

 

 

 

 

 

 

 

 

Modern Telephone

The Cellphone

Cellphones are the so called mobile phones. They are manufactured by a number of companies and they use radio waves for transmitting messages.

Mobile phone service providers in Kenya such as Safaricom and Kencell companies have established transmitter-receivers which detect radio signals sent by cellphones. The transmitter-receivers then send the signals back to the phones.

 

 

 

 

 

 

 

 

 

 

Cellphones

 

Cellphones vary in sizes and they are convenient as means of communication. They can be used anywhere so long as there is the network.

The only disadvantages of cellphones is that they are easily stolen. Some phones have poor reception while others are very delicate and can get damaged easily. cellphones cannot be used in places where there are no sources of electrical power because their batteries require continuous charging. They are expensive to buy and also to maintain.

 

Television

The invention of the cathode ray tube in USA enabled the development of the modern television to take place.

This enabled people to receive news through sound while seeing pictures on screen. The televisions also became educational and entertainment facilities. The first televisions showed black and white pictures. Later colour televisions were introduced.

Today televisions are important because they entertain people, provide educative programmes and provide local and international news. However, the televisions are expensive to buy and require power from electricity or batteries which are expensive to buy and maintain. It is only the middle and upper class people who can afford to purchase and maintain televisions.

 

Radio

The first wireless messages were sent in form of electromagnetic signals through frequencies by Guglielimo Marconi. The wireless telegraphy became popular and more experiments were carried out which led to the transmission of speech by radio waves.

During the First World War, more experiments were carried out. In 1920 the first radio broadcast was made in Britain by the Marconi Company. The same year the Westinghouse Company also begun sending out regular radio broadcasts in America.

The British Broadcasting Company (B.B.C) began its regular transmissions in 1922. The first BBC radio broadcast was transmitted in Kenya in 1928. Later during the Second World War English and Kiswahili programmes were introduced in Kenya. The radio transmitted local and foreign news.

 

 

 

 

 

 

 

 

 

 

Radio

 

Today the radio has become a very useful means of communication. It sends messages to distant places in the shortest possible time. The radio transmits educative programmes in form of Radio broadcast to schools as well as local and foreign news.

It also provides programmes to the general public, which give them awareness on HIV/AIDS, good morals, need for unity and how to become good law abiding citizens.

The radio serves a large number of people at the same time and it is cheaper to use than many other means of communication. It plays a big role in promoting trade through advertisement.

Lastly the radio entertains many people with songs and plays. This is possible because anybody can listen to the appropriate radio programme transmitted in a language he or she understands best.

 

Telegraph

Two scientists namely, Charles Wheatstone and William Coke invented the electric telegraph in 1837. The initial telephone wires were laid along railway lines in Britain inorder to alert railway officials about the movement of the locomotives.

Later an American scientist called Samuel Morse improved the telegraph communication by inventing one which never used needles but used a code of dots and dashes. This new device came to be known as Morse Code. It was used to send telegrams to many parts of the world. In Kenya the telegraph wires were laid down during the construction of the Kenya-Uganda railway.

 

Electronic Mail (E-mail)

Electronic mail sometimes called E-mail is a device which allows computer users locally and internationally to exchange messages. The E-mail allows distribution of messages (mails) to and from computers in a network. Each user of the E-mail has a mailbox address to which messages are sent. Messages sent through e-mail arrive within a very short period irrespective of the distance the sender is. Messages sent merely take seconds to reach.

The E-mail has some advantages when used as a means of communication:

 

  1. It delivers messages very fast.

 

  1. It is cheap because the cost of delivering messages far away is relatively low.

 

  1. Volumes or several copies of messages can be sent at the same time.

 

  1. The same message can be sent to many different people instantly.

 

  1. The E-mail messages are secure and one does not need to own a computer to use the facility. All one is required to do is to open an account through an Internet Service Provider.

 

 

Facsimile transreceivers (Fax)

This is a machine which enables transmission of written information like drawings, diagrams and maps in their exact form. Messages to be transmitted are fed into the machine which is connected by a telegraphic or telephone wire to a similar machine elsewhere which produces the message in photographic detail.

The sender makes first contact by telephone and then presses a button at the sending point. Both the sending machine and the receiving machine have drums with photographic papers. When the drums on both sides start to revolve, the facsimile copy is produced at the receiving end. The facsimile copy produced is exactly the same as the original copy at the sending end. It is transmitted in about half a minute.

 

 

 

 

 

 

 

 

 

Fax

 

This method of sending information is advantageous in that actual information is transmitted within a very short time.

One disadvantage is that it is more expensive to send messages using facsimile transreceiver compared with some other means of communication such as e-mail and telephone over short distances. However, the method is cheaper when used to transmit messages over long distances.

 

Telex

Telex uses a teleprinter which prints messages and send them to the other places instantly. Telex machines are switched on the whole day. The telex subscribers have numbers which must be typed and the exchange operator advises when the connection is made so as to start typing the messages.

When information is typed on a teleprinter, it is automatically typed and reproduced the same time by the machine at the receiving end in typescript. Today teleprinters are used all over the world to send urgent messages.

 

Pager

This is a device which enables the where about of a person to be located so that the person can be brought on telephone to hear a message and perhaps also reply to it immediately. It involves sending a signal that is received by a particular person who is alerted by the beeping of the pager.

It is common where people do not sit in offices but move from one place to another within a specified area. Its disadvantages are that it only receives a signal and one cannot send back the reply using the machine. It operates within a specified area where the signals can reach.

 

Internet

This is a computer network made up of thousands of networks world-wide. Millions of world computers are connected to the Internet and the number is still increasing at alarming rate.

There is no single individual, organisation or government which may claim ownership of the Internet. However, some organisations develop technical aspects of the Internet network and set standards for creating applications on it, but no single governing body is in control.

 

The backbone through which the Internet traffic flows is owned by private companies. All computers on the Internet communicate with one another using the transmission control protocol.

An Internet user has access to a wide variety of services which include shopping opportunities, real-time broadcasting, interactive collaboration, file transfer and electronic mail.

Users of Internet can search and find information of interest aided by special software and data stored in ready usable formats. This is called information browsing. Individuals are able to gain access to a wide range of information topics.

The Internet allows a person to use electronic mail and to transfer data in form of files across the Internet from one side to the other. The Internet also allows people to use other computers across the network. The use of computers is becoming popular in Kenya today. Many people and organisations are trying to connect their computers to the Internet so that they can interact with the rest of the world.

 

The impact of modern means of telecommunication

 

  1. The development of telecommunication has improved communication in the entire world by easing communication within countries, between various countries and between citizens and their governments as well as communication among individuals themselves.

 

  1. It has helped to improve travel. Pilots in ships and planes for instance communicate with others in control stations by use of telecommunication facilities.

 

  1. Trade has been promoted due to the development of telecommunication services which provide speed and efficiency of business transactions through advertisements.

 

  1. Radio and television provide mass entertainment to people all over the world. They have also kept people busy during their leisure time.

 

  1. Telecommunication technology has created employment opportunities for many people in the world.

 

  1. It has been used in modern warfare to communicate and to provide information to soldiers in war.

 

  1. It has enabled astronomers to explore the outer space in order to conduct space research. Satellite communication is mainly for this purpose.

 

  1. Many people have been able to learn a lot of new things as they watch the television and listen to radio programmes.

 

  1. Telecommunication services have enabled people to learn the cultures of other people in the world. The television has played a great role in achieving this therefore promoting cultural interaction.

 

  1. Means of communication such as the telephone enable direct delivery of messages to the recipients.

 

  1. The message can be delivered very fast within seconds to a person very far away by use of telephone, telex, fax and e-mail.

 

  1. The computers have enabled storage of information while the Internet has enabled access to other information in computers world wide. This is a great achievement in the development of telecommunication.

 

Print media

 

The print media includes communication through Newspapers, Magazines, Journals and Periodicals.

 

Newspapers

These are written messages containing local and foreign events. Before the introduction of regular newspapers, messages reached people through word of mouth and short letters posted to them or pinned on the notice boards for anyone to read.

The Germans were the first to introduce the newspaper system following the invention of the printing press by Johann Gutenberg in 1440. By the close of the 18th century almost all the countries in Europe except Britain had regular newspapers.

Britain however introduced the first newspaper entitled the Daily Courant in 1702. More and more publications followed in Britain after 1861 when printing of newspapers was legally allowed. Newspaper printing and circulation then spread to the rest of the world.

 

Newspapers are printed on daily or weekly basis. They contain news, advertisements and various articles on many fields.

 

In Kenya for example, we have daily newspapers such as the Daily Nation, The  East African Standard, Kenya Times, The People, Taifa Leo, and weekly newspapers such as Sunday Nation, Sunday Standard and Taifa Weekly.

 

Magazines

Magazines resemble newspapers except the fact that they are not published frequently. They may be published after a week, after a fortnight or after a month or even three months. Magazines cover articles, stories and announcements.

 

During the colonial rule Jomo Kenyatta was the editor of a magazine entitled, “Muigwithania”. Since independence, we have had magazines like the Kenya Gazette, Parents, Today, Weekly Review and Finance among others.

 

Journals

These are newspapers which deal with certain specialised subjects for instance they may deal with trade, medicine, education, science and specific topics in history. They are published at certain intervals.

We may therefore have titles such as ‘The Journal of African History’, The Medicine Journal and The Scientific Journal but each of them covering a specific area in a specified field.

 

Periodicals

These are magazines or other publications published at regular intervals for instance on weekly or monthly basis.

 

Advantages of print media

 

  1. Written information through the print media is preserved for a long period without being distorted, forgotten and damaged.

 

  1. Written of information through print media can be done any time because it is not effected by weather or any other physical aspects.

 

  1. It is cheap to store and also transport written material such as newspapers and magazines that contain written information.

 

  1. It is easy to use written information in the print media for future reference because one can easily review the message when necessary.

 

  1. It is easy for the literate to get information and directives from the government by use of newspapers and magazines.

 

  1. Newspapers and magazines are used to advertise business. This promotes business transactions.

 

  1. Ideas are able to spread fast.

 

  1. Printing and sale of newspapers and magazines has created employment opportunities.

 

  1. Print media provides foreign news therefore enabling people to be aware of what happens outside the country.

 

  1. Print media is not discriminative because it serves all the people who can read since newspaper and magazines are written using several languages. For instance, some newspapers are written in English, others in Kiswahili and some in various local languages (mother tongues)

 

Disadvantages of print media

  1. They can be used to spread propaganda.

 

  1. They can be used to tarnish the name of individuals for example the politicians.

 

  1. They sometimes include information that is not suitable for young children. This can affect the morals of the youth.

 

Review Questions

1        a)       Define transport and communication.

  1. b) Explain why the camel is regarded as the best beast of burden for use in deserts.

 

2        a)       Outline the impact of the invention of the wheel.

  1. b) Describe the main stages in the development of water transport.
  2. c) What is the impact of the development of modern water transport.
3        a)       List the inventions, which helped to promote road transport.
b)              What was the impact of the development of rail transport.

 

4        a)       Explain the development of space exploration.
b)              Describe the advantages of the development of air transport.

 

5        a)       Identify the traditional forms of communications.
b)              Explain the importance of radio as a means of communication.

 

6        a)       What is the print media?
b)              Discuss the impact of modern telecommunication.

 

Students’ Activities

1        In groups discuss the problems of various means of transport and communication.

  • Collect newspapers and magazines and then in groups classify the types of news reported.

 

 

CHAPTER 3

 

Development of Industry

 

Industrialisation is the process of producing goods from raw materials. Before the Industrial Revolution of the 19th century, wood, wind and water were the major sources of energy in the world.

 

The sources of energy

 

Wood

Before the 19th century wood was an important source of energy. Wood was used for cooking, boiling water and warming houses in winter. In the early 19th century, it was also used for making charcoal that was used for smelting iron. Wood was also used to heat water to prepare the steam power for driving steam engines and steam ships.

 

Wind

Energy from wind was used for pumping water from mines and wells. It was used to separate grains from husks (winnowing). Wind energy was used for driving ships and boats for instance the Arab dhows. Wind energy was also used to operate windmills used for grinding grains into flour. The balloons also used wind energy to fly.

 

Water

Water provided energy for operating spinning and weaving machines. It operated water mills for grinding flour. Water also provided energy for operating water pumps. It was heated to produce steam power.

 

 

Uses of metals in Africa

 

Bronze

Bronze is a mixture (alloy) of copper and tin. Bronze was used to make weapons such as daggers, arrowheads, swords, axes and spears. It was used to make tools which included chisels and hoes. It was used to make ornaments and utensils.

 

Bronze was also used to make containers, bronze sculptures and musical instruments such as flutes.

 

Lastly, bronze was used for making stones for constructing pyramids in Egypt and also for decorating king’s palaces.

Gold

Gold is an attractive metal that was used by rulers to decorate their palaces. It acted as a sign of wealth. The rulers of the Asante Kingdom in West Africa regarded gold as their sole property. Anyone who obtained a gold nugget had to hand it over to the king.

Gold was used to make golden ornaments and sculptures. It was an important commodity of trade among the people of the Mwene Mtapa Kingdom and the city-state of Kilwa that minted gold coins. Gold was also used to make knife handles, utensils and containers.

 

Copper

Copper was found in many parts of Africa such as Egypt, Zaire and Zambia. Copper was used to make ornaments such as bangles. It was used to make tools such as needles and to mint copper coins that acted as a sign of wealth and medium of exchange.

Copper utensils were also made from it. It was also used for decorating the kings’ palaces and for making brass and bronze alloys. Copper was used to make water pipes in Egypt. Lastly it was used for making weapons.

 

Iron

There were several early iron working centres in Africa such as Meroe, Nok, Taruga, Axum, Korotoro, Kwale and Kavirondo gulf. These early iron-working centres were famous for making a variety of iron tools such as hoes, knives and axes. In some places cattle bells and jingles for festivities were made.

Iron was widely used for making high quality weapons of the time such as daggers, swords, spearheads, arrowheads and stabbing knives.

Gold sculptures which represented people were made in West Africa in Nok and Taruga iron working sites. The Bantu are associated with the spread of iron working technology in Africa.

 

The spread of iron working technology had the following impact:

 

  1. More land was cultivated due to the introduction of better iron tools such as hoes and axes which cleared forests.
  2. Trade increased especially between the blacksmiths and the cultivators.

 

  1. It encouraged migrations because the iron weapons made the migrating communities to have confidence of conquering others and settling in their land since security was guaranteed.

 

  1. The iron weapons made some communities to expand through conquest. This led to the growth of strong states such as Nubia, Mwene Mtapa, Buganda, Axum and Ancient Ghana.

 

  1. The iron making in Africa encouraged wars because people acquired superior iron weapons which gave them courage to advance and conquer others.

 

  1. Iron working encouraged job specialisation. Some people became blacksmiths others began making specific items such as knives, daggers, axes, hoes and spear heads.

 

  1. There was rapid increase in food production because of increase in farmlands.

 

  1. The early mining centres attracted more people. This encouraged urbanisation.

 

  1. Iron weapons enables various communities to improve their systems of defence.

 

  1. The weak communities were displaced by the stronger ones and sometimes assimilated during migration.

 

  1. In some areas iron became a medium of exchange.

 

 

Uses of various sources of energy during the Industrial Revolution in Europe

 

Coal

Coal was the main source of energy in the 19th century. It heated water to very high temperatures to produce steam which drove water pumps for removing water in the coal mines. Coal was used to produce steam for driving steamships and the locomotives. It was also used for heating and lighting houses.

 

Today, coal is used for generating electricity and providing power for industries.

 

Oil

The use of petroleum became popular during the industrial revolution. At first oil was used to light lamps which were used in houses and streets.

When the first internal combustion engine which used petrol was invented by Gottlieb Daimler, petroleum began being used for driving motor vehicles. Petroleum was also used for lubricating machines in factories and for generating thermal – electricity. Petroleum was used as medicine by the Chinese and the Indians. Today petroleum products are used in industries to make drugs, synthetics, plastics and fertilisers.

The disadvantages of petroleum

It is expensive to mine. Once extracted and exhausted it cannot be renewed. Lastly it pollutes the environment.

Steam

Steam was produced by heating water to very high temperatures. When steam was produced it was used as follows:

 

  1. To drive heavy machines in factories.

 

  1. To pump out water out of mines.

 

  1. To drive steam driven vehicles.

 

  1. To drive steam driven trains and locomotives.

 

 

 

 

 

 

 

 

Steam locomotive

 

  1. To drive steamships and steam boats.

 

  1. To operate spinning and weaving machines.

 

Electricity

There are two forms of electricity, Hydro-electricity and Thermal electricity. Hydro-electricity is produced by converting the energy of moving water to electrical energy. Thermal electricity is produced by burning oil or coal to provide heat which is used to produce steam which turn steam turbines and hence generate electricity.

 

The electrical power was used and is still used as follows:

  1. To drive machines in industries and factories.

 

  1. To light houses.

 

  1. To drive electric trains and cars

 

  1. To heat houses.

 

  1. To supply power to radios, televisions, cinema and computers.

 

  1. To supply power to refrigerators and electric cookers.

 

  1. For welding.

 

  1. To boil water.

 

  1. To fence game parks.

 

Uses of iron and steel

The smelting of iron started very early when communities started separating it from rock. In the 18th and 19th centuries new iron smelting techniques were discovered. This came about because iron was very much in demand during the Industrial Revolution especially in the transport sector where it was used for making ships, trains, rails and bridges. Iron was also used to make textile machines, water pipes and ploughs.

 

In the mid 19th century, Henry Bessemer discovered the method of converting iron into steel. There after, steel replaced iron in the making of many equipment required in the transport industry. For instance rail bars, trains, ships and bridges were made by use of steel because it is stronger than iron. Later steel was used for reinforcing concrete during construction of permanent buildings.

 

 

 

 

 

 

 

 

 

 

 

 

 

Steel producing plant

 

Today steel has a wide range of uses for instance it is used in the motor vehicle industries, ship building industries, in the industries for making trains and also in the industries which make building materials such as iron sheets, roofing bars, nuts and bolts. Steel is therefore widely used to make many kinds of tools and machinery.

 

Industrialisation in Britain

Britain was the first European nation to industrialise. During the first half of the 19th century, it was the leading industrialised nation in the world. It manufactured textiles and a variety of items made of iron.

Britain had rich coal mines which provided enough coal for industrial power. The surplus was exported. This made Britain to be the leading trading nation during the first half of the 19th century.

The other European countries and USA borrowed the industrial technology from Britain. By 1870s Britain ceased to be the world’s leading industrialised nation.

The last half of the 19th century was associated with many scientific inventions and discoveries which promoted industrialisation not only in Britain but also in other nations like USA, France and Germany. Britain became the first nation to industrialise because of the following factors which contributed to the development of industries:

 

  1. Britain had good transport and communication network.

 

  1. It had enough capital to invest in industry.

 

  1. There was sufficient raw materials in Britain in form of coal, iron and cotton for use in the industries.

 

  1. Britain enjoyed a long period of peace and political stability.

 

  1. The British army was strong and superior. It defended the waters of Britain effectively from competitions by rival nations from sea pirates.

 

  1. Britain had well advanced insurance and banking systems.

 

  1. Trade barrier such as tariffs which could hinder trade never existed in Britain by then because it had adopted the policy of free trade.

 

  1. Britain had enterprising merchants who manned trade and also encouraged industrial growth and development.

 

  1. It had well developed cottage industries which laid the basis of the industrial take off.

 

  1. There was adequate skilled and unskilled labour.

 

  1. The acquisition of colonies overseas provided Britain with more raw materials for the industries.

 

  1. The rapid population growth in Britain expanded the internal market for the manufactured goods while the acquisition of colonies overseas provided external markets.

 

  1. The technological advancement of the people in Britain brought about new inventions which stimulated industrialisation.

 

  1. There was availability of energy from coal.

 

  1. The Agrarian Revolution had provided industrial workers with sufficient food.

 

The effects of the industrialisation in Britain in the 19th century

 

  1. The industrialisation of Britain in the 19th century stimulated the rural-urban migration of the landless who went to seek for employment in the emerging industrial centres. This led to expansion of industrial centres and hence urbanisation.

 

  1. Transport and communication facilities such as roads, railways, and telephones were developed to serve the industrial centres by facilitating trade and transportation of raw materials to the factories and manufacture of goods to the market.

 

  1. There was the expansion of the banking industry and insurance. These provided services to both industrial owners and workers. They also created new employment opportunities.

 

  1. The industrialisation in Britain led to enormous expansion of local and international trade. The manufactured goods were sold to the British citizens and the surplus was sold to the rest of Europe and to the British colonies overseas. The British colonies provided raw materials such as palm oil, iron, copper and cotton in return.

 

  1. Colonialism was encouraged as a means of acquiring sources of raw materials for the British industries. Britain was able to acquire colonies such as India, Egypt, Ghana and Nigeria.

 

  1. The standards of living of many Britons was raised due to income obtained from the industries. The rise of the standards of living of the middle class in particular resulted to the class struggle between the rich and the poor in Britain therefore sharpening the social stratification.

 

  1. The industrialisation in Britain led to development of agricultural production in Britain as well as in USA and other British colonies. The industrial workers in Britain required food. The machines required lubricating oil which was obtained from the palm oil grown along the West African coast. Cotton was obtained from America and used in the British textile industries to manufacture cotton cloth.

 

  1. The industrialisation in Britain encouraged establishment of many kinds of machines. These industrial machines produced fumes which polluted the environment. There was also excessive noise which made some people deaf.

 

  1. Poor living conditions of factory workers encouraged emergence of poor housing or slums. In these slums there was overcrowding of houses which were not properly ventilated. The poor living conditions were as a result of the low wages of the factory workers.

 

  1. The industrialisation in Britain also encouraged exploitation of labour. Children and women laboured for long hours in industries before manual labour was replaced by use of machines.

 

  1. Industrialisation in Britain caused unemployment especially after machines were introduced which could do the work formerly done by labourers. The jobless still remained living in slums but they turned to new careers which were immoral such as robbery and prostitution as a means of their survival.

 

  1. The overcrowding of people in towns and poor sanitary facilities resulted to outbreaks of diseases such as dysentery, cholera and tuberculosis.

 

 

Industrialisation in continental Europe

 

It is necessary to note that industrialisation technology spread to other countries of Europe from Britain in the second half of the 19th century. Countries such as Germany, France and Belgium which had abundant deposits of coal, iron and steel as well as the supply of both skilled and unskilled labour became industrialised next.

To achieve this, industrial research was carried out. The discovery of the method of converting iron into steel by Henry Bessemer revolutionised the industrial sector. Electricity and petroleum were also discovered and they became important sources of energy for the industries.

 

The rapid industrialisation of continental Europe was characterised by the following:

  • Improved transport and communication to ease transportation of raw materials and marketing of ready manufactured goods.
  • Increased exploitation of coal and iron ore.
  • Improvements in agriculture in order to produce enough food for urban dwellers and industrial workers and also to provide some industrial raw materials.
  • Mass production of manufactured goods as well as the coming up of many new inventions as a result of increased industrial research.

 

Problems the industrial workers experienced

 

  1. Workers were paid very low wages making them to experience poor living conditions.

 

  1. Workers were exposed to very dangerous machines, noise and chemicals which resulted to injuries, suffocation, accidents and deaths.

 

  1. Diseases attacked workers because their living conditions were very poor. Such diseases were typhoid, cholera, dysentery and tuberculosis.

 

  1. Women and children toiled in the factories and they were also subjected to long working hours which denied them leisure and rest.

 

  1. The environment they worked in was polluted due to improper disposal of industrial waste.

 

  1. Workers lived in overcrowded houses where there was inadequate lighting conditions and poor ventilation.

 

  1. The poverty as a result of low wages increased crime rate in towns. Workers were therefore exposed to constant robbery.

 

  1. The factory workers were not insured.

 

 

Effects of the industrial revolution in Europe

 

  1. The Industrial Revolution in Europe stimulated rural urban migration of the landless who wanted to look for jobs in the expanding urban centres.

 

  1. There was scramble for colonies as a means of acquiring sources of raw materials for the industries in Europe and looking for market for the surplus manufactured goods as well as suitable areas for investing their surplus capital.

 

  1. There was increased urbanisation because employment opportunities attracted many people. Trade that developed in towns attracted businessmen who opened other commercial activities that also attracted many people. The development of transport and communication systems and the use of machines in the cottage industry also made people to move to urban centres and hence promoting urbanisation.

 

  1. The standards of living of the people in Europe were raised due to income from the industries.

 

  1. It stimulated expansion of factories instead of cottage industries. Banking and insurance were established.

 

  1. Industrial Revolution in Europe created employment opportunities in the industrial sector in form of mechanics, plant operators, engineers and managers.

 

  1. The Industrial Revolution led to the rise of trade unionism in the European countries such as Britain, France and Germany.

 

  1. There was replacement of human labour with the use of machines.

 

  1. The Industrial Revolution in Europe led to production of goods in large quantities. These goods were exported in bulk.

 

  1. It encouraged the development of transport and communication systems such as railways and roads.

 

  1. The industries led to pollution of the environment, overcrowding of people and crime.

 

  1. The Industrial Revolution in Europe promoted the development of agriculture because the industrial workers needed food.

 

  1. The Industrial Revolution in Europe caused unemployment in the countries where the use of machines had replaced manual labour.

 

  1. The Industrial Revolution in Europe stimulated local and international trade.

 

  1. The Industrial Revolution finally led to exploitation of labour. Children worked in factories for long hours.

 

 

Emergence of the world industrial powers

The USA

The USA has led in industrialisation for a long period. Before it became industrialised the Americans were largely agricultural people. The Britons who migrated from Britain to America are the one who stimulated industrialisation in the USA.

 

Many factors however contributed to the success of the industrialisation in the USA. These factors are as follows:

 

  1. The USA had abundant natural resources such as iron ore and coal as well as forestry resources.

 

  1. There was adequate skilled and unskilled labour due to the high population in USA. Slaves also provided labour in the American farms leading to production of raw materials for use in the American industries.

 

  1. The USA had adequate energy resources such as coal and iron ore. Later uranium, petroleum, electricity and natural gas were introduced.

 

  1. There was the development of transport and communication in form of railways, roads, airways, telegraph, radio, telephones, telegrams and televisions.

 

  1. The technological advancement in North America in the 19th and 20th centuries contributed to the industrial advancement in the USA because a lot of discoveries and inventions on industry were made.

 

  1. Banks and insurance were introduced in the USA. They contributed a lot to the industrial sector.

 

  1. The government of the USA encouraged foreign investors from Germany and Japan to come and invest in industry.

 

  1. The USA had adequate capital obtained locally as a result of the Agrarian Revolution as well as from the foreigners who had invested there.

 

  1. The USA enjoyed a long period of political stability. Even in the 20th century the USA joined the two world wars almost the time they were ending. Also there were few strikes and industrial disputes.

 

  1. The British citizens who migrated to the USA introduced plantation agriculture that provided the initial industries with the agricultural raw materials. This laid the basis for heavy industries that used iron and steel.

 

  1. In the 20th century the USA embarked on intensive research aimed at promoting industry. The institutions of learning emphasised on Science and scientific research. The universities in particular became devoted to industrial development.

 

  1. The government policies favoured the growing industries. The USA government for example encouraged the home market by discouraging the imposition of tariffs on locally manufactured commodities.

 

  1. The USA had a strong agricultural base that contributed to her industrial take off. This is because the industrial labour force could get enough food supply and raw materials for the processing industries based on agricultural product.

 

The effects of industrialisation on the USA

  1. The people’s standards of living has been improved. The USA government supports the unemployed US citizens.

 

  1. The USA economy has been diversified. It now attains income from both agriculture and industry.

 

  1. The USA has been able to boost her industrial technology by encouraging education based on science and research.

 

  1. The USA has become the major world power after the break of the former USSR.

 

  1. The USA has been able to use its industrial product and technology to mechanise agriculture in order to increase the agricultural yields. This has enabled the USA to provide the growing population with sufficient food.

 

  1. The industrial development in the USA has enabled it to take part in space exploration. The first human being to land on the moon, Neil Armstrong, was from the USA.

 

  1. The USA has been able to earn foreign currency which has enabled it to acquire abundant foreign reserve. This has also enabled the USA to be one of the world’s leading donor states. For example the USA provided financial and technical aid to Brazil and Egypt which enabled them to industrialise.

 

  1. The US businessmen have been able to invest locally because of the wealth obtained from the industrial sector.

 

  1. Industrialisation has enabled the USA to develop its military might. This military might enabled US to oust Saddam Hussein of Iraq from power.

 

  1. Industrialisation has encouraged urbanisation.

 

  1. Industrialisation has encouraged pollution of the environment.

 

  1. Industrialisation created job opportunities for the Americans.

Germany

Germany began being industrialised in the 19th century. By 1900 it was second to USA in industrialisation.

 

Several factors facilitated the industrial development in Germany. These were as follows:

 

  1. The creation of German customs union (Zollverein) unified the Germans. This was followed by rapid economic development.

 

  1. Germany had large amounts of raw materials such as iron ore and coal. Iron ore was obtained from Alsace-Lorraine while coal was obtained from Ruhr and Saar mines.

 

  1. The USA through the Marshall plan provided Germany with financial aid for reconstruction after the Second World War.

 

  1. The German population was increased rapidly. This growing population provided skilled and unskilled labour.

 

  1. Germany had well-developed transport and communication facilities in form of railways, roads and canals.

 

  1. The German government supported industrialisation by encouraging ambitious Germans to invest locally in industry and also through protection of tariffs and subsidies.

 

  1. The industrial base that existed before the Second World War in Germany was revoked even after the war.

 

  1. Germany enjoyed political stability after the Second World War. This encouraged industrial development.

 

  1. There was sufficient power for the German industries from coal.

 

  1. The manufactured goods from Germany had markets in South America and Far East.

 

  1. The development of education based on science and technology in Germany enabled it to produce scientists and very skilled manpower.

 

  1. The second unification of East and West Germany widened the scope of industrial output.
  2. There were improved agricultural techniques in Germany that resulted to the increased yields that provided agricultural raw materials for the processing industries.

 

The impact of industrialisation of Germany

  1. Industrialisation improved the standards of living of the German society. Their purchasing power was raised.

 

  1. Germany was able to develop a network of transport and communication to be able to transport raw materials and manufactured goods.

 

  1. Industrialisation enabled Germany to become a strong power before the First World War. This made Germany to join other European nations to look for colonies overseas.

 

  1. Industrialisation diversified the economy of Germany because the country was able to manufacture vehicles, machinery, chemicals, electronics and textiles that were exported in the local and international markets.

 

  1. It created employment opportunities for the people in West Germany and the neighbouring states such as Yugoslavia, Turkey and Italy.

 

  1. Industrialisation in Germany encouraged the growth of urban centres such as Berlin and Warsaw.

 

  1. Germany’s foreign reserve was boosted due to sale of her manufactured goods for instance machinery of all kinds.

 

  1. Industrialisation boosted local and international trade.

 

  1. Industrialisation of Germany contributed in reducing inflation.

 

  1. Industrialisation in Germany also boosted foreign reserve due to sale of the manufactured goods.

 

Japan

Industrialisation of Japan began in the second half of the 19th century after the USA made treaties with Japan aimed at creating trade partnership. The introduction of compulsory primary and secondary education and the establishment of universities and other colleges followed this. Many students were sponsored abroad where they acquired education.

Japan was engaged in wars with China and Russia between 1894 and 1905. It also fought on one side with Britain, France and Russia during the First World War against Germany and her allies.

During the Second World War, Japan attacked the American naval base at Pearl Harbour in the Hawaiian Islands. The USA responded by bombing the Japanese cities of Hiroshima and Nagasaki in 1945. This act affected the economy of Japan but there was economic recovery and continued industrialisation in the later years.

 

Industrialisation in Japan was promote by the following factors:

  1. Japan had enough capital for carrying out research and for industrial development. Japan also benefited from the American aid obtained after the Second World War.

 

  1. There was ready internal and external market for the Japanese manufactured goods.

 

  1. Japan enjoyed a long term of political stability mainly after the Second World War. This peaceful atmosphere encouraged industrial progress.

 

  1. Japan has a network of transport and communication for instance railways and roads.

 

  1. The Japanese industrial base which existed before the first world war was improved and made better after the second world war.

 

  1. Power was available from coal, uranium and hydro-electric power for industrial use.

 

  1. Skilled and unskilled labour was readily available in Japan.

 

  1. Japan had abundant raw material for instance, iron ore and coal.

 

  1. Japanese are hardworking people. This promoted industrial development.

 

  1. Japanese goods are of very high quality and at the same time very cheap. This encouraged internal and external market.

 

  1. Japan natural harbours encouraged trade through export and import of goods.

 

  1. Japan has been politically neutral since the Second World War. It trades with any nation.

 

  1. Japanese introduced a new form of taxation aimed at raising funds for promoting industrialisation.

 

  1. The Japanese government encouraged home market and imposed tariffs on foreign goods to discourage them from competing with goods produced in other countries.

 

  1. Japan encouraged foreign investors to come and invest in the country. Japan also invested in other countries.

The effects of industrialisation in Japan

 

  1. Industrialisation has led to improvement of the standards of living of Japan

People.

 

  1. The Japan foreign reserve has been boosted due to sale of Japanese manufactured goods.

 

  1. Japan has been recognised as one of the developed industrialised country of the world.

 

  1. Japan has diversified her economy from a predominantly agricultural country to a country which also obtains wealth from Industry.

 

  1. Japan has promoted trade by using locally manufactured ships to carry imported raw materials and goods for export.

 

  1. Job opportunities have been created in the industrial sector.

 

  1. Industrialisation has encouraged development of better and sufficient means of transport and communications.

 

  1. Many people prefer Japanese manufactured goods mainly because they are of high quality and at the same time cheap.

 

Industrialisation in the third world

 

Brazil

Industrialisation in Brazil began in the last quarter of the 19th century. The country’s industrial process later developed tremendously because of the following factors.

 

  1. Large deposits of minerals such as iron ore, gold, bauxite and manganese were available for industrial use. Other raw materials in form of wood for lumbering and agricultural products were available for the Brazilian industries.

 

  1. The Brazilian government provided capital for developing industries.

 

  1. The U.S.A. also provided technical and financial aid to Brazil, such aid was used to develop heavy industries like the Volta and Rendonda steel works.

 

  1. Brazil had cottage industries that laid the basis of its modern industries.

 

  1. There was development of transport and communication in Brazil. This was through the construction of roads and railways for transporting raw materials to the industries.

 

  1. Brazil encouraged foreign investors who established companies from Europe and the U.S.A.

 

  1. The Brazilian government introduced five year development plans to promote industrial development.

 

  1. The first and the second world wars influenced the industrial take off in Brazil by encouraging mass production of locally manufactured goods, which were sold cheaply.

 

  1. Brazilian goods were in demand in Britain, which provided a ready market.

 

  1. The government nationalised industries to enable them to be supervised properly. It also encouraged industrialisation.

 

  1. Coal, petroleum and hydro- electric power were available for providing energy in the industries.

 

  1. There was internal market of the goods from the industries. For example the Brazilians purchase pharmaceuticals transport materials and spare parts, farm tools and machinery and textiles.

 

Obstacles to the industrialisation of Brazil

Industrialisation of Brazil has not been smooth A number of factors have undermined Brazilian effort to industrialise. These are:

 

  1. A large percentage of Brazilian citizens are poor and they can not establish industries or provide a high purchasing power for the industrial goods.

 

  1. Still there is inadequate transport and communication facilities even after the government’s efforts to improve transport and communication.

 

  1. The Brazilian wealth in owned and controlled by a majority group.

 

  1. The Brazilian population is concentrated along the coastal belt. The interior has labour problems because majority of the Brazilians prefer to work along the coastal belt.

 

  1. Constant inflation in Brazil makes goods to be expensive.

 

  1. Brazil has accumulated many foreign debts. This hinders steady progress of the country.

 

  1. The available resources in the Amazon forest are under exploited due to the sparse population there. These are resources that can be used in industries.

 

Impact of the industrial growth in Brazil

 

  1. The Brazilian industrial sector has boosted her foreign reserve.

 

  1. At least there is an improvement in the living standards of the local people in Brazil who survive from the spill of industrial gains. This has succeeded due to reduction of the inflation that has to the rise of the purchasing power of the Brazilians.

 

  1. Exports have been increased due to increase in manufactured goods.

 

  1. Brazil has emerged as one of the most industrialised third world countries.

 

  1. Industrialisation of Brazil has encouraged modernisation of port facilities in order to provide an outlet of goods being exported.

 

  1. It has accelerated the development of transport and communication in Brazil.

 

  1. Employment opportunities have been created especially in the heavy and light industries.

 

  1. Industrial growth has encouraged growth and expansion of urban centres especially those along the coastal belt such as Sao Paulo, Rio de Janeiro and Recife.

 

South Africa

South Africa first started as an agricultural country but later there was the discovery of gold and diamonds that promoted the industrialisation of the country.

 

The industries which developed in South Africa, included textile industries, iron and steel industries, chemical industries, cement industries and locomotive industries among others.

The factors which contributed to the industrialisation of South Africa:

  1. Availability of minerals such as coal, gold, diamonds, silver and iron ore some of which provided raw materials for the industries.

 

  1. Availability of capital from the sale of some minerals such as gold and diamonds.

 

  1. Availability of power for industries in form of coal and hydro-electric power.

 

  1. Availability of network of transport and communication in form of railways, roads, air transport and telephones.

 

  1. Encouragement of foreign investors who invested in the mining industry.

 

  1. Availability of skilled labour and unskilled labour obtained from the neighbouring states such as Malawi and Mozambique.

 

  1. Existence of local and international market especially after South African majority attained independence in 1994.

 

  1. There has been a considerable period of political stability after the majority Africans took over the government after independence was granted to them in 1994.

 

  1. The manufactured goods from South Africa are of high quality. These enable them to compete favourably with imported ones.

 

  1. The government of South Africa supported industrialisation by imposing tariffs on imported goods.

 

Factors that hindered industrialisation in South Africa

 

  1. Majority of Africans were impoverished by the colonial regime and for this reason their purchasing power is low.

 

  1. The international community banned South Africa from trading with countries that were United Nations (UN) members. Therefore, there was no external market for South African manufactured goods.

 

  1. There was no political stability during colonial rule because Africans were always fighting against apartheid. This affected industrial growth and also discouraged investment.

 

  1. South African goods have faced stiff competition from those from the developed nations like Japan and China.

 

  1. The high crime rate in the South African cities discouraged those who wanted to invest in industry.

 

India

India was colonised by Britain and it supplied the colonial master with cotton. It attained independence in 1947 and since then it engaged itself in industrial development.

 

A number of factors enabled India to industrialise. These are:

 

  1. India had raw materials such as cotton and iron ore for use in industries.

 

  1. India established a well developed infrastructure for instance its transport and communication facilities.

 

  1. The cottage industries existed in India. These industries formed a basis for industrial growth.

 

  1. There was adequate power from coal, natural gas and oil. Currently hydroelectricity and uranium are in use.

 

  1. India’s high population provided skilled and unskilled labours. The government of India trained people to acquire technical skills and industrial technology.

 

  1. The high population provided internal and external market for the manufactured goods.

 

  1. India embarked on a series of five-year economic plans aimed at developing industry. The first of these plans was the 1950 – 1955 development plan.

 

  1. India established state enterprises and assisted the private sector through loans. This boosted industrialisation.

 

  1. The Indian government encouraged foreign investment in the industrial sector.

 

  1. The political stability in India after the attainment of independence encouraged industrialisation.

 

  1. Protective tariffs were imposed to enable local industries to grow.

 

The main industrial cities in India

 

 

Impact of Industrialisation of India

 

  1. India’s foreign exchange earnings have been increased due to sale of cheap manufactured goods.

 

  1. There is a lot of improvement in the living standards of some sections of the Indian community. Even the purchasing power of the people has risen.

 

  1. India has boosted the agricultural sector through manufacturing of farm tools and machinery.

 

  1. India’s industrial development has created employment opportunities for the citizens.

 

  1. Local and international trade has been encouraged through sale of the manufactured goods.

 

  1. It has encouraged new urbanisation and expansion of the existing urban centres such as Bombay, Karachi and New Delhi.

 

  1. India’s revenue has been increased and its economy diversified as a result of establishment of light and heavy industries as well as development of agriculture.

 

  1. India has become technologically advanced and a nuclear power.

 

  1. India is now one of the most industrialised third world nations.

 

  1. India has used the income from industry to develop transport and communication network.

 

  1. Today India is able to provide public services such as education and health care to its citizens.

 

  1. Modern industrialisation in India has also boosted the cottage industries that include making of garments, plastics, shoes, hosiery and some household items.

 

 

 

 

 

 

 

 

 

 

Plastic buckets and shoes

 

 

Scientific Revolution

 

Scientific revolution refers to the period when man made many inventions and discoveries as a result of his improvement in knowledge and the interest to find out new thing about the universe. The scientific inventions began before the birth of Christ. A number of scientific discoveries and inventions were made in agriculture, industry and medicine. These discoveries and inventions improved man’s conditions of living after he indetified various ways of solving his problems.

 

The early civilizations for example in Greece, India, Iraq, Egypt and China influenced the development of early science. The Greeks and the Egyptians were great mathematicians. The Greek mathematician called Pythagoras came up with the right-angled triangle. The Egyptians used mathematical skills to construct pyramids. They also came up with Geometry and used it in farms.

 

The Chinese also contributed to scientific knowledge in that they discovered the way of making silk cloth, gunpowder and paper.

 

The Indians introduced ‘Zero’ in mathematics and also use of the decimal points.

 

The Iraq people were in ancient times called the Sumerians or the Mesopotamians. Their scientific inventions were mainly in the fields of medicine, architecture, mathematics and astronomy. During ‘Renaissance’, scientific knowledge spread to many countries especially in Europe. This was followed by Agrarian Revolution and Industrial Revolution.

 

Individual scientists contributed a lot to the scientific inventions as from the 15th century. Some of these notable scientists were:

  1. Nicolas Copernicus

He learnt that the earth went round the sun within a period of one year. He also discovered that the earth rotated on its own axis.

 

  1. Galileo Galilei

He agreed with the theory of Copernicus that the earth and the remaining planets moved round the sun in one year after using a telescope to observe the universe.

 

  1. Sir Isaac Newton

He discovered the force of gravity and the spectrum.

 

  1. Antoine Lavoisier

He found that air is composed of hydrogen and oxygen elements.

 

  1. John Dalton

He came up with the ‘Atomic Theory’ and also discovered colour blindness.

 

  1. Michael Faraday

He discovered electricity. This enabled him to make a dynamo which gave out electricity.

 

  1. Thomas Edison

He came up with electric lamp.

 

  1. Charles Darwin

He formulated the evolution theory which stated that all living things developed from simple life forms to complex ones over millions of years.

 

  1. Edward Jenner

He came up with the vaccine for small pox

 

  1. Louis Pastour

He found that diseases and decay were caused by microbes. He introduced pasteurisation as a method of conserving liquid foods.

 

  1. Alexander Graham Bell

He invented the telephone.

 

  1. George Stephenson

He invented the steam locomotive.

 

  1. The Wright Brothers (Wilber and Oville Wright)

They invented the first aeroplane.

 

Important scientific inventions on agriculture

 

  1. Jethro Tull

He invented seed drill which was used to plant seeds in rows and a horse drawn hoe.

 

  1. Robert Bakewell

He found out that the quality of animals could be improved through cross breeding. Using the method, he came up with quality sheep.

 

  1. Andrew Meikle

He came up with a mechanical thresher.

 

 

  1. Justus Von Liebig

He came up with the modern fertiliser industry. In his experiments, he found that plants obtain nitrogen phosphorus and salt from the soil.

 

  1. Cyrus Mc Comic

He invented the reaper which could be used for harvesting.

 

  1. Sir John Bennet Lawes

He began a super phosphate factory for making fertiliser.

 

Impact of scientific inventions on agriculture

 

  1. Scientific invention promoted agriculture leading to rapid increase in food production. Fertilisers added nutrients to the soils while farm machinery helped in ploughing, planting, harvesting and threshing.

 

  1. Scientific inventions improved farming techniques and livestock rearing. For instance cross-breeding brought about quality livestock breeds, while the invention of the seed drill encouraged farmers to plant in rows.

 

  1. Before the invention of agricultural machines such as tractors, combined harvesters and seed drills, human labour was very popular in farms. After the machines were introduced, manual labour was reduced. This resulted to unemployment of many people in the agricultural sector.

 

  1. It became easy to preserve foods and even transport them over long distances and over a long period of time because of the invention of refrigerators and the canning process. This led to increase in cultivation.

 

  1. The introduction of pesticides reduced crop destruction by pests while the development of fungicides reduced crop diseases. Food production therefore increased as a result of the reduction of crop diseases and pests.

 

  1. The invention of farm machinery led to increase in cultivated land. This was followed by the establishment of large estates leading to plantation farming.

 

  1. The desire to make more inventions and to improve what had already been established for instance the need to come up with better breeds of livestock and to come up with more efficient farm tools and machinery led to establishment of scientific research centres and schools which emphasised on science.

 

  1. There was diversification of agriculture as well as diversification of economy. This was important because people stopped depending on a single source of livelihood.

 

  1. Increase in food production led to increase in population growth. This is because the fertility rate rose as people obtained sufficient and nutritious food which also reduced the death rate.

 

  1. The invention of farm machinery which replaced manual labour resulted to rural urban migration of the unemployed. There were therefore large populations in towns which required food. For this more land had to be cultivated to feed the town folk. This therefore indirectly promoted the development of agriculture.

 

  1. Continuous application of fertilisers in farms have affected soils therefore leading to reduction in yields.

 

  1. Indigenous crops and livestock have been replaced by exotic breeds which are mainly hybrids.

 

  1. Inhaling of various chemicals and pesticides cause respiratory diseases e.g whooping cough and other diseases like tuberculosis and cancer.

 

 

Important discoveries in industry

 

  1. a) The textile industry had so many discoveries. These were:

 

  1. i) James Hargreaves

He invented the spinning jenny which prepared large amount of cotton threads.

 

  1. ii) Edmund Cartright

He invented the power loom which facilitated weaving.

 

iii)      Samuel Crompton

He invented the spinning mule. This machine produced high quality threads.

 

  1. iv) John Key

He invented the flying shuttle.

 

  1. v) Thomas Bell

He made a cylindrical calico printing machine.

 

  1. vi) Eli Whitney

He invented the cotton gin which removed seeds from cotton fibre.

 

  1. b) Others who made inventions on industry were:
  2. i) Michael Faraday

He discovered electricity and he made a dynamo for generating electricity.

 

  1. ii) Benjamin Franklin

He proved that lightning was a form of electricity.

 

iii)      Otto Hahn and Stressman

They discovered nuclear energy.

 

  1. iv) George Stephenson

He made the locomotive which was called ‘The Rocket’.

 

  1. v) James Watt

He invented the steam engine

 

 

 

Impact of scientific inventions on industry

 

  1. As a result of people getting exposed to the industrial goods, their living standards have improved.

 

  1. Jobs have been created in industries. The textile industries for example employ a large number of people.

 

  1. There is diversification of economy as a result of introduction of industries. This has stopped man from depending on agriculture only.

 

  1. New sources of energy were introduced as a result of scientific research. These were like solar energy, atomic and nuclear energy, and electric power.

 

  1. Space exploration has been carried out due to invention of rockets, satellites, and digital cameras.

 

  1. Dangerous weapons such as atomic and nuclear weapons have been invented. This has increased wars in the world.

 

  1. Inventions of engines, motorcars, supersonic planes and locomotives encouraged manufacture of spare parts and vehicles and also refining of oil to get fuel for vehicles. Transport has therefore been revolutionised through scientific inventions.

 

  1. Scientific inventions had reduced the labour burden. Machines do most of the work especially in developed countries.

 

  1. The invention of computers has helped workers to perform their duties efficiently and accurately for example in the banking sector where computers are used to process information and many other types of data.

 

  1. Trade has been encouraged due to the growing demand of the manufactured goods.

 

  1. The industries cause pollution in cities. Industrial fumes, noise and smell affect people. Some are affected by diseases like tuberculosis.

 

  1. Communication network has been improved through the use of Email and Internet.

 

  1. Some countries of the world have become highly industrialized. This has given them the opportunity of becoming world powers. They use the products of their industries to overpower others.

Important scientific inventions and discoveries in medicine

 

  1. Joseph Lister

He discovered he use of carbonic acid as an antiseptic to sterilise surgical apparatus. Then he developed an antiseptic spray for making the air clean during operations. He also discovered the use of carbonic acid for destroying microbes around the wound after an operation.

 

  1. William Marton

He discovered the use of chloroform sometimes refered to as carbonic acid during surgery.

 

  1. Edward Jenner

He invented the first vaccine for controlling smallpox.

 

  1. Lous Pasteur

He discovered that certain bacteria caused certain disease. He discovered that heat could kill bacteria. He therefore discovered that food could be preserved through the method he called pasteurisation. This is heating food to a certain temperature and then making it maintain the same temperature for a specific period of time before it is cooled quickly. He also came up with cures for anthrax and rabies.

 

  1. Sir Ronald Ross

He found out that the anopheles mosquitoes carried parasites that caused malaria. He also discovered that proper drainage systems could prevent the breeding of mosquitoes and therefore reduce malaria infections.

 

  1. Rontgen

He discovered the x-ray radiation which later enabled doctors to observe the internal organs of man and his bony framework..

 

  1. Alexander Flemming

He discovered penicillin, which was an antibiotic capable for curing coughs, pneumonia, sore throat and wounds.

 

  1. Dr Christian Bernard

He introduced the method of transplanting the heart of a death person to a body of a living patient with heart problem.

Impact of scientific inventions on medicine

 

  1. There has been rapid increase in life expectancy of human beings. This has resulted to rapid increase in human population.

 

  1. Drugs have been discovered which reduce pains therefore reducing human suffering. Others cure diseases completely.

 

  1. Machinery for use in hospitals have been invented. These are used by doctors for locating and treating diseases.

 

  1. Industries for manufacturing drugs (curatives) have been established. This has created employment opportunities in the pharmaceutical industries.

 

  1. Preventive measures have been applied such as vaccination which has led to eradication of many diseases.

 

  1. Excess use of drugs may affect the health of many people. This is because certain diseases become resistant to certain drugs.

 

Factors influencing scientific inventions in Africa and other developing nations

 

  1. Inadequate capital for the use in scientific research.

 

  1. Illiteracy of the people. Many people who are not educated cannot be able to apply scientific principles to come up with new findings.

 

  • Over-depending on donor countries. This occurs because African countries are poor.

 

  1. Little emphasis in the teaching of science in school. This occurs because of shortages of science equipment for experimental work.

 

  1. Failure for the governments to assist researchers. Many African countries cannot afford to fund researchers. Even those countries which may afford do not take research work as their first priority.

 

  1. Excessive dependence on items for instance engines, pharmaceuticals and other machinery reduce the importance of engaging on scientific research.

 

  • Lack of initiative on the side of researchers. Therefore others are not encouraged to carry out research.

 

Review Questions

1        a)       Identify the early sources of energy.

  1. How was energy from wind used?

 

  1. a) Give the uses of the following metals:
  2. i) Copper
  3. Iron
  4. Explain the effects of the spread of iron smelting in Africa?

 

  • What factors contributed to the industrialisation in Britain?

 

  1. What were the social and economic effects of industrialisation in continental Europe?

 

  1. a) What is scientific revolution?
  2. b) Discuss the impact of scientific inventions on:
  3. i) Agriculture
  4. Medicine

 

  1. a) What are the main factors which contributed to the industrialisation

of the developed countries?

  1. b) What are the major obstacles to the industrialisation of the developing nations?

 

Students’ Activities

 

  • Compare the type of industries found in the developed countries and those found in the third world (developing) countries.

 

  • In groups discuss various discoveries and inventions which have promoted Industry, Medicine and agriculture.

 

 

 

 

 

 

CHAPTER 4

 

 

Urbanisation

 

Urbanisation is the process of people’s migration from rural areas to live in towns or cities. It can also imply the establishment of towns or cities. It can also be defined as the concentration of people in settlements usually referred to as urban centres. An urban centre according to the United Nations is a settlement with a population of 20,000 people and above.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A modern town

 

 

Early urbanisation in Africa

 

Early urbanisation began in Africa before the birth of Christ. Early urban centres which declined such as Meroe and Aksum are suitable example of such towns.

Several factors led to the establishment of the early urban centres before the establishment of the colonial rule. These are:

 

  1. Due to development of trade, convergent centres emerged which became the meeting places for many people from different places. They later development into towns. Examples are Mombasa and Kilwa.

 

  1. There was development of ports and harbours where ships anchored such as Cape Town and Malindi.

 

  1. Some areas like Meroe where local industries were established attracted many people who settled there. These settlements later developed into towns.

 

  1. Areas which had reliable water for irrigation, industrial use and domestic use attracted people who established settlements which later developed into towns.

 

  1. Some administrative centres and palaces of rulers expanded to become towns after the subjects came to settle close to rulers for security reasons.

 

  1. Urban centres developed at major cross-roads and where several trade routes met. Examples are Tuat, Timbuktu and Sijilmasa.

 

  1. Notable religious centres became the meeting places for many people. They attracted people who settled nearby and thereafter towns developed.

 

  1. Development of early education centres such as Timbuktu, Gao and Cairo contributed to development of urbanisation in those centres.

 

  1. The development of Agriculture made people to settle permanently together because food was available.

 

  1. Areas that were secure and were sheltered from possible attacks attracted people who concentrated there. These settlements later developed into towns.

 

Cairo

 

Modern Cairo is situated at the delta of River Nile where some earlier settlements had been established about 2000 years ago. Egypt was invaded by the Fatimids who established a walled town. By mid 14th century Egypt had grown into a big city with many mosques and palaces. It served as an early religious centre.

The town had narrow streets, bazaars, shops and crowded living quarters. There was a market where people sold their produce.

The Ottoman Turks took control of Egypt in 1517 and remained under their control until 1798 when Napoleon Bonaparte of France captured it from the Turks. Three years later in 1801 the French were driven out of Cairo and it was thereafter made the capital of Egypt by the then ruler, Mohammed Ali.

During the reign of Ismaili, Egypt was first modernised. Later it expanded as more buildings reflecting the European style were constructed. Today it is the largest town in Egypt. It has a modern international airport and a railway network which links Cairo with the other towns. Cairo has many entertainment facilities and museums. It is an important religious centre.

 

 

Meroe

 

Meroe is an ancient city in Africa that emerged in an iron working site North of modern Khartoum. The inhabitants of Meroe developed the style of building in brick and plaster during the first century BC. They white-washed the outer walls of palaces and also decorated them with glowing mural-paintings. The inner walls were also painted and decorated with ornaments.

Meroe started expanding when it was made the capital of Kush instead of the former capital, Napata because the people of Kush had learnt the knowledge of iron working from the Assyrians and they also traded with the Greeks by exporting ivory, slaves, animal skins, ostrich feathers, timber and gold which provided them with income to expand the town.

The city of Meroe declined during the first century AD mainly due to trade rivalry from the growing kingdom of Axum in Ethiopia. When Meroe began becoming weak, the King of Axum known as Ezana attacked Meroe, burnt it and took everything of value. Ezana destroyed their stores of corn and cotton and the statues in their temples. This marked the decline of the great city of Meroe.

 

 

Kilwa

 

The origin of Kilwa is associated with the Persian immigrants who established settlements on the Indian Ocean coast. At the beginning of the 13th century Kilwa began expanding due to wealth obtained from the gold trade. From the end of the 13th century, it was the most important trading town on the East Coast of Africa.

It controlled the coastal settlement in the North as far as Pemba Island. Kilwa was a walled town which minted its own coins. It controlled the gold trade with Sofala and Zimbabwe. The inhabitants were mainly Muslims.

The town of Kilwa had beautiful buildings such as the Great Mosque and the large palace known as Husuni Kubwa. The town began declining first in the second hand of the 14th century. The fine buildings were ruined. Between 1420 and 1440 the mosque was renovated. The town of Kilwa lost its glory and prosperity and declined completely almost at the close of the 15th century because of the following reasons:

 

  1. There were dynastic quarrels in Kilwa.

 

  1. The Sofala gold trade was interrupted by wars in the interior.

 

  • Mombasa became a strong rival of Kilwa.

 

  1. The arrival of the Portuguese interfered with the gold trade because the Portuguese soldiers attacked and conquered all the coastal city states.

 

  1. There were constant rivalries between Kilwa and other coastal city states.

 

 

Early urbanisation in Europe

 

London

 

London is the capital city of the United Kingdom of Great Britain and Northern Ireland. It is in the continent of Europe. The city is situated in South East England.

The town of London originated before the first century AD. When the Romans occupied Britain in the 1st century AD, London was already a town of considerable importance.

The Romans expanded the town and made it an important religious centre. They also established Christianity which became the dominant religion in England.

London continued to expand even after it was burnt in the first century AD. When the Romans left England, London had already been established with a large population.

The withdrawal of the Romans did not affect the growth of London because what they did in Britain perished after they left.

In the 9th century, King Alfred made London the capital of his kingdom. Later King William I established himself in England and developed the town of London. He built the Tower of London and also rebuilt the London bridge. Initially it was built of wood but he rebuilt it using stone.

Throughout the Middle Ages the growth of London was slow as a result of wars, epidemics and commercial crisis.

When Queen Elizabeth I opened the Royal exchange in 1566 AD, the city of London grew into an important city of the world. By 1580 AD Queen Elizabeth I issued a proclamation which prohibited construction of any new buildings within a radius of about 4 kilometres outside the city gates.

In 1665 AD London was affected by plague. The following year a great fire burnt the city.

In 1667 the rebuilding act was enacted. It stipulated that all buildings be of stone and brick. In the 1760s the walls and gates of old medieval city of London were demolished. During the 19th century, London was modernised through the construction of many suburbs, rebuilding of bridges and through lighting of city streets. By the close of the century, London had grown into a beautiful city served by a well developed networked of transport and communication.

During the First World War, London became the German target. London was heavily bombed. The Tower of London and the British Museum were destroyed. Many other buildings were also damaged.

After the war, the British government reconstructed the war damage. Many tall storey buildings were constructed such as the Museum Radio Tower of the General Post Office building. This was followed by construction of shops, residential houses, school, hotels and cultural centres.

The city of London got most of its water from river Thames. There were several city markets which provided people with food, meat, fruits and flowers. Today the city of London is under the control of the local government headed by mayors.

 

Several factors contributed to the growth of the city of London. These were:

 

  1. Development of transport and communication. London had a network of roads and railways. Underground roads and railways were established in underground tunnels to reduce traffic congestion.

 

Modern international airports such as Heathrow airport were also established. London was connected to the rest of the world with telegraphs, telephones and radio transmissions.

 

  1. Trade enabled the town of London to grow into city status. Many people migrated to London to conduct business as a way of earning a living.

The success of their businesses made them wealthy and they settled permanently. As this process continued, the town also continued to expand.

 

  1. The establishment of industries attracted the people who came to seek for employment and those who came to survive on cheap manufactured goods.

 

  1. The development of port facilities in London encouraged many people to go and do the jobs of loading and unloading cargo. The sailors from England also started their journeys from the seaports like London. Those who came from abroad on their way to England regarded London as their port of call. This contributed to the growth of London.

 

  1. London served as a political and an administrative centre for a long time. The Romans constructed a fort and surrounded it with a wall for security reasons. The colonies Britain acquired were under the colonial secretary who was based in London.

 

  1. The city of London had several museums and theatres that made it an important cultural centre. Many people were attracted by the activities in the city making them to settle there in great numbers.

 

Functions of London

  1. London is the capital of the United Kingdom. It acts as an administrative headquarters.

 

  1. It is an industrial centre that has both heavy and light industries.

 

  1. It is a cultural and recreational centre. London has many theatres and museums.

 

  1. London is a centre of international transport and communication. This is because there are international airports in London and there is the harbour where ships from all over the world anchor.

 

  1. London is a centre of learning. It has international Universities and colleges.

 

  1. It is also a commercial centre that has many banks and insurance. It has many shopping centres.

 

  1. London is a religious centre. It has many churches and cathedrals.

 

  1. London is also the common wealth headquarter.

 

 

The problems London has encountered since it was founded

 

  1. Problem of overcrowding of houses, vehicles and people.

 

  1. Epidemics such as plague affected London during the Romans era and in 1665 AD.

 

  • London was burnt down in 1666 AD.

 

  1. There was the problem of unemployment.

 

  1. There was the problem of rural – urban migration of the jobless.

 

  1. There was inadequate housing facilities and poor sanitation.

 

  • There was high crime rate.

 

  • There was pollution of the environment due to fumes from industries and vehicles.

 

  1. London was bombed by the Germans during the First World War. This resulted to deaths of people and destruction of property.

 

  1. There was the demolition of the old city of London in the 1760’s.

 

 

Athens

 

The growth and prosperity of Athens is based on trade and commerce. The land surrounding Athens was rocky. It could not support a large population. The people of Athens depended mainly on imported food that they exchanged with olive oil, wine and wool.

 

Athens was a famous centre of learning. The city state provided education in such fields as philosophy, architecture, drama, science and medicine. The democracy that is enjoyed in the world today originated in Athens where it was actually practised.

 

Athens was surrounded by a protective wall for security purposes because of constant wars with the other city states. The town itself looked clumsy. The streets were merely narrow earth roads that became dusty during the dry spell and muddy during the rainy season.

 

Some houses were made of unbaked brick while others were made of mud. A few beautiful and well-built buildings such as Parthenon temple and the temple of Athena Nike existed.

 

There was a market place in the centre of the town which also acted as a meeting place for people and also the place where people assembled for debates. On top of the high cliff was the Acropolis (Fortress) which provided protection for the village below.

The biggest problem of Athens was that it had inadequate sanitary facilities for disposing human waste and refuse. Due to this the town was exposed to very bad smell from rotting garbage.

Athens weakened and lost its glory between 430 BC and 335 BC due to the following reasons:

  1. i) Athens was affected by constant rivalries and wars with other city states.

 

  1. Athens was conquered by King Philip of Macedonia and put under the Macedonian domination.

 

  • Constant epidemics like plague led to death of many Athenian citizens therefore weakening the military might of Athens.

 

  1. The final blow, which made the town to disintegrate, was the death of Alexander the Great whose empire controlled Athens. Other towns such as Rome and Cathage rose to power to fill the political vacuum left by Macedonia.

 

 

Emergence of modern urban centres in Africa

 

There are many urban centres in Africa that began when the Europeans acquired colonies and settled there. Such towns never existed in Africa before the coming of the Europeans.

Some of them began as administrative centres for the colonial authority. Some emerged as mining towns, others as commercial centres some as agricultural centres or farming centres while others began as industrial centres.

The Europeans at first settled in those places and established administrative and commercial buildings. The emerging settlements attracted rural people who also migrated there to look for employment, start business and seek for other fortunes. Examples of the modern urban centres in Africa are Nairobi and Johannesburg.

 

 

Nairobi

 

Nairobi began in 1899 during the construction of the Uganda railway. It first started as a depot for storing the railway equipment before approaching the steep rift valley escarpment.

The place looked suitable for a depot and for resting because of its mild climate that was preferable by Europeans. There was also the Nairobi River which provided water to the railway builders. The site was somehow flat for construction compared to the land ahead of them before they reached the Rift Valley. At the same time Nairobi was the midpoint between Mombasa and Lake Victoria.

In 1907 the Imperial British East Africa (IBEA) company transferred its capital from Mombasa to Nairobi. During the colonial period the Europeans and Asians dominated the town.

Migration of Africans to Nairobi was restricted but quite a number went there to work as labourers.

The town was associated with racial discrimination in employment, commerce and housing.

Today Nairobi lies at the heart of Kenya’s rail and road network. It has a modern international airport known as Kenyatta International Airport. It has several other small airports such as Eastleigh, Embakasi and Wilson airports.

Nairobi is the seat of the government and the commercial centre of Kenya. Nairobi is also industrial, cultural, educational, communication and transport centre.

It has modern buildings that are used as offices, hotels and shopping centres. The city attracts Kenyan citizens from all parts of the country and also foreigners who include tourists from many countries of the world. However, Nairobi City is facing a number of problems as below:

 

  1. The city has inadequate drainage and sanitary facilities.

 

  1. There is the problem of pollution as a result of many industries producing fumes and noise.
  2. There is acute problem of water.

 

  1. There are inadequate educational facilities such as schools for the rapid growing urban population.

 

  1. There is congestion of traffic leading to traffic jams.

 

  1. There is a high rate of crime such as robbery and prostitution.

 

  1. There is inadequate housing facilities leading to development of slums and overcrowding in residential areas.

 

  1. There is high rate of unemployment. School leavers flock in Nairobi to look for jobs.

 

Johannesburg

 

Johannesburg is a city of the Republic of South Africa, in Transvaal province.

 

The discovery of minerals during the second half of the 19th century was largely responsible for the emergence of a number of towns in South Africa.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Location of the city of Johannesburg

 

 

 

Johannesburg mushroomed after large gold deposits were discovered in Witwatersrand in September 1886. This was followed by a gold rush. At first Johannesburg began with a very small population. Within a very short time people flocked to Johannesburg on the Witwatersrand in great numbers from Britain, America, Australia and other countries of Europe.

 

At first the early settlements were mere shanties made of galvanised iron. These shanties were the basis of a miraculous growth of the city of Johannesburg. Within a decade, the town had a population of about 100,000 people.

 

Other factors that contributed to the growth of Johannesburg are:

 

  1. There was cheap labour from the Africans. Labour was also obtained from the neighbouring countries like Malawi, Namibia and Botswana. These labourers increased the population of the city.

 

  1. River Vaal provided enough water for mining, industry and domestic use.

 

  1. There was development of transport and communication in form of road and railway.

 

  1. The land surrounding Johannesburg was suitable for farming. This provided enough food for the people in the mining centre and industries.

 

  1. The availability of other minerals such as iron ore and flourspar in the outskirts of the city contributed in the industrial growth.

 

  1. The availability of coal, which provided energy also, promoted industrial development.

 

Today, Johannesburg is the largest city of the Republic of South Africa and the industrial and commercial centre. It is the centre of the country’s gold mining industries and the site of the Johannesburg stock exchange.

It is a strategic rail, road and air hub with an international airport. It is a mining as well as an industrial centre whose industries include manufacture of mining and railway equipment, automobile parts, chemicals, textiles, electrical and communication equipment.

Johannesburg is a cultural and educational centre of South Africa. It has a number of museums, theatres, a symphony, orchestra and an opera company. It has schools and universities.

 

Review Questions

 

1        a)       What is urbanisation?

  1. What favoured development of early urbanisation in Africa?

 

  1. a) Describe the factors which contributed to the growth of:
  2. i) London
  3. ii) Kilwa
  4. What problems did each of the two towns above encounter that affected its growth.

 

  1. Explain the factors which led to the decline of the city of Athens in the first millennium AD?

 

  1. Describe the major problems of the modern urban centres.

 

  1. Explain the growth of Johannesburg as an important urban centre.

 

  1. Describe the functions of Nairobi City.

 

Students’ Activities

 

  1. Compare the factors that led to the growth of the early urban centres with those which led to the growth of modern urban centres.

 

  1. Draw a map of Africa and indicate the locations of Nairobi, Cairo, Meroe, Johannesburg and Kilwa.

 

 

 

CHAPTER 5

 

 

SOCIAL, ECONOMIC AND POLITICAL ORGANISATION OF AFRICAN SOCIETIES IN THE 19TH CENTURY

 

 

Buganda

 

The Buganda Kingdom was one of the Kingdoms in Uganda. During the 19th century Buganda expanded to become the largest and most powerful kingdoms in Uganda. Several factors brought about the rise of Buganda. These were:

 

  1. The Baganda were agriculturists. They grew bananas which was their staple food. This enabled them to feed the army. The fertile soils and suitable climate enabled them to grow crops.

 

  1. During the 18th and 19th centuries, Buganda was under very strong and competent rulers entitled Kabaka. One such ruler was Kabaka Mtesa I.

 

  1. Buganda kingdom was centralised and it had a well-organised political system. The centralisation of Buganda enhanced effective control of the kingdom, enhanced loyalty to one single ruler, promoted control and unity of other traditional leaders and also led to emergence of able rulers who strengthened the Kingdom.

 

  1. Buganda had a strong army, which defended the kingdom, and a navy that conquered people living in the islands of Lake Victoria such as the people of Sese Island.

 

  1. The decline of Bunyoro Kitara Kingdom enabled Buganda to expand to fill the power vacuum left by Bunyoro.

 

  1. Participation in the long distance trade by the Baganda people enabled the kingdom to attain wealth that was used to maintain the kingdom. The rulers also taxed the Arab and Swahili traders who ventured into the kingdom to trade.

 

  1. The annexation of Buddu iron fields enabled Buganda to manufacture superior iron weapons.
  2. When the British occupied Uganda, she handed over the ‘lost counties’ of Bunyoro to Buganda. These counties included Bungaizi and Buyoga. This action of the British contributed to more expansion of Buganda.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Buganda at its peak in the 19th Century

 

 

Social organisation of Buganda

The social organisation of the Baganda was based on clans made up of members of several related families.

There were also social classes with members of the loyal family on top followed by local chief and then below were the commoners followed by slaves.

The Kabaka existed who played social roles such as presiding on various ceremonies and rituals, being the chief priest and therefore being in charge of all religious activities.

The Kabaka’s power was symbolised by his loyal regalia that included the royal drums, the stools and the spears.

The Baganda worshipped a god entitled Katonda. They believed in the spirits of the dead ancestors. They thought that the death affected the affairs of the living people.

They had a traditional religion they called Lubaale. They consulted the spirits of the dead through prophets. The mediums who consulted the spirits were usually given gifts. The Baganda had medicinemen and sorcerers.

They conducted marriage and initiation ceremonies. During the reign of Kabaka Mwanga, same people of Buganda were converted to Christianity while others were converted to Islam. After the arrival of many Christian Missionaries, Christianity took the dominance that was followed by rivalry between various religious groups.

 

Economic organisation of Buganda

Buganda Kingdom was located on the northern shores of Lake Victoria. The Kingdom’s geographical location, the nature of its environment and climate influenced the economic activities of the Baganda.

The Baganda were mainly cultivators. They grew bananas, millet and sorghum. Bananas (matoke) were the staple food of the Baganda. The high rainfall and fertile soils enabled them to cultivate. The Baganda kept livestock such as cattle, sheep, goats and chickens. They also conducted raids and captured slaves and cattle from the neighbouring weaker communities such as Bunyoro and Busoga.

The Baganda benefited by fishing due to their proximity to Lake Victoria that had a lot of fish. This supplemented their diet. The Baganda like many other Bantu communities in Uganda had acquired the skills of iron working from the Abachwezi. They conducted raids that exposed them to the iron-bearing field in the neighbouring lands. The iron obtained was used for making iron hoes, spear heads, arrowheads and a variety of other tools.

The Baganda also manufactured bark-cloth, weaved and built canoes for use in Lake Victoria for fishing and for the navy that was used to conquer people living in the islands of Lake Victoria such as the people of Sese Island.

Some of the Baganda hunted animals such as buffaloes and antelopes for meat. They also gathered fruits and roots that they used as food. The Baganda conducted local trade which involved exchange of goods within themselves or with their immediate neighbours. For example trade in salt existed with people around Lake Victoria.

The Baganda engaged themselves in the long distance trade mainly in the 19th century after the Arab and Swahili merchants from the coast penetrated into kingdom. This trade expanded rapidly during the era of Kabaka Mtesa I. Slaves and ivory were the main commodities the Arab and Swahili traders demanded. They in turn brought ammunitions, cloth, beads and swords that were demanded by the Baganda.

 

Political organisation of Buganda

Baganda is believed to have originally been a section of the Chwezi State. It is not known clearly whether it is Kintu or Kimera who established the early kingdom of Buganda.

What is clear is that Buganda was a centralised kingdom controlled by a ruler entitled Kabaka whose authority in those early days was limited by the power of the clan heads each entitled Bataka.

 

In the later years, the Kabakas assumed a lot of power because they played the following roles:

 

  1. They acted as the chief political and religious leaders and heads of government.

 

  1. They were considered as the supreme judges in the kingdom and also as the final court of appeal.

 

  1. They were regarded as the sole defenders of Buganda and protectors of their subjects.
  2. They commanded the army as well as all other juniors for instance, the Katikiros, the Saza chiefs and the Gombolora chiefs.

 

  1. It was their responsibility to appoint or fire senior officials like the Katikiro and the Chief Justice.

 

  1. They controlled trade to such an extent that they even taxed foreign traders.

 

The Kabaka was assisted to administer the kingdom by a Prime Minister entitled Katikiro.

In the Kabakas court, their existed the Chief Justice entitled Omulamuzi and the treasurer entitled Omuwanika, all appointed by the Kabaka. Together with the Katikiro, they formed the Kabakas advisory body.

There existed a legislature assembly called Lukiko, which acted like the modern day parliament. It discussed important issues affecting Buganda kingdom such as issues pertaining to external attacks, relations with foreigners, trade regulations and the ways to deal with the citizens.

The kingdom was split into counties each called Saza. Each county was headed by a Saza chief.

Counties were further split into sub-counties each entitled Gombolola. Each Gombolola was under the leadership of a Gombolola chief whose duty was to collect the taxes and remit to Kabaka as well to maintain law and order in his area of Jurisdiction.

Each Gombolola was further split into a small division called Miluka headed by Miluka chief.

Buganda had a strong standing army and navy. The army defended the kingdom while the navy controlled Buganda’s possessions in Lake Victoria such as Sese Island.

Leadership among the Baganda was hereditary (passed from father to son) at first but later the Kabaka could appoint a minor chief from the citizens who was royal to him.

The Kabaka strengthened the loyalty bestowed on him by all the people in the kingdom by marrying from all popular clans and accepting sons of popular people from various families to come and work in his court.

 

 

Shona

 

The Shona settled in central Africa south of River Zambezi in the present day Zimbabwe. It is believed that they migrated to the region from the Congo basin and they are related to the Kalanga.

 

Social organisation of the Shona

The Shona worshipped a god who was believed to be all-powerful. They called their god Mwari. The Shona had priest who presided over religious functions for instance during the time of offering sacrifices to the supreme being.

The priests also conducted rituals to appease their gods. The Rozwi clan provided the shona community with priests. Worship was conducted in shrines.

The shona believed in the existence of the ancestral spirits they referred to as clan spirit, Mhondoro, and the family spirits, Vadzimu. The spirits communicated through intermediaries referred to as Svikiro. The Shona communicated with the spirits through mediums.

They conducted a number of ceremonies and festivals. The shona were socially organised into families, several of which made a clan. The clan elders were highly respected. Polygamy was a very common practice among the Shona. It was common to find men with very many wives. This was one way of ensuring that the community had enough warriors and was provided with sufficient labour force.

 

The Economic Organisation of the Shona

The Shona grew a variety of subsistence crops such as beans, millets and vegetables. They also kept livestock such as cattle, sheep and goats, which provided them with milk and meat.

The Shona made iron tools such as spears, hoes and knives. They also weaved and made back cloth.

The Shona supplied the people of Sofala with gold. In return the Shona obtained cloth, glassware, and firearms obtained from the Portuguese.

 

The political Organisation of the Shona

An emperor who was the head of state and government controlled the Shona kingdom. When the emperor died, his son took over leadership. This implies that leadership among the Shona was hereditary.

 

The emperor administered the empire with the assistance of his immediate relatives and leading officials. These were queen’s mother, his principal wives, his sister, the head drummer, the chancellor, the supreme cook, the chief door keeper and the commander of his army.

The emperor was the overall military leader and for this reason he acted as the commander in chief of the standing army which not only defended the kingdom but also tried to conquer other neighbouring communities in order to expand it.

The Shona kingdom was divided into smaller divisions that were under the control of lesser kings who were answerable to the emperor.

The lesser kings ensured that trade was promoted. The emperor was the sole controller of the entire trade. The profit from trade maintained the army and also sustained the kingdom. Vassal states were made to pay tribute to the emperor.

The Shona priest played political roles in that they acted as the emperor’s spies. The priests also linked the people with the emperor. In so doing religion was used to create political unity among the Shona.

 

 

Asante (Ashanti)

 

The Asante is one of the Akan or Twi speaking peoples of the present day Ghana. The Asante kingdom is believed to have been established as a result of a number of states which united together and settled at a place called Asantemanso.

From Asantemanso they dispersed in clans and family groups to new settlements such as Bekwai, Tafo, Nsuta, Mampong, Amakom and Kwaman. Later in the 17th century these settlements united under the leadership of the Oyoko clan.

All the Asante states were established surrounding modern Kumasi in an area referred to as Kwaman forest. By the middle of the 18th century, the Asante had become a very large empire as a result of the efforts of Osei Tutu who introduced the golden stool, which became the symbol of Asante union. The Asante rulers were entitled Asantehene.

 

 

Factors that led to the rise and expansion of the Asante kingdom

 

We have already seen that the Asante kingdom rose from a number of clans and families who migrated and then settled together at Asantemanso. Those settlements later united into states.

 

The rise of the kingdom was therefore as a result of the unity of those states. The Asante emerged and expanded into a mighty kingdom because of the following reasons:

 

  1. The area the Asante people settled had abundant rainfall which enabled them to grow crops and gather wild fruits to sustain the growing population.

 

  1. Asantehehe Osei Tutu with an Akwamu priest, Okomfo Anokye cemented the Asante union when they introduced the golden stool as the symbol of Asante union.

 

  1. The Asante obtained income for expanding the empire from the trade they conducted with the Europeans at the coast.

 

  1. The Odwira Festival was organised which enabled the state rulers to gather together to pay allegiance to the Asantehehe.

 

  1. The Asante kingdom was controlled by strong and able rulers like Osei Tutu, Opoku Ware and Osei Bonsu who engaged themselves on expansionist missions aimed at enlarging and strengthening the kingdom.

 

  1. The fact that Asante kingdom was highly centralised enabled people to join in order to fight against a common enemy.

 

  1. The neighbouring states such as Denkyira and Fante were weaker that the Asante kingdom. This gave the Asante the advantage of expanding its empire.

 

  1. The Asante army was very strong and well organised. It was made up of soldiers from all the Asante states.

 

  1. The Asante used modern weapons such as guns which they bought from the Europeans along the west African coast.

 

  1. The Asante rulers obtained revenue from the tribute paid by conquered states. This enabled the Asantehene to maintain his army and his kingdom.

 

Social organisation of Asante

In the early beginning the Asante lived in separate clans and family groups. When the family and groups migrated from Asantemanso, they went to places where they lived in settlements. At first the settlements were not united but later they joined together into states.

An Akwamu priest named Okomfo Anokye together with Osei Tutu introduced the golden stool as a symbol of unity, which had religious symbolism. It united all the states not only politically but also socially.

The Asante introduced the national festival called Odwira that united the whole of Asante by making state rulers to be royal to the Asantehene. The Asante were polytheistic. They worshipped gods and goddesses. The Asantehene played both political and religious roles. He acted like a religious leader and presided over religious ceremonies.

The Asante people worshipped their gods through their ancestors. The ancestors acted as intermediaries between gods and the people. The Asante people sacrificed to their gods. They believed in life after death and in punishment of wrong doers and reward for those who did well.

By the first half of the 19th century, the Asante had embraced Islam. The Asante Muslim converts therefore adopted Islamic culture and law (sharia). This became the beginning of the Islamic influence in Asante.

 

Economic organisation of Asante

The Asante lived in the forest region in the west of River Volta. The land they occupied received heavy rainfall which enabled them to grow crops such as vegetables, kolanuts and grains.

The Asante also kept few livestock. They hunted and gathered fruits and red kolanuts from Kwaman forest for sale. The Asante also participated in the local trade. They traded with the Ga and the people of Benin.

They exchanged commodities such as salt, cloth and fish. Later they traded with the Europeans who had settled along the West African coast in settlements such as Accra, Anomabo, Cape Coast, Winneba and Elmina. The Asante traders gave Europeans ivory, slaves, gold and colanuts in exchange for firearms, cloth and ironware.

The Asante mined gold in the Kwaman forest and practised iron working. They used iron to manufacture tools, bangles, hoes and arrowheads. They practised traditional crafts such as cloth making, basketry, pottery and sculpture making. The Asante hunted elephants to obtain ivory. They also gathered fruits and edible roots.

 

Political organisation of Asante

The Asante Empire was centralised and divided into three parts. The first part was the metropolitan or Nucleus State that consisted of the Kumasi State that was directly under the Asantehehe.

The second part was the Amatoo or the states within a radius of about 30 to 40 miles of modern Kumasi. These states were outside Kumasi and they recognised the Golden stool as the symbol of unity of the Asante. Some of them were Dwaben, Adansi, Bekwai, Nsuta, Mampon and Kokofu.

The third part was the conquered states or provincial Asante states that consisted of all the outer circle of states which had earlier been conquered and controlled by the Asante. Examples of them are Akwamu, Akyem, Twifu, Wassa, Denkyira, Sefwi, Akwapem, Assin, Gonja, Dagomba, Gyaman and Takyiman.

 

 

 

 

 

 

Gonja                      Dagomba

 

 

 

 

 

 

Takyiman

                                             Kumasi

                                                   Sefwi                                         Akwamu

                                                                           Denkyira

 

 

 

 

 

 

Asante Kingdom in the 19th century

 

The Asante kingdom was ruled by kings entitled Asantehene. The Asantehene was the supreme ruler of the kingdom. He had direct control over Kumasi State. The Asantehene was the conmmander in – chief of the army. He presided over political and religious festivals and he acted as the final court of appeal because he was the supreme judge. Leadership among the Asante was hereditary.

The Asantehene ruled with the advice of the state rulers who formed the union of rulers. The conquered states were administered by their kings but they were regarded as the provinces of the Asante kingdom .A representative who was an appointee of the Asantehene was posted in each province where he acted as the eyes and ears of the Asantehene. He also levied taxes, supervised trade and mining of gold nuggets.

Each Asante State was under the rule of Omanhene who took the oath of allegiance to demonstrate loyalty to the Asantehene. The Omanhene represented the Asantehene in the provinces but they were required to pay tribute to the Asantehene and also to provide soldiers in times of conflicts.

The Asante states were all bound together by the golden stool which was the symbol of unity of the Asante. This stool was preserved in the capital, Kumasi. Every state ruler was presented with a symbolic black stool to signify unity of the provinces.

There was a national festival organised particularly for state rulers to pay allegiance to the Asantehene. This festival was known as Odwira festival.

The Asante had a strong standing army consisting of an infantry and a calvary wing. The Asante army was divided into four segments which included the left wing, the right wing the van and the rear. Every king of a state was given a position within the wings. This position was taken by the army he controlled in his state a thing which made him remain powerful.

At its peak, the Asante kingdom consisted of the area surrounding Kumasi which was directly under the Asantehene, the states outside Kumasi which were part of the original Asante union and lay about 90 kilometre radius of present day Kumasi and the vassal or conquered states.

 

The Asante government finally collapsed due to the following reasons:

 

  1. Constant rebellions by the vassal states who wanted to reassert their independence.

 

  1. The British supported the Fante to flight against the Asante.

 

  • The kingdom had grown too large for the rulers to control effectively.

 

  1. Asante strained relations with Fante and the British affected Asante trade and source of income.

 

  1. There was weakness in the system of provincial administration because vassal states were not fully incorporated to the kingdom.

 

  1. The Asante ruler, Osei Tutu was forced to grant independence to the southern states.

 

  • Asantehene Prempe I was exiled.

 

Review Questions

 

  1. Explain the roles of the following in the 19th century:
  2. i) Kabaka of Buganda
  3. ii) Asantehene of Asante

 

  1. Describe the political and social organisation of Buganda.

 

  1. a) Explain the factors that led to the rise and growth of Asante

Empire.

  1. b) Describe the political organisation of the Asante Kingdom up to the 19th

 

  1. Describe the Shona kingdom under the following headings:
  2. Economic organisation
  3. Political organisation
  4. Social organisation

 

  1. What factors contributed to the decline of the Asante Kingdom.

 

  1. Identify the economic and social activities of the Asante in the 19th

 

Students’ Activities

  1. Draw maps to show the location of the Asante and Buganda kingdoms

 

  1. Discuss in groups the factors which contributed to the rise and decline of the Asante and Buganda Kingdoms.

 

  1. Compare the administration of Buganda kingdom with the administration of Asante Kingdom.

 

CHAPTER 6

 

 

Constitutions and constitution making

 

A constitution is a set of fundamental principals and laws established to govern and regulate the behaviour of citizens of a particular state as they relate to each other in their daily activities as well as regulating the conduct of the people who are entrusted with the responsibility of managing the affairs of the state.

 

A constitution therefore clarifies the duties and rights of the citizens as well as the duties, rights and responsibilities of the rulers.

 

The constitution regulates the powers of government by controlling the way it behaves as it manages the country’s affairs. The constitution also regulates the relationship between the government and the citizens of the state.

 

A country’s constitution has the following functions:

 

  1. It clarifies the powers, duties and responsibilities of those in power (rulers) and their subjects.

 

  1. It protects the rights and freedoms of all citizens.

 

  1. It limits the powers of rulers who would attempt to oppress their subjects. It also limits the possibilities of the subjects to insurbodinate the rulers. This is done by limiting some of their rights and freedoms.

 

  1. A constitution enables a country to follow a well defined cause by spelling out the powers of the government. This helps to control national instability.

 

  1. A constitution defines and spells out the formal structure of government and the functions and powers of each state organ for example the powers of the regional government in relation to the central government and also the powers and duties of the executive, the legislature and the judiciary.

 

  1. A constitution offers the legal framework from which the country’s laws are made.

 

  1. A constitution also reflects the wishes of the people and their social, cultural, economic and political aspects.

 

Characteristics of a good constitution

 

  1. A good constitution must define and spell out clearly the structure of government and the functions and powers of each level and arm of government.

 

  1. The fundamental rights and duties of all citizens must be clearly spelt out and the way the rights will be guaranteed specified.

 

  1. Roles and powers of specific rulers such as Presidents and Prime Ministers must be stipulated.

 

  1. The separation of powers of the Judiciary, the Legislature and the Executive must be very clear to avoid conflicts of roles.

 

  1. The composition, functions and powers of all laws to be enacted by parliament must be made clear.

 

 

Types of constitution

 

There are various kinds of constitutions in the world. Some of them are democratic constitutions, others are undemocratic constitutions. There are also unitary or federal constitutions. We also have two other types of constitutions. These are written constitutions and unwritten constitutions.

 

Written constitutions

A written constitution is the one in which the basic principles and laws are written down and are therefore available in a formal document. Examples of the countries with written constitutions are Kenya, USA and France.

 

The following are the characteristics of a written constitution:

 

  1. It is written in an official volume that one can buy in order to study.

 

  1. It is rigid and not easy to alter. Any amendment is made using a procedure that is usually slow and cumbersome.

 

  1. A written constitution is usually simple, clear and consistent. A special body of experts is therefore given the responsibility of drafting it using a well formulated procedure.

 

  1. It sets clearly the powers of the judiciary, the executive and the legislature in a particular state.

 

  1. It spells out the fundamental rights and freedoms of the citizens. To ensure this is accomplished the draft constitution is taken to the legislature for approval.

 

  1. In some written constitutions, rules are found in traditions. Some of them are based on conventions and customs of the people.

 

  1. A written constitution is prepared in such a way that one can be able to compare the actions and day to day activities of the government with what is written and expected to be achieved and maintained.

 

Advantages of written constitution

 

The following are the advantages of a written constitution:

 

  1. Once prepared, it is not easy to change or amend it so as to favour particular personalities in power.

 

  1. It becomes easy for the literates to know the expectations of the government because they can buy the official copies and read themselves. This is because it is readily available for reference and use.

 

  1. No individual can alter or manipulate any part of the written constitution. The legislative body is the one which has a right of making even a minor amendment or alteration.

 

  1. The legislators and delegates are able to incorporate the traditions, conventions and customs of the citizens into a written constitution which is people driven and which recognises people’s ethnic groupings.

 

  1. A well written and acceptable constitution can play the role of uniting all the people in a nation.

 

  1. A written constitution provides a smooth procedure of handing over power after general elections, death of rulers or resignation. This is because it provides a clear guideline of what should be done if such a thing happens.

 

  1. A written constitution enables a country to operate in favourable and orderly manner.

 

  1. A written constitution spells out the fundamental rights of citizens very clearly therefore making them aware of their rights and also making them have a reference when their rights are infringed.

 

Disadvantages of written constitution

 

  1. It is too rigid to be easily altered without a lot of consultation.

 

  1. Amending a written constitution is slow and cumbersome.

 

  • The language used to write the constitution volumes is difficult for people who have not learnt disciplines such as law. Yet it becomes difficult to simplify without altering the meaning and the stress.

 

  1. If the constitution is not properly formulated, it can make various arms of the government to conflict.

 

  1. For a good lasting written constitution, very qualified experts are required. These may not be available in some countries.

 

  1. The constitution making process is costly and very involving if all the procedures are followed to the dot.

 

Unwritten constitution

 

An unwritten constitution is one which does not exist in a single formal official document. Britain is an example of a country with unwritten constitution. The sources of the British constitution are the Act of Parliament, British conventions, the Hansard, Legal publications by reputable authorities, decisions made by the British law courts from time to time and Royal prerogatives of the King or Queen to declare war or make treaties of peace.

 

Advantages of unwritten constitutions

 

  1. It is easy to make amendments in order to cope with the prevailing situations.

 

  1. It is not rigid. Therefore it can be altered without a lot of consultation.

 

  1. This constitution is long lasting because it is native and therefore acceptable by the majority.

 

Disadvantages of unwritten constitution

 

 

  1. Fundamental rights of citizens are not clearly spelt out in an unwritten constitution.

 

  1. Unwritten constitution requires very qualified judges and lawyers of the law courts who are able to cope with the tedious work of referring to many constitutional documents e.g. statutes, historical documents and customs in order to make any judgement.

 

  1. An unwritten constitution is not clearly expressed as compared to the written constitution.

 

 

The independence constitution

 

The first constitution in Kenya was established during the British colonial rule. This may be referred to as the colonial constitution. The colonial constitution discriminated against the Africans while it favoured the whites.

As the Africans continued to be aware of their rights they appealed to the colonial government to grant them their rights. Due to political pressure from the Africans, the colonial government unwillingly tried to change the constitution.

In 1960 and 1962, constitutional conferences were held in London. African representatives attended. The Lancaster House conference held in London in 1962 concluded the constitution for independent Kenya. The date for independence was also set. The constitution made is the one we are calling the independence constitution.

The conference was attended by representatives of the African political parties such as Kenya African National Union (KANU), Kenya African Democratic Union (KADU) and African People’s Party (APP). KANU and KADU differed in the structure of government they wanted.

 

KANU preferred a strong unitary constitution while KADU wanted a majimbo or Federal constitution. KADU was in favour of majimbo constitution because it feared that smaller communities would be dominated by large ones such as the Luo and the Kikuyu. KANU believed that a unitary government would protect the interests of the smaller communities.

The outcome of the 1962 conference was a federal form of constitution. This was followed by the formation of a coalition government between KANU and KADU.

 

Provisions of the independence constitution

 

The independence constitution provided a regional (majimbo) government. The country (Kenya) was therefore split into six regions each with its own regional government and assembly with full legislative powers.

There was a central government consisting of two chamber national assembly namely the senate and the House of Representatives. The central government was headed by a Prime Minister from the party with majority seats. Nairobi was the headquarters of the central government.

The Queen remained as the head of state. She was represented by the Governor General whose duties were to approve legislation, to ensure there was internal security, to deal with all foreign affairs and to give assent to bills to become laws.

The independent constitution recommended a multi-party system of government. The party with the majority was to form the government. It recommended a Bill of Rights whose role was to protect the fundamental interests of the individuals.

It also recommended formation of a Central Land Board for dealing with all issues concerning land and an independent public Service Commission for appointing, disciplining and firing civil servants.

The independence constitution recommended the setting up of an independent electoral commission for setting constitutional boundaries and conducting elections.

An electoral commission was established. It was made up of the speakers of both the House of Representatives and the Senate, nominated representatives of each region and a nominated representative of the Prime Minister.

 

The independence constitution provided an independent judiciary that showed complete impartiality when judging cases. No one was allowed to influence the decisions of judges and they enjoyed security of tenure.

Lastly, the independence constitution organised for the protection of the minority rights. This was mainly to ensure that the European and Asian minorities were protected and their properties were safeguarded.

 

 

The Kenya Constitution

Kenya is governed by a democratic constitution. A democratic constitution recognises and protects human rights for instance the right to acquire and own property, right to life and the rights safeguarding the individual’s freedom of expression, association, conscience, movement and assembly. It also recognises the freedom of worship, belief and opinion.

The Kenya constitution ensures that people have full and equal enjoyment of all rights and freedoms.

It also ensures that all people are equal before the law. An individual has right to equal protection and equal benefit of the law. He has the right to a fair trial. According to the Kenya constitution, no person may be required to perform forced labour or be held in slavery.

 

 

Constitutional making process

 

Constitution making can take place in a number of ways as follows:

  1. Having it done by Parliament whereby at least 65% of all parliamentary members must vote for a change to the Kenya constitution.

 

  1. Using a constitutional review commission. This commission may be set up by the President or by Parliament.

 

  1. Having a constitutional conference attended by selected people from various interests in society. They then make a draft constitution that can if necessary pass through a referendum.

 

  1. Having a national convention composed of representatives from all walks of life who identify and discuss important national issues in order to prepare a constitution.

 

Constitutions are therefore made through established procedures that are agreed upon by the majority. In Kenya the constitutional making process is as follows:

 

  1. The general public is provided with civic education to enable them to take part in the constitution making process. To begin with, they are made to understand what a constitution is and why it is necessary in any state. They are then enlightened on the shortcomings of the current constitutions and also its strength.

People are then requested to give their views on various aspects of the constitution. A commission is set to visit all the constituencies in Kenya to listen and record the views of the public.

All the views obtained from the constituencies of Kenya are compiled together. The wishes of the majority are isolated and used to prepare a draft constitution which is forwarded for further discussion.

 

  1. The recommendations are printed, published and circulated to the public. The commission once more visit the public to give their remarks. All the provinces are covered to ensure that the outcome reflects the will of the people.

 

  1. A national constitutional conference is organised and attended by delegates from each district in Kenya. The commission then submits the recommendations which are largely the opinions of the public for further discussion and careful scrutiny.

Some of the recommendations may be rejected. Other recommendations are accepted while some are amended. The National Constitution conference members may reject some recommendations and replace them with their own.

 

  1. Sometimes the National Constitutional Conference members are unable to reach a consensus concerning certain recommendations. If this happens the recommendations causing disagreement are referred back to the public to be resolved through a referendum which is organised by the Constitution of Kenya Review Commission. The referendum is conducted within two months.

 

  1. After this is done the draft constitution is forwarded to the National Assembly by the Attorney General after receiving it from the Commission. The draft constitution is treated as a bill and then published for discussion. Once it is recommended by the Members of Parliament after passing through all the stages a bill undergoes before becoming law, it is finally presented to the President for assent.

 

  1. Finally, the constitution is published in the Kenya Gazette and after this implementation begins.

 

 

Features of Kenya constitution

 

  1. a) The constitution is democratic

Due to the wishes and ambitions of the people since Kenya attained independence, the country has developed a democratic constitution based on the principles of separation of powers between the Judiciary, the Legislature and the Executive. This is aimed at reducing conflicts between the three arms of government. The arms of government are therefore required to work independently without excessive interference from each other.

 

 

  1. b) There is supremacy of the constitution and the rule of law

Kenya is established on the principles of the supremacy of the constitution and the rule of law. It is governed in accordance with the constitution that acts as the supreme law that binds all authorities and individuals throughout the country.

However, the rule of the law emphasises on handling all legal matters in accordance with the Kenyan laws. Every individual suspects is supposed to be given an opportunity for self-defence before a competent court of law after being arrested. The prosecution is supposed to prove the defendant guilty within a specific period and until the victim is proved guilty beyond reasonable doubt, he should be presumed innocent.

 

  1. c) Recognition for and protection of individual human rights and freedom

The Kenya constitution accommodates this distinctive characteristic in order to preserve the dignity of individuals and communities, to promote the realisations of the potential of all the people and also to promote social justice. The rights and freedom of the individuals are contained in the Bill of Rights.

 

  1. d) A government must have relationship with the constitution

It is unlawful to establish a system of government that is contrary to the constitution.

Constitutional amendments since independence

 

Kenya attained internal self-government on 1st June 1963. The constitution which the country adopted in 1963 was the independence constitution.

 

  1. a) In 1964, the independence (majimbo) constitution was abolished. Kenya became a republic with an executive President. The President was the head of state and government. The country adopted a republican constitution with a unitary system of government.

 

  1. b) In 1966, the two houses of parliament, that is the senate and the House of Representatives were abolished and replaced with a single chamber National Assembly (Parliament).

 

  1. In 1966, a member who resigned from the party that sponsored him or her was required to seek fresh mandate from the electorate on the ticket of the new party. Also a member who missed eight consecutive parliamentary sittings or who served a prison sentence of over six months would automatically lose his seat.

 

  1. d) In 1966, for any constitutional amendment to be affected there had to be a 2/3 majority of the members of Parliament.

 

  1. e) In 1966, the Public Security Act stated that people could be detained on public interest without trial. For example, a citizen who was considered to be a danger to state security was detained without trial.

 

  1. f) In 1966, it was declared that if the Presidency fell vacant, the Vice-President would take over and act as President for the remaining term of office. The President was given power to nominate 12 members of parliament.

 

  1. g) In 1968, the President was empowered to make changes on the administrative boundaries. In this case, the Parliament lost control over the changing of administrative boundaries.

 

  1. h) In 1968, voting age was lowered from 21 to 18 years. One could qualify to contest for Presidency at the age of 35 years. Before one could contest at the age of 40 years and above.

 

  1. i) In 1968, the presidential election was to be done directly by the people who qualified to vote.

 

  1. j) In 1968, If the presidency fell vacant, elections were to be held within 90 days. The Vice – President acted as President for a period not going beyond 90 days. The President was also given power to postpone elections when and if he or she found it necessary. He could also shorten the life of the Parliament.

 

  1. k) In 1975, the President was empowered to pardon election offenders enabling them to contest in future elections.

 

  1. l) In 1977, the Kenya Court of Appeal was established to replace the East African Court of Appeal.

 

  1. m) In 1978, Public officers who wanted to contest during parliamentary elections had to resign six months before election time.

 

  1. In 1982, Kenya was changed from a de-facto one-party state to a de jure one-party state. This was done through the constitutional amendments which brought about the ‘Section 2A’. KANU was to be the only legal political party.

 

  1. In 1982, the security tenure of office of the Attorney General and Controller Audit General was established.

 

  1. In 1982, The office of the Chief Secretary and Head of Civil Service was established.

 

  1. In 1987, The post of Chief Secretary was abolished and replaced by the office of the secretary to the cabinet. This occurred because the office of the Chief Secretary was too powerful.

 

  1. In 1987, The President was empowered to dismiss government officers such as the Attorney General and the Controller and Audit General at will.

 

  1. In 1988, The President was empowered to dismiss the High Court judges and the chairman of the Public Service Commission at will.

 

  1. In 1988, The Police department was empowered to hold suspected criminals for a maximum of 14 days before presenting them to a court of law for hearing and trial.

 

  1. In 1990, The tenure of office of the Attorney General, The Chairman of the Public Service Commission and the Controller and Audit General were guaranteed.

 

  1. In 1990, The Presidency was limited to 2 five-year terms. For one to qualify as President he or she had to win 25% of the votes cast in at least 5 provinces of Kenya.

 

  1. In 1991, The section 2A of the constitution was repealed and Kenya became a multi-party state. The voting age was lowered from 21 years to 18 years.

 

  1. In 1997, Political parties were given the mandate to appoint nominated members of parliament.

 

The Kenya electoral commission commissioners were increased while certain oppressive laws were either amended or repealed. Such laws were:

  1. i) The public order act

 

  1. The Chief’s Act

 

  • The Preservation of Public Security Act

 

  1. The Vagrancy Act

 

 

Review Questions

 

  1. a) Define the term ‘constitution’.
  2. b) Explain the advantages and disadvantages of a written constitution.

 

  1. Outline the provisions of the independence constitution of Kenya.

 

  1. Discuss the main constitutional amendments in Kenya since independence.

 

  1. Identify the differences between written and unwritten constitution.

 

  1. What are the main features of the Kenya constitution?

 

  1. Give reasons why a constitution is necessary in any country.

 

Students’ Activities

 

  1. Describe the stages in the constitution making in Kenya.

 

  1. Discuss the factors that determine a country’s constitution.

 

  1. Have a class debate on whether Kenya should have a Prime Minister with more powers than that of the President or not.

 

 

 

 

 

CHAPTER 7

 

 

Democracy and human rights

 

Democracy is a Greek term derived from the Greek words demos, which means people and Kratia signifies power or rule.

The word democracy may mean people’s rule. It may also imply a system of government where the people of a country take part in decision making through elected representatives. Abraham Lincoln defined democracy as ‘a government of the people, for the people and by the people.’

His definition is very popular and easy to comprehend. Any country with a true democratic system of government allows the people to enjoy the rights and freedoms such as rights to life, right to liberty and freedom of speech, freedom of political opinion and freedom of religion. It handles legal matters in accordance with the law. All people in the country are regarded as equal before the law irrespective of their status, race or religion.

In a democratic country, people’s opinions are taken very seriously because the government has to live to people’s expectations. A country which does not honour the opinions of the people (public opinion) becomes unpopular and it is disowned by the majority who later vote it out of power.

From the above explanation we may summarise the main features of democracy as below:

 

  1. Democracy gives room for consent to various aspects. This is either done directly or through people’s representatives.

 

  1. Democracy emphasises on equality of all the people. The government therefore tries to provide all the people with equal opportunities.

 

  1. Democracy gives people freedom to organise and enjoy their rights.

 

 

Types of democracy

 

The two common types of democracy are:

 

  1. Direct democracy

 

  1. Indirect democracy

 

Direct democracy

A direct democracy is one which people in a country are allowed to participate directly in all decision making. It is sometimes called pure democracy. This kind of decision making was very common among the Bushmen of South Africa and the people of the Greek city states.

Unfortunately direct democracy cannot work in countries with large populations because all the people cannot be consulted before decisions are made. It therefore succeeds in countries or communities with very few people where the opinion of every person is considered to be very useful before final decisions on various issues are made. What is agreed upon by all is accepted by all of them without any question.

Direct democracy principles have been applied in Kenya in the attempt to allow people to exercise their democratic rights. Kenyans for example have been consulted to give their opinion concerning the constitutional review.

Incase some issues are not agreed upon by members of the constitutional conference, a referendum has to be used so as to act according to the will of the people.

 

Indirect democracy

 

This is sometimes referred to as representative democracy.

In this case, people do not participate directly in decision making. They normally use their representatives. The people by way of voting elect the representatives and they specifically express people’s feelings on public issues. Indirect democracy is practical in large modern states because there are huge in size and population.

The disadvantages of this method are that the people who are elected can easily ignore the people who elected them. They can also fail to consult the electorate in order to be able to air their views in the parliament.

 

There are two types of representative democracy. These are:

 

  1. Parliamentary democracy
  2. Presidential democracy

 

Parliamentary democracy

 

Here people cast votes to elect their representatives. Those who are elected choose one person to take leadership as Prime Minister.

The one who is chosen appoints the other ministers from among the members of parliament. Those appointed forms the cabinet. The Prime Minister can be forced to resign if the other legislators cast a vote of no confidence on him. If this is done, another Prime Minister is elected to form the government.

 

Presidential Democracy

Here the President and other members of Parliament are elected directly by the electorate. They then form a government that lasts for a specified period of time. In the Kenyan case, it is 5 years. Non of the two arms of the government, executive and legislature has full control over the other in this type of democracy. They only act as checks and balances therefore ensuring that non of them tries to overshadow the other.

 

Principles of democracy

 

Democratic principles are the moral professional standards that are necessary in a democracy.

They play the role of showing whether a country is democratic or not. The principles of democracy are found in the Bill of Rights that is the framework for the adoption of social, economic and cultural policies.

 

The principles of democracy are:

 

  1. Rule of law

This implies that there must be equality before the law. All people in a country are subject to the same law. People must obey the law. Those who violate the established laws are prosecuted and punished if found guilty. The law should apply to all people equally without any discrimination on the basis of gender, race, ethnicity, religion, political affiliation, colour, disability, social status and other physical or social characteristics.

 

  1. People’s participation in governance

In a democratic country, people should participate in the governing of their country. They should be involved in the decision-making processes.

A person can participate in government by getting involved in voting to elect the most responsible representative of the people in the country’s parliament. A person can also contest for a parliamentary or civic post.

One can be a member of a non-governmental organisation or association that is free to hold discussions on matters affecting the country e.g. Maendeleo ya Wanawake. Such an organisation can help to control the activities of the government inorder to prevent it from abusing its powers.

 

  1. Economic liberty

Democratic governments allow their citizens to have freedom of action, choice and decision when dealing with issues pertaining to their economic status. This may be achieved through allowing privatisation of business partners, and market for selling one’s goods. All this gives individuals lawful authority to genuinely attain and control their own wealth.

 

  1. Respect for and protection of human rights

Human rights should be respected and protected because they are essential aspects of democracy which promote the respect for human life and dignity. Human rights are recognised and protected to preserve the dignity of individuals and communities and to promote social justice and the realisation of the potential of all human beings.

 

  1. Need to conduct free and fair elections

Elections should be held every time after an agreed period of time. In Kenya elections are held after every five years. Elections should not involve some unfair practices such as corruption, intimidation and rigging.

 

  1. Respect of other people’s opinions

In a democratic country, the opinions of political opponents should never be dismissed.

The opinions of political opponents should help those in control to streamline or even adjust their actions.

 

  1. Bill or Rights

Every democratic country should have a Bill of Rights, which contain the rights and freedoms of all the citizens and the limitations of these rights and freedoms.

 

  1. Equal status of all people (citizens)

There should be no discrimination based on colour, race, gender, political position or ethnic group.

All people should be regarded as equal before the law and therefore be provided with equal opportunities and privileges.

 

  1. Transparency and Accountability

Any country which claims to be democratic must operate in such a way that the citizens are aware of what the government is doing and what it is intending to do. There should be high degree of openness on the side of the government. The government should listen to and respect the views of its citizens and otherwise act accordingly.

Transparency and accountability may be achieved through constant meetings of the authorities with the people and through advertisements done through the mass media and print media.

 

  1. Application of democratic principles such as liberty and social justice.

 

  1. Separation of functions between the Executive, the Legislature and the Judiciary.

 

  1. Provision of equal opportunities for all citizens without discrimination.

 

NB:   The process of building a democracy is referred to as democratisation. The agents of democratisation are interest groups, political parties, civil society, the mass media and state institutions such as Judiciary, Parliament, the civil service and other state sponsored bodies such as human rights commission and anti-corruption authorities

 

 

Human rights

 

Human rights can be defined as set of basic rules of justice to which each human being is entitled. They can also be defined as things that any individual is allowed to do or have by the law. One is legally allowed to do or have those things irrespective of race, religion, political opinion, creed, sex, language, place of origin, age, one’s tribe, colour or other local connections.

In Kenya, every person is guaranteed freedom of speech, religion, association and movement. He or she is also guaranteed the right to life, right to own property and right to personal liberty. Governments do not give these rights. They are the rights needed to live a human life.

As one enjoys these fundamental rights, he or she should follow the law. He or she should not interfere with other people’s rights or with the functioning of the government or the whole society’s enjoyment of rights. The rights of the individuals are contained in chapter five of the constitution. The functions of Human Rights are:

 

  1. To safeguard the individual’s security, life and liberty.

 

  1. To safeguard the individual’s freedom of conscience, movement, association and speech, etc.

 

  1. To safeguard the individual’s private property and home.

 

  1. Human rights empower people to air their own views independently without fear. People should have the freedom of expression.

 

  1. They ensure that the weak and the poor are not oppressed by the rich and powerful.

 

  1. The human rights fulfil the moral and spiritual requirements of individuals.

 

  1. They limit conflicts between people therefore inculcating to people the need for unity.

 

  1. The human rights guide the government on how to deal with its citizens so that the citizens can gain confidence with the government.

 

 

Features of human rights

 

The main features of human rights are:

 

  1. Human rights affect all the people in the world. Every human being therefore has the right to enjoy these fundamental human rights.

 

  1. There are limitations of human rights. This simply means that sometimes people abuse the human rights when they fail to honour the rights of others. Due to this, the law has put some limitations on some of the rights and freedoms of the individuals.

 

  1. Human rights are interdependent in that sometimes you must be having a certain right in order to enjoy the other. You cannot enjoy the freedom of speech if you are denied the freedom of association because you will not get somebody to talk to. If you are living in a state of insecurity and your life is in danger then you cannot enjoy many other rights such as right to liberty, freedom of association and freedom of movement.

 

  1. If the country is at war, certain provisions of the fundamental rights can be suspended. Examples of the provisions which can be suspended are:
  2. i) The protection in respect to the rights to liberty

 

  1. ii) Freedom of expression (speech)

 

  • Freedom of movement

 

  1. Right against forced search or entry.

 

  1. Freedom of association

 

  1. Anti-discrimination provision

 

 

Violation of human rights

 

In order to ensure that human rights are not violated, the government of Kenya set up a standing committee on human rights aimed at providing citizens with a way they can report abuses of human rights. The role of this committee is to receive complaints on human rights abuses from the public. It then makes reports and suggestions to the government on the action to be taken against those who violate the rights.  The Kenyan Human Rights Commission also draws attention to human rights abuses.

Other groups that observe and report issues on the abuse of human rights are religious groups, police, newspaper journalists, judges, educators, lawyers, trade unionists and the civil society organisations.

 

The Bill of Rights

 

The Bill of Rights is a statement of human or civil rights in a constitution. It explains and guarantees the rights of the individuals. It also clarifies the circumstances which may force the government to deny an individual his rights and freedoms.

The Bill of rights in the Kenya constitution is derived from the International Bill of Rights that is found in the International Covenant on Civil and Political Rights.

 

Some of the provisions of the International Bill of rights are:

 

  1. It states clearly the right to self-determination. Here people are allowed to determine their political position and to continue with their socio-economic and cultural advancement.

 

  1. There should be equal rights for both men and women as they enjoy civil and political rights.

 

  1. All people have right to freedom of association.

 

  1. No person shall be subjected to arbitrary interference of his family or privacy.

 

  1. All people are equal before the law. Therefore no person is above the law and the law should apply to all people equally without any discrimination.

 

  1. All people have a right to freedom of conscience and religion.

 

  1. No person shall be subjected to inhuman treatment or torture.

 

  1. All people have right to liberty.

 

  1. All people living in a particular state lawfully have freedom of movement in that particular state.

 

  1. Every person has the right to life that must be protected by law.

 

  1. No person should be enslaved because all people have a right to freedom.

 

  1. Every person has the right of being recognised every where in the world as a human being (person) before the law.

 

  1. A couple has freedom to marry and start a family so long as they agree to do so.

 

  1. Minority groups should never be denied their rights for instance religious rights and cultural rights.

 

  1. Everyone has the right to take part in the public affairs of the state he belongs either directly or indirectly. So the right to vote and to be voted for is provided.

 

The Bill of Rights was included in the constitution of many democratic states that include Kenya. However the Bill of Rights in Kenya had a number of limitations in connection to the constitution in use from independent up to 2003. These are:

 

  1. Some bills lost their power due to use of clauses or exceptions. For instance in the constitution there was the freedom of movement at the same time the parliament was empowered to make laws that could restrict that freedom.

 

  1. The ways of making sure that the rights in the Bill of Rights were carried out were not clarified.

 

  1. The Bill of Rights did not include or protect persons with disabilities against discrimination.

 

  1. The provisions of suspending some of the rights contained in the Bill of Rights were generally very wide.

 

  1. The marginalised communities were not very well protected because the Bill of Rights did not provide clear protection guidelines for such communities.

 

  1. The Kenyan Bill of Rights did not mention the socio-economic and cultural rights as well as the rights to development and the rights to a clean environment.

 

  1. Some sections of the laws allowed discrimination. For example section 91 of the constitution discriminated against women when it allowed the child of a Kenyan father married to a foreign woman to get citizenship automatically while the child of a Kenyan woman married to a foreigner could not be awarded citizenship automatically.

 

 

 

The UN charter on human rights

 

The United Nations Organisation (UNO) sometimes referred to as UN was established after the Second World War to promote international co-operation by encouraging the respect for human rights and freedoms.

The Charter of the UN was signed on 26th June 1945 and came into force on 24th October 1945. It provided the constitutional basis for establishing international peace and security.

The need to have international peace and security arose as a result of people’s concern due to the damages caused by the first world war and the second world war. During these two world wars, many people were killed and property worth millions of shillings destroyed.

To prevent such damages occurring again, the Universal Declaration of Human Rights was written.

The Declaration of Human Rights states that, “all human beings are born free and equal in dignity and rights”.

 

The General Assembly of the United Nations adopted this declaration. It declares:

 

  1. i) Civil and political rights

 

  1. Cultural rights

 

  • Economic rights

 

  1. Social rights

1.       Civil and political rights

The aliens are protected from expulsion. People are prevented from being forced to testify against themselves or confess their guilt. It also provides for a right to be compensated in case of misuse or error of justice. There is prohibition of racial or religious hatred and ban of wars. Lastly, protection of ethnic, religious or different language minorities is provided.

 

  1. Cultural Rights, Economic Rights and Social Rights

The rights included here are the right to work, the right to education, the right to form trade unions, the right to strike, the right to participate in cultural life, the right to have an adequate standard of living, the right to social security, the right to fair and favourable conditions of work and the rights of minorities.

 

 

 

 

 

 

 

 

 

 

 

 

Kenyans enjoying the right to education

 

Some of the human rights contained in the Universal Declaration of Human Rights document

 

  1. Nobody shall be subjected to arbitrary detention, arrest or exile.

 

  1. Nobody should be enslaved.

 

  1. All human beings are born free and equal.

 

  1. All people have a right to life and liberty.

 

  1. All people have a right to freedom of association and assembly.

 

  1. Any person charged with an offence must be presumed innocent until proved guilty in a court of law.

 

  1. Every person has a right to own property. No property should be taken away without proper compensation.

 

  1. Every person is entitled with the right to a fair hearing by an impartial and independent court.

 

  1. The right to freedom of movement within one’s country is provided.

 

  1. Anybody has a right to seek refuge in another country for political reasons.
  2. Anybody has a right to freedom of expression (speech).

 

  1. Anybody has a right to belong to a particular nation. One can also change his nationality if he wants.

 

  1. All people are equal before the law.

 

  1. Anybody is allowed to marry another person and start a family irrespective of their nationality, religion, colour or race.

 

 

The Universal Declaration of Human Rights document is important because:

 

  1. i) It provides an international standard by which governments can be judged on issues of human rights so that they can be accused of violating them and therefore be cut off internationally or certain sanctions put in place to punish them.

 

  1. It encourages some countries to form regional blocs so as to be able to introduce and protect human rights.

 

The rights of the child

 

Children like any other human beings are entitled to certain rights that provide special protection to them. Children differ from adults in that they have limited capabilities. For this reason they require protection and support of adults.

The rights of children are contained in the United Nations Convention on the Rights of the Child.

The Children’s Act in Kenya was passed by Parliament in the year 2002. It contained a number of rights for children. Some of them are as below:

 

  1. Right to life

Every child is entitled to the right to life. The parents and the government should therefore ensure that the children grow up without any obstacles that may affect their lives.

 

  1. Right to education

Children have a right to be educated. The parents must therefore ensure that their children obtain basic primary education that is now free. The government is ensuring that successful primary school pupils acquire secondary school education by providing bursary funds to students from poor families.

 

  1. Protection from exploitation

Children can easily be exploited as cheap labour. There should be regulations that protect children against exploitation. Children should not be forced to do any work that is likely to negatively affect them morally, physically and mentally.

 

  1. Protection from discrimination

Children should be protected against various kinds of discrimination such as being discriminated on the bases of colour, race, religion, sex and many others.

 

  1. Right to good medical care

Parents and the government should ensure that children are provided with medical care. For instance they can be vaccinated against certain diseases. Specialists for treating children should also be available.

 

  1. Right to religious guidance

The parents should guide their children on how to practice their religion and also instruct them on religious matters.

 

 

  1. Protection from sexual abuse

Children should be protected from rape and from being given money in exchange for sex by adults.

 

  1. Right to basic requirements like food, shelter and clothing

Children have a right to be provided with food, shelter and clothing by their parents. In times of famine, the government should provide children with food if their parents are not able to do so.

 

  1. Right to adoption

The government has put in place guidelines on the way adoption should be done.

 

  1. Right to play

Children should be allowed to play. It is when they play that they make discoveries and also settle their minds. Playing also enables them to socialise with others.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Children socialising

 

 

Classification of human rights

 

Human rights may be categorised as follows:

 

  1. i) Political and civil rights

 

  1. Social and cultural rights

 

  • Economic Rights

 

  1. Development and group rights

 

Political and civil rights

Political and civil rights are generally referred to as “Civil rights” or “Fundamental rights, freedoms and protections”.

They enable individuals to follow their values and interests. They provide individuals with basic freedoms. Examples of civil rights are:

 

  1. i) The right to life

 

  1. The right to personal liberty

 

  • Freedom of expression

 

  1. Freedom of conscience

 

  1. Freedom of association and assembly

 

  1. Freedom of movement

 

  • Freedom of discrimination

 

  • Protection against slavery and forced labour

 

  1. Protection from arbitrary search and entry

 

  1. Right to the secure protection of law.

 

Social and cultural rights

They provide people with social freedom and basic needs such as education and health. They also provide people with the right to take part in cultural activities. They encourage fair treatment of all citizens and discourage inhuman treatment and interference with one’s body, premises or private life therefore ensuring security to the people. Examples of social and cultural rights are:

 

  1. i) Right to education

 

  1. Right to start a family or marry

 

  • Right to health or medical care

 

  1. Right to housing or good shelter

 

  1. Right to good food

 

  1. Right to good clothing

 

  • Right to play and leisure

 

  • Right to social security

 

  1. Right to parental love

 

  1. Right to association

 

  1. Protection from discrimination, sexual abuse, drugs and disaster.

 

Economic rights

These provide people with economic freedom. They enable people to take part in the economic activities freely without harassment. Economic rights provide people with the right to own and use property and the chance to work and provide for their livelihood. They also provide people with the right to freedom from forced labour and slavery. Examples of economic rights are:

 

  1. i) Right to form and become a trade union member

 

  1. Right to own property

 

  • Right to work and to fair judgement

 

  1. Right to start and operate a business

 

  1. Right to form and join a trade union

 

Developmental and group rights

These help people to have better life. One of the ways of having a better life is living in a clean environment which is free from all forms of pollution for instance excessive noise, excessive fumes and smoke, bad smell from rotting objects and contaminated water due to careless dumping of pollutants. Group rights represent a specific group of people. Examples of development and group rights are:

 

  1. i) The right to culture

 

  1. The right to clean environment

 

  • The right to development

 

  1. The right of persons with disabilities

 

  1. The right of minorities

 

In conclusion, it is vital to note that the new government which took over leadership after 2002 immediately began addressing itself to the issue of discrimination against women and other minorities which is an important issue on human rights. For decades women and women’s groups have been disadvantaged yet they contribute greatly to the economy of the country.

There were also other groups that are marginalised on the basis of gender, disability, age, customs and traditions.

The new government responded positively after power was handed over by the previous regime by taking Affirmative action (measures to accelerate equality and reverse discrimination) which resulted to nomination of more women to parliament after the general election.

It is hoped that the government will continue to encourage fairness to both genders in the assignment of responsibilities and leadership roles as well as making opportunities available for the marginalised groups. By so doing, there will be fair sharing, distribution and allocation of jobs and resources for everyone’s benefit and also for the good of everyone in the country.

When this is achieved all Kenyans will begin thinking, talking, trying and acting to achieve all the goals set by the practical democratic leaders of our country.

 

Review Questions

  1. a) Define the term ‘Democracy’.
  2. b) Describe the two types of democracy below:
  3. i) Direct Democracy
  4. ii) Indirect or Representative Democracy

 

  1. a) What are Human Rights?
  2. b) Describe the UN Charter on Human Rights

 

  1. Identify the Rights of the Child which are contained in the Children’s Act.

 

  1. a) How can we classify Human Rights?
  2. b) Identify the ways the government is adopting Affirmative Action to deal with the past discrimination.

 

  1. What are the sources of Kenya’s Bill of Rights?

 

  1. Discuss the following:
  2. i) Presidential democracy
  3. ii) Parliamentary democracy

Students’ Activities

  1. Discuss the principles of democracy.

 

  1. In groups identify various human rights abuses in Kenya.

 

  1. Have a class debate whether it is right or wrong to compel all street children to join the National Youth Service.

Form 3 Maths Free Notes

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QUADRATIC EXPRESSION AND EQUATIONS

                  CHAPTER FOURTY FOUR

Specific Objectives

By the end of the topic the learner should be able to:

(a) Factorize quadratic expressions;

(b) Identify perfect squares;

(c) Complete the square;

(d) Solving quadratic equations by completing the square;

(e) Derive the quadratic formula;

(f) Solve quadratic equations using the formula;

(g) Form and solve quadratic equations from roots and given situations;

(h) Make tables of values from a quadratic relation;

(i) Draw the graph of a quadratic relation;

(j) Solve quadratic equations using graphs;

(k) Solve simultaneous equations (one linear and one quadratic) analytically and graphically;

(1) Apply the knowledge of quadratic equations to real life situations.

Content

(a) Factorization of quadratic expressions

(b) Perfect squares

(c) Completion of the squares

(d) Solution of quadratic equations by completing the square

(e) Quadratic formula x = -b ±

(f) Solution of quadratic equations using the formula.

(g) Formation of quadratic equations and solving them

(h) Tables of values for a given quadratic relation

(i) Graphs of quadratic equations

(j) Simultaneous equation – one linear and one quadratic

(k) Application of quadratic equation to real life situation.

Perfect square

Expressions which can be factorized into two equal factors are called perfect squares.

Completing the square

Any quadratic expression can be simplified and written in the form  where a, b and c are constant and a is not equal to zero. We use the expression    to make a perfect square.

We are first going to look for expression where   coefficient of   x = 1

Example

What must be added to + 10 x to make it a perfect square?

Solution

  • Let the number to be added be a constant c.
  • Then + 10x + c is a perfect square.
  • Using
  • (10 /2 = c
  • C = 25 (25 must be added)

Example

What must be added to + _ + 36 to make it a perfect square

Solution

  • Let the term to be added be bx where b is a constant
  • Then + bx +36 is a perfect square.
  • Using
  • b =12 x or -12 x

 

 

 

 

 

We will now consider the situations where a  eg

 

 

In the above you will notice that   ac . We use this expression to make perfect squares where  a is not one and its not zero.

Example

What must be added to + _ + 9 to make it a perfect square?

Solution

  • Let the term to be added be bx.
  • Then, + bx + 9 is a perfect square.
  • .
  • The term to be added is thus .

Example

What must be added to _ – 40x + 25 to make it a perfect square?

Solution

  • Let the term to be added be a
  • Then – 40x + 25 is a perfect square.
  • Using

 

 

 

 

Solutions of quadratic equations by completing the square methods

Example

Solve  + 5x+ 1 = 0 by completing the square.

 

 

solution

+ 5x+ 1 = 0                      Write original equation.

+ 5x = -1 Write the left side in the form + bx.

+ 10x + ( (    Add  to both sides

+ 10x + =

=   Take square roots of each side and factorize the left side

= Solve for x.

Simplify

Therefore x = – 0.2085 or 4.792

Cannot be solved by factorization.

Example

Solve  + 4x+ 1 = 0 by completing the square

Solution

+ 4x =-1   make cooeffiecient of  one by dividing both sides by 2

+ 2x = -1/2

+ 2x + 1 = –  + 1

                                  Adding 1 to complete the square on the LHS

 

 

 

 

The quadratic formula

Example

Using quadratic formula solve

Solution

Comparing this equation to the general equation  we get;a =2  b =-5  c =-5

Substituting in the quadratic formulae

X =

 

=

=

=

=

X = 3 or –

 

Formation of quadratic equations

Peter travels to his uncle’s home,30 km away from his place. He travels for two thirds of the journey before the bicycle developed mechanical problems an he had to push it for the rest of the journey. If his cycling speed is 10 km\h faster than his walking speed and he completes the journey in 3 hours 30 minutes, determine his cycling speed .

 

 

Solution

Let Peters cycling speed be x km\ h , then his walking speed is (x-10 ) km/h.

Time taken in cycling

Time taken in walking = (30 – 20) ( x -10 )

Total time h

Therefore

 

60(x-10) + 30 (x) = 10(x) (x-10)

– 190x + 600 = 0

– 19x + 60 = 0

If his cycling speed is 4 km/h , then his walking speed is (4 -10 ) km/h, which gives – 6 km/h.Thus,

4 is not a realistic answer to this situation.therefore his cycling speed is 15 km/h.

Example

A posite two digit number is such that the product of the digit is 24.When the digits are reversed , the number formed is greater than than the original number by 18. Find the number

 

 

 

Solution

Let the ones digit of the number be y and the tens digit be x,

Then , xy = 24…………..1

When the number is reversed, the ones digit is x and the tens digit is y.

Therefore;

(10y + x) – (10x +y) = 18

9y- 9x = 18

 

 

Substituting 2 in equation 1 gives;

 

Since the required number is positive x =4 and y = 4 + 2 =6

Therefore the number is 46

 

 

 

 

Graphs of quadratic functions

A quadratic function has the form y = ax2 + bx + c where a ≠ 0. The graph of a quadratic function isU-shaped and is called a parabola. For instance, the graphs of y = and y = e

Shown below. The origin (0, 0) is the lowest point on the graph of y =    and the highest point on the graph of y =   . The lowest or highest point on the graph of a quadratic function is called the vertex.

The graphs of y =  and y =   are symmetric about the y-axis, called the axis of symmetry. In general, the axis of symmetry for the graph of a quadratic function is the vertical line through the vertex..

 

 

Notes;

The graph of y =  and y = or .

Example

Draw the graph of y =

Solution

Make a table showing corresponding value of  x and y.

X   -1  0 1 2 3
Y   – 8 -1 2 1 -4

 

Note ; To get the values replace the value of x in the equation to get the corresponding value of x

  1. g y = -2 ( -1

y = -2 ( 0

 

Example

Draw the graph of y =

x 0 1 2 3 5 7
y 2 -4 -8 -10 -8 2

 

 

 

 

 

 

 

 

 

Graphical solutions of simultaneous equations

We should consider simultaneous equation one of which is linear and the other one is quadratic.

Example

Solve the following simultaneous equations graphically:

Solution

Corresponding values of x and y

x -2 -1 0 1 2 3 4 x
y 9 4 1 0 1 4 9 y

 

We use the table to draw the graph as shown below, on the same axis the line y = 5-2x is drawn. Points where the line y =5 -2x and the curve  intersect give the solution. The points are (- 2, 9) and (2,1).Therefore , when x = -2, y = 9 and when x = 2, y= 1

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

 

Past KCSE Questions on the topic.

 

 

  1. The table shows the height metres of an object thrown vertically upwards varies with the time t seconds

The relationship between s and t is represented by the equations s = at2 + bt + 10 where b are constants.

 

t 0 1 2 3 4 5 6 7 8 9 10
s 45.1
  • (i) Using the information in the table, determine the values of a and b

(2 marks)

(ii) Complete the table                                                                    (1 mark)

(b)(i)    Draw a graph to represent the relationship between s and t         (3 marks)

(ii)   Using the graph determine the velocity of the object when t = 5 seconds

  1. (a) Construct a table of value for the function y = x2 – x – 6 for -3≤ x ≤ 4

(b)        On the graph paper draw the graph of the function

Y=x2 – x – 6 for -3 ≤ x ≤4

(c)        By drawing a suitable line on the same grid estimate the roots of the equation   x2 + 2x – 2 =0

  1. (a) Draw the graph of y= 6+x-x2, taking integral value of x in -4 ≤ x ≤ 5. (The

grid is provided. Using the same axes draw the graph of y = 2 – 2x

(b)        From your graphs, find the values of X which satisfy the simultaneous

equations y = 6 + x  – x2

y = 2 – 2x

(c)        Write down and simplify a quadratic equation which is satisfied by the

values of x where the two  graphs intersect.

  1. (a) Complete the following table for the equation y = x3 – 5x2 + 2x + 9
x -2 -1.5 -1 0 1 2 3 4 5
x2 -3.4 -1 0 1 27 64 125
-5x2 -20 -11.3 -5 0 -1 -20 -45
2x -4 -3 0 2 4 6 8 10
9 9 9 9 9 9 9 9 9 99
-8.7 9 7 -3

 

(b) On the grid provided draw the graph of y = x3 – 5x2 + 2x + 9 for -2 ≤ x ≤ 5

(c) Using the graph estimate the root of the equation x3 – 5x2 + 2 + 9 = 0 between x =

2 and x = 3

(d) Using the same axes draw the graph of y = 4 – 4x and estimate a solution to the

equation x2 – 5x2 + 6x + 5 =0

  1. (a) Complete the table below, for function y = 2x2 + 4x -3
x -4 -3 -2 -1 0 1 2
2x2 32 8 2 0 2
4x – 3 -11 -3 5
y -3 3 13

(b)        On the grid provided, draw the graph of the function y=2x2 + 4x -3 for

-4 ≤ x ≤ 2 and use the graph to estimate the rots of the equation 2x2+4x – 3 = 0 to 1 decimal place.                                                               (2mks)

(c)        In order to solve graphically the equation 2x2 +x -5 =0, a straight line must be drawn to intersect the curve y = 2x2 + 4x – 3. Determine the equation of this straight line, draw the straight line hence obtain the roots.

2x2 + x – 5 to 1 decimal place.

  1. (a) (i)         Complete the table below for the function y = x3 + x2 – 2x         (2mks)

 

x -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 2 2.5
x3 15.63 -0.13 1
x2 4 0.25 6.25
-2x 1 -2
y 1.87 0.63 16.88

 

(ii)        On the grid provided, draw the graph of y = x3 + x2 – 2x for the values of x in the interval – 3 ≤ x ≤ 2.5

(iii)       State the range of negative values of x for which y is also negative

(b)        Find the coordinates of two points on the curve other than (0, 0) at which x- coordinate and y- coordinate are equal

  1. The table shows some corresponding values of x and y for the curve represented by Y = ¼ x3 -2

 

X -3 -2 -1 0 1 2 3
Y -8.8 -4 -2.3 -2 -1.8 0 4.8

 

On the grid provided below, draw the graph of y = ¼ x2 -2 for -3 ≤ x ≤3. Use the graph to estimate the value of x when y = 2

  1. A retailer planned to buy some computers form a wholesaler for a total of Kshs 1,800,000. Before the retailer could buy the computers the price per unit was reduced by Kshs 4,000. This reduction in price enabled the retailer to buy five more computers using the same amount of money as originally planned.

(a)        Determine the number of computers the retailer bought

(b)        Two of the computers purchased got damaged while in store, the rest were sold and the retailer made a 15% profit Calculate the profit made by the retailer on each computer sold

  1. The figure below is a sketch of the graph of the quadratic function y = k

( x+1) (x-2)

 

 

 

 

 

 

Find the value of k

  1. (a) Draw the graph of y= x2 – 2x + 1 for values -2 ≤ x ≤ 4

(b) Use the graph to solve the equations x2 – 4= 0 and line y = 2x +5

  1. (a) Draw the  graph  of y = x3 + x2 – 2x for -3≤ x ≤ 3 take scale of 2cm to

represent 5 units as the horizontal axis

(b)        Use the graph to solve x3 + x 2 – 6 -4 = 0 by drawing a suitable linear graph on the same axes.

 

  1. Solve graphically the simultaneous equations 3x – 2y = 5 and 5x + y = 17

 

 

    APPROXIMATION AND ERROR

CHAPTER FOURTY TWO

 

Specific Objectives

By the end of the topic the learner should be able to:

 

(a) Perform various computations using a calculator;

(b) Make reasonable approximations and estimations of quantities incomputations and measurements;

(c) Express values to a given number of significant figures;

(d) Define absolute, relative, percentage, round-off and truncation errors;

(e) Determine possible errors made from computations;

(f) Find maximum and minimum errors from operations.

 

Content

(a) Computing using calculators

(b) Estimations and approximations

(c) Significant figures

(d) Absolute, relative, percentage, round-off (including significant figures)and truncation errors

(e) Propagation of errors from simple calculations

(f) Maximum and minimum errors.

 

 

 

 

 

Approximation

Approximation involves rounding off and truncating numbers to give an estimation

Rounding off

In rounding off the place value to which a number is to be rounded off must be stated. The digit occupying the next lower place value is considered. The number is rounded up if the digit is greater or equal to 5 and rounded down if it’s less than 5.

Example

Round off 395.184 to:

  1. The nearest hundreds
  2. Four significant figures
  3. The nearest whole number
  4. Two decimal places

Solution

  1. 400
  2. 395 .2
  3. 395
  4. 395.18

 

Truncating

Truncating means cutting off numbers to the given decimal places or significant figures, ignoring the rest.

Example

Truncate 3.2465 to

  1. 3 decimal  places
  2. 3 significant figures

Solution

  1. 3.246
  2. 3.24

 

 

 

Estimation

Estimation involves rounding off numbers in order to carry out a calculation faster to get an approximate answer .This acts as a useful check on the actual answer.

Example

Estimate the answer to

Solution

The answer should be close to

The exact answer is 1277.75. 1277.75 writen to 2 significant figures is 1300 which is close to the estimated answer.

 

ACCURACY AND ERROR

Absolute error

The absolute error of a stated measurement is half of the least unit of measurement used. When a measurement is stated as 3.6 cm to the nearest millimeter ,it lies between 3.55 cm and 3.65 cm.The least unit of measurement is milliliter, or 0.1 cm.The greatest possible error is 3.55 – 3.6 = -0.05 or 3.65 – 3.6 = + 0.05.

To get the absolute error we ignore the sign. So the absolute error is 0.05 thus,|-0.05| =| +0.05|= 0.05.When a measurement is stated as 2.348 cm to the nearest thousandths of a centimeters (0.001) then the absolute error is .

Relative error

Relative error =

 

Example

An error of 0.5 kg was found when measuring the mass of a bull.if the actual mass of the bull was found to be 200kg.Find th relative error

Solution

Relative error =

 

 

 

 

Percentage error

Percentage error = relative error x 100%

Example

The thickness of a coin is 0.20 cm.

  1. The percentage error
  2. What would be the percentage error if the thickness was stated as 0.2 cm ?

 

Solution

The smallest unit of measurement is 0.01

Absolute error

 

Percentage error

The smallest unit of measurement is 0.1

Absolute error

Percentage error

= 25 %

 

Rounding off and truncating errors

An error found when a number is rounded off to the desired number of decimal places or significant figures, for example when a recurring decimal 1.  is rounded to the 2 significant figures, it becames 1.7 the rounde off error is;

1.7 -1.

 

Note;

1.6 converted to a fraction .

 

Truncating error

The error introduced due to truncating is called a truncation error.in the case of 1.6 truncated to 2 S.F., the truncated error is; |1.6 -1. |  =

Propagation of errors

Addition and subtraction

What is the error in the sum of 4.5 cm and 6.1 cm, if each represent a measure measurement.

Solution

The limits within which the measurements lie are 4.45, i.e. ., 4.55 or  and 6.05 to 6.15, i.e. 6.1 .

The maximum possible sum is 4.55 10.7cm

The minimum possible sum is 4.45 10.5 cm

The working sum is 4.5 + 6.1 = 10.6

The absolute error = maximum sum – working sum

=| 10.7 – 10.6 |

=0.10

Example

What is the error in the difference between the measurements 0.72 g and 0.31 g?

Solution

The measurement lie within  and   respectively the maximum possible difference will be obtained if we substract the minimum value of the second measurement from the maximum value of the first, i.e ;

0.725 – 0.305 cm

The minimum possible difference is 0.715 – 0.315 = 0.400.the working difference is 0.72 – 0.31 =0.41 , which has an absolute error of |0.420 -0.41| or |0.400 – 0.41| = 0.10. Since our working difference is 0.41, we give the absolute error as 0.01 (to 2 s.f)

Note:

In both addition and subtraction, the absolute error in the answer is equal to the sum of the absolute errors in the original measurements.

 

 

Multiplication

Example

A rectangular card measures 5.3 cm by 2.5 cm. find

  1. The absolute error in the rea of the card
  2. The relative error in the area of the cord

Solution

  • The length lies within the limits
  • The length lies within the limits

The maximum possible area is 2.55 x 5.35 =13.6425

The minimum possible area is 2.45 x 5.25 =12.8625

The working area is 5.3 x 2.5 = 13.25

Maximum area – working area = 13.6425 – 1325 = 0.3925.

Working area  minimum area = 13.25 – 12.8625 = 0.3875

We take the absolute error as the average of the two.

Thus, absolute error

= 0.3900

The same can also be found by taking half the interval between the maximum area and the minimum area

The relative error in the area is :

 

 

Division

Given 8.6 cm .Find:

  1. The absolute error in the quotient
  2. The relative error in the quotient

 

Solution

  1. 8.6 cm has limits 8.55 cm and 8.65 cm. 3.4 has limits 3.35 cm and 3.45 cm.The maximum possible quotient will be given by the maximum possible value of the  numerator and the smallest possible value of the denominator, i.e.,

 

= 2.58 (to 3 s.f)

The minimum possible quotient will be given by the minimum possible value of the numerator ad the biggest possible value of the denominator, i.e.

 

= 2.48 (to 3 s.f)

The working quotient is;  = 2.53 (to 3 .f.)

The absolute error in the quotient is;

X 0.10

 

  1. Relative error in the working quotient ;

 

= 0.0197

= 0.020 (to 2 s.f )

 

Alternatively

Relative error in the numerator is

Relative error in the denominator is

Sum of the relative errors in the numerator and denominator is

0.00581 + 0.0147 = 0.02051s

=0.021 to 2 S.F

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

 

Past KCSE Questions on the topic.

 

  1. (a) Work out the exact value of R =               1_________

0.003146 – 0.003130

(b)        An approximate value of R may be obtained by first correcting each of the decimal in the denominator to 5 decimal places

  • The approximate value

(ii)        The error introduced by the approximation

  1. The radius of circle is given as 2.8 cm to 2 significant figures
  • If C is the circumference of the circle, determine the  limits between which C/π lies
  • By taking ∏ to be 3.142, find, to 4 significant figures the line between which the circumference lies.
  1. The length and breadth of a rectangular floor were measured and found to be 4.1 m and 2.2 m respectively. If possible error of 0.01 m was made in each of the measurements, find the:
  • Maximum and minimum possible area of the floor
  • Maximum possible wastage in carpet ordered to cover the whole floor
  1. In this question Mathematical Tables should not be used

The base and perpendicular height of a triangle measured to the nearest centimeter

are 6 cm and 4 cm respectively.

 

Find

(a) The absolute error in calculating the area of the triangle

(b) The percentage error in the area, giving the answer to 1 decimal place

  1. By correcting each number to one significant figure, approximate the value of 788 x 0.006. Hence calculate the percentage error arising from this approximation.
  2. A rectangular block has a square base whose side is exactly 8 cm. Its height measured to the nearest millimeter is 3.1 cm

Find in cubic centimeters, the greatest possible error in calculating its volume.

  1. Find the limits within the area of a parallegram whose base is 8cm and height is 5 cm lies. Hence find the relative error in the area
  2. Find the minimum possible perimeter of a regular pentagon whose side is 15.0cm.
  3. Given the number 0.237

(i)         Round off to two significant figures and find the round off error

(ii)        Truncate to two significant figures and find the truncation error

  1. The measurements a = 6.3, b= 15.8, c= 14.2 and d= 0.00173 have maximum possible errors of 1%, 2%, 3% and 4% respectively. Find the maximum possible percentage error in ad/bc correct to 1sf.

 

                 TRIGONOMETRY

   CHAPTER FOURTY THREE

 

 

Specific Objectives

By the end of the topic the learner should be able to:

(a) Define and draw the unit circle;

(b) Use the unit circle to find trigonometric ratios in terms of co-ordinates of points for 0 < 9 < 360°;

(c) Find trigonometric ratios of negative angles;

(d) Find trigonometric ratios of angles greater than 360° using the unit circle;

(e) Use mathematical tables and calculators to find trigonometric ratios of angles in the range 0 < 9 < 360°;

(f) Define radian measure;

(g) Draw graphs of trigonometric functions; y = sin x, y = cos x and y ~ tan x using degrees and radians;

(h) Derive the sine rule;

(i) Derive the cosine rule;

(j) Apply the sine and cosine rule to solve triangles (sides, angles and area),

(k) Apply the knowledge of sine and cosine rules in real life situations.

 

 

 

 

 

 

 

Content

(a) The unit circles

(b) Trigonometric rations from the unit circle

(c) Trigonometric ratios of angles greater than 360° and negative angles

(d) Use of trigonometric tables and calculations

(e) Radian measure

(f) Simple trigonometric graphs

(g) Derivation of sine and cosine rule

(h) Solution of triangles

(i) Application of sine and cosine rule to real situation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The unit circle

It is circle of unit radius and centre O (0, 0).

An angle measured anticlockwise from positive direction of x – axis is positive. While an angle measured clockwise from negative direction of x – axis  is negative.

 

 

 

 

In general, on a unit circle

 

 

 

Trigonometric ratios of negative angles

In general

 

Use of calculators

Example

Use a calculator to find

  1. Tan

Solution

  • Key in tan
  • Key in 30
  • Screen displays 0.5773502
  • Therefore tan = 0.5774

To find the inverse of sine cosine and tangent

  • Key in shift
  • Then either sine cosine or tangent
  • Key in the number

Note;

Always consult the manual for your calculator. Because calculators work differently

Radians

One radian is the measure of an angle subtended at the centre by an arc equal in length to the radius of the circle.

Because the circumference of a circle is 2πr, there are 2π radians in a full circle. Degree measure and radian measure are therefore related by the equation 360° = 2π radians, or 180° = π radians.

The diagram shows equivalent radian and degree measures for special angles from 0° to 360° (0 radians to 2π radians).You may find it helpful to memorize the equivalent degree and radian measures of special angles in the first quadrant. All other special angles are just multiples of these angles.

 

Example

Convert into radians

Solution

If  = 57.29

Therefore =  = 2.182 to 4 S.F

Example

Convert the following degrees to radians, giving your answer in terms

Solution

Therefore

 

Example

What is the length of the arc that that subtends an angle of 0.6 radians at the centre of a circle of radius 20 cm.

Solution

 

 

 

 

 

 

 

Simple trigonometric graphs

Graphs of y=sin x

The graphs can be drawn by choosing a suitable value of x and plotting the values of y against theCorresponding values of x.

 

 

 

 

 

 

 

 

 

 

The black portion of the graph represents one period of the function and is called one cycle of the sine curve.

Example

 

Sketch the graph of y = 2 sin x on the interval [– , 4 ].

 

Solution:

Note that y = 2 sin x = 2(sin x) indicates that the y-values for the key points will have twice the magnitude of those on the graph of y = sin x.

 

x 3 2
Y=2sin x 2 0 -2 0

To get the values of y substitute the values of x in the equation y =2sin x as follows

                     y=2 sin (360) because 2  is equal to 36

 

 

Note;

  • You can change the radians into degrees to make work simpler.
  •  By connecting these key points with a smooth curve and extending the curve in both directions over the interval       [– , 4 ], you obtain the graph shown in below.

 

 

 

Example

 

Sketch the graph of y = cos x for using an  interval of

 

Solution:

The values of  x and the corresponding values of y are given in the table below

 

 

x
 Y=cos x 1 0.8660 0.5 0 -0.5 -0.8660 -1 -0.8660 -0.5

 

x
Y=cosx 0 0.5 0.8660 1

 

 

 

Graph of tangents

Note;

  • As the value of  x approaches  and 27  tan x becames very large
  • Hence the graph of y =tan x approaches the lines x =  without touching them.
  • Such lines are called asymptotes

 

Solution of triangles

Sin rule

If a circle of radius R is circumscribed around the  triangle ABC ,then  =2R.

The  sine rule applies to both acute and obtuse –angled triangle.

 

 

 

Example

Solve triangle ABC, given that CAB =42. , c= 14.6 cm and a =11.4 cm

Solution

To solve a triangle means to find the sides and angles not given

 

Sin c =  = 0.8720

Therefore c =60.6

Note;

The sin rule is used when we know

  • Two sides and a non-included angle of a triangle
  • All sides and at least one angle
  • All angles and at least one side.

 

 

 

 

 

 

 

 

Cosine rule

 

 

 

Example

Find AC in the figure below, if AB= 4 cm , BC = 6 cm and ABC =7

 

Solution

Using the cosine rule

= 16 + 36 – 48

= 52 – 9.979

= 42.02 cm

Note;

The cosine rule is used when we know

  • Two sides and an included angle
  • All three sides of a triangle

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

 

Past KCSE Questions on the topic.

 

  1. Solve the equation

Sin 5 θ = –1 for 00 ≤ 0 ≤ 1800

2         2

  1. Given that sin θ = 2/3 and is an acute angle find:
    • Tan θ giving your answer in surd form
    • Sec2 θ
  1. Solve the 1

equation 2 sin2(x-300) = cos 600 for – 1800 ≤ x ≤ 1800

  1. Given that sin (x + 30)0 = cos 2x0for 00, 00 ≤ x ≤900 find the value of x. Hence find the value of cos 23x0.
  2. Given that sin a =1 where a is an acute angle find, without using

√5

Mathematical tables

(a) Cos a in the form of a√b, where a and b are rational numbers

(b) Tan (900 – a).

  1. Give that xo is an angle in the first quadrant such that 8 sin2 x + 2 cos x -5=0

Find:

  1. a) Cos x
  2. b) tan x
  3. Given that Cos 2x0 = 0.8070, find x when 00 ≤ x ≤ 3600

8          The figure below shows a quadrilateral ABCD in which AB = 8 cm, DC = 12 cm, < BAD = 450, < CBD = 900 and BCD = 300.

 

 

 

 

 

 

 

 

 

 

 

Find:

(a)        The length of BD

(b)        The size of the angle ADB

 

 

 

 

 

 

 

  1. The diagram below represents a school gate with double shutters. The shutters are such opened through an angle of 630.

The edges of the gate, PQ and RS are each 1.8 m

 

 

 

 

 

 

 

Calculate the shortest distance QS, correct to 4 significant figures

10…The figure below represents a quadrilateral piece of land ABCD divided into three triangular plots. The lengths BE and CD are 100m and 80m respectively. Angle ABE = 300ÐACE = 450 and Ð ACD = 1000

 

 

 

 

 

 

 

(a)  Find to four significant figures:

(i)         The length of AE

(ii)        The length of AD

(iii)       The perimeter of the piece of land

 

(b) The plots are to be fenced with five strands of barbed wire leaving an entrance of 2.8 m wide to each plot. The type of barbed wire to be used is sold in rolls of lengths 480m. Calculate the number of rolls of barbed wire that must be bought to complete the fencing of the plots.

  1. Given that x is an acute angle and cos x = 2Ö 5, find without using mathematical

5

tables or a calculator, tan ( 90 – x)0.

  1. In the figure below ÐA = 620, ÐB = 410, BC = 8.4 cm and CN is the bisector of ÐACB.

 

 

 

 

 

 

 

 

 

Calculate the length of CN to 1 decimal place.

  1. In the diagram below PA represents an electricity post of height 9.6 m. BB and RC represents two storey buildings of heights 15.4 m and 33.4 m respectively. The angle of depression of A from B is 5.50 While the angle of elevation of C from B is 30.50 and BC = 35m.

 

 

 

 

 

 

 

 

(a)        Calculate, to the nearest metre, the distance AB

(b)        By scale drawing find,

(i)         The distance AC in metres

(ii)        Ð BCA and hence determine the angle of depression of A from C

More questions

 

  1. Solve the equation:        (2 mks)

for

  1. (a) Complete the table below, leaving all your values correct to 2 d.p. for the functions y = cos x and y = 2cos (x + 30)0        (2 mks)
X0 00 600 1200 1800 2400 3000 3600 4200 4800 5400
cosX 1.00 -1.00 0.50
2cos(x+30) 1.73 -1.73 0.00

(b) For the function y = 2cos(x+30)0

State:

  • The period (1 mk)
  • Phase angle (1 mk)

(c) On the same axes draw the waves of the functions y = cos x and y = 2cos(x+30)0 for . Use the scale 1cm rep 300 horizontally and 2 cm rep 1 unit vertically                                                                                          (4 mks)

(d) Use your graph above to solve the inequality (2 mks)

  1. Find the value of x in the equation.

Cos(3x – 180o) =   √3              in the range Oo < x < 180o (3 marks)

2

  1. Given that and ө is an acute angle, find without using tables cos (90 –ө)                                                                                                                                                    (2mks)
  2. Solve for ө if -¼ sin (2x + 30) = 0.1607, 0 ≤ө≥ 3600 (3mks)
  3. Given that Cos q = 5/13 and that 2700£q£ 3600 , work out the value of Tan q + Sin q without using a calculator or mathematical tables.                                                         (3 marks)
  4. Solve for x in the range 00£ x £ 1800             (4mks)

-8 sin2x – 2 cos x = -5.

  1. If tan xo = 12/5 and x is a reflex angle, find the value of 5sin x + cos x without using a

calculator or mathematical tables

  1. Find q given that 2 cos 3q -1 = 0 for 0o £q£ 360o
  2. Without a mathematical table or a calculator, simplify: Cos300o x Sin120ogiving your answer in

Cos330o – Sin 405orationalized surd form.

  1. Express in surds form and rationalize the denominator.

1

Sin 60o Sin 45o –  Sin 45o

 

  1. Simplify the following without using tables;

Tan 45 + cos 45sin 60

 

 

 

 

 

 

 

 

                      SURDS

CHAPTER FOURTY FOUR

 

Specific Objectives

By the end of the topic the learner should be able to:

(a) Define rational and irrational numbers,

(b) Simplify expressions with surds;

(c) Rationalize denominators with surds.

 

Content

(a) Rational and irrational numbers

(b) Simplification of surds

(c) Rationalization of denominators.

 

 

 

 

 

 

 

 

 

 

 

 

 

Rational and irrational numbers

 

Rational numbers

A rational number is a number which can be written in the form   , where p and q are integers and q .The integer’s p and q must not have common factors other than 1.

Numbers such as 2, are examples of rational numbers .Recurring numbers are also rational numbers.

Irrational numbers

Numbers that cannot be written in the form   .Numbers such as   are irrational numbers.

Surds

Numbers which have got no exact square roots or cube root are called surds e.g.  , ,

The product of a surd and a rational number is called a mixed surd. Examples are ;

,   and

Order of surds

,

,

Simplification of surds

A surd can be reduced to its lowest term possible, as follows ;

Example

Simplify

Solution

 

 

Operation of surds

Surds can be added or subtracted only if they are like surds (that is, if they have the same value under the root sign).

Example 1

Simplify the following.

  1. 3 √2 + 5√2
  2. 8 √5 − 2√5

 

Solution

 

  1. 3 √2 + 5√2 = 8 √2
  2. 8 √5 − 2√5 = 6√5

Summary

Let a =

Therefore  = a + a

=2 a

But   a =

Hence   =

 

Multiplication and Division of surds

Surds of the same order can be multiplied or divided irrespective of the number under the root sign.

 

 

Law 1: √a x √b = √ab   When multiplying surds together, multiply their values together.

 

e.g.1                 √3 x √12 = √ (3 x 12) = √36  =  6

 

e.g.2                 √7 x  √5   =  √35

 

This law can be used in reverse to simplify expressions…

 

e.g.3                 √12  =  √2 x √6   or  √4 x √3 = 2√3

 

 

 

   Law 2:√a ÷ √b   or   =  √(a/b)                When dividing surds, divide their values (and vice versa).

 

e.g.1                 √12   =   √(12 ÷ 3)  =  √4  =  2

√3

 

 

e.g.2

 

 

 

Law 3: √ (a2) or (√a) 2   = a       When squaring a square-root, (or vice versa), the symbols cancel

 

Each other out, leaving just the base.

 

e.g.1                 √122  =  12

 

e.g.2                 √7 x √7 = √72 = 7

 

Note:

If you add the same surds together you just have that number of surds. E.g.

√2 + √2 + √2= 3√2

If a surd has a square number as a factor you can use law 1 and/or law 2 and work backwards to take that out and simplify the surd.  E.g.  √500   = √100 x √5 = 10√5

 

Rationalization of surds

Surds may also appear in fractions.  Rationalizing the denominator of such a fraction means finding an equivalent fraction that does NOT have a surd on the bottom of the fraction (though it CAN have a surd on the top!).

If the surd contains a square root by itself or a multiple of a square root, to get rid of it, you must multiply BOTH the top and bottom of the fraction by that square root value.

 

e.g.                   6                     x √7                 =          6√7

√7                    x √7                             7

 

e.g.2                 6 + √2  x √3                 =          6√3 + √2 x √3   =          6√3 + √6

2√3                 x √3                               2 x √3 x √3                 6

i.e. 2  x         3

 

If the surd on the bottom involves addition or subtraction with a square root, to get rid of the square root part you must use the ‘difference of two squares’ and multiply BOTH the top and bottom of the fraction by the bottom surd’s expression but with the inverse operation.

 

e.g.3                     7                  x (2 – √2)          =          14 – 7√2            =          14 – 7√2

2 + √2  x (2 – √2)                      22 – (√2)2                      2

i.e. 4   –     2

 

Notes on the ‘Difference of two squares’…

 

Squaring…       (2 + √2)(2 + √2)            = 2(2 + √2) + √2(2 + √2)

(ops the same)                                      =  4  + 2√2  + 2√2 + √2√2

=  4      +      4√2      +    2                     = 6 + √2  (still a surd)

 

Multiplying…    (2 + √2)(2 – √2)           = 2(2 – √2) + √2(2 – √2)

(opposite ops)                                                   =   4  – 2√2 + 2√2 – √2√2

=   4     (cancel out)  –    2   =  2   (not a surd)

 

In essence, as long as the operation in each brackets is the opposite, the middle terms will always cancel each other out and you will be left with the first term squared subtracting the second term squared.

i.e.       (5 + √7)(5 – √7)  à  52 – (√7)2  =  25 – 7 = 18

 

 

 

Example

Simplify by rationalizing the denominator

Solution

Note

If the product of the two surds gives a rational number then the product of the two surds gives conjugate surds.

 

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

 

Past KCSE Questions on the topic.

  1. Without using logarithm tables, find the value of x in the equation

Log x3 + log 5x = 5 log2 – log 2                                                                                                                                5

  1. Simplify (1 ÷ √3) (1 – √3)

Hence evaluate           1          to 3 s.f. given that √3 = 1.7321

1 + √3

  1. If √14      –      √ 14        =  a√7 + b√2

√7-√2         √ 7 + √ 2

Find the values of a and b where a and b are rational numbers.

  1. Find the value of x in the following equation 49(x+1) + 7(2x) = 350
  2. Find x if 3 log 5 + log x2 = log 1/125
  3. Simplify as far as possible leaving your answer inform of a surd

 

            1            –                    1          

√14   – 2 √3                   √14 + 2 √3

  1. Given that tan 750 = 2 + √3, find without using tables tan 150 in the form p+q√m, where p, q and m are integers.
  2. Without using mathematical tables, simplify

 

 

63        +          72

32        +          28

  1. Simplify  +   1   leaving the answer in the form a + b Öc, where a, b and c  Ö5 -2    Ö5      are rational numbers

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

      FURTHER LOGARITHMS

CHAPTER FOURTY FIVE

 

Specific Objectives

By the end of the topic the learner should be able to:

 

(a) Derive logarithmic relation from index form and vice versa;

(b) State the laws of logarithms;

(c) Use logarithmic laws to simplify logarithmic expressions and solvelogarithmic equations;

(d) Apply laws of logarithms for further computations.

Content

(a) Logarithmic notation (eg. an=b, log ab=n)

(b) The laws of logarithms: log (AB) = log A + log B, log(A^B) = log A -log B and Log A n = n x log A.

(c) Simplifications of logarithmic expressions

(d) Solution of logarithmic equations

(e) Further computation using logarithmic laws.

 

 

 

 

 

 

 

 

 

If then we introduce the inverse function logarithm and define

(Read as log base  of equals ).

 

        In general

 

Where Û means “implies and is implied by” i.e. it works both ways!

 

Note this means that, going from exponent form to logarithmic form:

Þ Þ
Þ Þ
Þ Þ

 

And in going from logarithmic form to exponent form:

Þ Þ
Þ Þ
Þ Þ

 

Laws of logarithms

Product and Quotient Laws of Logarithms:

 

The Product Law

The Quotient Law

 

 

Example.

 

 

 

= 2                                                      

 

                   

The Power Law of Logarithms:

 

 

Example.

2log 5 + 2log 2

 

 

 

= 2                              

 

Logarithm of a Root

 

or

 

 

 

Example.

PROOF OF PROPERTIES

Property Proof Reason for Step
1.     logb b = 1 and logb 1 = 0 b1 = b   and b0 = 1  Definition of logarithms
2.(product rule)

logb xy = logb x + logb y

 

a.  Let  logb x = m and logb y = n

b.  x = bm  and y = b n

c.  xy = bm * bn

d.  xy = b m + n

e.  logb xy = m + n

f  logb xy = logb x + logb y  

 

a.  Setup

b.  Rewrite in exponent form

c.  Multiply together

d.  Product rule for exponents

e.  Rewrite in log form

f.  Substitution

3.     (quotient rule)

logb  = logb x – logb y

a.  Let  logb x = m and logb y = n

b.  x = bm  and y = b n

c.   =

d.  =

e.  logb = m – n

f.  logb logb x – logb y 

a.  Given:  compact form

b.  Rewrite in exponent form

 

c.  Divide

 

d.  Quotient rule for exponents

 

e.  Rewrite in log form

 

f.  Substitution

4.     (power rule)

logb xn = n logb x

 

 

a.  Let  m = logb x  so x = bm

b.  xn = bmn

c.  logb x n = mn

d.  logb xn = n logb x

a.  Setup

b.  Raise both sides to the nth power

c.  Rewrite as log

d.  Substitute

5.  Properties used to solve log equations:

 

a.  if bx = by, then x = y

 

 

b.  if logb x = logb y, then x = y

 

 

 

a. This follows directly from the properties for exponents.

 

b.  i.  logb x – logb y = 0

ii. logb

iii. =b0

   iv.  1 so x = y

 

 

 

 

 

 

 

b.  i.  Subtract from both sides

 

ii. Quotient rule

 

 

iii. Rewrite in exponent form

 

 

   iv.  b0 = 1

 

 

 

Solving exponential and logarithmic equations

By taking logarithms, and exponential equation can be converted to a linear equation and solved.  We will use the process of taking logarithms of both sides.

 

Example.

  1. a)

 

 

x = 1.792         

Note;

A logarithmic expression is defined only for positive values of the argument. When we solve a logarithmic equation it is essential to verify that the solution(s) does not result in the logarithm of a negative number.  Solutions that would result in the logarithm of a negative number are called extraneous, and are not valid solutions.

 

Example.

Solve for x:

(the one becomes an exponent : )

 

 

 

 

 

Verify:

not possible

Solving equations using logs

 

Examples

(i) Solve the equation

The definition of logs says if then  or

Hence  (to 5 decimal places)

Check (to 5 decimal places)

In practice from  we take logs to base 10 giving

 

(ii) Solve the equation

 

 

Check , , we want  so the value of  lies between 3 and 4 or  which means  lies between 1.5 and 2. This tells us that  is roughly correct.

(iii) Solve the equation

 

Check   very close!

Note you could combine terms, giving,

 

 

 

(iv) Solve the equation

 

 

Take logs of both sides

Expand brackets

Collect terms

Factorise the left hand side

 

divide

(Note you get the same answer by using the ln button on your calculator.)

 

Check and

 

Notice that you could combine the log-terms in

to give

It does not really simplify things here but, in some cases, it can.

(v) Solve the equation

 

 

Take logs of both sides

Expand brackets

Collect terms

 

Factorize left hand side

 

simplify

 

 

divide

 

Check

LHS =                       (taking )

RHS =           (taking )

The values of LHS and RHS are roughly the same.  A more exact check could be made using a calculator.

 

 

 

 

 

 

 

 

Logarithmic equations and expressions

Consider the following equations

The value of x in each case is established as follows

Therefore

 

X =4

Example

Solve

Solution

Let  = t. then = 2

Introducing logarithm to base 10 on both sides

 

Therefore

 

 

 

Example

Taking logs on both sides cannot help in getting the value of x, since  cannot be combined into a single expression. However if we let  then the equation becomes quadratic in y.

Solution

Thus, let …………….. (1)

Therefore

Substituting for y in equation (1);

Let    or let

There is no real value of x for which    hence

Example

Solve for x in

Solution

Let

Therefore

solve the quadratic equation using any method

 

Substituting for t in the equation (1).

= x

Note;

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

 

Past KCSE Questions on the topic.

 

  1. Solve for ( – ½  = 3/2
  2. Find the values of x which satisfy the equation 52x – 6 (5x) + 5 =0

 

  1. Solve the equation

Log (x + 24) – 2 log 3 = log (9-2x)

  1. Find the value of x in the following equation 49(x+1) + 7(2x) = 350
  2. Find x if 3 log 5 + log x2 = log 1/125
  3. Without using logarithm tables, find the value of x in the equation

Log x3 + log 5x = 5 log2 – log 2                                                                                                                                               5

  1. Given that P = 3y express the questions 32y -1) + 2 x 3(y-1) = 1 in terms of P
  2. Hence or otherwise find the value of y in the equation: 3(2y-1) + 2 x 3(y-1)=1

 

 

 

COMMERCIAL ARITHMETIC II

CHAPTER FOURTY SIX

 

Specific Objectives

By the end of the topic the learner should be able to:

(a) Define principal, rate and time in relation to interest;

(b) Calculate simple interest using simple interest formula;

(c) Calculate compound interest using step by step method;

(d) Derive the compound interest formula;

(e) Apply the compound interest formula for calculating interest;

(f) Define appreciation and depreciation;

(g) Use compound interest formula to calculate appreciation and depreciation;

(h) Calculate hire purchase;

(i) Calculate income tax given the income tax bands.

Content

(a) Principal rate and time

(b) Simple interest

(c) Compound interest using step by step method

(d) Derivation of compound interest formula

(e) Calculations using the compound interest formula

(f) Appreciation and depreciation

(g) Calculation of appreciation and depreciation using the compound interestformula

(h) Hire purchase

(i) Income tax.

 

 

 

Simple interest

Interest is the money charged for the use of borrowed money for a specific period of time. If money is borrowed or deposited it earns interest, Principle is the sum of money borrowed or deposited P, Rate is the ratio of interest earned in a given period of time to the principle.

The rate is expressed as a percentage of the principal per annum (P.A).When interest is calculated using only the initial principal at a given rate and time, it is called simple interest (I).

Simple interest formulae

Simple interest =

 

Example

Franny invests ksh 16,000 in a savings account. She earns a simple interest rate of 14%, paid annually on her investment. She intends to hold the investment for 1  years. Determine the future value of the investment at maturity.

 

Solution

I =

= sh. 16000 x

= sh 3360

Amount = P + I

= sh.16000 + sh 3360

= sh.19360

Example

Calculate the rate of interest if sh 4500 earns sh 500 after 1  years.

 

 

 

 

Solution

From the simple interest formulae

I =

 

R=

 

P = sh 4500

I = sh 500

T = 1  years

Therefore R =

R 7.4 %

Example

Esha invested a certain amount of money in a bank which paid 12% p.a. simple interest. After 5 years, his total savings were sh 5600.Determine the amount of money he invested initially.

Solution

Let the amount invested be sh P

T = 5 years

R = 12 % p.a.

A =sh 5600

But A = P + I

Therefore 5600 = P + P X

= P + 0.60 P

= 1.6 P

Therefore p =

= sh 3500

 

 

 

Compound interest

Suppose you deposit money into a financial institution, it earns interest in a specified period of time. Instead of the interest being paid to the owner it may be added to (compounded with) the principle and therefore also earns interest. The interest earned is called compound interest. The period after which its compounded to the principle is called interest period.

The compound interest maybe calculated annually, semi-annually, quarterly, monthly etc. If the rate of compound interest is R% p.a and the interest is calculated n times per year, then the rate of interest per period is

Example

Moyo lent ksh.2000 at interest of 5% per annum for 2 years. First we know that simple interest for 1st year and 2nd year will be same

i.e. = 2000 x 5 x 1/100 = Ksh. 100

Total simple interest for 2 years will be = 100 + 100 = ksh. 200

In Compound Interest (C I) the first year Interest will be same as of Simple Interest (SI) i.e. Ksh.100. But year II interest is calculated on P + SI of 1st year i.e. on ksh. 2000 + ksh. 100 = ksh. 2100.

So, year II  interest in Compound Interest  becomes

= 2100 x 5 x 1/100 = Ksh. 105

So it is Ksh. 5 more than the simple interest. This increase is due to the fact that SI is added to the principal and this ksh. 105 is also added in the principal if we have to find the compound interest after 3 years. Direct formula in case of compound interest is

A = P (1 + )t

Where A = Amount

P = Principal

R = Rate % per annum

T = Time

A = P + CI

P (1 + ) t = P + CI

 

Types of Question:

Type I: To find CI and Amount

Type II: To find rate, principal or time

Type III: When difference between CI and SI is given.

Type IV: When interest is calculated half yearly or quarterly etc.

Type V: When both rate and principal have to be found.

Type 1

Example

Find the amount of ksh. 1000 in 2 years at 10% per annum compound interest.

Solution.

A = P (1 + r/100)t

=1000 (1 + 10/100)2

= 1000 x 121/100

=ksh. 1210

Example

Find the amount of ksh. 6250 in 2 years at 4% per annum compound interest.

Solution.

A = P (1 + r/100) t

= 6250 (1 + 4/100)2

=6250 x 676/625

= ksh. 6760

Example

What will be the compound interest on ksh 31250 at a rate of 4% per annum for 2 years?

 

 

Solution.

CI = P (1 + r/100) t – 1

=31250 { (1 + 4/100)2 – 1}

=31250 (676/625 – 1)

=31250 x 51/625  = ksh. 2550

Example

A sum amounts to ksh. 24200 in 2 years at 10% per annum compound interest.

Find the sum ?

Solution.

A = P (1 + r/100)t

24200 = P (1 + 10/100)2

= P (11/10)2

= 24200 x 100/121

= ksh. 20000

 

Type II

Example.

The time in which ksh. 15625 will amount to ksh. 17576 at 45 compound interest is?

Solution

A = P (1 + r/100)t

17576 = 15625 (1 + 4/100)t

17576/15625 = (26/25)t

(26/25)t = (26/25)3

t = 3 years

 

 

Example

The rate percent if compound interest of ksh. 15625 for 3 years is Ksh. 1951.

Solution.

A = P + CI

= 15625 + 1951 = ksh. 17576

A = P (1 + r/100)t

17576 = 15625 (1 + r/100)3

17576/15625 = (1 + r/100)3

(26/25)3 = (1 + r/100)3

26/25 = 1 + r/100

26/25 – 1 = r/100

1/25 = r/100

r = 4%

 

Type IV

  1. Remember

When interest is compounded half yearly then Amount = P (1 + R/2)2t

———–

100

I.e. in half yearly compound interest rate is halved and time is doubled.

  1. When interest is compounded quarterly then rate is made ¼ and time is made 4 times.

Then A = P [(1+R/4)/100]4t

  1. When rate of interest is R1%, R2%, and R3% for 1st, 2nd and 3rd year respectively; then A = P (1 + R1/100) (1 + R2/100) (1 + r3/100)

 

 

 

Example

Find the compound interest on ksh.5000 at 205 per annum for 1.5 year compound half yearly.

Solution.

When interest is compounded half yearly

Then Amount = P [(1 +R/2)/100]2t

Amount = 5000 [(1 + 20/2)/100]3/2

= 5000 (1 + 10/100)3

=5000 x 1331/1000

= ksh 6655

CI = 6655 – 5000 = ksh. 1655

e.g.

Find compound interest ksh. 47145 at 12% per annum for 6 months, compounded quarterly.

Solution.

As interest is compounded quarterly

A =[ P(1 + R/4)/100)]4t

A = 47145 [(1 + 12/4)/100] ½ x 4

= 47145 (1 + 3/100)2

= 47145 x 103/100 x 103/100

= ksh. 50016.13

CI = 50016.13 – 47145

= ksh. 2871.13

Example

Find the compound interest on ksh. 18750 for 2 years when the rate of interest for 1st year is 45 and for 2nd year 8%.

 

 

Solution.

A = P (1 + R1/100) (1 + R1/100)

= 18750 * 104/100 * 108/100

=ksh. 21060

CI = 21060 – 18750

= ksh. 2310

Type V

Example

The compound interest on a certain sum for two years is ksh. 52 and simple interest for the same period at same rate is ksh.50 find the sum and the rate.

Solution.

We will do this question by basic concept. Simple interest is same every year and there is no difference between SI and CI for 1st year. The difference arises in the 2nd year because interest of 1st year is added in principal and interest is now charged on principal + simple interest of 1st year.

So in this question

2 year SI = ksh. 50

1 year SI = ksh. 25

Now CI for 1st year = 52 – 25 = Rs.27

This additional interest 27 -25 = ksh. 2 is due to the fact that 1st year SI i.e. ksh. 25 is added in principal. It means that additional ksh. 2 interest is charged on ksh. 25. Rate % = 2/25 x 100 = 8%

Shortcut:

Rate % = [(CI – SI)/ (SI/2)] x 100

= [(2/50)/2] x 100

2/25 x 100

=8%

P = SI x 100/R x T = 50 x 100/8 x 2

= ksh. 312.50

Example

A sum  of money lent CI amounts in 2 year to ksh. 8820 and in 3 years to ksh. 9261. Find the sum and rate %.

Solution.

Amount after 3 years = ksh. 9261

Amount after 2 years = ksh. 8820

By subtracting last year’s interest ksh. 441

It is clear that this ksh. 441 is SI on ksh. 8820 from 2nd to 3rd year i.e. for 1 year.

Rate % = 441 x 100/8820 x 1

=5 %

Also A = P (1 + r/100)t

8820 = P (1 + 5/100)2

= P (21/20)2

P = 8820 x 400/441

= ksh. 8000

 

 

Appreciation and Depreciation

Appreciation is the gain of value of an asset while depreciation is the loss of value of an asset.

Example

An iron box cost ksh 500 and every year it depreciates by 10% of its value at the beginning of that that year. What will its value be after value 4 years?

 

 

 

Solution

Value after the first year = sh (500 –  x 500)

= sh 450

Value after the second year = sh (450 –  x 450)

= sh 405

Value after the third year = sh (405 –  x 405)

= sh 364.50

Value after the fourth year = sh (364.50 –  x 364.50)

= sh 328.05

In general if P is the initial value of an asset, A the value after depreciation for n periods and r the rate of depreciation per period.

A=P (

Example

A minibus cost sh 400000.Due to wear and tear, it depreciates in value by 2 % every month. Find its value after one year,

Solution

A=P (

Substituting P= 400,000 , r = 2 , and n =12 in the formula ;

A =sh.400000 (1- 0.02

=sh.400, 000(0.98

= sh.313700

Example

The initial cost of a ranch is sh.5000, 000.At the end of each year, the land value increases by 2%.What will be the value of the ranch at the end of 3 years?

Solution

The value of the ranch after 3 years =sh 5000, 000(1 +

= sh. 5000000(

= sh 5,306,040

Hire Purchase

Method of buying goods and services by instalments. The interest charged for buying goods or services on credit is called carrying charge.

Hire purchase = Deposit + (instalments x time)

Example

Aching wants to buy a sewing machine on hire purchase. It has a cash price of ksh 7500.She can pay a cash price or make a down payment of sh 2250 and 15 monthly instalments of sh.550 each. How much interest does she pay under the instalment plan?

 

Solution

Total amount of instalments = sh 550 x 15

= sh 8250

Down payment (deposit)    = sh 2250

Total payment                      = sh (8250 + 2250)

= sh 10500

Amount of interest charged = sh (10500-7500)

= sh3000

Note;

Always use the above formula to find other variables.

 

 

 

 

 

 

 

 

 

Income tax

Taxes on personal income is income tax. Gross income is the total amount of money due to the individual at the end of the month or the year.

Gross income = salary + allowances / benefits

Taxable income is the amount on which tax is levied. This is the gross income less any special benefits on which taxes are not levied. Such benefits include refunds for expenses incurred while one is on official duty.

In order to calculate the income tax that one has to pay, we convert the taxable income into Kenya pounds K£ per annum or per month as dictated by the by the table of rates given.

Relief

  • Every employee in kenya is entitled to an automatic personal tax relief of sh.12672 p.a (sh.1056 per month)
  • An employee with a life insurance policy on his life, that of his wife or child, may make a tax claim on the premiums paid towards the policy at sh.3 per pound subject to a maximum claim of sh .3000 per month.

Example

Mr. John earns a total of  K£12300 p.a.Calculate how much tax he should pay per annum.Using the tax table below.

Income tax K£ per annum Rate (sh per pound)
1 -5808 2
5809 – 11280 3
11289 – 16752 4
16753 – 22224 5
Excess over 22224 6

 

Solution

His salary lies between £ 1 and £12300.The highest tax band is therefore the third band.

For the first £ 5808, tax due is sh 5808 x 2 = sh 11616

For the next £ 5472, tax due is sh 5472 x 2 = sh 16416

Remaining £ 1020, tax due sh. 1020 x 4     = sh 4080 +

Total tax due                                                   sh 32112

 

Less personal relief of sh.1056 x 12          =   sh.12672

Sh 19440

Therefore payable p.a is sh.19400.

Example

Mr. Ogembo earns a basic salary of sh 15000 per month.in addition he gets a medical allowance of sh 2400 and a house allowance of sh 12000.Use the tax table above to calculate the tax he pays per year.

Solution

Taxable income per month = sh (15000 + 2400 + 12000)

= sh.29400

Converting to K£ p.a = K£ 29400 x

= K£ 17640

Tax due

First £ 5808 = sh.5808 x 2 = sh.11616

Next £ 5472 = sh.5472 x 3 = sh.16416

Next £ 5472 = sh.5472 x 4 = sh.21888

Remaining £ 888 = sh.888 x 5 = sh 4440 +

Total tax due                                        sh 54360

Less personal relief                             sh 12672

Therefore, tax payable p.a          sh41688

 

 

PAYE

In Kenya, every employer is required by the law to deduct income tax from the monthly earnings of his employees every month and to remit the money to the income tax department. This system is called Pay As You Earn (PAYE).

 

 

Housing

If an employee is provided with a house by the employer (either freely or for a nominal rent) then 15% of his salary is added to his salary (less rent paid) for purpose of tax calculation. If the tax payer is a director and is provided with a free house, then 15% of his salary is added to his salary before taxation.

Example

Mr. Omondi who is a civil servant lives in government house who pays a rent of sh 500 per month. If his salary is £9000 p.a, calculate how much PAYE he remits monthly.

Solution

Basic salary                                                            £ 9000

Housing £

Less rent paid               =    £ 300

£ 1050 +

Taxable income                                                   £ 10050

 

Tax charged;

First £ 5808, the tax due is sh.5808 x 2   =         sh 11616

Remaining £ 4242, the tax due is sh 4242 x 3 = sh 12726 +

Sh 24342

Less personal relief                                              Sh 12672

Sh 11670

PAYE = sh

 

= sh 972.50

Example

Mr. Odhiambo is a senior teacher on a monthly basic salary of Ksh. 16000.On top of his salary he gets a house allowance of sh 12000, a medical allowance of Ksh.3060 and a hardship allowance of Ksh 3060 and a hardship allowance of Ksh.4635.He has a life insurance policy for which he pays Ksh.800 per month and claims insurance relief.

  1. Use the tax table below to calculate his PAYE.
Income in £ per month Rate  %
1 – 484 10
485 – 940 15
941 – 1396 20
1397 – 1852 25
Excess over 1852 30

 

  1. In addition to PAYEE the following deductions are made on his pay every month
  2. WCPS at 2% of basic salary
  3. HHIF ksh.400
  4. Co – operative shares and loan recovery Ksh 4800.

Solution

  1. Taxable income = Ksh (16000 + 12000 +3060 +4635)

= ksh 35695

Converting to K£          =

= K

Tax charged is:

First £ 484 = £484 x  = £ 48.40

Next £ 456 = £456 x  = £ 68.40

Next £ 456 = £456 x  = £ 91.20

Remaining £ 388 = £388 x  = £ 97.00.

Total tax due = £305.00

= sh 6100

Insurance relief = sh  = sh 120

Personal relief                       = sh 1056 +

Total relief                            sh 1176

 

Tax payable per month is sh 6100

Sh 1176 –

Sh   4924

Therefore, PAYE is sh 4924.

Note;

For the calculation of PAYE, taxable income is rounded down or truncated to the nearest whole number.

If an employee’s due tax is less than the relief allocated, then that employee is exempted from PAYEE

  1. Total deductions are

Sh (

Net pay = sh (35695 – 11244)

= sh 24451

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

Past KCSE Questions on the topic.

 

  1. A business woman opened an account by depositing Kshs. 12,000 in a bank on 1st July 1995. Each subsequent year, she deposited the same amount on 1st July. The bank offered her 9% per annum compound interest. Calculate the total amount in her account on

(a)        30th June 1996

(b)        30th June 1997

  1. A construction company requires to transport 144 tonnes of stones to sites A and
  2. The company pays Kshs 24,000 to transport 48 tonnes of stone for every 28
  3. Kimani transported 96 tonnes to a site A, 49 km away.

(a)        Find how much he paid

(b)        Kimani spends Kshs 3,000 to transport every 8 tonnes of stones to site.

Calculate his total profit.

(c)        Achieng transported the remaining stones to sites B, 84 km away. If she made 44% profit, find her transport cost.

  1. The table shows income tax rates
Monthly taxable pay Rate of tax Kshs in 1 K£
1 – 435

436 – 870

871-1305

1306 – 1740

Excess Over 1740

2

3

4

5

6

 

A company employee earn a monthly basic salary of Kshs 30,000 and is also given taxable allowances amounting to Kshs 10, 480.

(a)        Calculate the total income tax

(b)        The employee is entitled to a personal tax relief of Kshs 800 per month.

Determine the net tax.

(c)        If the employee received a 50% increase in his total income, calculate the

corresponding percentage increase on the income tax.

  1. A house is to be sold either on cash basis or through a loan. The cash price is Kshs.750, 000. The loan conditions area as follows: there is to be down payment

of 10% of the cash price and the rest of the money is to be paid through a loan

at 10% per annum compound interest.

A customer decided to buy the house through a loan.

  1. a) (i)         Calculate the amount of money loaned to the customer.

(ii)        The customer paid the loan in 3 year’s. Calculate the total amount

paid for the house.

  1. b) Find how long the customer would have taken to fully pay for the house

if she paid a total of Kshs 891,750.

  1. A businessman obtained a loan of Kshs. 450,000 from a bank to buy a matatu valued at the same amount. The bank charges interest at 24% per annum compound quarterly
  2. a) Calculate the total amount of money the businessman paid to clear the loan in 1 ½ years.
  3. b) The average income realized from the matatu per day was Kshs. 1500. The matatu worked for 3 years at an average of 280 days year. Calculate the total income from the matatu.
  4. c) During the three years, the value of the matatu depreciated at the rate of 16% per annum. If the businessman sold the matatu at its new value, calculate the total profit he realized by the end of three years.
  5. A bank either pays simple interest as 5% p.a or compound interest 5% p.a on deposits. Nekesa deposited Kshs P in the bank for two years on simple interest terms. If she had deposited the same amount for two years on compound interest terms, she would have earned Kshs 210 more.

Calculate without using Mathematics Tables, the values of P

  1. (a) A certain sum of money  is deposited in  a bank that pays simple interest at

a certain rate. After 5 years the total amount of money in an account is Kshs 358 400. The interest earned each year is 12 800

Calculate

  • The amount of money which was deposited (2mks)
  • The annual rate of interest that the  bank  paid             (2mks)

(b)        A computer whose marked price is Kshs 40,000 is sold at Kshs 56,000 on hire purchase terms.

(i)         Kioko bought the computer on hire purchase term. He paid a deposit of 25% of the hire purchase price and cleared the balance by equal monthly installments of Kshs 2625. Calculate the number of installments       (3mks)

(ii)        Had Kioko bought the computer on cash terms he would have been allowed a discount of 12 ½ % on marked price. Calculate the difference between the cash price and the hire purchase price and express as a percentage of the cash price

(iii)       Calculate the difference between the cash price and hire purchase price and express it as a percentage of the cash price.

  1. The table below is a part of tax table for monthly income for the year 2004

 

Monthly taxable income

In ( Kshs)

Tax rate percentage

(%) in each shillings

Under Kshs 9681 10%
From Kshs 9681 but under 18801 15%
From Kshs 18801 but 27921 20%

In the tax year 2004, the tax of Kerubo’s monthly income was Kshs 1916.

Calculate Kerubo’s monthly income

  1. The cash price of a T.V set is Kshs 13, 800. A customer opts to buy the set on hire purchase terms by paying a deposit of Kshs 2280.

If simple interest of 20 p. a is charged on the balance and the customer is required to repay by 24 equal monthly installments. Calculate the amount of each installment.

  1. A plot of land valued at Ksh. 50,000 at the start of 1994.

Thereafter, every year, it appreciated by 10% of its previous years value find:

(a)        The value of the land at the start of 1995

(b)        The value of the land at the end of 1997

 

  1. The table below shows Kenya tax rates in a certain year.

 

Income K £ per annum Tax rates Kshs per K £
1- 4512 2
4513 – 9024 3
9025 – 13536 4
13537 – 18048 5
18049 – 22560 6
Over 22560 6.5

 

In that year Muhando earned a salary of Ksh. 16510 per month. He was entitled to a monthly tax relief of Ksh. 960

Calculate

(a)        Muhando annual salary in K £

(b)        (i)         The monthly tax paid by Muhando in Ksh

  1. A tailor intends to buy a sewing machine which costs Ksh 48,000. He borrows the money from a bank. The loan has to be repaid at the end of the second year. The bank charges an interest at the rate of 24% per annum compounded half yearly. Calculate the total amount payable to the bank.

 

  1. The average rate of depreciation in value of a water pump is 9% per annum. After three complete years its value was Ksh 150,700. Find its value at the start of the three year period.

 

  1. A water pump costs Ksh 21600 when new, at the end of the first year its value depreciates by 25%. The depreciation at the end of the second year is 20% and thereafter the rate of depreciation is 15% yearly. Calculate the exact value of the water pump at the end of the fourth year.

 

 

 

 

 

 

  CIRCLES, CHORDS AND TANGENTS

CHAPTER FOURTY SEVEN

 

 

 

Specific Objectives

By the end of the topic the learner should be able to:

(a) Calculate length of an arc and a chord;

(b) Calculate lengths of tangents and intersecting chords;

(c) State and use properties of chords and tangents;

(d) Construct tangent to a circle,

(e) Construct direct and transverse common tangents to two circles;

(f) Relate angles in alternate segment;

(g) Construct circumscribed, inscribed and escribed circles;

(h) Locate centroid and orthocentre of a triangle;

(i) Apply knowledge of circles, tangents and chords to real life situations.

Content

(a) Arcs, chords and tangents

(b) Lengths of tangents and intersecting chords

(c) Properties of chords and tangents

(d) Construction of tangents to a circle

(e) Direct and transverse common tangents to two circles

(f) Angles in alternate segment

(g) Circumscribed, inscribed and escribed circles

(h) Centroid and orthocentre

(i) Application of knowledge of tangents and chords to real life situations.

 

 

 

 

Length of an Arc

The Arc length marked red is given by ;

Example

Find the length of an arc subtended by an angle of  at the centre of the circle of radius 14 cm.

Solution

Length of an arc =

=

Example

The length of an arc of a circle is 11.0 cm.Find the radius of the circle if an arc subtended  an angle of at the centre .

Solution

Arc length =

Therefore 11 =

 

 

 

 

 

Example

Find the angle subtended at the centre of a circle by an arc of 20 cm, if the circumference of the circle is 60 cm.

Solution

=

But 2

Therefore,

Chords

Chord of a circle: A line segment which joins two points on a circle. Diameter: a chord which passes through the center of the circle. Radius: the distance from the center of the circle to the   circumference of the circle

 

Perpendicular bisector of a code

A perpendicular drawn from the centre of the circle to a chord bisects the chord.

 

 

Note;

  • Perperndicular drawn from the centre of the circle  to chord  bisects the cord ( divides it into two equal parts)
  • A straight line joining the centre of a circle to the midpoint of a chord is perpendicular to the chord.

 

 

 

 

 

 

The radius of a circle centre O is 13 cm.Find the perpendicular distance from O to the chord, if AB is 24 cm.

 

Solution

OC bisects chord AB at C

Therefore, AC =12 cm

In O

Therefore

, OM =  = 5 cm

 

Parallel chords

Any chord passing through the midpoints of all parallel chords of a circle is a diameter

Example

In the figure below CD and AB are parallel chords of a circle and 2 cm apart. If CD = 8 cm and AB= 10 cm, find the radius of the circle

Solution

  • Draw the perpendicular bisector of the chords to cut them at K and L .
  • Join OD and OC
  • In triangle ODL,
  • DL = 4 cm and KC =5 cm
  • Let OK = X cm
  • Therefore (

In triangle OCK;

  • Therefore (
  • 4x = 5
  • X =

Using the equation

=

=

= 5.154 cm

 

 

 

 

 

 

 

 

 

 

 

Intersecting chords

In general

 

 

Example

In the example above AB and CD are two chords that intersect in a circle at Given that AE = 4 cm, CE =5 cm and DE = 3 cm, find AB.

 

Solution

Let EB = x cm

4

Since AB = AE + EB

AB = 4 + 3.75

= 7.75 cm

 

Equal chords.

  • Angles subtended at the centre of a circle by equal chords are equals
  • If chords are equal they are equidistant from the centre of the circle

 

 

Secant

A chord that is produced outside a circle is called a secant

 

Example

Find the value of AT in the figure below. AR = 4 cm, RD = 5 cm and TC = 9 cm.

Solution

AC x AT

(x + 9) x = (5 + 4) 4

(x + 12) (x- 3) = 0

Therefore, x = – 12 or x = 3

Tangent and secant

Tangent

A line which touches a circle at exactly one point is called a tangent line and the point where it touches the circle is called the point of contact

Secant

A line which intersects the circle in two distinct points is called a secant line (usually referred to as a secant).The figures below  A shows a secant while B shows a tangent .

A                                               B

Construction of a tangent

  • Draw a circle of any radius and centre O.
  • Join O to any point P on the circumference
  • Produce OP to a point P outside the circle
  • Construct a perpendicular line SP through point P
  • The line is a tangent to the circle at P as shown below.

Note;

  • The radius and tangent are perpendicular at the point of contact.
  • Through any point on a circle , only one tangent can be drawn
  • A perpendicular to a tangent at the point of contact passes thought the centre of the circle.

 

Example

In the figure below  PT = 15 cm  and PO = 17 cm, calculate the length of PQ.

 

Solution

OT = 8 cm

 

Properties of tangents to a circle from an external point

If two tangents are drawn to a circle from an external point

  • They are equal
  • They subtend equal angles at the centre
  • The line joining the centre of the circle to the external point bisects the angle between the tangents

 

s

 

Example

The figure below represents a circle centre O and radius 5 cm. The tangents PT is 12 cm long. Find: a.) OP      b.) Angle TP

 

 

Solution

  • Join O to P

 

 

  • <

<OTP    =

= 0.9231

Therefore, <TPO = 22.6

Hence <

Two tangent to a circle

Direct (exterior) common tangents                Transverse or interior common tangents

 

 

Tangent Problem

The common-tangent problem is named for the single tangent segment that’s tangent to two circles. Your goal is to find the length of the tangent. These problems are a bit involved, but they should cause you little difficulty if you use the straightforward three-step solution method that follows.

 

The following example involves a common external tangent (where the tangent lies on the same side of both circles). You might also see a common-tangent problem that involves a common internal tangent (where the tangent lies between the circles). No worries: The solution technique is the same for both.

Given the radius of circle  A is 4 cm and the radius of circle Z is 14 cm and the distance between the two circles is 8 cm.

Here’s how to solve it:

1.)Draw the segment connecting the centers of the two circles and draw the two radii to the points of tangency (if these segments haven’t already been drawn for you).

Draw line AZ and radii AB and ZY.

The following figure shows this step. Note that the given distance of 8 cm between the circles is the distance between the outsides of the circles along the segment that connects their centers.

 

 

 

 

2.) From the center of the smaller circle, draw a segment parallel to the common tangent till it hits the radius of the larger circle (or the extension of the radius in a common-internal-tangent problem).

 

 

You end up with a right triangle and a rectangle; one of the rectangle’s sides is the common tangent. The above figure illustrates this step.

3.)You now have a right triangle and a rectangle and can finish the problem with the Pythagorean Theorem and the simple fact that opposite sides of a rectangle are congruent.

 

The triangle’s hypotenuse is made up of the radius of circle A, the segment between the circles, and the radius of circle Z. Their lengths add up to 4 + 8 + 14 = 26. You can see that the width of the rectangle equals the radius of circle A, which is 4; because opposite sides of a rectangle are congruent, you can then tell that one of the triangle’s legs is the radius of circle Z minus 4, or 14 – 4 = 10.

You now know two sides of the triangle, and if you find the third side, that’ll give you the length of the common tangent.

You get the third side with the Pythagorean Theorem:

(Of course, if you recognize that the right triangle is in the 5 : 12 : 13 family, you can multiply 12 by 2 to get 24 instead of using the Pythagorean Theorem.)Because opposite sides of a rectangle are congruent, BY is also 24, and you’re done.

 

 

Now look back at the last figure and note where the right angles are and how the right triangle and the rectangle are situated; then make sure you heed the following tip and warning.

 

Note the location of the hypotenuse. In a common-tangent problem, the segment connecting the centers of the circles is always the hypotenuse of a right triangle. The common tangent is always the side of a rectangle, not a hypotenuse.

 

In a common-tangent problem, the segment connecting the centers of the circles is never one side of a right angle. Don’t make this common mistake.

 

HOW TO construct a common exterior tangent line to two circles

 

In this lesson you will learn how to construct a common exterior tangent line to two circles in a plane such that no one is located inside the other using a ruler and a compass.

 

 

Problem 1

For two given circles in a plane such that no one is located inside the other,  to construct the common exterior tangent line using a ruler and a compass.

 

Solution

 

We are given two circles in a plane such that no one is located inside the other  (Figure 1a).

We need to construct the common exterior tangent line to the circles using a ruler and a compass.

 

First,  let us  analyze  the problem and make a sketch  (Figures 1a  and  1b).  Let  AB  be the common tangent line to the circles we are searching for.

Let us connect the tangent point  A  of the first circle with its center  P  and the tangent point  B  of the second circle with its center  Q  (Figure 1a  and  1b).

 

Then the radii  PA  and  QB  are both perpendicular to the tangent line  AB  (lesson  A tangent line to a circle is perpendicular to the radius drawn to the tangent point  under the topic  Circles and their properties  ).  Hence, theradii PA and QB are parallel.

 

 

Figure 1a.  To the Problem 1

 

 

 

 

 

Figure 1b.  To the solution of the Problem 1

 

Figure 1c.  To the construction step 3

 

Next,  let us draw the straight line segment  CQ  parallel to  AB  through the point  Q  till the intersection with the radius  PA  at the point  C  (Figure 1b).  Then the straight line  CQ  is parallel to  AB.  Hence, the quadrilateral  CABQ  is a parallelogram  (moreover,  it is a rectangle)  and has the opposite sides  QB  and  CA  congruent.  The point  C  divides the radius  PA  in two segments of the length   (CA)  and   (PC).  It is clear from this analysis that the straight line  QC  is the tangent line to the circle of the radius   with the center at the point  P  (shown in red in  Figure 1b).

 

It implies that the procedure of constructing the common exterior tangent line to two circles should be as follows:

1)  draw the auxiliary circle of the radius    at the center of the larger circle  (shown in red in  Figure 1b);

2)  construct the tangent line to this auxiliary circle from the center of the smaller circle  (shown in red in  Figure 1b).  In this way you will get the tangent point  C  on the auxiliary circle of the radius    ;

3)  draw the straight line from the point  P  to the point  C  and continue it in the same direction till the intersection with the larger circle  (shown in blue in  Figure 1b).  The intersection point  A  is the tangent point of the common tangent line and the larger circle.  Figure 1c  reminds you how to perform this step.

4)  draw the straight line  QB  parallel to  PA  till the intersection with the smaller circle  (shown in blue in  Figure 1b).

The intersection point  B  is the tangent point of the common tangent line and the smaller circle;

5)  the required common tangent line is uniquely defined by its two points  A  and  B.

 

Note that all these operations  1)  –  4)  can be done using a ruler and a compass.  The problem is solved.

 

 

 

Problem 2

Find the length of the common exterior tangent segment to two given circles in a plane,  if they have the radii  and  and the distance between their centers is  d.

No one of the two circles is located inside the other.

 

Solution

Let us use the  Figure 1b  from the solution to the previous  Problem 1.

This  Figure  is relevant to the  Problem 2.  It is copied and reproduced

in the  Figure 2  on the right for your convenience.

figure 2

 

It is clear from the solution of the  Problem 1  above that the common

exterior tangent segment  |AB|  is congruent to the side  |CQ|  of the

quadrilateral (rectangle)  CABQ.

 

From the other side,  the segment  CQ  is the leg of the right-angled

triangle  DELTAPCQ.  This triangle has the hypotenuse’s measure  d  and

the other leg’s measure  .  Therefore,  the length of the common

exterior tangent segment  |AB|  is equal to

|AB| =

 

Note that the solvability condition for this problem is  d > .

It coincides with the condition that no one of the two circles lies inside the other.

 

Example 1

Find the length of the common exterior tangent segment to two given circles in a plane,  if their radii are  6 cm  and  3 cm  and the distance between their centers

is  5 cm.

 

 

 

Solution

Use the formula  (1)  derived in the solution of the  Problem 2.

According to this formula,  the length of the common exterior tangent segment to the two given circles is equal to

 

 

=   =

= 4 cm

 

Answer.

The length of the common exterior tangent segment to the two given circles is  4 cm

 

Contact of circles

Two circle are said to touch each other at a point if they have a common tangent at that point.

Point T is shown by the red dot.

Internal tangent                   externally tangent

Note;

  • The centers of the two circles and their point of contact lie on a straight line
  • When two circles touch each other internally, the distance between the centers is equal to the difference of the radii i.e. PQ= TP-TA
  • When two circles touch each other externally, the distance between the centers is equal to the sum of the radii i.e.  OR =TO +TR

.

 

Alternate Segment theorem

The angle which the chord makes with the tangent is equal to the angle subtended by the same chord in the alternate segment of the circle.

Angle a = Angle b

Note;

The blue line represents the angle which the chord CD makes with the tangent PQ which is equal to the angle b which is subtended by the chord in the alternate segment of the circle.

 

Illustrations

  • Angle s = Angle t
  • Angle a = Ange b

 

 

 

Tangent – secant segment length theorem

If a tangent segment and secant segment are drawn to a circle from an external point, then the square of the length of the tangent equals the product of the length of the secant with the length of its external segment.

Example

In the figure above ,TW=10 cm and XW = 4 cm. find TV

Solution

=

TV =

Circles and triangles

 

Inscribed circle

  • Construct any triangle ABC.
  • Construct the bisectors of the three angles
  • The bisectors will meet at point I
  • Construct a perpendicular from O to meet one of the sides at  M
  • With the centre I and radius IM draw a circle
  • The circle will touch the three sides of the triangle ABC
  • Such a circle is called an inscribed circle or in circle.
  • The centre of an inscribed circle is called the incentre

 

Circumscribed circle

  • Construct any triangle ABC.
  • Construct perpendicular bisectors of AB , BC, and AC to meet at point O.
  • With O as the centre and using  OB as radius, draw  a circle
  • The circle will pass through the vertices A , B and C as shown in the figure below

Escribed circle

  • Construct any triangle ABC.
  • Extend line BA and BC
  • Construct the perpendicular bisectors of the two external angles produced
  • Let the perpendicular bisectors meet at O
  • With O as the centre draw the circle which will touch all the external sides of the triangle

Note;

Centre O is called the ex-centre

AO and CO are called external bisectors.

 

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

Past KCSE Questions on the topic.

  1. The figure below represents a circle a diameter 28 cm with a sector subtending an angle of 750 at the centre.

 

 

 

 

 

 

 

Find the area of the shaded segment to 4 significant figures

(a) <PST

  1. The figure below represents a rectangle PQRS inscribed in a circle centre 0 and radius 17 cm. PQ = 16 cm.

 

 

 

 

 

 

 

 

Calculate

  • The length PS of the rectangle
  • The angle POS
  • The area of the shaded region
  1. In the figure below, BT is a tangent to the circle at B. AXCT and BXD are

straight lines. AX = 6 cm, CT = 8 cm, BX = 4.8 cm and XD = 5 cm.

 

 

 

 

 

 

 

 

 

Find the length of

(a) XC

(b) BT

  1. The figure below shows two circles each of radius 7 cm, with centers at X and Y. The circles touch each other at point Q.

 

 

 

 

 

 

 

 

 

 

 

Given that <AXD = <BYC = 1200 and lines AB, XQY and DC are parallel, calculate the area of:

  1. a) Minor sector XAQD (Take π 22/7)
  2. b) The trapezium XABY
  3. c) The shaded regions.
  4. The figure below shows a circle, centre, O of radius 7 cm. TP and TQ are tangents to the circle at points P and Q respectively. OT =25 cm.

 

 

 

 

 

Calculate the length of the chord PQ

 

O
Q
  1. The figure below shows a circle centre O and a point Q which is outside the circle

 

 

 

 

Using a ruler and a pair of compasses, only locate a point on the circle such that angle OPQ = 90o

 

  1. In the figure below, PQR is an equilateral triangle of side 6 cm. Arcs QR, PR and PQ arcs of circles with centers at P, Q and R respectively.

 

 

 

 

 

 

 

 

 

 

 

Calculate the area of the shaded region to 4 significant figures

 

 

 

 

 

 

  1. In the figure below AB is a diameter of the circle. Chord PQ intersects AB at N. A tangent to the circle at B meets PQ produced at R.

 

 

 

 

 

 

 

 

 

 

 

 

Given that PN = 14 cm, NB = 4 cm and BR = 7.5 cm, calculate the length of:

(a)        NR

(b)        AN

 

 

 

 

 

 

 

                  MATRICES

CHAPTER FOURTY EIGHT

 

Specific Objectives

By the end of the topic the learner should be able to:

(a) Define a matrix;

(b) State the order of a matrix;

(c) Define a square matrix;

(d) Determine compatibility in addition and multiplication of matrices;

(e) Add matrices;

(f) Multiply matrices;

(g) Identify matrices;

(h) Find determinant of a 2 x 2 matrix;

(i) Find the inverse of a 2 x 2 matrix;

(j) Use matrices to solve simultaneous equations.

 

Content

(a) Matrix

(b) Order of a matrix

(c) Square matrix

(d) Compatibility in addition and multiplication of matrices

(e) Multiplication of a matrix by a scalar

(f) Matrix multiplication

(g) Identify matrix

(h) Determinant of a 2 x 2 matrix

(i) Inverse of a 2 x 2 matrix

(j) Singular matrix

(k) Solutions of simultaneous equations in two unknowns.

 

(i)

 

Introduction

 

A matrix is a rectangular arrangement of numbers in rows and columns. For instance, matrix A below has two rows and three columns. The dimensions of this matrix are 2 x 3 (read “2 by 3”). The numbers in a matrix are its entries. In matrix A, the entry in the second row and third column is 5.

A =

Some matrices (the plural of matrix) have special names because of their dimensions or entries.

 

Order of matrix

Matrix consist of rows and columns. Rows are the horizontal arrangement while columns are the vertical arrangement.

Order of matrix is being determined by the number of rows and columns. The order is given by stating the number of rows followed by columns.

 

Note;

If the number of rows is m and the number of columns n, the matrix is of order .

E.g. If a matrix has m rows and n columns, it is said to be order m´n.

 

e.g.        is a matrix of order 3´4.

 

e.g.        is a matrix of order 3.

e.g.        is a 2´3 matrix.

e.g.        is a 3´1 matrix.

Elements of matrix

The element of a matrix is each number or letter in the matrix. Each element is locating by stating its position in the row and the column.

 

 

For example, given the 3 x 4 matrix

 

  • The element 1 is in the third row and first column.
  • The element 6 is in the first row and forth column.

Note;

A matrix in which the number of rows is equal to the number of columns is called a square matrix.

 

 

 

Is called a row matrix or row vector.

 

Is called a column matrix or column vector.

 

Is a column vector of order 3´1.

is a row vector of order 1´3.

Two or more matrices re equal if they are of the same order and their corresponding elements are equal. Thus, if  then, a = 3, b =4 and d=5.

Addition and subtraction of matrices

Matrices can be added or subtracted if they are of the same order. The sum of two or more matrices is obtained by adding corresponding elements. Subtraction is also done in the same way.

Example

 

  • A + B ) A – B

Solution

  • A+B =

 

  • A – B =

 

Example

–   +

=

 

Note;

After arranging the matrices you must use BODMAS

The matrix above cannot be added because they are not of the same order

Matrix multiplication

To multiply a matrix by a number, you multiply each element in the matrix by the number.

Example

3

solution

=

 

Example

-2

Solution

=

Example

A woman wanted to buy one sack of potatoes, three bunches of bananas and two basket of onion. She went to kikuyu market and found the prices as sh 280 for the sack of potatoes ,sh 50 for a bunch of bananas and sh 100 for a basket of onions. At kondelee market the corresponding prices were sh 300, sh 48 and sh 80.

  • Express the woman’s requirements as a row matrix
  • Express the prices in each market as a column matrix
  • Use the matrices in (a) and (b) to find the total cost in each market

 

Solution

  • Requirements in matrix form is (1 3 2)
  • Price matrix for Kikuyu market is

 

 

Price matrix for kondelee market

  • Total cost in shillings at Kikuyu Market is;

 

(1 3 2) = (1 x 280 + 3 x 50 +2 x 100) = (630)

 

Total cost in shillings at Kondelee Market is;

(1 3 2 )  = ( 1 x 300 + 3 x 48 + 2 x 80) =(604)

The two results can be combined into one as shown below

(1 3 2)

Note;

The product of two matrices A and B is defined provided the number of columns in A is equal to the number of rows in B.

If A is an m n matrix and B is an n p matrix, then the product AB is an m a p matrix.

A X B = AB

                        m X n   n X p = m p

Each time a row is multiplied by a column

Example

Find AB if A =  and B=

 

 

 

 

 

 

Solution

Because A is a 3 x 2 matrix and B is a 2 x 2 matrix, the product AB is defined and is a 3 x 2 matrix. To write the elements in the first row and first column of AB, multiply corresponding elements in the first row of A and the first column of B. Then add. Use a similar procedure to write the other entries of the product.

 

AB=

=

 

=

 

Identity matrix

For matrices, the identity matrix or a unit matrix is the matrix that has 1’s on the main diagonal and 0’s elsewhere. The main diagonal is the one running from top left to bottom right .It is also called leading or principle diagonal. Examples are;

I=

2 X 2 identity matrix                                                                      3 x 3 identity matrix

If A is any n x n matrix and I is the n x n identity matrix, then IA = A and AI = A.

Determinant matrix

The determinant of a matrix is the difference of the products of the elements on the diagonals.

Examples

The determinant of A, det A or |A| is defined as follows:

(a)        If n=2,

 

 

Example

Find the determinant

Solution

Subtract the product of the diagonals

1 x 5 – 2 x 3 = 5 – 6 = -1

Determinant is -1

Inverse of a matrix

Two matrices of order n x n are inverse of each other if their product (in both orders) is theidentity matrix of the same order n x n. The inverse of A is written as

Example

Show that B=

Solution

AB=

=

=

BA=

=            AB=BA=I. Hence, A is the inverse of B

Note;

To get the inverse matrix

  • Find the determinant of the matrix. If it is zero, then there is no inverse
  • If it is non zero, then;
  • Interchange the elements in the main diagonal
  • Reverse the signs of the element in the other diagonals
  • Divide the matrix obtained by the determinant of the given matrix

 

 

In summary

The inverse of the matrix A =  is

=

 

Example

Find the inverse of A=

Solution

Check

You can check the inverse by showing that A

And

 

Solutions of simultaneous linear equations using matrix

Using matrix method solve the following pairs of simultaneous equation

Solution

 

 

We need to calculate the inverse of A =

=

Hence

=

=

Hence the value of x = 2 and the value of y = 1 is the solution of the simultaneous equation

 

 

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

 

Past KCSE Questions on the topic

 

  1. A and B are two matrices. If A = 1     2     find B given that A2 = A + B

4      3

  1. Given that A= 1 3  , B= 3   1  , C = p   0    and AB =BC, determine the value of P

5   3          5  -1           0    q

  1. A matrix A is given by A = x 0

5     y

  1. a) Determine A2

 

1   0    ,

0   1

  1. b) If A2 = determine the possible pairs of values of x and y
  2. (a) Find the inverse of the matrix   9   8

7    6

(b)        In a certain week a businessman bought 36 bicycles and 32 radios for total of Kshs 227 280. In the following week, he bought 28 bicycles and 24 radios for a total of Kshs 174 960. Using matrix method, find the price of each bicycle and each radio that he bought

 

(c)        In the third week, the price of each bicycle was reduced by 10% while the price of each radio was raised by 10%. The businessman bought as many bicycles and as many radios as he had bought in the first two weeks.

Find by matrix method, the total cost of the bicycles and radios that the businessman bought in the third week.

 

 

  1. Determine the inverse T-1 of the matrix 1    2

1   -1

Hence find the coordinates to the point at which the two lines x + 2y=7 and x-y=1

 

  1. Given that A = 0         -1         and B =   -1      0

3       2                         2      -4

Find the value of x if

(i)         A – 2x = 2B

(ii)        3x – 2A = 3B

(iii)       2A – 3B = 2x

  1. Find the non- zero value of k for which k + 1          2      is an inverse.

4k        2k

  1. A clothes dealer sold 3 shirts and 2 trousers for Kshs. 840 and 4 shirts and 5 trousers for Kshs 1680. Form a matrix equation to represent the above information. Hence find the cost of 1 shirt and the cost of 1 trouser.

 

 

 

  FORMULAE AND VARIATION

CHAPTER FOURTY NINE

 

Specific Objectives

By the end of the topic the learner should be able to:

  1. a) Rewrite a given formula by changing its subject
  2. b) Define direct, inverse, partial and joint variations
  3. c) Determine constants of proportionality
  4. d) Form and solve equations involving variations
  5. e) Draw graphs to illustrate direct and inverse proportions
  6. f) Use variations to solve real life problems

 

Content

  • Change of the subject of a formula
  • Direct, inverse, partial and joint variation
  • Constants of proportionality
  • Equations involving variations
  • Graphs of direct and inverse proportion
  • Formation of equations on variations based on real life situations

 

 

 

 

 

 

 

 

Formulae

A Formula is an expression or equation that expresses the relationship between certain quantities.

 

For Example  is the formula to find the area of a circle of radius r units.

 

From this formula, we can know the relationship between the radius and the area of a circle. The area of a circle varies directly as the square of its radius. Here is the constant of variation.

 

Changing the subject of a formulae

Terminology

In the formula

                                        C = d

            Subject: C                                 Rule: multiply by diameter

 

The variable on the left, is known as the subject: What you are trying to find.

The formula on the right, is the rule, that tells you how to calculate the subject.

So, if you want to have a formula or rule that lets you calculate d, you need

to make d, the subject of the formula.

This is changing the subject of the formula from C to d.

 

 

So clearly in the case above where

                     C = d

 

We get C by multiplying by the diameter

To calculate d, we need to divide the Circumference C by

So      d   and now we have d as the subject of the formula.

 

 

 

 

 

 

 

Method:

A formula is simply an equation, that you cannot solve, until you replace the letters with their

values (numbers). It is known as a literal equation.

To change the subject, apply the same rules as we have applied to normal equations.

  1. Add the same variable to both sides.
  2. Subtract the same variable from both sides.
  3. Multiply both sides by the same variable.
  4. Divide both sides by the same variable.
  5. Square both sides
  6. Square root both sides.

 

 

Examples:

Make the letter in brackets the subject of the formula

x + p = q [ x ]

(subtract p from both sides)

x = q p

 

y r = s [ y ]

(add r to both sides)

y = s + r

 

P = RS [ R ]

(divide both sides by S)

 

S =

 

= L           [ A ]

(multiply both sides by B)

A = LB

 

2w+ 3 = [ w ]

(subtract 3 from both sides)

2w = y −3

(divide both sides by 2)

W=

 

P = Q     [ Q ]

(multiply both sides by 3get rid of fraction)

3P = Q

 

 

 

 

T = k [ k ]

(multiply both sides by 5get rid of fraction)

5T = 2k

(divide both sides by 2)

= k      Note that: is the same as

 

A = r [ r ]

(divide both sides by p)

 (square root both sides)   

 

L = h t [ h ]

(multiply both sides by 2)

2L = h t

(add t to both sides)

2L + t = h

 

Example

Make d the subject of the formula G=

Solution

Squaring both sides

Multiply both sides by d-1

Expanding the L.H.S

Collecting the terms containing d on the L.H.S

Factorizing the L.H.S

Dividing both sides by

 

 

 

 

Variation

In a formula some elements which do not change (fixed) under any condition are called constants while the ones that change are called variables. There are different types of variations.

 

  • Direct Variation, where both variables either increase or decrease together
  • Inverse or Indirect Variation, where when one of the variables increases, the other one decreases
  • Joint Variation, where more than two variables are related directly
  • Combined Variation, which involves a combination of direct or joint variation, and indirect variation

Examples

  • Direct:   The number of money I make varies directly (or you can say varies proportionally) with how much I work.
  • Direct:   The length of the side a square varies directly with the perimeter of the square.
  • Inverse:   The number of people I invite to my bowling party varies inversely with the number of games they might get to play (or you can say is proportional to the inverse of).
  • Inverse:  The temperature in my house varies indirectly (same as inversely) with the amount of time the air conditioning is running.
  • Inverse:   My school marks may vary inversely with the number of hours I watch TV.

Direct or Proportional Variation

When two variables are related directly, the ratio of their values is always the same.  So as one goes up, so does the other, and if one goes down, so does the other.  Think of linear direct variation as a “y = mx” line, where the ratio of y to x is the slope (m).  With direct variation, the y-intercept is always 0 (zero); this is how it’s defined.

Direct variation problems are typically written:

→       y= kx      where k is the ratio of y to x (which is the same as the slope or rate).

Some problems will ask for that k value (which is called the constant of variation or constant of proportionality ); others will just give you 3 out of the 4 values for x and y and you can simply set up a ratio to find the other value.

Remember the example of making ksh 1000  per week (y = 10x)?  This is an example of direct variation, since the ratio of how much you make to how many hours you work is always constant.

 

Direct Variation Word Problem:

The amount of money raised at a school fundraiser is directly proportional to the number of people who attend.  Last year, the amount of money raised for 100 attendees was $2500.   How much money will be raised if 1000 people attend this year?

Solution:

Let’s do this problem using both the Formula Method and the Proportion Method:

Formula method            Explanation

 

Proportional method      Explanation

 

Direct Square Variation Word Problem

Again, a Direct Square Variation is when y is proportional to the square of x, or   .

Example

If yvaries directly with the square ofx, and if y = 4 when x= 3, what is y when x= 2?

Solution:

Let’s do this with the formula method and the proportion method:

Formulae method               notes

 

 

 

Proportional method                       Notes

 

 

Example

The length (l) cm of  a wire varies directly  as the temperature c.The length of the wire is 5 cm when the temperature is .Calculate the length of the wire when the temperature is c.

 

 

Solution

l

Therefore l =Kt

Substituting l =5 when T= .

5 =k x 65

K =

Therefore l =

When t = 69

L =

 

Direct variation graph

 

Inverse or Indirect Variation

Inverse or Indirect Variation is refers to relationships of two variables that go in the opposite direction.  Let’s supposed you are comparing how fast you are driving (average speed) to how fast you get to your work.The faster you drive the earlier you get to your work. So as the speed increases time reduces and vice versa .

 

So the formula for inverse or indirect variation is:

→    y =      or K =xy  where k is always the same number or constant.

(Note that you could also have an Indirect Square Variation or Inverse Square Variation, like we saw above for a Direct Variation.  This would be of the form→    y =      or k=      .)

 

Inverse Variation Word Problem:

So we might have a problem like this:

The value of yvaries inversely with x, and y = 4 when x = 3.  Find x when y = 6.

The problem can also be written as follows:

Let = 3,   = 4, and   = 6.  Let yvary inversely as x.  Find .

 

Solution:

We can solve this problem in one of two ways, as shown.  We do these methods when we are given any three of the four values for x and y.

Product Rule Method:

Inverse Variation Word Problem:

For the club, the number of tickets Moyo can buy is inversely proportional to the price of the tickets.  She can afford 15 tickets that cost $5 each.  How many tickets can she buy if each cost $3?

Solution:

Let’s use the product method:

.

Example

If 16 women working 7 hours day can paint a mural in 48 days, how many days will it take 14 women working 12 hours a day to paint the same mural?

Solution:

The three different values are inversely proportional;  for example, the more women you have, the less days it takes to paint the mural, and the more hours in a day the women paint, the less days they need to complete the mural:

 

Joint Variation and Combined Variation

Joint variation is just like direct variation, but involves more than one other variable.  All the variables are directly proportional, taken one at a time.  Let’s do a joint variation problem:

Supposed x varies jointly with y and the square root of z.  When x = ­–18 and y = 2, then z = 9.  Find y when x = 10 and z = 4.

Combined variation involves a combination of direct or joint variation, and indirect variation.  Since these equations are a little more complicated, you probably want to plug in all the variables, solve for k, and then solve back to get what’s missing.  Here is the type of problem you may get:

(a)   yvaries jointly as x and w and inversely as the square of zFind the equation of variation when y = 100, x = 2, w = 4, and z = 20.

(b)   Then solve for y when x = 1, w = 5, and z = 4.

Solution:

 

 

 

Example

The volume of wood in a tree (V) variesdirectly as the height (h) and inversely as the square of the girth (g).  If the volume of a tree is 144 cubic meters when the height is 20 meters and the girth is 1.5 meters, what is the height of a tree with a volume of 1000 and girth of 2 meters?

Solution:

 

 

Example

The average number of phone calls per day between two cities has found to be jointly proportional to the populations of the cities, and inversely proportional to the square of the distance between the two cities.  The population of Charlotte is about 1,500,000 and the population of Nashville is about 1,200,000, and the distance between the two cities is about 400 miles.  The average number of calls between the cities is about 200,000.

(a)   Find the k and write the equation of variation.

(b)   The average number of daily phone calls between Charlotte and Indianapolis (which has a population of about 1,700,000) is about 134,000.  Find the distance between the two cities.

Solution:

It may be easier if you take it  one step at a time:

Math’s                                                                 Explanation

Example

A varies directly as B and inversely as the square root of C. Find the percentage change in A when B is decreased by  10 %  and C increased by  21%.

Solution

A= K

A change in B and C causes a change in A

= 1.21C

Substituting

 

=

Percentage change in A =

=

= – 18

Therefore A decreases 18

Partial variation

The general linear equation y =mx +c, where m and c are constants, connects two variables x and y.in such case we say that y is partly constant and partly varies as x.

Example

A variable y is partly constant and partly varies as if x = 2 when y=7 and x =4 when y =11, find the equation connecting y and x.

Solution

The required equation is y = kx + c where k and c are  constants

Substituting x = 2 ,y =7 and x =4, y =11 in the equation gives ;

7 =2k +c …………………..(1)

11 = 4k +c …………………(2)

Subtracting equation 1 from equation 2 ;

4 = 2 k

Therefore k =2

Substituting k =2 in the equation 1 ;

C =7 – 4

C =3

Therefore the equation required is y=2x +3

 

 

 

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

 

Past KCSE Questions on the topic.

 

  1. The volume Vcm3 of an object is given by

 

V = 2 π r31 – 2

3            sc2

 

Express in term of π r, s and V

  1. Make V the subject of the formula

T = 1 m (u2 – v2)

2

  1. Given that y =b – bx2 make x the subject

cx2 – a

  1. Given that log y = log (10n) make n the subject
  2. A quantity T is partly constant and partly varies as the square root of S.
  1. Using constants a and b, write down an equation connecting T and S.
  2. If S = 16, when T = 24 and S = 36 when T = 32,  find  the values of the constants a and b,
  3. A quantity P is partly constant and partly varies inversely as a quantity q, given that p = 10 when q = 1.5 and p = 20, when q = 1.25, find the value of p when q= 0.5
  4. Make y the subject of the formula p = xy

x-y

  1. Make P the subject of the formula

P2 = (P – q) (P-r)

  1. The density of a solid spherical ball varies directly as its mass and inversely as the cube of its radius

When the mass of the ball is 500g and the radius is 5 cm, its density is 2 g per cm3

Calculate the radius of a solid spherical ball of mass 540 density of 10g per cm3

  1. Make s the subject of the formula

 

 

√P = r     1 – as2

  1. The quantities t, x and y are such that t varies directly as x and inversely as the  square root of y. Find the percentage  in t if x decreases by 4% when y  increases  by 44%
  2. Given that y is inversely proportional to xn and k as the constant of proportionality;

(a)        (i)         Write down a formula connecting y, x, n and k

(ii)        If x = 2 when y = 12 and x = 4 when y = 3, write down two expressions for k in terms of n.

Hence, find the value of n and k.

(b)        Using the value of n obtained in (a) (ii) above, find y when x = 5 1/3

 

  1. The electrical resistance, R ohms of a wire of a given length is inversely proportional to the square of the diameter of the wire, d mm. If R = 2.0 ohms when d = 3mm. Find the vale R when d = 4 mm.

 

  1. The volume Vcm3 of a solid depends partly on r and partly on r where rcm is one of the dimensions of the solid.

When r = 1, the volume is 54.6 cm3 and when r = 2, the volume is 226.8 cm3

(a) Find an expression for V in terms of r

(b) Calculate the volume of the solid when r = 4

(c) Find the value of r for which the two parts of the volume are equal

 

  1. The mass of a certain metal rod varies jointly as its length and the square of its radius. A rod 40 cm long and radius 5 cm has a mass of 6 kg. Find the mass of a similar rod of length 25 cm and radius 8 cm.

 

  1. Make x the subject of the formula

P =       xy

z + x

  1. The charge c shillings per person for a certain service is partly fixed and partly inversely proportional to the total number N of people.

(a)        Write an expression for c in terms on N

(b)        When 100 people attended the charge is Kshs 8700 per person while for 35 people the charge is Kshs 10000 per person.

(c)        If a person had paid the full amount charge is refunded. A group of people paid but ten percent of organizer remained with Kshs 574000.

Find the number of people.

 

  1. Two variables A and B are such that A varies partly as B and partly as the square root of B given that A=30, when B=9 and A=16 when B=14, find A when B=36.

 

  1. Make p the subject of the formula

A =      -EP      

√P2 + N

 

 

 

 

       SEQUENCE AND SERIES

CHAPTER FIFTY

 

Specific Objectives

By the end of the topic the learner should be able to:

(a) Identify simple number patterns;

(b) Define a sequence;

(c) Identify the pattern for a given set of numbers and deduce the general rule;

(d) Determine a term in a sequence;

(e) Recognize arithmetic and geometric sequences;

(f) Define a series;

(g) Recognize arithmetic and geometric series (Progression);

(h) Derive the formula for partial sum of an arithmetic and geometric series(Progression);

(i) Apply A.P and G.P to solve problems in real life situations.

Content

(a) Simple number patterns

(b) Sequences

(c) Arithmetic sequence

(d) Geometric sequence

(e) Determining a term in a sequence

(f) Arithmetic progression (A.P)

(g) Geometric progression (G.P)

(h) Sum of an A.P

(i) Sum of a G.P (exclude sum to infinity)

(j) Application of A.P and G.P to real life situations.

Introduction

Sequences and Series are basically just numbers or expressions in a row that make up some sort of a pattern; for example,  Monday, Tuesday, Wenesday,, Friaday is a sequence that represents the days of the week.   Each of these numbers or expressions are called terms or elements of the sequence.

Sequences are the list of these items, separated by commas, and series are the sum of the terms of a sequence.

Example

Sequence                                                                           Next two terms

1, 8, 27, – , –                                Every term is cubed .The next two terms are

3, 7, 11, 15 – , – ,                   every term is 4 more than the previous one. To get the next term add 4

15 + 4 = 19, 19 +4 =23

On the numerator, the next term is 1 more than the previous one, and the                                             denominator, the next term is multiplied by 2 the next two terms are

Example

For the term of a sequence is given by 2n + 3, Find the first, fifth, twelfth terms

Solution

First term, n = 1 substituting (2 x 1 +3 =5)

Fifth term, n = 5 substituting (2 x 5 +3 =13)

Twelfth term, n = 12 substituting (2 x 12 +3 =27)

 

 

 

 

 

Arithmetic and geometric sequence

Arithmetic sequence.

Any sequence of a number with common difference is called arithmetic sequence

To decide whether a sequence is arithmetic, find the differences of consecutive terms. If each  differences are not constant,the it is arithmetic sequence

Rule for an arithmetic sequence

The nth term of an arithmetic sequence with first term   and common difference d is given by:

=   + (n – 1)d

 

 

Example Illustrations

 

 

Example

Write a rule for the nth term of the sequence 50, 44, 38, 32, . . . . Then find .

Solution

The sequence is arithmetic with first term  = 50 and common difference

d = 44 – 50 = -6. So, a rule for the nth term is:

 

= + (n – 1)d    Write general rule.

= 50 + (n – 1)(-6) Substitute for a1 and d.

= 56 – 6n                Simplify.

The 20th term is  = 56 – 6(20) = -64.

 

Example

The 20 th term of arithmetic sequence is 60 and the 16 th term is 20.Find the first term and the common difference.

 

 

Solution

  • – (2) gives

4d = 40

d= 10

 

Therefore a + 15 x 10 =20

a + 150 = 20

a = -130

Hence, the first term is – 130 and the common difference is 10.

Example

Find the number of terms in the sequence – 3 , 0 , 3 …54

Solution

The n th term is a + ( n – 1)d

a = -30 , d =3

n th term = 54

therefore  – 3 + ( n – 1) = 54

3 (n – 1 ) = 57

 

Arithmetic series/ Arithmetic progression A.P

The sum of the terms of a sequence is called a series. If the terms of sequence are 1, 2, 3, 4, 5, when written with addition sign we get arithmetic series

1 + 2 + 3 + 4 + 5

The general formulae for finding the sum of the terms is

Note;

If th first term (a) and the last term l are given , then

 

 

Example

The sum of the first eight terms of an arithmetic Progression is 220.If the third term is 17, find the sum of the first six terms

Solution

= 4( 2a + 7d )

So , 8a + 28d = 220…………………….1

The third term is  a + (3 – 1)d = a + 2d =17 …………….2

Solving 1  and 2 simultaneously;

8a + 28 d =220  …………1

8a + 16 d = 136 …………2

12 d = 84

Substituting d =7 in equation 2 gives a = 3

Therefore,

= 3(6 x 35)

= 3 x 41

= 123

 

Geometric sequence

It is a sequence with a common ratio.The ratio of any term to the previous term must be constant.

Rule for Geometric sequence is;

The nth term of a geometric sequence with first term a1 and common ratio r is given by:

 

 

Example

Given the geometric sequence 4 , 12 ,36 ……find the 4th , 5th  and the n th terms

Solution

The first term , a =4

The common ratio , r =3

Therefore the 4th term = 4 x

= 4 x

= 108

The 5th term                = 5 x

= 5 x

= 324

The  term         =4 x

 

 

Example

The  4th term of geometric sequence is 16 . If the first term is 2 , find;

  • The common ration
  • The seventh term

Solution

The common ratio

The first term, a = 2

The 4th term is 2 x

Thus, 2

 

The common ratio is 2

The seventh term =

 

 

 

Geometric series

The series obtained by the adding the terms of geometric sequence is called geometric series or geometric progression G.P

The sum of the first n terms of a geometric series with common ratio r > 1 is:

The sum of the first n terms of a geometric series with common ratio r < 1 is:

Example

Find the sum of the first 9 terms of G.P. 8 + 24 + 72 +…

Solution

Example

The sum of the first three terms of a geometric series is 26 .If the common ratio is 3 , find the sum of the first six terms.

Solution

 

=

                                                                            a       =

 

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

 

Past KCSE Questions on the topic.

 

 

 

  1. The first, the third and the seventh terms of an increasing arithmetic progression are three consecutive terms of a geometric progression. In the first term of the arithmetic progression is 10 find the common difference of the arithmetic progression?
  2. Kubai saved Ksh 2,000 during the first year of employment. In each subsequent year, he saved 15% more than the preceding year until he retired.

(a) How much did he save in the second year?

(b) How much did he save in the third year?

(c) Find the common ratio between the savings in two consecutive years

  • How many years did he take to save the savings a sum of Ksh 58,000?

(e) How much had he saved after 20 years of service?

  1. In geometric progression, the first term is a and the common ratio is r. The sum of the first two terms is 12 and the third term is 16.
  • Determine the ratio ar2

a + ar

(b) If the first term is larger than the second term, find the value of r.

  1. (a) The first term of an arithmetic progression is 4 and the last term is 20. The

Sum of the term is 252. Calculate the number of terms and the common differences of the arithmetic progression

(b)        An Experimental culture has an initial population of 50 bacteria. The population increased by 80% every 20 minutes. Determine the time it will take to have a population of 1.2 million bacteria.

  1. Each month, for 40 months, Amina deposited some money in a saving scheme. In the first month she deposited Kshs 500. Thereafter she increased her deposits by Kshs. 50 every month.

Calculate the:

  1. a) Last amount deposited by Amina
  2. b) Total amount Amina had saved in the 40 months.
  3. A carpenter wishes to make a ladder with 15 cross- pieces. The cross- pieces are to diminish uniformly in length from 67 cm at the bottom to 32 cm at the top.

Calculate the length in cm, of the seventh cross- piece from the bottom

 

  1. The second and fifth terms of a geometric progression are 16 and 2 respectively. Determine the common ratio and the first term.

 

  1. The eleventh term of an arithmetic progression is four times its second term. The sum of the first seven terms of the same progression is 175

(a)        Find the first term and common difference of the progression

(b)        Given that pth term of the progression is greater than 124, find the least

value of P

  1. The nth term of sequence is given by 2n + 3 of the sequence

(a)        Write down the first four terms of the sequence

(b)        Find sn the sum of the fifty term of the sequence

(c)        Show that the sum of the first n terms of the sequence is given by

Sn = n2 + 4n

Hence or otherwise find the largest integral value of n such that Sn <725

 

 

      BINOMIAL EXPANSION

CHAPTER FIFTY ONE

 

Specific Objectives

By the end of the topic the learner should be able to:

(a) Expand binomial expressions up to the power of four by multiplication;

(b) Building up – Pascal’s Triangle up to the eleventh row;

(c) Use Pascal’s triangle to determine the coefficient of terms in a binomialexpansions up to the power of 10;

(d) Apply binomial expansion in numerical cases.

Content

(a) Binomial expansion up to power four

(b) Pascal’s triangle

(c) Coefficient of terms in binomial expansion

(d) Computation using binomial expansion

(e) Evaluation of numerical cases using binomial expansion.

 

 

 

 

 

 

 

 

 

 

 

 

 

A binomial is an expression of two terms

Examples

(a + y), a + 3, 2a + b

It easy to expand expressions with lower power but when the power becomes larger, the expansion or multiplication becomes tedious. We therefore use pascal triangle to expand the expression without multiplication.

We can use Pascal triangle to obtain coefficients of expansions  of the form( a + b

Pascal triangle

 

1

1                1

1          2            1

1      3             3         1

1    4        6            4        1

Note;

  • Each row starts with 1
  • Each of the numbers in the next row is obtained by adding the two numbers on either side of it in the preceding row
  • The power of first term (a ) decreases as you move to right while the powers of the second term (b ) increases as you move to the right

Example

Expand (p +

Solution

The terms without coefficients are;

From Pascal triangle, the coefficients when n =5 are; 1    5    10      10     5      1

Therefore (p +  =

 

Example

Expand (x

Solution

(x

The terms without the coefficient are;

From Pascal triangle, the coefficients when n =7 are;

1 7 21 35 35 21 7 1

Therefore (x =

Note;

When dealing with negative signs, the signs alternate with the positive sign but first start with the negative sign.

Applications to Numeric cases

Use binomial expansion to evaluate (1.02

Solution

(1.02) = (1+0.02)

Therefore (1.02  = (1+ 0.02

The terms without coefficients are

From Pascal triangle, the coefficients when n =6 are;

1 6   15   20    15 6     1

Therefore;

(1.02  =

1 + 6 (0.02) +   15

=1 + 0.12 + 0.0060 + 0.00016 + 0.0000024 + 0.0000000192 + 0.000000000064

=1.1261624

=1.126 (4 S.F)

Note;

To get the answer just consider addition of up to the 4th term of the expansion. The other terms are too small to affect the answer.

Example

Expand (1 +  up to the term .Use the expansion to estimate (0.98  correct to 3 decimal places.

Solution

(1 +

The terms without the coefficient are;

From Pascal triangle, the coefficients when n =9 are;

1    9   36   84   126    126   84   36   9    1

Therefore (1 + = 1 + 9x + 36  + 84 ………………..

(0.98

= 1 – 0.18 + 0.0144 – 0.000672

= 0.833728

= 0.834 ( 3 D.P)

Example

Expand (  in ascending powers of hence find the value of (  correct to four decimal places.

Solution

=

=

Here

Substituting for x = 0.01 in the expansion

= 1 + 0.05 +0.001125 +0.000015

= 1.051140

= 1.0511 (4 decimal places)

 

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

Past KCSE Questions on the topic.

 

  1. (a) Write down the simplest expansion ( 1 + x)6

(b)        Use the expansion up to the fourth term to find the value of (1.03)6 to the nearest one thousandth.

  1. Use binomial expression to evaluate (0.96)5 correct to 4 significant figures.
  2. Expand and simplify (3x – y)4 hence use the first three terms of the expansion to proximate the value of (6 – 0.2)4
  3. Use binomial expression to evaluate

2 + 15+       2 – 15

√2    √2

  1. (a) Expand the expression 1 + 1x    5  in ascending powers of x, leaving

2

the coefficients as fractions in their simplest form.

  1. (a) Expand (a- b)6

(b)        Use the first three terms of the expansion in (a) above to find the approximate value of (1.98)6

  1. Expand (2 + x)5 in ascending powers of x up to the term in x3 hence approximate  the value of (2.03)5 to 4 s.f

 

  1. (a) Expand (1 + x)5

Hence use the expansion to estimate (1.04)5 correct to 4 decimal places

(b)        Use the expansion up to the fourth term to find the value of (1.03)6 to the nearest one thousandth.

  1. Expand and Simplify (1-3x)5 up to the term in x3

Hence use your expansion to estimate (0.97)5 correct to decimal places.

  1. Expand (1 + a)5

Use your expansion to evaluate (0.8)5 correct to four places of decimal

 

  1. (a) Expand (1 + x)5

(b)        Use the first three terms of the expansion in (a) above to find the approximate value of (0.98)5

 

 

 

 

 

 

CHAPTER FIFTY TWO

 COMPOUND PROPRTION AND RATES OF WORK

 

 

 

 

Specific Objectives

By the end of the topic the learner should be able to:

(a) Solve problems involving compound proportions using unitary and ratiomethods;

(b) Apply ratios and proportions to real life situations;

(c) Solve problems involving rates of work.

Content

(a) Proportional parts

(b) Compound proportions

(c) Ratios and rates of work

(d) Proportions applied to mixtures.

 

 

 

 

 

 

 

 

 

 

 

 

Introduction

Compound proportions

The proportion involving two or more quantities is called compound proportion. Any four quantities a , b , c  and d are in proportion if;

Example

Find the value of a that makes 2, 5, a and 25 to be in proportion;

Solution

Since 2 , 5 ,a , and 25 are in proportion

 

Continued proportions

In continued proportion, all the ratios between different quantities are the same; but always remember that the relationship exists between two quantities for example:

 

P  :   Q                    Q  :  R                     R  :  S

 

10:    5                    16  : 8                     4  :   2

 

Note that in the example, the ratio between different quantities i.e. P:Q, Q:R and R:S are the same i.e. 2:1 when simplified.

 

Continued proportion is very important when determining the net worth of individuals who own the same business or even calculating the amounts of profit that different individual owners of a company or business should take home.

 

 

Proportional parts

In general, if n is to be divided in the ratio a: b: c, then the parts of n proportional to a, b, c are

 

Example

Omondi, Joel, cheroot shared sh 27,000 in the ratio 2:3:4 respectively. How much did each get?

Solution

The parts of sh 27,000 proportional to 2, 3, 4 are

 

Example

Three people – John, Debby and Dave contributed ksh 119, 000 to start a company. If the ratio of the contribution of John to Debby was 12:6 and the contribution of Debby to Dave was 8:4, determine the amount in dollars that every partner contributed.

 

Solution

Ratio of John to Debby’s contribution = 12:6 = 2:1

 

Ratio of Debby to Dave’s contribution = 8:4 = 2:1

 

As you can see, the ratio of the contribution of John to Debby and that of Debby to Dave is in continued proportion.

Hence

To determine the ratio of the contribution between the three members, we do the calculation as follows:

 

John: Debby: Dave

12   :      6

8   :     4

 

We multiply the upper ratio by 8 and the lower ratio by 6, thus the resulting ratio will be:

 

John: Debby: Dave

96:     48   :     24

= 4 :      2     :      1

The total ratio = 7

 

The contribution of the different members can then be found as follows:

John

Debby

Dave

John contributed ksh 68, 000 to the company while Debby contributed ksh 34, 000 and Dave contributed ksh 17, 000

Example 2

You are presented with three numbers which are in continued proportion. If the sum of the three numbers is 38 and the product of the first number and the third number is 144, find the three numbers.

Solution

Let us assume that the three numbers in continued proportion or Geometric Proportion are a, ar and a  where a is the first number and r is the rate.

 

a+ar+a  = 38 ………………………….. (1)

The product of the 1st and 3rd is

a × a  = 144

Or

(ar)2 = 144………………………………..(2)

If we find the square root of (a , then we will have found the second number:

=

Since the value of the second number is 12, it then implies that the sum of the first and the third number is 26.

We now proceed and look for two numbers whose sum is 26 and product is 144.

Clearly, the numbers are 8 and 18.

Thus, the three numbers that we were looking for are 8, 12 and 18.

Let us work backwards and try to prove whether this is actually true:

 

8 + 12 + 18 = 18

What about the product of the first and the third number?

 

8 × 18 = 144

What about the continued proportion

The numbers are in continued proportion

Example

Given that x: y =2:3, Find the ratio (5x – 4y): (x + y).

Solution

Since x: y =2: 3

(5x – 4y): (x + y) = (10k – 12 k) 🙁 2k + 3 k)

=-2k: 5k

= – 2: 5

 

Example

If show that .

Solution

Substituting kc for a and kd for b in the expression

 

Therefore expression

 

 

 

 

 

 

Rates of work and mixtures

Examples

195 men working 10 hour a day can finish a job in 20 days. How many men employed to finish the job in 15 days if they work 13 hours a day.

Solution:

Let x be the no. of men required

Days         hours         Men

20             10               195

15              13                x

 

20 x 10 x 195

Example

Tap P can fill a tank in 2 hrs, and tap Q can fill the same tank in 4 hrs. Tap R can empty the tank in 3 hrs.

  1. If tap R is closed, how long would it take taps P and Q to fill the tank?
  2. Calculate how long it would take to fill the tank when the three taps P, Q and R. are left running?

Solution

  1. Tap P fills of the tank in 1 h.

Tap Q fills  of the tank in 1 h.

Tap R empties   of the tank in 1 h.

In one hour, P and Q fill

Therefore

Time taken to fill the tank

  1. In 1 h, P and Q fill of tank while R empties  of the tank.

When all taps are open , of the tank is filled in 1 hour.

= 2

Example

In what proportion should grades of sugars costing sh.45 and sh.50 per kilogram be mixed in order to produce a blend worth sh.48 per kilogram?

 

 

Solution

Method 1

Let n kilograms of the grade costing sh.45 per kg be mixed with 1 kilogram of grade costing sh.50 per kg.

Total cost of the two blends is sh.

The mass of the mixture is

Therefore total cost of the mixture is

45n + 50 = 48 (n +1)

45n + 50 = 48 n + 48

50 = 3n + 48

2 = 3n

The two grades are mixed in the proportion

 

 

Method 2

Let x kg of grade costing sh 45 per kg be mixed with y kg of grade costing sh.50 per kg. The total cost will be sh.(45x + 50 y)

Cost per kg of the mixture is sh.

The proportion is x : y = 2:3

 

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

Past KCSE Questions on the topic.

 

  1. Akinyi bought and beans from a wholesaler. She then mixed the maize and beans the ratio 4:3 she brought the maize as Kshs. 12 per kg and the beans 4 per kg. If she was to make a profit of 30% what should be the selling price of 1 kg of the mixture?
  2. A rectangular tank of base 2.4 m by 2.8 m and a height of 3 m contains 3,600 liters of water initially. Water flows into the tank at the rate of 0.5 litres per second

Calculate the time in hours and minutes, required to fill the tank

  1. A company is to construct a parking bay whose area is 135m2. It is to be covered with concrete slab of uniform thickness of 0.15. To make the slab cement. Ballast and sand are to be mixed so that their masses are in the ratio 1: 4: 4. The mass of m3 of dry slab is 2, 500kg.

Calculate

(a)        (i)         The volume of the slab

(ii)        The mass of the dry slab

(iii)       The mass of cement to be used

(b)        If one bag of the cement is 50 kg, find the number of bags to be purchased

  • If a lorry carries 7 tonnes of sand, calculate the number of lorries of sand

to be purchased.

  1. The mass of a mixture A of beans and maize is 72 kg. The ratio of beans to maize

is 3:5 respectively

(a)        Find the mass of maize in the mixture

(b)        A second mixture of B of beans and maize of mass 98 kg in mixed with A. The final ratio of beans to maize is 8:9 respectively. Find the ratio of beans to maize in B

  1. A retailer bought 49 kg of grade 1 rice at Kshs. 65 per kilogram and 60 kg of grade II rice at Kshs 27.50 per kilogram. He mixed the tow types of rice.
  • Find the buying price of one kilogram of the mixture
  • He packed the mixture into 2 kg packets
    • If he intends to make a 20% profit find the selling price per packet
    • He sold 8 packets and then reduced the price by 10% in order to attract customers. Find the new selling price per packet.
    • After selling 1/3 of the remainder at reduced price, he raised the price so as to realize the original goal of 20% profit overall. Find the selling price per packet of the remaining rice.
  1. A trader sells a bag of beans for Kshs 1,200. He mixed beans and maize in the ration 3: 2. Find how much the trader should he sell a bag of the mixture to realize the same profit?
  2. Pipe A can fill an empty water tank in 3 hours while, pipe B can fill the same tank in 6 hours, when the tank is full it can be emptied by pipe C in 8 hours. Pipes A and B are opened at the same time when the tank is empty.

If one hour later, pipe C is also opened, find the total time taken to fill the tank

  1. A solution whose volume is 80 litres is made 40% of water and 60% of alcohol. When litres of water are added, the percentage of alcohol drops to 40%

(a)        Find the value of x

(b)        Thirty litres of water is added to the new solution. Calculate the percentage

(c)        If 5 litres of the solution in (b) is added to 2 litres of the original solution, calculate in the simplest form, the ratio of water to that of alcohol in the resulting solution

  1. A tank has two inlet taps P and Q and an outlet tap R. when empty, the tank can be filled by tap P alone in 4 ½ hours or by tap Q alone in 3 hours. When full, the tank can be emptied in 2 hours by tap R.

(a)        The tank is initially empty. Find how long it would take to fill up the tank

  • If tap R is closed and taps P and Q are opened at the same time                                                                                     (2mks)
  • If all the three taps are opened at the same time

(b)        The tank is initially empty and the three taps are opened as follows

P at 8.00 a.m

Q at 8.45 a.m

R at 9.00 a.m

(i)         Find the fraction of the tank that would be filled by 9.00 a.m

(ii)        Find the time the tank would be fully filled up

 

  1. Kipketer can cultivate a piece of land in 7 hrs while Wanjiru can do the same work in 5 hours. Find the time they would take to cultivate the piece of land when working together.

 

  1. Mogaka and Ondiso working together can do a piece of work in 6 days. Mogaka, working alone, takes 5 days longer than Onduso. How many days does it take Onduso to do the work alone.

 

  1. Wainaina has two dairy farms A and B. Farm A produces milk with 3 ¼ percent fat and farm B produces milk with 4 ¼ percent fat.

(a)        (i)         The total mass of milk fat in 50 kg of milk from farm A and 30kg

of milk from farm B.

(ii)        The percentage of fat in a mixture of 50 kg of milk A and 30 kg of milk from B

(b)        Determine the range of values of mass of milk from farm B that must be used in a 50 kg mixture so that the mixture may have at least 4 percent fat.

 

  1. A construction firm has two tractors T1 and T2. Both tractors working together can complete the work in 6 days while T1 alone can complete the work in 15 days. After the two tractors had worked together for four days, tractor T1­ broke down.

Find the time taken by tractor T2 complete the remaining work.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

           GRAPHICAL METHODS

CHAPTER FIFTY THREE

 

Specific Objectives

By the end of the topic the learner should be able to:

(a) Makes a table of values from given relations;

(b) Use the table of values to draw the graphs of the relations;

(c) Determine and interpret instantaneous rates of change from a graph;

(d) Interpret information from graphs;

(e) Draw and interpret graphs from empirical data;

(f) Solve cubic equations graphically;

(g) Draw the line of best fit;

(h) Identify the equation of a circle;

(i) Find the equation of a circle given the centre and the radius;

(j) Determine the centre and radius of a circle and draw the circle on acartesian plane.

Content

(a) Tables and graphs of given relations

(b) Graphs of cubic equations

(c) Graphical solutions of cubic equations

(d) Average rate of change

(e) Instantaneous rate of change

(f) Empirical data and their graphs

(g) The line of best fit

(h) Equation of a circle

(i) Finding of the equation of a circle

(j) Determining of the centre and radius of a circle.

Introduction

These are ways or methods of solving mathematical functions using graphs.

Graphing solutions of cubic Equations

A cubic equation has the form

ax3 + bx2 + cx + d = 0

where a, b , c and d are constants

It must have the term in x3 or it would not be cubic (and so a  0), but any or all of b, c and d can be zero. For instance,

x3 −6x2 +11x −6 = 0,                 4x3 +57 = 0,              x3 +9x = 0

are all cubic equations.

The graphs of cubic equations always take the following shapes.

 

3
2
1
-1
-2
-3
1
2
3
-1
y
x

Y =x3 −6x2 +11x −6 = 0.

Notice that it starts low down on the left, because as x gets large and negative so does x3 and it finishes higher to the right because as x gets large and positive so does x3. The curve crosses the x-axis three times, once where x = 1, once where x = 2 and once where x = 3. This gives us our three separate solutions.

Example

(a) Fill in the table below for the function y = -6 + x + 4x2 + x3 for -4 £x £ 2

 

x -4 -3 -2 -1 0 1 2
-6 -6 -6 -6 -6 -6 -6 -6
x -4 -3 -2 -1 0 1 2
4x2 16 4
x3
y

(b) Using the grid provided draw the graph for y = -6 + x + 4x2 + x3 for -4£ x £ 2         

(c)         Use the graph to solve the equations:-

 

-6 + x + 4x2 + x3 = 0

.x3 + 4x2 + x – 4 = 0

-2 + 4x2 + x3 = 0

 

Solution

The table shows corresponding values of x and y for y=  -6 + x + 4x2 + x3

X -4 -3 -2 -1 0 1 2
-6 -6 -6 -6 -6 -6 -6 -6
X -4 -3 -2 -1 0 1 2
4x2 64 36 16 4 0 4 16
X3 -64 -27 -8 -1 0 1 8
Y=-6+x+4x2+x3 -10 0 0 -4 -6 0 20

From the graph the solutions for x are x =-3 , x = -2, x = 1

 

  1. To solve equation y = x3 + 4x2 + x -6 we draw a straight line from the diffrence of the two equations and then we read the coordinates at the point of the intersetion of the curve and the straight line

y = x3 + 4x2 + x -6

             0 = x3 + 4x2 + x -4

                           y = -2                        solutions 0.8 ,-1.5 and -3.2

 

                                                                                    x     1     0     -2

               y = x3 + 4x2 + x – 6                                    y    -3   -4     -8              

            0 = x3 + 4x2 + 0 – 2 

                        y =    x – 4                   

 

 

y=-6 + 4x2 +x

                        

 

 

 

 

 

 

 

 

 

y=x-4

 

 

 

Y=-2

 

 

c          (i) solution 0.8

-1.5                                                                             

And -3.2

Average Rate of change

 

 

 

Defining the Average Rate of Change

The notion of average rate of change can be used to describe the change in any variable with respect to another. If you have a graph that represents a plot of data points of the form (x, y), then the average rate of change between any two points is the change in the y value divided by the change in the x value.

 

Populationinmillions
50
100
150
200
250
300
90
years

 

change in y

The average rate of change of y with respect to x

change in x

 

Note;

  • The rate of change of a straight  ( the slop)line is the same between all points along the line
  • The rate of change of a quadratic function is not constant (does not remain the same)

Example

The graph below shows the rate of growth of a plant,from the graph, the change in height between day 1 and day 3 is given by 7.5 cm – 3.8 cm = 3.7 cm.

Average rate of change is

The average rate of change for the next two days is  = 0.65cm/day

Note;

  • The rate of growth in the first 2 days was 1.85 cm/day while that in the next two days is only 0.65 cm /day.These rates of change are represented by the gradients of the lines PQ and QR respectively.

Number of days

The gradient of the straight line is 20 ,which is constant.The gradient represents the rate of distance with time (speed) which is 20 m/s.

Rate of change at an instant

We have seen that to find the rate of change at an instant  ( particular point),we:

  • Draw a tangent to the curve at that point
  • Determine the gradient of the tangent

The gradient of the tangent to the curve at the point is the rate of change at that point.

 

Empirical graphs

An Empirical graph is a graph that you can use to evaluate the fit of a distribution to your data by drawing the line of best fit. This is because raw data usually have some errors.

Example

The table below shows how length l cm of a metal rod varies with increase in temperature T ( .

 

 

 

Temperature

Degrees C

O 1 2 3 5 6 7 8
Length cm 4.0 4.3 4.7 4.9 5.0 5.9 6.0 6.4

 

Solution

NOTE;

  • There is a linear relation between length and temperature.
  • We therefore draw a line of best fit that passes through as many points as possible.
  • The remaining points should be distributed evenly below and above the line

 

 

 

 

 

 

The line cuts   the y – axis at (0, 4) and passes through the point (5, 5.5).Therefore, the gradient of the line is  = 0.3.The equation of the line is l =0.3T + 4.

 

 

Reduction of Non-linear Laws to Linear Form.

When we plot the graph of xy=k, we get a curve.But when we plot y against , w get a straight line whose gradient is k.The same approach is used to obtain linear relations from non-linear relations of the form y .

 

Example

The table below shows the relationship between A and r

 

 

r 1 2 3 4 5
A 3.1 12.6 28.3 50.3 78.5

 

 

 

It is suspected that the relation is of the form A= By drawing a suitable graph,verify the law connecting A and r and determine the value of K.

Solution

If we plot A against  ,we should get a straight line.

r 1 2 3 4 5
A 3.1 12.6 28.3 50.3 78.5
1 4 9 16 25

 

 

 

 

 

Since the graph of A against is a straight line, the law A =k holds.The gradient of this line is 3.1 to one decimal place. This is the value of k.

 

 

 

Example

From  1960 onwards, the population P of  Kisumu  is believed to obey a law of the form P = ,Where k and A are constants and t is the time in years reckoned from 1960.The table below shows the population of the town since 1960.

r 1960 1965 1970 1975 1980 1985 1990
p 5000 6080 7400 9010 10960 13330 16200

 

 

By plotting a suitable graph, check whether the population growth obeys the given law. Use the graph to estimate the value of A.

Solution

The law to be tested is P= .Taking logs of both sides we get log P = .Log P = log K + t log A, which is in the form y = mx + Thus we plot log P against t.(Note that log A is a constant).The below shows the corresponding values of  t and log p.

r 1960 1965 1970 1975 1980 1985 1990
Log P 3.699 3.784 3.869 3.955 4.040 4.125 4.210

 

 

Since the graph is a straight line ,the law P = holds.

Log  A is given by the gradient of the straight line.Therefore, log A = 0.017.

Hence,A = 1.04

Log k is the vertical intercept.

Hence log k =3.69

Therefore k = 4898

Thus, the relationship is P = 4898 (1.04

Note;

  • Laws of the form y=  can be written in the linear form as: log y = log k + x log A (by taking logs of both sides)
  • When log y is plotted against x , a straight line is obtained.Its gradient is log A  and the intercept is log k.
  • The law of the form y = ,where k and n are constants can be written in linear form as;
  • Log y =log k + n log x.
  • We therefore plot log y is plotted against log x.
  • The gradient of the line gives n while the vertical intercept is log k

 

 

Summary

For the law y = d + cx2 to be verified it is necessary to plot a graph of the variables in a modified

Form as follows y =d  is compared with y = mx + c   that is y =

  • Y is plotted on the y axis
  • is plotted on the x axis
  • The gradient is c
  • The vertical axis intercept is d

 

For the law y – a = to be verified it is necessary to plot a graph of the variables in a x

Modified form as follows

y a =  , i.e. y =  + a which is compared with y = mx + c

 

  • y should be plotted on the y axis
  • should be plotted on the x axis
  • The gradient is b
  • The vertical axis intercept is a

 

For the law y e =  to be verified it is necessary to plot a graph of the variables in a

Modified form as follows. The law y e =  is f  compared with y = mx + c.

  • y should be plotted on the vertical axis
  • should be plotted on the horizontal axis
  • The gradient is f
  • The vertical axis intercept is e

For the law y cx = bx2 to be verified it is necessary to plot a graph of the variables in a

Modified form as follows. The law y cx = b  is = b x + c compared with y = mx + c,

  • should be plotted on y axis
  • X should be plotted on x axis
  • The gradient is b
  • The vertical axis intercept is c

 

For the law y =  + bx to be verified it is necessary to plot a graph of the variables in a ax

Modified form as follows. The law   = a  compared with y = mx + c

 

  • should be plotted on the vertical axis
  • should be plotted on the horizontal axis
  • The gradient is a
  • The vertical intercept is b

 

Equation of a circle

A circle is a set of all points that are of the same distance r from a fixed point. The figure below is a circle centre ( 0,0) and radius 3 units

 

 

P ( x ,y ) is a point on the circle. Triangle PON is right – angled at N.

By Pythagoras’ theorem;

But ON = x, PN = y and OP =3 .Therefore,

 

Note;

The general equation of a circle centre ( 0 ,0 ) and radius r is

 

Example

Find the equation of a circle centre (0, 0) passing through   (3, 4)

 

 

 

 

 

Solution

Let the radius of the circle be r

From Pythagoras theorem;

 

 

Example

Consider a circle centre ( 5 , 4 ) and radius 3 units.

 

 

Solution

In the figure below triangle CNP is right angled at N.By pythagoras theorem;

But  CN= ( x – 5), NP = (y – 4) and CP =3 units.

Therefore, .

Note;

The equation of a circle centre ( a,b) and radius r units is given by;

 

Example

Find the equation of a circle centre (-2 ,3) and radius 4 units

 

 

 

 

Solution

General equation of the circle is  .Therefore a = -2 b =3 and r = 4

 

 

 

Example

Line AB is the diameter of a circle such that the co-ordinates of A and B are ( -1 ,1) and(5 ,1) respectively.

  • Determine the centre and the radius of the circle
  • Hence, find the equation of the circle

 

Solution

Radius =

=  = 3

  • Equation of the circle is ;

 

 

Example

The equation of a circle is given by – 6x + .Determine the centre and radius of the circle.

 

Solution

– 6x +

Completing the square on the left hand side;

– 6x +

Therefore centre of the circle is (3,-2) and radius is 4 units. Note that the sign changes to opposite positive sign becomes negative while negative sign changes to positive.

 

Example

Write the equation of the circle that has   and  as endpoints of a diameter.

Method 1:         Determine the center using the Midpoint Formula:

 

Determine the radius using the distance formula (center and end of diameter):

 

Equation of circle is:

Method 2:         Determine center using Midpoint Formula (as before):

Thus, the circle equation will have the form

Find  by plugging the coordinates of a point on the circle in for

Let’s use

Again, we get this equation for the circle:

 

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

Past KCSE Questions on the topic.

 

 

  1. The table shows the height metres of an object thrown vertically upwards varies with the time t seconds

The relationship between s and t is represented by the equations s = at2 + bt + 10 where b are constants.

 

T 0 1 2 3 4 5 6 7 8 9 10
S 45.1 49.9 -80
  • (i) Using the information in the table, determine the values of a and b

(ii) Complete the table

(b) (i)   Draw a graph to represent the relationship between s and t

(ii)   Using the graph determine the velocity of the object when t = 5 seconds

  1. Data collected form an experiment involving two variables X and Y was recorded as shown in the table below
x 1.1 1.2 1.3 1.4 1.5 1.6
y -0.3 0.5 1.4 2.5 3.8 5.2

The variables are known to satisfy a relation of the form y = ax3 + b where a and b are constants

  • For each value of x in the table above,  write  down the value  of  x3
  • (i) By drawing a suitable straight line graph, estimate the values of a and b

(ii) Write down the relationship connecting y and x

  1. Two quantities P and r are connected by the equation p = krn. The table of values

of P and r is given below.

 

P 1.2 1.5 2.0 2.5 3.5 4.5
R 1.58 2.25 3.39 4.74 7.86 11.5

 

  1. a) State a liner equation connecting P and r.
  2. b) Using the scale 2 cm to represent 0.1 units on both axes, draw a suitable

line graph on the grid provided. Hence estimate the values of K and n.

  1. The points which coordinates (5,5) and (-3,-1) are the ends of a diameter of  a circle centre A

Determine:

(a)        The coordinates of A

The equation of the circle, expressing it in form x2 + y2 + ax + by + c = 0

where a, b, and c are constants each computer sold

  1. The figure below is a sketch of the graph of the quadratic function y = k

(x+1) (x-2)

 

 

 

 

 

 

Find the value of k

  1. The table below shows the values of the length X ( in metres ) of a pendulum and the corresponding values of the period T ( in seconds) of its oscillations  obtained  in an experiment.
X ( metres) 0.4 1.0 1.2 1.4 1.6
T ( seconds) 1.25 2.01 2.19 2.37 2.53

(a)       Construct a table of values of log X and corresponding values of log T,

correcting each value to 2 decimal places

  1. b) Given that the relation between the values of log X and log T approximate to a linear law of the form m log X + log a where  a and b are constants

(i)         Use the axes on the grid provided to draw the line of best fit for the graph of log T against log X.

 

 

 

 

 

 

 

 

(ii)        Use the graph to estimate the values of a and b

(iii)       Find, to decimal places the length of the pendulum whose period is 1 second.

 

  1. Data collection from an experiment involving two variables x and y was recorded as shown in the table below

 

X 1.1 1.2 1.3 1.4 1.5 1.6
Y -0.3 0.5 1.4 2.5 3.8 5.2

 

The variables are known to satisfy a relation of the form y = ax3 + b where a and b

are constants

(a)        For each value of x in the table above. Write down the value of x3

(b)        (i) By drawing s suitable straight line graph, estimate the values of  a and b

(ii) Write down the relationship connecting y and x

 

  1. Two variables x and y, are linked by the relation y = axn. The figure below shows part of the straight line graph obtained when log y is plotted against log x.

 

 

 

 

Calculate the value of a and n

  1. The luminous intensity I of a lamp was measured for various values of voltage v across it. The results were as shown below
V(volts) 30 36 40 44 48 50 54
L (Lux ) 708 1248 1726 2320 3038 3848 4380

 

It is believed that V and l are related by an equation of the form l = aVn where a and n are constant.

(a)        Draw a suitable linear graph and determine the values of a and n

(b)        From the graph find

(i)         The value of I when V = 52

(ii)        The value of V when I = 2800

  1. In a certain relation, the value of A and B observe a relation B= CA + KA2 where C and K are constants. Below is a table of values of A and B
A 1 2 3 4 5 6
B 3.2 6.75 10.8 15.1 20 25.2

 

(a) By drawing a suitable straight line graphs, determine the values of C and K.

(b) Hence write down the relationship between A and B

(c) Determine the value of B when A = 7

  1. The variables P and Q are connected by the equation P = abq where a and b are constants. The value of p and q are given below
P 6.56 17.7 47.8 129 349 941 2540 6860
Q 0 1 2 3 4 5 6 7

 

(a)        State the equation in terms of p and q which gives a straight line graph

(b)        By drawing a straight line graph, estimate the value of constants a and b and give your answer correct to 1 decimal place.

 

 

 

                PROBABILITY

CHAPTER FIFTY FOUR

 

Specific Objectives

By the end of the topic the learner should be able to:

(a) Define probability;

(b) Determine probability from experiments and real life situations;

(c) Construct a probability space;

(d) Determine theoretical probability;

(e) Differentiate between discrete and continuous probability;

(f) Differentiate mutually exclusive and independent events;

(g) State and apply laws of probability;

(h) Use a tree diagram to determine probabilities.

Content

(a) Probability

(b) Experimental probability

(c) Range of probability measure 0 ^ P (x) ^1

(d) Probability space

(e) Theoretical probability

(f) Discrete and continuous probability (simple cases only)

(g) Combined events (mutually exclusive and independent events)

(h) Laws of probability

(i) The tree diagrams.

 

 

 

Introduction

The likelihood of an occurrence of an event or the numerical measure of chance is called probability.

Experimental probability

This is where probability is determined by experience or experiment. What is done or observed is the experiment. Each toss is called a trial and the result of a trial is the outcome. The experimental probability of a result is given by (the number of favorable outcomes) / (the total number of trials)

Example

A boy had a fair die with faces marked 1to6 .He threw this die up 50 times and each time he recorded the number on the top face. The result of his experiment is shown below.

face 1 2 3 4 5 6
Number of times a face has shown up 11 6 7 9 9 8

 

 

 

 

What is the experimental provability of getting?

a.)1   b.) 6

Solution

a.) P(Event) =

P(1)= 11/50

b.) P(4)= 9/50

Example

From the past records, out of the ten matches a school football team has played, it has won seven.How many possible games might the school win in thirty matches ?.

 

Solution

P(winning in one math) = 7/10.

Therefore the number of possible wins in thirty matches = 7/10 x 30 = 21 matches

 

Range of probability Measure

If P(A) is the probability of an event A happening and P(A’) is the probability of an event A not happening, Then P(A’)= 1 – P(A)  and P(A’) + P(A)= 1

Probability are expressed as fractions, decimals or percentages.

Probability space

A list of all possible outcomes is probability space or sample space .The coin is such that the head or tail have equal chances of occurring. The events head or tail are said to be equally likely or eqiprobable.

Theoretical probability

This can be calculated without necessarily using any past experience or doing any experiment. The probability of an event happening #number of favorable outcomes /total number of outcomes.

Example

A basket contains 5 red balls, 4green balls and 3 blue balls. If a ball is picked at random from the basket, find:

a.)The probability of picking a blue ball

b.) The probability of not picking a red ball

 

Solution

a.)Total number of balls is 12

The number of blue balls is 3

Solution

a.) therefore, P (a blue ball) =3/12

b.)The number of balls which are not red is 7.

Therefore P ( not a red ball)= 7/12

 

 

Example

A bag contains 6 black balls and some brown ones. If a ball is picked at random the probability that it is black is 0.25.Find the number of brown balls.

Solution

Let the number of balls be x

Then the probability that a black ball is picked at random is 6/x

Therefore 6/x = 0.25

x = 24

The total number of bald is 24

Then the number of brown balls is 24 – 6 =18

Note:

When all possible outcomes are count able, they are said to be discrete.

Types of probability

Combined Events

These are probability of two or more events occurring

Mutually Exclusive Events

Occurrence of one excludes the occurrence of the other or the occurrence of one event depend on the occurrence of the other.. If A and B are two mutually exclusive events, then ( A or B) = P (A) + P (B). For example when a coin is tossed the result will either be a head or a tail.

Example

  • If a coin is tossed ;

P(head) + P( tail)

=

Note;

If [OR] is used then we add

 

 

 

Independent Events

Two events A and B are independent if the occurrence of A does not influence the occurrence of B and vice versa. If A and B are two independent events, the probability of them occurring together is the product of their individual probabilities .That is;

P (A and B) = P (A) x P(B)

Note;

When we use [AND] we multiply ,this is the multiplication law of probability.

 

Example

A coin is tosses twice. What is the probability of getting a tail in both tosses?

Solution

The outcome of the 2nd toss is independ of the outcome of the first .

Therefore;

P (T and T ) = P( T) X P( T)

= =

Example

A boy throws  fair coin and a regular tetrahedron with its four faces marked 1,2,3 and 4.Find the probability that he gets a 3 on the tetrahedron and a head on the coin.

Solution

These are independent events.

P (H) =  P(3) =

Therefore;

P (H and 3) = P (H) x P (3)

= ½ x ¼

= 1/8

 

 

Example

A bag contains 8 black balls and 5 white ones.If two balls are drawn from the bag, one at a time,find the probability of drawing a black ball and a white ball.

  • Without replacement
  • With replacement

Solution

  • There are only two ways we can get a black and a white ball: either drawing a white then a black,or drawing a black then a white.We need to find the two probabilities;

P( W followed by B) = P (W and B)

=

  • P(B followed by W) = P (B and W)

Note;

The two events are mutually exclusive, therefore.

P (W followed by B) or ( B followed by W )= P( W followed by B ) + P ( B followed by W)

= P (W and B) + P( B and W)

=

Since we are replacing, the number of balls remains 13.

Therefore;

P (W and B) =

P ( B and W) =

Therefore;

P [(W and B) or (B and W)] = P (W and B) + P (B and W)

=

 

 

 

Example

Kamau ,Njoroge and Kariuki are practicing archery .The probability of Kamau hitting the target is 2/5,that of Njoroge hitting the target is ¼ and that of Kariuki hitting the target is 3/7 ,Find the probability that in one attempt;

  • Only one hits the target
  • All three hit the target
  • None of them hits the target
  • Two hit the target
  • At least one hits the target

Solution

  • P(only one hits the target)

=P (only Kamau hits and other two miss) =2/5 x 3/5 x 4/7

= 6/35

P (only Njoroge hits and other two miss) = 1/4 x 3/5 x 4/7

= 3/35

P (only Kariuki hits and other two miss)   = 3/7 x 3/5 x ¾

= 27/140

P (only one hits) = P (Kamau hits or Njoroge hits or Kariuki hits)

= 6/35 + 3/35 +27/140

= 9/20

  • P ( all three hit) = 2/5 x 1/4 x 3/7

= 3/70

  • P ( none hits) = 3/5 x 3/4 x 4/7

= 9/35

  • P ( two hit the target ) is the probability of ;

Kamau and Njoroge hit the target and Kariuki misses = 2/5 x 3/7 x 4/7

Njoroge and Kariuki hit the target and Kamau misses = 1/4 x 3/7 x 3/5

 

Or

 

Kamau and Kariuki hit the target and Njoroge misses = 2/5 x 3/7 x 3/4

Therefore P (two hit target) = (2/5 x 1/4 x 4/7) + (1/4 x 3/7 x 3/5) + (2/5 x 3/7 x 3/4)

= 8/140 + 9/140 + 18/140

= ¼

  • P (at least one hits the target) = 1 – P ( none hits the target)

= 1 – 9/35

= 26/35

Or

 

P (at least one hits the target) = 1 – P (none hits the target)

= 26/35

Note;

P (one hits the target) is different from P (at least one hits the target)

 

Tree diagram

Tree diagrams allows us to see all the possible outcomes of an event and calculate their probality.Each branch in a tree diagram represents a possible outcome .A tree diagram which represent a coin being tossed three times look like this;

 

 

From the tree diagram, we can see that there are eight possible outcomes. To find out the probability of a particular outcome, we need to look at all the available paths (set of branches).

 

The sum of the probabilities for any set of branches is always 1.

 

Also note that in a tree diagram to find a probability of an outcome we multiply along the branches and add vertically.

 

The probability of three heads is:

 

P (H H H) = 1/2 × 1/2 × 1/2 = 1/8

 

P (2 Heads and a Tail) = P (H H T) + P (H T H) + P (T H H)

 

= 1/2 × 1/2 × 1/2 + 1/2 × 1/2 × 1/2 + 1/2 × 1/2 × 1/2

 

= 1/8 + 1/8 + 1/8

 

= 3/8

Example

Bag A contains three red marbles and four blue marbles.Bag B contains 5 red marbles and three blue marbles.A marble is taken from each bag in turn.

  • What is the probability of getting a blue bead followed by a red
  • What is the probability of getting a bead of each color

Solution

  • Multiply the probabilities together

P( blue and red) =4/7 x 5/8 = 20/56

=5/14

  • P(blue and red or red and blue) = P( blue and red ) + P (red and blue)

= 4/7 x 5/8 + 3/7 x 3/8

= 20/56 + 9/56

=29/56

Example

The probability that Omweri goes to Nakuru is ¼ .If he goes to Nakuru, the probability that he will see flamingo is ½ .If he does not go to Nakuru, the probability that he will see flamingo is 1/3 .Find the probability that;

  • Omweri will go to Nakuru and see a flamingo.
  • Omweri will not go to Nakuru yet he will see a flamingo
  • Omweri will see a flamingo

Solution

Let N stand for going to Nakuru ,N’  stand for not going to Nakuru, F stand for seeing a flamingo and F’ stand for not seeing a flamingo.

  • P (He goes to Nakuru and sees a flamingo) = P(N and F)

= P(N) X P(F)

= ¼   X ½

= 1/8

  • P( He does not go to Nakuru and yet sees a flamingo) =P( N’) X P( F)

= P (N’ and F)

= 3/4 X 1/3

= ¼

  • P ( He sees a flamingo) = P(N and F) or P ( N’ and F)

= P (N and F) + P (N’ and F)

= 1/8 + 1/4

= 3/8

 

End of topic

                            Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

 

Past KCSE Questions on the topic.

 

 

  1. The probabilities that a husband and wife will be alive 25 years from now are 0.7 and 0.9 respectively.

Find the probability that in 25 years time,

  • Both will be alive
  • Neither will be alive
  • One will be alive
  • At least one will be alive
  1. A bag contains blue, green and red pens of the same type in the ratio 8:2:5 respectively. A pen is picked at random without replacement and its colour noted

(a)        Determine the probability that the first pen picked is

(i)         Blue

(ii)        Either green or red

(b)        Using a tree diagram, determine the probability that

(i)         The first two pens picked are both green

(ii)        Only one of the first two pens picked is red.

  1. A science club is made up of boys and girls. The club has 3 officials. Using a tree diagram or otherwise find the probability that:

(a) The club officials are all boys

(b) Two of the officials are girls

  1. Two baskets A and B each contain a mixture of oranges and limes, all of the same size. Basket A contains 26 oranges and 13 limes. Basket B contains 18 oranges and 15 limes. A child selected a basket at random and picked a fruit at a random from it.

(a)        Illustrate this information by a probabilities tree diagram

(b)        Find the probability that the fruit picked was an orange.

  1. In form 1 class there are 22 girls and boys. The probability of a girl completing the secondary education course is 3 whereas that of a boy is 2/3

(a)        A student is picked at random from class. Find the possibility that,

  • The student picked is a boy and will complete the course
  • The student picked will complete the course

(b)        Two students are picked at random. Find the possibility that they are a boy

and a girl and that both will not complete the course.

  1. Three representatives are to be selected randomly from a group of 7 girls and 8

boys. Calculate the probability of selecting two girls and one boy.

  1. A poultry farmer vaccinated 540 of his 720 chickens against a disease. Two months later, 5% of the vaccinated and 80% of the unvaccinated chicken, contracted the disease. Calculate the probability that a chicken chosen random contacted the disease.
  2. The probability of three darts players Akinyi, Kamau, and Juma hitting the bulls eye are 0.2, 0.3 and 1.5 respectively.

(a)        Draw a probability tree diagram to show the possible outcomes

(b)        Find the probability that:

(i)         All hit the bull’s eye

(ii)        Only one of them hit the bull’s eye

(iii)       At most one missed the bull’s eye

  1. (a) An unbiased coin with two faces, head (H)  and tail (T), is tossed three

times, list all the possible outcomes.

Hence determine the probability of getting:

(i)         At least two heads

(ii)        Only one tail

  • During a certain motor rally it is predicted that the weather will be either dry (D) or wet (W). The probability that the weather will be dry is estimated to be 7/10. The probability for a driver to complete (C) the rally during the dry weather is estimated to be 5/6. The probability for a driver to complete the rally during wet weather is estimated to be 1/10. Complete the probability tree diagram given below.

 

 

 

 

 

 

 

 

 

 

 

 

 

What is the probability that:

(i)         The driver completes the rally?

(ii)        The weather was wet and the driver did not complete the rally?

  1. There are three cars A, B and C in a race. A is twice as likely to win as B while B is twice as likely to win as c. Find the probability that.
  2. a) A wins the race
  3. b) Either B or C wins the race.
  4. In the year 2003, the population of a certain district was 1.8 million. Thirty per cent of the population was in the age group 15 – 40 years. In the same year, 120,000 people in the district visited the Voluntary Counseling and Testing (VCT) centre for an HIV test.

If a person was selected at random from the district in this year. Find the probability that the person visited a VCT centre and was in the age group 15 – 40 years.

  1. (a) Two integers x and y are selected at random from the integers 1 to 8. If the

same integer may be selected twice, find the probability that

  • |x – y| = 2
  • |x – y| is 5 or more

(iii)       x>y

(b)        A die is biased so that when tossed, the probability of a number r showing up, is given by p ® = Kr where K is a constant and r = 1, 2,3,4,5 and 6 (the number on the faces of the die

(i)         Find the value of K

(ii)        If the die is tossed twice, calculate the probability that the total

score is 11

  1. Two bags A and B contain identical balls except for the colours. Bag A contains 4 red balls and 2 yellow balls. Bag B contains 2 red balls and 3 yellow balls.
    • If a ball is drawn at random from each bag, find the probability that both balls are of the same colour.
    • If two balls are drawn at random from each bag, one at a time without replacement, find the probability that:

(i)         The two balls drawn from bag A or bag B are red

(ii)        All the four balls drawn are red

 

  1. During inter – school competitions, football and volleyball teams from Mokagu high school took part. The probability that their football and volleyball teams would win were 3/8 and 4/7 respectively.

Find the probability that

(a)        Both their football and volleyball teams

(b)        At least one of their teams won

 

  1. A science club is made up of 5 boys and 7 girls. The club has 3 officials. Using a tree diagram or otherwise find the probability that:

(a)        The club officials are all boys

(b)        Two of the officials are girls

 

  1. Chicks on Onyango’s farm were noted to have either brown feathers brown or black tail feathers. Of those with black feathers 2/3 were female while 2/5 of those with brown feathers were male. Otieno bought two chicks from Onyango. One had black tail feathers while the other had brown find the probability that Otieno’s chicks were not of the same gender

was

  1. Three representatives are to be selected randomly from a group of 7 girls and 8 boys. Calculate the probability of selecting two girls and one boy
  2. The probability that a man wins a game is ¾. He plays the game until he wins. Determine the probability that he wins in the fifth round.

 

  1. The probability that Kamau will be selected for his school’s basketball team is ¼. If he is selected for the basketball team. Then the probability that he will be selected for football is 1/3 if he is not selected for basketball then the probability that he is selected for football is 4/5. What is the probability that Kamau is selected for at least one of the two games?

 

  1. Two baskets A and B each contains a mixture of oranges and lemons. Baskets A contains 26 oranges and 13 lemons. Baskets B contains 18 oranges and 15 lemons. A child selected a basket at random and picked at random a fruit from it. Determine the probability that the fruit picked an orange.

 

 

 

 

 

 

 

 

 

 

 

 

                      VECTORS

CHAPTER FIFTY FIVE

 

Specific Objectives

By the end of the topic the learner should be able to:

(a) Locate a point in two and three dimension co-ordinate systems;

(b) Represent vectors as column and position vectors in three dimensions;

(c) Distinguish between column and position vectors;

(d) Represent vectors in terms of i, j , and k;

(e) Calculate the magnitude of a vector in three dimensions;

(f) Use the vector method in dividing a line proportionately;

(g) Use vector method to show parallelism;

(h) Use vector method to show collinearity;

(i) State and use the ratio theorem,

(j) Apply vector methods in geometry.

Content

(a) Coordinates in two and three dimensions

(b) Column and position vectors in three dimensions

(c) Column vectors in terms of unit vectors i, j , and k

(d) Magnitude of a vector

(e) Parallel vectors

(f) Collinearity

(g) Proportional division of a line

(h) Ratio theorem

(i) Vector methods in geometry.

 

Vectors in 3 dimensions:

3 dimensional vectors can be represented on a set of 3 axes at right angles to each other (orthogonal), as shown in the diagram.

Note that the z axis is the vertical axis.

To get from A to B you would move:

4 units in the x-direction, (x-component)

3 units in the y-direction, (y-component)

2 units in the z-direction. (z-component)

In component form:  =

In general:  = ,

 

 

 

 

 

Column and position vectors

In three dimensions, a displacement is represented b a column vector of the form  where p,q and r are the changes in x,y,z directions respectively.

Example

The displacement from A ( 3, 1, 4 ) to B ( 7 ,2,6) is represented b the column vector,

The position vector of A written as OA is  where O is the origin

Addition of vectors in three dimensions is done in the same way as that in two dimensions.

Example

If a = then

  • 3a + 2b =

 

  • 4a – ½ b =

 

Column Vectors in terms of unit Vectors

In three dimension the unit vector in the x axis direction is = ,that in the dirction of the y axis is  while that in the direction of z – axis is  .

Diagrammatic representation of the vectors.

 

Three unit vectors are written as ; i =

 

 

Express vector  in terms of the unit vector I , j and k

Solution

5

=5i – 2j +7k

Note;

The column vector can be expressed as a i  + b j + ck

 

 

Magnitude of a 3 dimensional vector.

Given the vector AB = xi + y j + 2 k,then the magnitude of AB is written as |AB| =

This is the length of the vector.

Use Pythagoras’ Theorem in 3 dimensions.

AB2 = AR2 + BR2

= (AP2 + PR2) + BR2

=

and if u =   then the magnitude of u,   | u | = length of AB

 

 

 

 

Distance formula for 3 dimensions

Recall that since:  = , then if    then

Since  x =

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Example:

  1. If A is (1, 3, 2) and B is (5, 6, 4)

Find

  1. If Find

 

 

Solution

 

 

 

 

Parallel vectors and collinearity

Parallel vectors

Two vectors are parallel if one is scalar multiple of the other.i.e vector a is a scalar multiple of b ,i.e .

a =kb then the two vectors are parallel.

Note;

Scalar multiplication is simply multiplication of a regular number by an entry in the vector

Multiplying by a scalar

 

A vector can be multiplied by a number (scalar).e.g.      multiply    by 3   is  written  as  3 a.Vector 3a  has three times the length but is in the same direction as a .In column form, each component will be multiplied by 3.

We can also take a common factor out of a vector in component form. If a vector is a scalar multiple of another vector, then the two vectors are parallel, and differ only in magnitude. This is a useful test to see if lines are parallel.

Example  if

 

 

 

 

 

 

 

 

Collinear Points

Points are collinear if one straight line passes through all the points. For three points A, B, C – if the line AB is parallel to BC, since B is common to both lines, A, B and C are collinear.

Test for collinearity

 

Example

A is (0, 1, 2),   B is (1, 3, –1) and C is (3, 7, –7) Show that A, B and C are collinear.

 

are scalar multiples, so AB is parallel to BC.Since B is a common point, then A, B and C are collinear.

In general the test of collinearity of three points consists of two parts

  • Showing that the column vectors between any two of the points are parallel
  • Showing that they have a point in common.

Example

A (0,3), B (1,5) and C ( 4,11) are three given points. Show that they are collinear.

Solution

AB and BC are parallel if AB = kBC ,where k is a scalar

AB=                         BC =

Therefore AB//BC and point B (1,5) is common. Therefore A,B,and C are collinear.

Example

Show that the points A (1,3,5) ,B( 4,12,20)  and C are collinear.

Solution

Consider vectors AB and AC

AB =

AC =

 

 

 

Hence k =

AC =

Therefore AB//AC and the two vectors share a common point A.The three points are thus collinear.

Example

In the figure above OA = a OB = b and OC = 3OB

 

  • Express AB and AC in terms of a and b
  • Given that AM = ¾ AB and AN = , Express OM and O in terms of a and b
  • Hence ,show that OM and N are collinear

Solution

  • AB = OA + OB

= – a + b

AC = – a + 3b

 

  • OM =OA + AM

= OA +

= a +

= a – b

= b

 

ON =OA +AN

=OA +  AC

a a +

=  b

 

  • OM =

Comparing the coefficients of a;

=

Thus, OM = ON.

Thus two vectors also share a common point ,O .Hence, the points are collinear.

Proportional Division of a line

In the figure below, the line is divided into 7 equal parts

The point R lies 4/7  of the ways along PQ if we take the direction from P to Q to be positive, we say R divides PQ internally in the ratio 4 : 3..

 

If Q to P is taken as positive,then R divides QP internally in the ratio 3 : 4 .Hence,QR : RP = 3 : 4 or ,4 QR = 3RP.

 

 

 

External Division

In internal division we look at the point within a given interval while in external division we look at points outside a given interval,

In the figure below point P is produced on AB

 

The line AB is divided into three equal parts with BP equal to two of these parts. If the direction from A to B is taken as positive, then the direction from P to B is negative.

Thus AP : PB = 5 : -2.In this case we say that P divides AB externally in the ratio 5 : -2 or P divides AB in the ratio 5 : -2.

Points, Ratios and Lines

Find the ratio in which a point divides a line.

 

Example:

The points A(2, –3, 4), B(8, 3, 1) and C(12, 7, –1) form a straight line. Find the ratio in which B divides AC.                                                                                 Solution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

B divides AC in ratio of 3 : 2

 

Points dividing lines in given ratios.

 

Example:

P divides AB in the ratio 4:3.  If A is (2, 1, –3) and B is (16, 15, 11), find the co-ordinates of P.

 

 

 

 

 

 

Solution:

\   3(pa) = 4(bp)

3p – 3a = 4b – 4p

7p = 4b + 3a

     

 

Points dividing lines in given ratios externally.

Example:

Q divides MN externally in the ratio of 3:2. M is (–3, –2, –1) and N is (0, –5, 2).Find the co-ordinates of Q.

Note that QN is shown as –2 because the two line segments are MQ and QN, and QN is in the opposite direction to MQ.

 

\   –2(qm) = 3(nq)

–2q  + 2m = 3n – 3q

q  = 3n – 2m

     

 

 

P is P(10, 9, 5)

 

 

 

 

The Ration Theorem

 

The figure below shows a point S which divides a line AB in the ratio m : n

Taking any point O as origin, we can express s in terms of a and b the positon vectors of a and b respectively.

OS = OA + AS

But AS =

Therefore, OS = OA +

Thus S = a +

 

= a –

 

= (1  –

 

=

 

=  +

 

 

This is called the ratio theorem. The theorem states that the position vectors s of a point which divides a line AB in the ratio m: n is given by the formula;

S = , where a and b are positon vectors of A and B respectively. Note that the sum of co-ordinates  1

Thus ,in the above example if the ratio m : n = 5 : 3

Then m = 5 and n = 3

OR =

Thus ,r = a +

Example

A point R divides a line QR externally in the ratio 7 : 3 .If q and r are position vectors of point Q and R respectively, find the position vector of p in terms of q and r.

Solution

We take any point O as the origin and join it to the points Q, R and P as shown below

 

QP: PR = 7: -3

Substituting m =7 and n = -3 in the general formulae;

OP =

P =

Vectors can be used to determine the ratio in which a point divides two lines if they intersect

 

 

Example

In the below OA = a and OB = B.A point P divides OAin the ratio 3:1 and another point O divides AB in the ratio 2 : 5 .If OQ meets BP at  M Determine:

  • OM : MQ
  • BM : MP

 

Let OM : MQ = k : ( 1 – k) and BM –MP = n : ( 1 – n )

Using the ratio theorem

OQ =

OM

Also by ratio theorem;

OM = n OP +( 1 – n ) OB

But OP = a

Therefore , OM = n (

 

 

 

 

Equating the two expressions;

Comparing the co-efficients

2

 

 

= 10: 3

 

 

End of topic

 

                                   Did you understand everything?

If not ask a teacher, friends or anybody and make sure you understand before going to sleep!

 

Past KCSE Questions on the topic

 

  1. The figure below is a right pyramid with a rectangular base ABCD and VO as the height. The vectors AD= a, AB = b and DV = v

 

 

 

 

 

 

 

 

  1. Express

(i)         AV in terms of a and c

(ii)        BV in terms of a, b and c

(b)  M is point on OV such that OM: MV=3:4, Express BM in terms of a, b and c.

Simplify your answer as far as possible

  1. In triangle OAB, OA = a OB = b and P lies on AB such that AP: BP = 3.5
  • Find the terms of a and b the vectors
  • AB
  • AP
  • BP
  • OP
  • Point Q is on  OP such AQ = -5 + 9

8a  40b

Find the ratio OQ: QP

  1. The figure below shows triangle OAB in which M divides OA in the ratio 2: 3 and N divides OB in the ratio 4:1 AN and BM intersect at X

 

 

 

 

 

 

 

 

 

 

 

 

 

(a) Given that OA = a and OB = b, express in terms of a and b:

(i)         AN

(ii)        BM

(b) If AX = s AN and BX = tBM, where s and t are constants, write two expressions

for OX in terms of a,b s and t

Find the value of s

Hence write OX in terms of a and b

  1. The position vectors for points P and Q are 4 I + 3 j + 6 j + 6 k respectively. Express vector PQ in terms of unit vectors I, j and k. Hence find the length of PQ, leaving your answer in simplified surd form.
  2. In the figure below, vector OP = P and OR =r. Vector OS = 2r and OQ = 3/2p.

 

 

 

 

 

 

 

 

 

 

 

  1. a) Express in terms of p and r (i) QR and (ii) PS
  2. b) The lines QR and PS intersect at K such that QK = m QR and PK = n PS, where m and n are scalars. Find two distinct expressions for OK in terms of p,r,m and n. Hence find the values of m and n.
  3. c) State the ratio PK: KS
  4. Point T is the midpoint of a straight line AB. Given the position vectors of A and T are i-j + k and 2i+ 1½ k respectively, find the position vector of B in terms of  i, j  and k
  5. A point R divides a line PQ internally in the ration 3:4. Another point S, divides the line PR externally in the ration 5:2. Given that PQ = 8 cm, calculate the length of RS, correct to 2 decimal places.
  6. The points P, Q, R and S have position vectors 2p, 3p, r and 3r respectively, relative to an origin O. A point T divides PS internally in the ratio 1:6

(a)        Find, in the simplest form, the vectors OT and QT in terms p and r

(b)        (i)         Show that the  points Q, T, and R lie on a straight line

(ii)        Determine the ratio in which T divides QR

  1. Two points P and Q have coordinates (-2, 3) and (1, 3) respectively. A translation map point P to P’ (10, 10)
  • Find the coordinates of Q’  the image of Q under the translation
  • The position vector of P and Q in (a) above are p and q respectively given that mp – nq = -12

9

 

Find the value of m and n

  1. Given that q i + 1/3 j + 2/3 k is a unit vector, find q
  2. In the diagram below, the coordinates of points A and B are (1, 6) and (15, 6) respectively). Point N is on OB such that 3 ON = 2 OB. Line OA is produced to L such that OL = 3 OA

 

 

 

 

 

 

 

 

(a) Find vector LN

(b) Given that a point M is on LN such that LM: MN = 3: 4, find the coordinates of M

(c) If line OM is produced to T such that OM: MT = 6:1

(i)         Find the position vector of T

(ii)        Show that points L, T and B are collinear

  1. In the figure below, OQ = q and OR = r. Point X divides OQ in the ratio 1: 2 and Y divides OR in the ratio 3: 4 lines XR and YQ intersect at E.

 

 

 

 

 

 

 

 

  • Express in terms of q and r

(i)         XR

(ii)        YQ

(b) If XE = m XR and YE = n YQ, express OE in terms of:

(i)         r, q and m

(ii)        r, q and n

(c) Using the results in (b) above, find the values of m and n.

  1. Vector q has a magnitude of 7 and is parallel to vector p. Given that

p= 3 i –j + 1 ½ k, express vector q in terms of i, j, and k.

 

  1. In the figure below, OA = 3i + 3j ABD OB = 8i – j. C is a point on AB such that AC:CB 3:2, and D is a point such that OB//CD  and 2OB = CD (T17)

 

 

 

 

 

Determine the vector DA in terms of I and j

  1. In the figure below, KLMN is a trapezium in which KL is parallel to NM and KL = 3NM

 

 

 

 

 

 

 

 

Given that KN = w, NM = u and ML = v. Show that 2u = v + w

  1. The points P, Q and R lie on a straight line. The position vectors of P and R are 2i + 3j + 13k and 5i – 3j + 4k respectively; Q divides SR internally in the ratio 2: 1. Find the

(a) Position vector of Q

(b) Distance of Q from the origin

  1. Co-ordinates of points O, P, Q and R are (0, 0), (3, 4), (11, 6) and (8, 2) respectively. A point T is such that the vector OT, QP and QR satisfy the vector equation OT = QP ½ QT. Find the coordinates of T.

 

  1. In the figure below OA = a, OB = b, AB = BC and OB: BD = 3:1

 

 

 

 

 

 

 

 

(a)        Determine

(i)         AB in terms of a and b

(ii)        CD, in terms of a and b

(b)        If CD: DE = 1 k and OA: AE = 1m determine

(i)         DE in terms of a, b and k

(ii)        The values of k and m

  1. The figure below shows a grid of equally spaced parallel lines

 

 

 

 

 

 

 

 

 

AB = a and BC = b

(a)        Express

(i)         AC in terms of a and b

(ii)        AD in terms of a and b

(b)        Using triangle BEP, express BP in terms of a and b

(c)       PR produced meets BA produced at X and PR = 1/9b – 8/3a

By writing PX as kPR and BX as hBA and using the triangle BPX determine the ratio PR: RX

 

  1. The position vectors of points x and y are x = 2i + j – 3k and y = 3i + 2j – 2k respectively. Find XY

 

  1. Given that X = 2i + j -2K, y = -3i + 4j – k and z= 5i + 3j + 2k and that p= 3x – y + 2z, find the magnitude of vector p to 3 significant figures.

 

KCSE Computer Studies Mokasa Joint Exams Plus Free Marking Schemes

 

MOKASA JOINT EXAMINATION

Kenya Certificate of Secondary Education

 

451/1 – COMPUTER STUDIES – Paper 1

2½hrs

MARKING SCHEME

 

SECTION A (40 MARKS)

ANSWER ALL QUESTIONS IN THIS SECTION

  1. Name the two common types of system units and differentiate them.       (2 marks)
  • Tower
  • Desktop

Desktop -the monitor is placed on top of the system unit. The tower type the monitor rests on the table  

  1. Define the following characteristics of a computer system.                   (2 marks)
  • Versatile
  • Reliable

Versatile– Computers are flexible in that they can be used to carry out different types of activities such as typing, calculations and playing music.

Reliable – Computers are more reliable because they do not get tired or bored in the processing repetitive activities

  1. Digital computers work with digital content. Describe a digital device.                               (2 marks)
  • A digital device processes electronic signals that represent either a one (“on”) or a zero (“off”)
  • digital deviceis an electronic device that can receive, store, process or send digital information IN discrete formats in binary representation.
  1. Differentiate between third and fourth generation computers                               (2marks)
  • Third generation computers used electronic component called Integrated circuits (ICS) which is a single component that consist of thousands of transistors etched on a semiconductor called a Silicon Chip. It emitted less heat, were smaller in size, easier to program and maintain compared to second generation computers
  • Fourth generation computers used an electronic component called microprocessor. It was designed to allow thousands of transistors embedded into a silicon chip made up very large scale integration(VLSI) giving birth to central processing unit that power microcomputer. Fourth generation computers are characterized by very low emission of heat and are small in size and easier to use and maintain
  1. (a) Mamboleo company is in the process of computerizing its services. List four measures that should be put into consideration to protect the users in their computerized areas.                         (2marks)
  • Power cables should be insulated
  • Providing standard furniture
  • Proper ventilation
  • Painting the wall with less reflective paints.
  • Overcrowding should be avoided.
  • Give two reasons why powder and liquid extinguishers are not recommended unlike gaseous extinguishers.                                     (2marks)
  • Liquid –based extinguisher may cause rusting and corrosion of computer components
  • Powder particles may increase friction, clogging and wearing of movable computer parts
  1. Without proper marketing, a business cannot survive in a competitive environment hence computers are being used in a number of ways to enhance marketing. List any three ways of ensuring this is effected.                                                                   (3 marks)
  • Electronic Commerce or e-business
  • Electronic presentation
  • Advertising
  1. Differentiate between the following as used in computers.       (3 marks)
  • Tab Key
  • Spacebar
  • Clicking

Tab Key– It is used to move the cursor at set horizontal intervals on the same line such as 0.5inch,1.0 inch e.t.c.

Space bar– It is used to insert spaces between characters on words when typing

Clicking– Pressing and releasing the left mouse button once. A click  often selects an Icon or Menu.

  1. Control unit is an essential component of the CPU. Describe the functions of the control unit.                                                                                                       (2 marks)
  • The control unit is responsible for coordinating all the  activities of the C.P.U
  • To coordinate these activities, the control unit uses a system clock that sends command signals
  1. (a)Differentiate between buffers and Registers       (2 marks)

 

 (i)Buffers are special memories that are found in input/output devices. Input data are held in the input buffer while processed output is held in output buffer.

(ii) A register is located inside the microprocessor hold one piece of data at a time one inside the C.P.U e.g Accumulator, Instruction Register, Address Register and storage register

 

(b)Speech recognition devices are used to capture natural sound and convert the input into digital form. State two problems related to speech recognition devices.                                          (2 marks)

  • Recognition rate is slow – the number of words in English and the number of words which can be said at a given point (known as branching factor) mean that response rates are still relatively slow.
  • Limited vocabularies – most systems are still limited to words in isolation; connected speech is much harder to get right than segmented speech. A computer may not respond to a voice command that has speech related problems like accents, Inflations and varying tones.
  • Speaker variability–The speed, pitch, range, rhythm. Intonation, loudness and pronunciation of an individual can vary (especially if they a have a cold).
  • Homophones – Some words e.g. see and sea, sound the same.
  • Problems of speech context – A computer cannot understand different contexts and meanings of speech because it is ‘literal minded’.
  • Background noise –Can upset voice input without a shielded mouthpiece on the microphone.

 

 

 

  1. Define Solid-state storage and give two examples.       (2 marks)
  • A non-volatile storage that employ integrated circuits rather than mechanical, magnetic or optical technology. They are referred to solid state because they do not have movable parts in its read/write storage mechanism.
  1. (a) Explain how a pixel affects the resolution of a monitor.                   (1 mark)
  • A pixel is the smallest unit of a digital image or graphic that can be displayed and represented on a digital display device. The higher the number of pixel, the clearer and excellent images formed on the screen. Less pixel results to less clearer and poorer display on the screen.

(b) List two types of computer output on microform (COM).                                              (2marks)

  • Microfiche
  • Microfilm
  1. Differentiate between high definition multimedia interface and Firewire       (2 marks)
  • High definition interface is an interface used for transmitting digital audio and video data from computer to a projector, TV or audio device.

 

  • Firewire It is similar to USB but has a higher transmission rate hence it is suitable for streaming video from digital cameras to a computer
  1. A warranty is an agreement between the buyer and the seller. It spells out terms and conditions after selling a product in case of failure or malfunction. Describe any three basic requirements a good warranty should cover.                                                                                                             (3 marks)

 

  • Scope of cover for example 4 months, 2years
  • Callout response and liability agreement. For how long should the supplier take to repair a fault or replace the product and if he/she delays who beams the cost.
  • Preventive maintenance for example regulating of service at intervals.
  1. (a)Differentiate between pasteboard and master page as used in DTP                               (2 marks)

 

  • Pasteboard: The background that lies behind your document. It is a convenientspace to put things if you need to move text or images between pages. You can also place items on the pasteboarduntil you decide where to position them on the page. Any text or images that you place on the pasteboard won’t be printed.
  • Master page: A page used in designing the general layout that will be replicated in all other pages in the publication.
  • Differentiate between graphic-based and layout based desktop publishing software. (2 marks)
  • Graphic based- They are specifically developed to edit and format graphic objects such as pictures and vector drawings.
  • Layout based- Are specifically developed to create different page layout designs for text and
  1. Differentiate between Network database and Relational database.       (2 marks)

 

  • Network model links are used to express the relationship between different data items, forming a network of items. Access to one item can be through multiple paths and from any item. Used to express the relationship between different data items forming a network of items. Access to one item can be through multiple paths from any item
  • Relational – Data items are stored together in structures called relations. In Relational database related data items are stored together in structures (relations or tables). Relationship can be created between tables such that a record or records from one table relates to another or other records in another table.

SECTION B (60 MARKS)

 

ANSWER QUESTION 16 AND ANY OTHER THREE QUESTIONS IN THIS SECTION

 

  1. (a) Define the following terms as used in programming                                                                 (2 marks)

(i) Source code

  • The program instructions entered in the program editor window that is not yet translated into machine readable form (binary language).

(ii) Object code

  • The program or source code that is already translated into machine readable form (binary language).It is produced by the assembly process (the production of a source code to machine form/binary).

(b) Differentiate between Assembler and Interpreter as used in programming.                              (2 marks)

 

Assembler(s) – it is a program or language processor that translates assembly language into machine language that the computer can understand and execute.

Interpreters – It is a translator program that translates source program one instruction at a time, completely translating and executing each instruction before it goes onto the next. Interpreters seldom produce object code but temporarily produce intermediate code which is not stored in main memory.

(c) Identify the type of programming language used in the codes below;                            (1 mark)

(i)        1101 1101                     1011 1011        

1110 0001                     1100 0111

0010 1110                     1011 0011

Machine Language

………………………………………………………………………………………..………………………

 

(ii)        LDA    A, 20  

ADD    A, 10  

STO    B, A    

NOP                                                    Assembly Language

………………………………………………………………………………………..………………………

 

 

(d) On the Nairobi-Nakuru highway, the Kenya Police have put speed cameras at a certain point to read         the time a vehicle passes a point (A) on the road and then reads the time it passes a second point (B)         on the same road. (Points A and B are 200 meters apart). The speed of the vehicle is calculated          using:

  • Speed = (Km/ hr)
  • The maximum allowed speed is 100 kilometers per hour.
  • 500 vehicles were monitored using these cameras over a 1-hour period.

 

  • Write a pseudo code, which:                   (5 marks)
  • Inputs the start time and the end time for the 500 vehicles that were monitored
  • Calculates the speed for each vehicle using the formula above.
  • Outputs the speed for each vehicle and a message if the speed exceeded 100 km/hour.

>=100km/hr “High Speed”

<100km/hr “Normal Speed”

 

 

 

Start

starttime=0

Endtime=0

Speed=0

For Vehicles=1 To 500 Do

Input Start Time

Input Stop Time

Speed =100/(End Time-Start Time)

Print Speed

If Speed >100 Then

Print Over Speeding

Else

Print Normal Speed

ENDIF

NEXT VEHICLE

ENDFOR

STOP

 

 

 

 

 

 

 

 

 

  • Draw a flow chart for the above pseudo code. (5 marks)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. (a) In order to generate information from data items, a set of processing activities have to be performed on the data items in a specific sequence depending on the desired result.Draw a well labeled           diagram to illustrate data processing cycle.                                                                    (2 marks)

(b) A data entry clerk experiences some common errors when typing. Most of the time, she finds that:

  • After every calculation, the result is less than the expected number of digits required e.g.345.7896543 the result is given as 345.789.
  • Different charactersare typed wrongly, for example instead of typing12873457 she types 128734S7.

 

Identify the two types of errors commonly experienced by the clerk during data processing in (i)   and (ii) above respectively.                                                                                              (2 marks)

 

  1. Truncation error
  2. Misreading error

(c) State two ways a user can ensure data accuracy is maintained during data processing.            (2 marks)

  • Using modern data capture devices (direct data capture) such as barcode readers, optical character readers, digital cameras etc., which capture/enter data with minimum user involvement.
  • Design user interfaces that minimizes chances of invalid data entry.
  • Double entry checks
  • Use of error detection and correction software when transmitting and processingdata.
  • Use of automated data verification and validation routines in the data processing system.

(d)(i) State three advantages of a computerized filing system as used in data processing.      (3 marks)

  1. information takes up much less space than the manual filing
  2. it is much easier to update or modify information
  3. it offers faster access and retrieval of data
  4. It enhances data integrity and reduces duplication
  5. It enhances security of data if proper care is taken to secure it.

(ii) State two disadvantages of a serial file organization method in computing.       (2 marks)

  • Itis cumbersome to access because you have to access all proceeding records before retrieving the one being searched.
  • Wastage of space on medium in form due inter-record gaps in storage.
  • It cannot support modern high speed requirements for quick record access.

(iii) Differentiate between distributed processing and interactive processing modes; stating one                           application area of each.                                                                                               (4 marks)

Distributed:

  • Various geographically dispersed computers arelinked by communication lines and all the computers linked belong to the same organization.
  • The computers are located at various departments or business sites for the individual departments or the business site to be served individually by its own computer resources.
  • All the branches have intelligent terminals (usually micro computers) linked to a big computer at the head office. Data from the branches is sent to the master where it is processed.

Interactive:

  • Occurs if the computer & the terminal user can communicate with each other.
  • It allows a 2-way communication between the user & the computer.
  • As the program executes, it keeps on prompting the user to provide input or respond to prompts displayed on the screen.
  • The user makes the requests and the computer gives the responses.
  • The data is processed individually and continuously, as transactions take place and output is generated instantly according totherequest made by user.

 

  1. (a) Write the following acronyms in full as used in operating systems.
  • GUI – Graphical User Interface                                                          (½ mark)
  • WIMP – Windows, Icons, Menus and Pointers/ pointing devices.       (½ mark)

(b) State three factors considered when choosing an operating system for use in a computer. (3 marks)

 

  1. The hardware configuration of the computer e.g. Memory Capacity, processor speed & hard disk capacity.
  2. The application software intended for the computer.
  3. The user friendliness
  4. The documentation available
  5. The cost of the operating system.
  6. Reliability and security provided by the operating system.
  7. The number of processors & hardware it can support.
  8. The number of users it can support.
  9. The type of computers in terms of size and make. For example some earlier Apple computers would not run Microsoft Operating System.

(c) An operating system manages and organizes a computer system using the following structures:

File, Folder and Drive. State the meaning of theunderlined items respectively.                 (3 marks)

 

Files

  • A file is a collection of related data given a unique name for ease of access, manipulation and storage on a backing storage.

Folder

  • A named storage location where files are stored.
  • A container of files.
  • Also referred to as directories – Directories originate form a special directory called the root directory or folder.

Drives

  • driveis a medium that is capable of storing and reading information that is not easily removed like a disk.

 

 

(d)(i) Differentiate between error handling and interrupt handling as used in operating systems.

(2 marks)

Error handling .

  • The OS has many ways of reporting to the user of any errors that occur during program execution. It does this by monitoring the status of the computer system & performing error checks on both hardware and software.
  • When the user makes an error, the OS through the Kernel determines the cause of the error, and prints diagnostic messages on the screen suggesting appropriate routines of how the error can be corrected.
  • In case of a fatal error that cannot be corrected, the program will be suspended permanently. g., the user program will prematurely terminate when it encounters an illegal operation, such as, dividing a no. by 0 or if it attempts to read a data file that had not been opened.

Interrupt handling

  • An Interrupt is a break from the normal sequential processing of instructions in a program.

Each hardware device communicates to the processor using a special number called the Interrupt Request number (IRQ).  Therefore, when an interrupt occurs, control is passed to the Kernel, which determines the cause of the interrupt.  The processor stops executing the current program to wait for the corrective response of the user.  Control is returned to the program that was interrupted once corrective action has been taken.

(ii) State three reasons why most network technicians prefer using command line operating systems to configure networking equipment.                                                                         (3 marks)

 

  • CLIcan be a lot faster and efficient than any other type of interface.
  • It is secure since the expert only knows the commands.
  • CLIrequires less memory to use in comparison to other interfaces.
  • CLIdoesn’t require high graphics, hence a low-resolution monitor can be used.
  • A CLI does not require Windows to run

(e)Disk management is one important aspect insecondary storage in computer systems. Explain the following tools used by an operating system to manage disks in the computer.                    (3 marks)

 

  • Formatting
  • Writing electronic information (tracks and sectots) on the disk so that the computer can recognise the disk as a valid storagedevice and data can be stored.
  • The formatting process sets up a method of assigning addresses to the different areas. It also sets up an area for keeping the list of addresses. Without formatting there would be no way to know what data is where.
  • Partitioning
  • The act or practice of dividing the storage space of a hard disk drive into separate data areas known as partitions.
  • Defragmentation

 

  • Sometimes called defragging or disk optimisation is a software-controlled operation that reduces the amount of fragmentation in file systems by moving the scattered parts of files so that they once again are contiguous (attached).
  • the OS does this by physically organising the contents of the disk to store the pieces of each file close together and contiguously (elements of memory are said to be contiguous if they are adjacent to one another and appear to beconnected).

 

 

  1. (a) Define the following terms as used in networking.       (3marks)
  • Network
  • A collection 2 or more computers connected together using transmission media (e.g., telephone cables, or Satellites) for the purpose of communication and sharing of resources.
  • Intranet
  • Internal corporate network that uses the infrastructure of the Internet and the World Wide Web.
  • Browser
  • A browser (short for web browser) is a computer program/software that accesses webpages and displays them on the computer screen. It is the basic software that is needed to find,retrieve, view and send information over the internet.

 

(b) The World Health Organization is global entity that deals with health issues around the world. It has computer networks linking its regional and continental offices using internet. State two importance of the internet to such organization.                                                              (2 marks)

  • Communication with other organizations, with your members, with your staff, with your supporters and donors through e-mails, messenger, web pages, mail lists, web site message boards. The Internet greatly offers rapid communication on a global scale. It even delivers an integrated multimedia entertainment that any other mass medium cannot offer.
  • Publishing your message to the world using online books, journals, press releases, workshops, conferences, lectures. Websites with conference proceedings, PDF (Portable Document Format) files of your publications, blogs, newsfeeds e.t.c. support publishing.
  • Customer support – the people you are helping through your organization. It can help them when you aren’t there: email, messenger, web pages, mail lists, and web site message boards. With video-conferencing, podcasting and other great web tools, you can even have workshopsand classes online.
  • Research on news, issues, papers and literature relevant to your cause. Use of search engines tofind materials world-wide, mail lists e.t.c.
  • Leisure activities – e.g. online games, videos or music.
  • A place to do business and many other commercial activities. E.g. e-bay, amazon.com,e.t.c.

(c) Mr. Zuma, the Principal of a school wishes his school to have an internet connection in a bid to improve its service delivery. Mention fourinternet connectivity requirements that must be presentto enable the connection.                                                                                                            (2 marks)

 

  • Transmission/Telecommunication/Network media
  • Data Terminal Equipments – A TCP/IP enabled computer with a web browser.
  • An account with an Internet Service Provider (ISP).
  • Networking equipment such as a modem, router or switch to connect the computer transmission media.

(c) Explain the following as used in e-mail:

  • Inbox: Stores incoming mails             (1 mark)
  • Drafts: Stores a saved copy of e-mails (usually composed but unsent) for later use. (1 mark)

 

(e)  (i) Failure of information systems is a major concern in the security of data in computing systems. State twocauses of such failure.                                                                                     (2 marks)

  • Hardware failure due to improper use.
  • Unstable power supply as a result of brownout or blackout and vandalism.
  • Network breakdown
  • Natural disaster
  • Program failure/crash

(ii) Explain the following computer crimes.

  • Fraud             (1 mark)
  • Fraud is the use of computers to conceal information or cheat other people with the intention of gaining money or information.
  • Industrial espionage             (1 mark)
  • Involves spying on a competitor to get or steal information that can be used to finish the competitor or for commercial gain.The main aim of espionage is to get ideas on how to counter by developing similar approach or sabotage.

(f) Excluding passwords, state two other security control measures used to guard against unauthorized access to computers in a network.                                                         (2 marks)

 

  1. Audit trails
  2. Firewalls
  3. Proxy servers
  4. Log files/security monitors
  5. Encryption
  6. User access levels/Multilevel access
  7. Biometric security
  8. (a) Convert the 1010.0112 to decimal equivalent.                                                                ( 3 marks)
23 22 21 20   2-1 2-2 2-3
1 0 1 0 . 0 1 1
8 0 2 0   0.5 0.25 0.125

8+0+2+0                                 0+0.25+0.125              Ans = 10.37510

(b) Perform the following number system conversions.                                                       (3 marks)

(i) 342.258 tobinary.

3 4 2 . 2 5  
011 100 010   010 101  
011100010 . 010 101  

                                                                                                            Ans = 11100010.0101012

(ii) 50310 to hexadecimal                                                                               (3 marks)

  Divide Result INT DEC PART *16 Hex
Ignore decimal parts 503/16 31.4375 31 0.4375 X16 =7 7=7
31/7 1.9375 1 0.9375 X 16 =15 15=F
1/16 0.0625 0 0.0625 X 16 =1 1=1

Ans = 1F7

(c) (i)Compute the binary arithmetic given below:                                                               (3 marks)

10111 + 10001 + 101

Carry digit ˃ 1 1 1 1 1  
  1 0 1 1 1 1
+   1 0 0 0 1
  1 0 0 0 0 0 0

 

Carry digit ˃   1 1 1 1 1 1,1
  1 0 0 0 0 0 0
        1 0 1
    1 1 1 0 1 1

 

                                                                                Ans = 111011

(ii)       Using 8-bit notation, perform the twos complementof 2510 -1510 , leaving your answer in binary.                                                                                                                                    (4 marks)

25 = 00011001

15 = 00001111

 

Ones complement/Bitwise NOT 15 = 11110000

Twos complement 15(11110000 + 1) = 11110001

 

Add the binary of 25 to the twos complement of 15 i.e. 00011001 + 11110001

 

 

Carry digit ˃ 1 1 1       1  
  0 0 0 1 1 0 0 1
  1 1 1 1 0 0 0 1
  (1)0 0 0 0 1 0 1 0

 

Ignore overflow bit.                Ans = 00001010

 

 

THIS IS THE LAST PRINTED PAGE

______________________________

 

MOKASA JOINT EXAMINATION

Kenya Certificate of Secondary Education

 

 

 

 

451/1 – COMPUTER STUDIES – Paper 1

2½hrs

 

 

Name……………………………………………………… Index Number……………………

Admission Number………….………………………………Class…………………………..

Date………………….……………..………

 

 

 

Instruction to candidates

  1. Write your name and index number in the space provided above.
  2. Sign and write the date of examination in the spaces provided above.
  3. This paper consists of two sections A and B.
  4. Answer all the questions in section
  5. Answer question 16 and any other three questions from section
  6. All answers should be written in the space provided in the question paper.
  7. This paper consists of 14 printed pages.
  8. Do not remove and pages from this booklet.
  9. Candidates should check the question paper to ascertain that all the pages are printed as indicated and that no questions are missing.
  10. Candidates should answer the questions in English.

 

For Examiner’s Use Only

Section Question Number Candidate’s Score
A 1-15  
 

 

B

16  
17  
18  
19  
20  
                                Total Score  

 

 

 

SECTION A (40 MARKS)

ANSWER ALL QUESTIONS IN THIS SECTION

  1. Name the two common types of system units and differentiate them.       (2 marks)

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

  1. Define the following characteristics of a computer system.                   (2 marks)
  • Versatile
  • Reliable

………………………………………………………………………………………………….………….………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

  1. Digital computers work with digital content. Describe a digital device.                               (2 marks)

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

  1. Differentiate between third and fourth generation computers                               (2marks)

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

  1. (a) Mamboleo company is in the process of computerizing its services. List four measures that should be put into consideration to protect the users in their computerized areas.                         (2marks)

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

 

  • Give two reasons why powder and liquid extinguishers are not recommended unlike gaseous extinguishers.                                                 (2marks)

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

  1. Without proper marketing, a business cannot survive in a competitive environment hence computers are being used in a number of ways to enhance marketing. List any three ways of ensuring this is effected.                                                                   (3 marks)

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

………………………………………………………………………………………………….………….

  1. Differentiate between the following as used in computers.       (3 marks)
  • Tab Key
  • Spacebar
  • Clicking

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  1. Control unit is an essential component of the CPU. Describe the functions of the control unit.                                                                                                                   (2 marks)

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  1. (a)Differentiate between buffers and Registers       (2 marks)

 

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(b)Speech recognition devices are used to capture natural sound and convert the input into digital form. State two problems related to speech recognition devices.                                          (2 marks)

 

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  1. Define Solid-state storage and give two examples.       (2 marks)

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  1. (a) Explain how a pixel affects the resolution of a monitor.                               (1 mark)

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(b) List two types of computer output on microform (COM).                                              (2marks)

 

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  1. Differentiate between high definition multimedia interface and Firewire       (2 marks)

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  1. A warranty is an agreement between the buyer and the seller. It spells out terms and conditions after selling a product in case of failure or malfunction. Describe any three basic requirements a good warranty should cover.                                                                                                             (3 marks)

 

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  1. (a)Differentiate between pasteboard and master page as used in DTP                               (2 marks)

 

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  • Differentiate between graphic-based and layout based desktop publishing software. (2 marks)

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  1. Differentiate between Network database and Relational database.                               (2 marks)

 

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SECTION B (60 MARKS)

 

ANSWER QUESTION 16 AND ANY OTHER THREE QUESTIONS IN THIS SECTION

 

  1. (a) Define the following terms as used in programming                                                                 (2 marks)
  2. i) Source code

 

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  1. ii) Object code

 

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(b) Differentiate between Assembler and Interpreter as used in programming.                             (2 marks)

 

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(c) Identify the type of programming language used in the codes below;                            (1 mark)

(i)        1101 1101                     1011 1011        

1110 0001                     1100 0111

0010 1110                     1011 0011

 

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(ii)        LDA    A, 20  

ADD    A, 10  

STO    B, A    

NOP

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(d) On the Nairobi-Nakuru highway, the Kenya Police have put speed cameras at a certain point to read         the time a vehicle passes a point (A) on the road and then reads the time it passes a second point (B)         on the same road. (Points A and B are 200 meters apart). The speed of the vehicle is calculated          using:

  • Speed = (Km/ hr)
  • The maximum allowed speed is 100 kilometers per hour.
  • 500 vehicles were monitored using these cameras over a 1-hour period.

 

  • Write a pseudo code, which:                   (5 marks)
  • Inputs the start time and the end time for the 500 vehicles that were monitored
  • Calculatesthe speed for each vehicle using the formula above.
  • Outputs the speed for each vehicle and a message if the speed exceeded 100 km/hour.

>=100km/hr “High Speed”

<100km/hr “Normal Speed”

 

 

 

 

 

 

 

 

 

 

 

 

 

  • Draw a flow chart for the above pseudo code. (5 marks)

 

 

 

 

 

 

 

 

 

 

 

 

  1. (a) In order to generate information from data items, a set of processing activities have to be performed on the data items in a specific sequence depending on the desired result.Draw a well labeled           diagram to illustrate data processing cycle.                                                                    (2 marks)

 

 

 

 

 

 

 

(b) A data entry clerk experiences some common errors when typing. Most of the time, she finds that:

  • After every calculation, the result is less than the expected number of digits required e.g.345.7896543 the result is given as 345.789.
  • Different charactersare typed wrongly, for example instead of typing12873457 she types 128734S7.

 

Identify the two types of errors commonly experienced by the clerk during data processing in (i)   and (ii) above respectively.                                                                                              (2 marks)

 

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(c) State two ways a user can ensure data accuracy is maintained during data processing.            (2 marks)

 

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(d)(i) State three advantages of a computerized filing system as used in data processing.      (3 marks)

 

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(ii) State two disadvantages of a serial file organization method in computing.

(2 marks)

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(iii) Differentiate between distributed processing and interactive processing modes; stating one                           application area of each.                                                                                               (4 marks)

 

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  1. (a) Write the following acronyms in full as used in operating systems.
  • GUI    (½ mark)

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  • WIMP    (½ mark)

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(b) State three factors considered when choosing an operating system for use in a computer. (3 marks)

 

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(c) An operating system manages and organizes a computer system using the following structures:

File, Folder and Drive. State the meaning of theunderlined items respectively.                 (3 marks)

 

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(d)(i) Differentiate between error handling and interrupt handling as used in operating systems.

(2 marks)

 

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(ii) State three reasons why most network technicians prefer using command line operating systems to configure networking equipment.                                                                         (3 marks)

 

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(e)Disk management is one important aspect insecondary storage in computer systems. Explain the following tools used by an operating system to manage disks in the computer.                    (3 marks)

 

  • Formatting

 

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  • Partitioning

 

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  • Defragmentation

 

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  1. (a) Define the following terms as used in networking.       (3marks)
  • Network

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  • Intranet

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  • Browser

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(b) The World Health Organization is global entity that deals with health issues around the world. It has computer networks linking its regional and continental offices using internet. State two importance of the internet to such organization.                                                                                      (2 marks)

 

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(c) Mr. Zuma, the Principal of a school wishes his school to have an internet connection in a bid to improve its service delivery. Mention fourinternet connectivity requirements that must be presentto enable the connection.                                                                                                            (2 marks)

 

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(c) Explain the following as used in e-mail:

  • Inbox             (1 mark)

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  • Drafts             (1 mark)

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(e)  (i) Failure of information systems is a major concern in the security of data in computing systems. State twocauses of such failure.                                                                                     (2 marks)

 

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(ii) Explain the following computer crimes.

  • Fraud             (1 mark)

 

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  • Industrial espionage             (1 mark)

 

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(f) Excluding passwords, state two other security control measures used to guard against unauthorized access to computers in a network.                                                         (2 marks)

 

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  1. (a) Convert the 1010.0112 to decimal equivalent.       ( 3 marks)

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(b) Perform the following number system conversions.                                                       (3 marks)

(i) 342.258tobinary.

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(ii) 50310 to hexadecimal                                                                                                       (3 marks)

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(c) (i) Compute the binary arithmetic given below:                                                             (3 marks)

10111 + 10001 + 101

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(ii)       Using 8-bit notation, perform the twos complementof 2510 -1510, leaving your answer in binary.                                                                                                                                    (4 marks)

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THIS IS THE LAST PRINTED PAGE

________________________________

QN Section/Activity Marks Max mark Marks awarded
1. a)     Creating workbook MASL REPS

–        Naming Worksheet 1 As Sales

–        Typing data accordingly,into rows/columns

–        Input validation, with correct parameters

1 mark

1 mark

18 marks

3 marks

23 marks  
b)     Using correctformulae to:

(i)     Total Sales for each sales rep

(ii)   Total Sales for each product

 

2 marks

2 marks

 

4 marks  
c)      Inserting Bonus Points column& Computing points

–        Create column

–        Using appropriate function or formulae

Calculate/compute bonus

1 mark

1 mark

2 marks

 

4 marks  
d)     Inserting column Awards

–        Use of IF function to display remarks

1 mark

4 marks

5 marks  
e)      Formatting worksheet

–        Double underline

–        Font type – Algerian

–        Font size – 26pts

–        Applying borders to data in worksheet

 

1 mark

1mark

1 mark

1 mark

4 marks  
f)      Rotating headings: All Product Type heading labels(Sales Rep., Faiba, Gateway, Vodafone, SAF, Total Sales). 1mark 1 mark  
g)     Inserting chart: Total sales vs Sales representatives

–        Chart title

–        X axis title

–         Y axes title

–        Legend

–        Data labels (Minimum & maximum ranges)

Renaming worksheet 2 as CHART

1 mark

1mark

1 mark

1 mark

1 mark

1 mark

1 mark

7 marks  
h)     Printing worksheets:

–        MASL

–        CHART

 

1 mark

1 mark

2 marks  
  TOTAL MARKS  

50 MARKS

 

 

 

 

 

 

 

 

 

Qestion 2 -Word Processing
No. Particulars Marks Award
a. fully typed text 5  
4 Paragraphs indication @ 1/2 Mark each 2  
dropcap 1  
columns 1  
Bullets 1  
line between columns 1  
paragraph title italics & bolding 2  
Correctly filled table 3  
table correct outer border 1  
table row shading and text color( white) 1  
correctly drawn diagram 3  
saving with correct file name 1  
b creating a copy 1  
saving with correct file name 1  
c heading format @ 1/2 Mark each 3  
d correct header 1  
correct footer 1  
e spelling error free 2  
f correct alignment 1  
g finding and replacing all 1  
h resizing diagram 1  
object placement 1  
text readability over graphics 1  
j i cell splitting 1  
ii inserting row 1  
cell merging 1  
appropriate row heading 1  
k i total score 2  
ii number of students 2  
iii highest score 2  
iv average total score 2  
l i print EDUC AI 1  
ii print EDUC AI2 1  
TOTAL MARKS 50  

 

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451/2 COMPUTER STUDIES- PAPER 2

(PRACTICAL)

2 ½ hours

 

 

 

MOKASA 1 JOINT EXAMINATION

Kenya Certificate of Secondary Education

(K.C.S.E)

 

Instructions to candidates

 

  • Indicate your name and index number at the top right hand corner of each printout
  • Write your name and index number on the CD/Removable storage medium provided.
  • Answer all the questions
  • All questions carry equal marks
  • Passwords should to be used while saving in the CD/Removable storage medium
  • All answers must be saved in your CD/Removable storage medium
  • Make a printout of the answers on the answer sheet
  • Arrange your printouts and tie/staple them together
  • Hand in all the printouts and the CD/Removable storage medium used
  • This paper consist of 5 printed pages
  • Candidates should check the question paper to ascertain that all the pages are printed as indicated and that o questions are missing

 

 

 

 

 

 

 

 

 

 

 

  1. MASL is a company thatengages in the sales of the following Mobile service providers: Faiba, Gateway, vodafone and SAF. The company uses sales representatives who operate at various regions in Nakuru town. Each sales representative presents monthly sales to the manager (Values are in Ksh).

 

  A B C D E F  
1 Mobile_Accessories Sales LTD
2   Product  type  
3 Sales Rep. Faiba Gateway Vodafone SAF Total Sales  
4 Kipkulei 24000 37500 39500 49500    
5 Tom 15000 26500 21500 25500    
6 Sharon 5500 14800 3500 16500    
7 Oscar 7000 15500 14500 64500    
8 Linda 11000 69000 2200 64500    
9 Danelaw 33500 12000 14500 25500    
10 Muriithi 15500 80000 17200 23500    
               

 

  • Using spreadsheet package,
  • Enter the information given in the table 1 into a worksheet.Save workbook as MASLREPSand rename sheet 1 as (20 marks)
  • Validate all the cells in the Product Type columns to allow entry of numeric data only.

A message, “Invalid data! Enter numbers” should be displayed whenever a cell is typed with non-numeric data.                                                               (3 marks)

  • Using formulae, determine the;
  • Total sales for each Sales representative (2 marks)
  • Producttype Total Sales for each month. (2 marks)
  • Each sales person earns Bonus points for the sales of each product type based on the following criteria.
  • 1 point if sales are greater than 50,000 for Faiba,
  • 2 points if sales are greater than 60,000 Gateway,
  • 3 points if sales are greater than 50,000 Vodafone
  • 2 points if sales are greater than 60,000 for SAF

Insert a column BonusPoints and compute the points of each sales Person.        (4 marks)

  • Insert a blank column Awardsand based on the TotalSales earned by each sales representative. Use a function to display the remarks on Awards as follows: (5 marks)

Total Sales                                                                               Awards

More than 250,000                                                                    Cash

More than 100, 000 and less than 250,000                                 Voucher

Less than 100,000                                                                     Try again

  • Format the figures in worksheet as follows: (4 marks)
  • Title and subtitle:
  • Double underline
  • Font type – Algerian
  • Font size 26
  • Apply borders to the data in the workbook.

 

 

  • Rotate Up, all the Product Type heading labels in the worksheet. (1 mark)
  • Generate a column chart to representthe Total sales for each salesrepresentative. Label your chart accordingly and place it in worksheet 2 renamed as CHART. (7 marks)
  • Print MASL and CHART (2 marks)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Using word processing program type the document as it appears and save it asEDUC AI

 

ARTIFICIAL INTELLIGENCE IN EDUCATION

 

For decades, science fiction authors, futurists, and movie makers alike have been predicting the amazing (and sometimes catastrophic) changes that will arise with the advent of widespread artificial intelligence. So far, AI hasn’t made any such crazy waves, and in many ways has quietly become ubiquitous in numerous aspects of our daily lives. From the intelligent sensors that help us take perfect pictures, to the automatic parking features in cars, to the sometimes frustrating personal assistants in smartphones, artificial intelligence of one kind of another is all around us, all the time.

 

W

hile we may not see humanoid robots acting as teachers within the next decade, there are many projects already in the works that use computer intelligence to help students and teachers get more out of the educational experience. Here are just a few of the ways those tools, and those that will follow them, will shape and define the educational experience of the future.

 

  • Automation of basic activities in education, like grading.
  • Educational software can be adapted to student needs.
  • It can point out places where courses need to improve.
  • Students could get additional support from AI tutors.
  • AI may change where students learn and how they acquire basic skills.
  • It is altering how we find and interact with information.

 

 

Automation basic activities in education, like grading.
In lower grades, teachers often find that grading takes up a significant amount of time, time that could be used to interact with students, prepare for class, or work on professional development.A1 can be used to automate grading systems and present the output in tables .

GRADE THREE COMMON EXAMINATION
SIR NAME LANGUAGE  SKILLS COMPUTING SKILLS ENVIRONMENTAL SKILLS Total Score
Macmillan 87 50 78  
Trevor 92 95 76
Johnstone 73 85 90
Kathleen 67 56 75
Count        
Highest Scores        

 

Educational software can be adapted to student needs.

From kindergarten to graduate school, one of the key ways artificial intelligence will impact education is through the use of application programs.learners can draw 3D diagramssuch as the one shown below

 

 

 

 

 

 

Teachers may not always be aware of gaps in their lectures and educational materials that can leave students confused about certain concepts. Artificial intelligence offers a way to solve that problem.

  1. using a word processing application software type the document below as it appears and save it as EDUC AI                                                                                                       (22 Marks)
  2. Copy the document EDUC AI in a new document and save it as EDUC AI2 then use it to answer the questions that follows                                                                                  (2 Marks)
  3. Format the heading as follows;
  • Center align, font size – 14, font color – red, font type – Algerian, double underline, scale – 130%             (3 Marks)
  1. Insert your name, Adm No ,system time as a header and your class and page number as a footer                                                                                                                  (2 Marks)
  2. Spell check the document to remove all typing errors                                         (2 Marks)
  3. Center align the first paragraph                                                                                     (1 Mark)
  4. Find all occurrences of the word AI in the document and replace with “Artificial Intelligence “                                                                                                                (1 Mark)
  5. Resize the diagram  between the last two paragraphs and move it to the second paragraph and send it behind text                                                                                      (3 Marks)
  6. On the grade three table,
  1. Split the cells in the total score column to separate each students’ marks (1 Mark)
  2. Insert a new row at the bottom of the table to display the average total scores and merge the first four columns of the row (3 Marks)
  1. Use appropriate function to calculate:
  1. Total score (2 Marks)
  2. Number of students who did each exam (2 Marks)
  • Highest score attained in each subject (2 Marks)
  1. Average total scores (2 Marks)
  2. PrintEDUC AI (1 Mark)
  3. EDUC AI2 (1 Mark)

Mukumu Girls Tragedy- Kuppet’s detailed reaction, response

THE GOVERNMENT’S OVERREACTION TO MUKUMU GIRLS EPIDEMIC SMACKS OF A MASSIVE COVER-UP OPERATION

Early this week, KUPPET dispatched a team of medical experts to Mukumu Girls High School in Kakamega County where four students and a teacher have died while more than 600 students, teachers and workers were hospitalised with a yet-unidentified ailment.

The expert team, which was reinforced by our partners from the doctors’ union, held consultations with the school administration, teachers, other staff and local KUPPET officials. They also reviewed investigative reports by the Public Health Department and the County Education Board.

The official report form the Ministry of Health indicates that the outbreak at Mukumu Girls was caused by Enterotoxigenic E. coli and Samonella typhi, an indication that water ingested by the students at the school were contaminated with these micro-organisms.

Based on the team’s findings, the union has made the following four determinations on the disease outbreak and government response to date:

  1. The cause of this disease and the deaths has not been conclusively established. There are claims that the school compromised on the public health report on the suitability of the water in the school. Scientific tests are needed on the safety of the school’s water systems. We await the post-mortem results and more expert investigations for greater insights into the disease.
  2. The outbreak of the disease characterised by fever, cramps, vomiting and diarrhoea seems to go beyond Mukumu Girls. Other schools from Kakamega, Bungoma, and Vihiga Counties have reported similar symptoms in students, leading to the closure of the institutions.
  3. Rather than systematically addressing an emerging epidemic, the government is engaged in a massive operation to cover up evident gaps in school health, contrary to policy. The forcible retirement of the school principal, Madam Fridah Ndolo, and dissolution of the Board of Management smack of a cover-up effort. Sending sick students home before the disease is properly understood could potentially transmit an epidemic to communities.
  4. Instead of kneejerk reactions, the Cabinet Secretary for Education, Hon Ezekiel Machogu, should convene a multi-agency team to review compliance with the Kenya School Health Policy 2018, which provides guidelines on ensuring healthy environments in learning institutions.

Among the main goals of the Kenya School Health Policy is managing access to water, sanitation and hygiene. The Policy recognises the right of all learners to safe and clean drinking water and adequate sanitation. This is to ensure disease prevention and control in schools.

Circumstantial evidence total non-compliance with this Policy at Mukumu Girls High School. Our team observed that the water that is being used in the school is stored in an underground tank, close to which runs a sewer line. The possibility of sewer contaminating water in the tank due to sewer seepage is very high.

Secondly, with 2,028 students, Mukumu Girls High School is clearly overpopulated. Learning resources and other facilities are strained. This is attributable to the government policy of 100% transition from primary school to secondary school. Uncontrolled sharing of resources due to the scarcity of the same plays a critical role in disease transmission in the event of an outbreak.

In such an environment, where resources are strained, putting in place systems to prevent transmission of communicable diseases, morbidity and mortality can be a very big challenge for the school management.

Recognising this, the Kenya School Health Policy Implementation document charges the Ministry of Health with the responsibility to “Provide technical advice on the required health standards including infrastructure, water and sanitation facilities in schools.”

The same ministry cannot come back and tell us that water was contaminated. The Directorate of Public Health must account for the negligence by its officers in such a scenario. The Directorate must answer the question of whether it has systems in place (including resources and manpower) to conduct routine public health checks in our schools.

Since this disease outbreak has been reported at Buture Boys High in Kakamega County and Khasoko Boys Secondary School in Bungoma, there clearly is a systemic lapse in the public health surveillance as opposed to failure by the school administration in adhering to public health guidelines.

Punishing Madam Ndolo only serves to undermine efforts to find lasting solutions to the problem over which she had no control. Regrettably, her forcible retirement fits in a pattern where our hard-working principals are used as sacrificial lambs to assuage public anger at the whiff of any malfunction in the school system regardless of the enormity of the situation.

KUPPET calls upon the Ministries of Education and Health to account for their responsibilities under the Kenya School Health Policy 2018. In case the Minister is unaware, the MOE’s Quality Assurance Directorate is in a sorry state, crippled by contradictory policies that have rendered the established standards useless.

A key example is the government’s policy on 100 percent transition from primary to secondary schools. The increased numbers have upended most existing guidelines on school establishment and health and safety policies. Before using the sledgehammer on the victims of the Ministry’s dysfunction, Hon Machogu must clean his office first and ensure that his Quality Assurance officers understand and are accountable for their work.

In the same vein, we urge the Teachers Service Commission to defend the rights of its employees from political fiat.

Amid the huge misfortune that has befallen the Mukumu Girls community, we urge politicians to exercise restraint and avoid inflaming the people’s passions. We take great exception to comments by the Senator for Kakamega, Hon Bonny Khalwale, who has repeatedly misdirected his ire from the county government to an innocent principal.

For the avoidance of doubt, water services are a devolved function. For that matter, the construction and maintenance of sewer systems in Mukumu Girls High School is a responsibility of the Kakamega County Government. Madam Ndolo had no power whatsoever over sewer systems developed by the county government.

To achieve disease prevention and control in schools, routine school inspection should be allocated more resources. Laboratory investigation of keys public health concerns should be part of routine school inspection. Capacity building for both the school community and the public health professionals need to be treated as a priority area to enhance disease surveillance and reporting.

Dr. Gurracha Memorial Girls High School’s KCSE Results, KNEC Code, Admissions, Location, Contacts, Fees, Students’ Uniform, History, Directions and KCSE Overall School Grade Count Summary

Dr. Gurracha Memorial Girls High School is a Girls’ secondary school located in Marsabit County; within the Eastern Region of Kenya. Get to know the school’s KCSE Results, KNEC Code, contacts, Admissions, physical location, directions, history, Form one selection criteria, School Fees and Uniforms. Also find a beautiful collation of images from the school’s scenery; including structures, signage, students, teachers and many more.

 For all details about other schools in Kenya, please visit the link below;

DR.GURRACHA MEMORIAL GIRLS SECONDARY SCHOOL’S KCSE RESULTS

Individual candidates can check their KCSE results by sending an SMS with their full index number (11digits) followed by the word KCSE. The SMS can be sent from any subscriber’s line (Safaricom, Airtel or any other) to 20076. For example, send the SMS in the format 23467847002KCSE to 20076. There should be no space left between the index number and the word KCSE.

One can also download the whole school’s KCSE results by Visiting the Official KNEC exams portal; https://www.knec-portal.ac.ke/.  This one requires the school’s log in credentials.

Finally, candidates can visit the school for their results. This is usually a day after the results have been released. It is important that you check your result slip to ensure there are no errors on it. Be keen to see that details such as your name, index number and sex are accurate. In case of any discrepancy, please notify your principal or KNEC immediately for correction.

DR.GURRACHA MEMORIAL GIRLS SECONDARY SCHOOL’S KCSE PERFORMANCE ANALYSIS/ GRADES COUNT

The school has maintained a good run in performance at the Kenya National Examinations Council, KNEC, exams. In the 2019 Kenya Certificate of Secondary Education, KCSE, exams the school posted good results to rank among the best schools in the County. This is how and where you can receive the KCSE results.

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DR.GURRACHA MEMORIAL GIRLS SECONDARY SCHOOL’S BASIC INFO & CONTACTS AT A GLANCE

In need of more information about the school? Worry not. Use any of the contacts below for inquiries and/ or clarifications. Here is a collation of the school’s basic details:

  • SCHOOL’S NAME: Dr. Gurracha Memorial Girls High School
  • SCHOOL’S TYPE: Girls’ only boarding school
  • SCHOOL’S CATEGORY: Extra County school.
  • SCHOOL’S LEVEL: Secondary
  • SCHOOL’S KNEC CODE: 16340202
  • SCHOOL’S OWNERSHIP STATUS: Public/ Government owned
  • SCHOOL’S PHONE CONTACT:
  • SCHOOL’S POSTAL ADDRESS:
  • SCHOOL’S EMAIL ADDRESS:
  • SCHOOL’S WEBSITE:
DR.GURRACHA MEMORIAL GIRLS SECONDARY SCHOOL’S BRIEF HISTORY

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DR.GURRACHA MEMORIAL GIRLS SECONDARY SCHOOL’S VISION
DR.GURRACHA MEMORIAL GIRLS SECONDARY SCHOOL’S MISSION
DR.GURRACHA MEMORIAL GIRLS SECONDARY SCHOOL’S MOTTO
DR.GURRACHA MEMORIAL GIRLS SECONDARY SCHOOL’S FORM ONE SELECTION CRITERIA & ADMISSIONS

Being a public school, form one admissions are done by the Ministry of Education. Vacancies are available on competitive basis. Those seeking admissions can though directly contact the school or pay a visit for further guidelines.

You have been selected to join form one at high school? Well. Congratulations. In case you need to see your admission letter, then click on this link to download it; Official Form one admission letter download portal.

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BEST LINKS TO TSC SERVICES & DOCUMENTS; ONLINE

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DR.GURRACHA MEMORIAL GIRLS SECONDARY SCHOOL’S PHOTO GALLERY

Planning to pay the school a visit? Below are some of the lovely scenes you will experience.

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