Category Archives: Teachers’ Resources

Week	LSN	strand	Sub-strand	Specific Learning Outcomes	Key Inquiry Question(s)	Learning Experiences	Learning Resources	Assessment Methods	Ref
1	1	Human Excretory System-Skin and Urinary System	Healthy living for Good skin and kidney	By the end of the lesson the learner should be able to: a) Identify causes of skin diseases b) Adopt a healthy lifestyle to promote skin health. c) Appreciate the importance of proper use of cosmetics for a health.	Why is excretion important to the human body?	Learners are guided to: • Learners are guided to discuss healthy lifestyles that promote kidney and skin health, for instance, adequate hydration.	• Basic Laboratory Apparatus, equipment and selected specimens • Charts • salts and water • Course book *Active Integrated Scie. Gr 7 T.G pg. 97-98* *Active Integrated Scie. Gr 7 P.B pg.118-119*	• Practical Work • Observation • Oral Questions and Answers • Assessment Rubrics • Checklist • Anecdotal Records • Written Test
	2		Importance of proper use of cosmetics	By the end of the lesson the learner should be able to: a. Define the term cosmetics b. Discuss the importance of cosmetics c. State the effects of cosmetics on the human skin d. Appreciate the importance of proper use of cosmetics	What are cosmetics?	Learners are guided to: • Search for information and brainstorm on examples of cosmetics and their health effects on human body (e.g. skin lightening creams and lotions).	• Basic Laboratory Apparatus, equipment and selected specimens • Charts • salts and water • Course book *Active Integrated Scie. Gr 7 T.G pg. 98-100* *Active Integrated Scie. Gr 7 P.B pg.119-121*	• Practical Work • Observation • Oral Questions and Answers • Assessment Rubrics • Checklist • Anecdotal Records • Written Test
	3		Homemade cosmetics	By the end of the lesson the learner should be able to: a. Define the term cosmetics b. List various homemade ingredients that can be used in making cosmetics c. Make homemade cosmetics using the available materials d. Appreciate the importance of proper use of cosmetics	What are cosmetics?	Learners are guided to: Make cosmetics using locally available materials at home like ginger, charcoal among others.	• Basic Laboratory Apparatus, equipment and selected specimens • Charts • salts and water • Course book Active Integrated Scie. Gr 7 T.G pg. 98-100 Active Integrated Scie. Gr 7 P.B pg.119-121	• Practical Work • Observation • Oral Questions and Answers • Assessment Rubrics • Checklist • Anecdotal Records • Written Test
	4		Model of a urinary system	By the end of the lesson the learner should be able to: a) Describe the various parts of the urinary system. b) Acquire locally available materials for modelling a urinary system c) Adopt a healthy lifestyle to promote kidney and skin health.	Why is excretion important to the human body?	Learners are guided to: Project Model of the urinary system.	• Basic Laboratory Apparatus, equipment and selected specimens • Charts • salts and water • Course book Active Integrated Scie. Gr 7 T.G pg. 100-101 Active Integrated Scie. Gr 7 P.B pg.122-123	• Practical Work • Observation • Oral Questions and Answers • Assessment Rubrics • Checklist • Anecdotal Records • Written Test
2	1	FORCE AND ENERGY	Static Electricity	By the end of the lesson the learner should be able to: a) demonstrate the existence of static charges in objects b) define the term static electricity c) appreciate the use of static charges in daily life	How do materials get charged?	The learner is guided to: • rub different objects to show the presence of static charges in objects	• Basic Laboratory Apparatus, equipment and selected specimens • Course book Active Integrated Scie. Gr 7 T.G pg. 103-105 Active Integrated Scie. Gr 7 P.B pg.124-125	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
	2		Types of charges	By the end of the lesson the learner should be able to: a) state the different types of charges b) demonstrate by showing the different types of charges c) appreciate the use of static charges in daily life	How do materials get charged?	The learner is guided to: • search for, play and watch videos showing types of charges	• Basic Laboratory Apparatus, equipment and selected specimens • Course book Active Integrated Scie. Gr 7 T.G pg. 105-106 Active Integrated Scie. Gr 7 P.B pg.126-127	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
	3		Charging objects by rubbing	By the end of the lesson the learner should be able to: a) state the methods used in charging objects b) charge objects using rubbing method c) appreciate the use of static charges in daily life	How do materials get charged?	The learner is guided to: • charge different objects by rubbing	• Basic Laboratory Apparatus, equipment and selected specimens • Course book Active Integrated Scie. Gr 7 T.G pg. 106-107 Active Integrated Scie. Gr 7 P.B pg.127-129	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
	4		Charging objects by rubbing	By the end of the lesson the learner should be able to: a) state the methods used in charging objects b) charge objects using rubbing method c) appreciate the use of static charges in daily life	How do materials get charged?	The learner is guided to: • charge different objects by rubbing	-• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 106-107 Active Integrated Scie. Gr 7 P.B pg.127-129	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
3	1		Charging objects by induction	By the end of the lesson the learner should be able to: a) state the methods used in charging objects b) charge objects using induction method c) appreciate the use of static charges in daily life	How do materials get charged?	The learner is guided to: • charge different objects by induction	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 106-107 Active Integrated Scie. Gr 7 P.B pg.127-129	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
	2		Charging objects by induction	By the end of the lesson the learner should be able to: a) state the methods used in charging objects b) charge objects using induction method c) appreciate the use of static charges in daily life	How do materials get charged?	The learner is guided to: • charge different objects by induction	• Basic Laboratory Apparatus, equipment and selected specimens • Course book Active Integrated Scie. Gr 7 T.G pg. 106-107 Active Integrated Scie. Gr 7 P.B pg.127-129	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
	3		effects of force between charged objects- attraction	By the end of the lesson the learner should be able to: a) define the term force b) demonstrate the effects of force between charged objects d) appreciate the use of static charges in daily life	What are the dangers of static charges?	The learner is guided to: • show attraction and repulsion between charged objects	• Basic Laboratory Apparatus, equipment and selected specimens • Course book Active Integrated Scie. Gr 7 T.G pg. 108-109 Active Integrated Scie. Gr 7 P.B pg.129-131	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
	4		effects of force between charged objects- attraction	By the end of the lesson the learner should be able to: a) define the term force b) demonstrate the effects of force between charged objects d) appreciate the use of static charges in daily life	What are the dangers of static charges?	The learner is guided to: • show attraction and repulsion between charged objects	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 108-109 Active Integrated Scie. Gr 7 P.B pg.129-131	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
4	1		effects of force between charged objects- repulsion	By the end of the lesson the learner should be able to: a) define the term force b) demonstrate the effects of force between charged objects d) appreciate the use of static charges in daily life	What are the dangers of static charges?	The learner is guided to: • show attraction and repulsion between charged objects	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 108-109 Active Integrated Scie. Gr 7 P.B pg.129-131	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
	2		effects of force between charged objects- repulsion	By the end of the lesson the learner should be able to: a) define the term force b) demonstrate the effects of force between charged objects d) appreciate the use of static charges in daily life	What are the dangers of static charges?	The learner is guided to: • show attraction and repulsion between charged objects	• Basic Laboratory Apparatus, equipment and selected specimens • Course book Active Integrated Scie. Gr 7 T.G pg. 108-109 Active Integrated Scie. Gr 7 P.B pg.129-131	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
	3		safety measures when dealing with static charges	By the end of the lesson the learner should be able to: a) identify safety measures when handling static electricity b) demonstrate the safety measures when dealing with static electricity c) appreciate the use of static charges in daily life	What are the dangers of static charges?	The learner is guided to: • discuss safety measures when dealing with static charges (include lightning).	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 109-111 Active Integrated Scie. Gr 7 P.B pg.131-133	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
	4		Uses of static charges in everyday life	By the end of the lesson the learner should be able to: a. Identify sources of static charges b. Discuss the application and uses of static charges c. Appreciate the existence of static charges	What are the uses of static charges?	The learner is guided to: Discuss the application and uses of static charges.	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 111-113 Active Integrated Scie. Gr 7 P.B pg.134-135	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
5	1	Electrical Energy	Sources of electricity	By the end of the lesson the learner should be able to: a) identify various sources of electricity in their environment b) watch a video clip on sources of electricity c) appreciate the use of electricity in their daily life	What are the sources of electricity?	The learner is guided to: • discuss and identify sources of electricity (hydro-electric power, geothermal, solar, wind power) • search for and observe videos and photographs on sources of electricity	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 115-116 Active Integrated Scie. Gr 7 P.B pg.136-137	• Assessment Rubrics • Checklist • Written Test • Practical Work • Observation Schedule • Portfolio
	2		Electrical circuit in series	By the end of the lesson the learner should be able to: a) identify the two types of electrical connections b) set up simple electrical circuits in series using dry cells, bulbs, ammeters and voltmeters c) appreciate the use of electricity in their daily life	What are the sources of electricity?	The learner is guided to: • Set up simple electrical circuits. (Series arrangement of cells and bulbs), in a group • search for and observe videos and animations showing how to set-up simple electrical circuits, in a group	• Basic Laboratory Apparatus, equipment and selected specimens • Course book Active Integrated Scie. Gr 7 T.G pg. 117-120 Active Integrated Scie. Gr 7 P.B pg.138-141	• Written Test • Assessment Rubrics • Checklist • Practical Work • Observation Schedule
	3		Electrical circuit in series	By the end of the lesson the learner should be able to: a) identify the two types of electrical connections b) set up simple electrical circuits in series using dry cells, bulbs, ammeters and voltmeters c) appreciate the use of electricity in their daily life	What are the sources of electricity?	The learner is guided to: • Set up simple electrical circuits. (Series arrangement of cells and bulbs), in a group • search for and observe videos and animations showing how to set-up simple electrical circuits, in a group	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 117-120 Active Integrated Scie. Gr 7 P.B pg.138-141	• Written Test • Assessment Rubrics • Checklist • Practical Work • Observation Schedule
	4		Electrical circuit in parallel	By the end of the lesson the learner should be able to: a) identify the two types of electrical connections b) set up simple electrical circuits in parallel using dry cells, bulbs, ammeters and voltmeters c) appreciate the use of electricity in their daily life	What are the sources of electricity?	The learner is guided to: • Set up simple electrical circuits. (parallel arrangement of cells and bulbs), in a group • search for and observe videos and animations showing how to set-up simple electrical circuits, in a group	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 117-120 Active Integrated Scie. Gr 7 P.B pg.138-141	• Written Test • Assessment Rubrics • Checklist • Practical Work • Observation Schedule
6	1		Electrical circuit in parallel	By the end of the lesson the learner should be able to: a) identify the two types of electrical connections b) set up simple electrical circuits in parallel using dry cells, bulbs, ammeters and voltmeters c) appreciate the use of electricity in their daily life	What are the sources of electricity?	The learner is guided to: • Set up simple electrical circuits. (parallel arrangement of cells and bulbs), in a group • search for and observe videos and animations showing how to set-up simple electrical circuits, in a group	• Basic Laboratory Apparatus, equipment and selected specimens • Course book Active Integrated Scie. Gr 7 T.G pg. 117-120 Active Integrated Scie. Gr 7 P.B pg.138-141	• Written Test • Assessment Rubrics • Checklist • Practical Work • Observation Schedule
	2		classification of materials as conductors	By the end of the lesson the learner should be able to: a) differentiate between conductors and non-conductors of electricity b) classify materials as conductors of electricity c) appreciate the use of electricity in their daily life	What are the differences between conductors and non-conductors of electricity?	The learner is guided to: • carry out experiments to classify materials as conductors of electricity	• Basic Laboratory Apparatus, equipment and selected specimens • Course book Active Integrated Scie. Gr 7 T.G pg. 120-121 Active Integrated Scie. Gr 7 P.B pg.141-142	• Written Test • Assessment Rubrics • Checklist • Practical Work • Observation Schedule
	3		classification of materials as conductors	By the end of the lesson the learner should be able to: a) differentiate between conductors and non-conductors of electricity b) classify materials as conductors of electricity c) appreciate the use of electricity in their daily life	What are the differences between conductors and non-conductors of electricity?	The learner is guided to: • carry out experiments to classify materials as conductors of electricity	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 120-121 Active Integrated Scie. Gr 7 P.B pg.141-142	• Written Test • Assessment Rubrics • Checklist • Practical Work • Observation Schedule
	4		classification of materials as non-conductors	By the end of the lesson the learner should be able to: a) differentiate between conductors and non-conductors of electricity b) classify materials as non-conductors of electricity c) appreciate the use of electricity in their daily life	What are the differences between conductors and non-conductors of electricity?	The learner is guided to: • carry out experiments to classify materials as non-conductors of electricity	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 120-121 Active Integrated Scie. Gr 7 P.B pg.141-142	• Written Test • Assessment Rubrics • Checklist • Practical Work • Observation Schedule
7	1		Electrical appliances in the locality	By the end of the lesson the learner should be able to: a) classify materials as conductors and non-conductors of electricity b) identify electrical appliances in their locality c) appreciate the use of electricity in their daily life	What are the sources of electricity?	The learner is guided to: • discuss and identify various electrical appliances in their locality. • explore uses of electricity in their environment	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 121-122 Active Integrated Scie. Gr 7 P.B pg.142-143	• Written Test • Assessment Rubrics • Checklist • Practical Work • Observation Schedule
	2		Electrical appliances in the locality	By the end of the lesson the learner should be able to: a) classify materials as conductors and non-conductors of electricity b) identify electrical appliances in their locality c) appreciate the use of electricity in their daily life	What are the sources of electricity?	The learner is guided to: • discuss and identify various electrical appliances in their locality. • explore uses of electricity in their environment	• Basic Laboratory Apparatus, equipment and selected specimens • Course book Active Integrated Scie. Gr 7 T.G pg. 121-122 Active Integrated Scie. Gr 7 P.B pg.142-143	• Written Test • Assessment Rubrics • Checklist • Practical Work • Observation Schedule
	3		safety measures when handling electrical appliances	By the end of the lesson the learner should be able to: a) identify electrical appliances in their locality b) identify safety measures when handling electrical appliances c) appreciate the use of electricity in their daily life	What are the sources of electricity?	The learner is guided to: • identify safety measures to observe when using electrical appliances • explore uses of electricity in their environment	• Basic Laboratory Apparatus, equipment and selected specimens • Course book Active Integrated Scie. Gr 7 T.G pg. 122-123 Active Integrated Scie. Gr 7 P.B pg.144-145	• Written Test • Assessment Rubrics • Checklist • Practical Work • Observation Schedule
	4		Uses of electricity in daily life	By the end of the lesson the learner should be able to: a. State the sources of electricity b. Observe pictures on uses of electricity c. Discuss the uses of electricity in daily life d. Appreciate the importance of electricity	What are the uses of electricity?	The learner is guided to: Discuss the uses of electricity in day to day life.	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 123-124 Active Integrated Scie. Gr 7 P.B pg.145-147	• Written Test • Assessment Rubrics • Checklist • Practical Work • Observation Schedule
8	1	Magnetism	Classification of materials	By the end of the lesson the learner should be able to: a) classify materials in the environment as magnetic or non-magnetic b) differentiate between magnetic and non-magnetic materials c) develop curiosity in using magnetic materials	How do we identify magnetic materials in our environment?	The learner is guided to: • identify and collect materials within their environment, sort and group them as magnetic and non-magnetic materials	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 127-128 Active Integrated Scie. Gr 7 P.B pg.148	Portfolio • Written Test • Observation Schedule • Assessment Rubrics • Checklist • Practical Work
	2		force between like and unlike poles	By the end of the lesson the learner should be able to: a) watch a video clip of force between like and unlike poles of a magnet b) investigate the force between like poles of magnets c) appreciate the applications of magnets in day-to-day life	How do we identify magnetic materials in our environment?	The learner is guided to: • carry out activities showing repulsion between two like poles of magnets. • Search for and watch animations showing force between like and unlike poles of magnets.	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 129-130 Active Integrated Scie. Gr 7 P.B pg.149-151	Portfolio • Written Test • Observation Schedule • Assessment Rubrics • Checklist • Practical Work
	3		force between like and unlike poles	By the end of the lesson the learner should be able to: a) watch a video clip of force between like and unlike poles of a magnet b) investigate the force between like poles of magnets c) appreciate the applications of magnets in day-to-day life	How do we identify magnetic materials in our environment?	The learner is guided to: • carry out activities showing repulsion between two like poles of magnets. • Search for and watch animations showing force between like and unlike poles of magnets.	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 129-130 Active Integrated Scie. Gr 7 P.B pg.149-151	Portfolio • Written Test • Observation Schedule • Assessment Rubrics • Checklist • Practical Work
	4		Uses of a magnet in daily life	By the end of the lesson the learner should be able to: a) Watch a video clip on the uses of a magnet b) identify the uses of magnets in day-to-day life c) appreciate the applications of magnets in day-to-day life	How are magnets used in day-to-day life?	The learner is guided to: • discuss the uses of magnets with peers	• Basic Laboratory Apparatus, equipment and selected specimens Active Integrated Scie. Gr 7 T.G pg. 131-134 Active Integrated Scie. Gr 7 P.B pg.151-156	Portfolio • Written Test • Observation Schedule • Assessment Rubrics • Checklist • Practical Work
9	END TERM ASSESSMENT/CLOSING

Teachers' Resources

Grade 4 score sheet pdf

October 5, 2025 Maverick John Leave a comment

GRADE 4 REPORT CARD

Download a free copy of the report book here; Grade 4 Report Card.

MINISTRY OF EDUCATION

STATE DEPARTMENT OF EARLY LEARNING AND BASIC EDUCATION SCHOOL TERMLY REPORT

GENERAL INFORMATION

NAME OF THE SCHOOL

LEARNERS NAME

DATE OF BIRTH ADMISSION NUMBER

LEARNERS GRADE LEARNERS UPI

YEAR

LEARNERS RATING SCALE

PERFOMANCE LEVEL	RATING
EXCEEDING EXPECTATION	4
MEETING EXPECTATION	3
APPROACHING EXPECTATION	2
BELOW EXPECTATION	1

LEARNERS ACHIEVEMENT (MATHEMATICS)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
MATHEMATICS
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 NUMBERS
Whole Numbers
Addition
Multiplication
Division
Fractions
Decimals
Comment on the Strand/Sub-strand:
2.0 MEASUREMENT
Length
Area
Mass
Volume
Capacity
Time
Money
Comment on the Strand/Sub-strand:
3.0 GEOMETRY
Positions and Direction
Angles
2-D shapes
Comment on the Strand/Sub-strand:
4. 0 DATA HANDLING
Data
Comment on the Strand/Sub-strand:
5.0 ALGEBRA
Use of Letters
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (SCIENCE AND TECHNOLOGY)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
SCIENCE AND TECHNOLOGY
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 LIVING THINGS
Plants
Animals
Human Body
Comment on the Strand/Sub-strand:
2.0 ENVIRONMENT
Air pollution
Water Pollution
Comment on the Strand/Sub-strand:
3.0 DIGITAL TECHNOLOGY
Digital Devices
Coding
Comment on the Strand/Sub-strand:
4.0 MATTER
States of matter
Properties of matter
Comment on the Strand/Sub-strand:
5.0 FORCE & ENERGY
Force
Energy
Comment on the Strand/Sub-strand:
6.0 EARTH AND SPACE
Weather and sky
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (ENGLISH ACTIVITES)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
ENLGLISH
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 LISTENING AND SPEAKING
Pronunciation
Vocabulary
Comment on the Strand/Sub-strand:
2.0 READING
Intensive reading
Extensive reading
Comment on the Strand/Sub-strand:
3.0 GRAMMAR
Language pattern
Comment on the Strand/Sub-strand:
4.0 WRITING
Hand writing
Guided writing
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (KISWAHILI LANGUAGE)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
KISWAHILI LANGUAGE
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 KUSIKILIZA NA KUZUNGUMZA
Matamshi bora
Maamkuzi na maagano
Tamathali za semi
Comment on the Strand/Sub-strand:
2.0 KUSOMA
Kusoma kwa ufahamu
Kusoma kwa mapana
Kusoma kwa kina
Comment on the Strand/Sub-strand:
3.0 KUANDIKA
Kuandika insha
Kuandika kutumia tarakilishi
Comment on the Strand/Sub-strand:
4.0 SARUFI
Aina za maneno
Umoja na wingi
Ngeli za Nomino
Mnyambuliko
Vinyume vya maneno
Nyakati na Hali
Ukanusho
Ukubwa na Udogo
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (SOCIAL STUDIES)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
MATHEMATICS
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 NATURAL & BUILT ENVIRONMENTS
Natural Environment
Built Environment
Comment on the Strand/Sub-strand:
2.0 PEOPLE & POPULATION
Interdependence of people
Population distribution
Comment on the Strand/Sub-strand:
3.0 CULTURE & SOCIAL ORG.
Culture
School
Comment on the Strand/Sub-strand:
4.0 RESOURCES & ECONOMIC ACT.
Resources in the county
Economic activities in the county
Trade in the county
Industries in the county
Enterprise project at school
Comment on the Strand/Sub-strand:
5.0 POLITICAL SYSTEMS & CHANES
Community Leadership
Comment on the Strand/Sub-strand:
6.0 CITIZENSHIP
Good citizenship in school
Human rights

Peace
Peace education project
Comment on the Strand/Sub-strand:
7.0 GOVERNANCE IN KENYA
Democracy in school
Children’s Government in school
Government in Kenya
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (AGRICULTURE)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
AGRICULTURE
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 CONSERVING OUR ENVIRONMENT
Soil
Water
Living better with wild animals
Growing fruit trees
Conservation project
Comment on the Strand/Sub-strand:
2.0 DOMESTIC ANIMALS
Domestic animals
Uses of Domestic animals
Comment on the Strand/Sub-strand:
3.0 GARDENING PRACTICES
Crops for gardening
Selected gardening practices
Innovative Gardening project
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (HOME SCIENCE)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
HOME SCIENCE
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 HEALTHY PRACTICES
Play
Comment on the Strand/Sub-strand:
2.0 HEALTHY LIVING
Common illness in the locality
Care of the home
Care and cleaning of shoes
Fuels used at home
Comment on the Strand/Sub-strand:
3.0 CONSUMER EDUCATION
Consumer awareness
Comment on the Strand/Sub-strand:
4.0 FOODS & NUTRITION
Choosing foods
Variety in the diet
Preservation of milk
Fragile kitchen utensils
Cooking food
Comment on the Strand/Sub-strand:
5.0 CLOTHING
Needlework tools
Stitches
Fixing a button
Laundry work
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (PHYSICAL AND HEALTH EDUCATION)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
PHE
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 BASIC MOVEMENT SKILLS
Locomotor skills
Manipulative skills
Comment on the Strand/Sub-strand:
2.0 GYMNASTICS
Rolls
Individual balances
Sequences
Comment on the Strand/Sub-strand:
3.0 SWIMMING
Basic strokes
Basic dives
Comment on the Strand/Sub-strand:
4.0 INVASION GAMES
Frisbee skills
Comment on the Strand/Sub-strand:
5.0 HEALTH AND PHYSICAL FITNESS
Components of health related fitness
Nutrition and sports performance
Wellness
Comment on the Strand/Sub-strand:
6.0 FIRST AID IN GAMES & SPORTS
Common injuries in games and sports
Transporting an injured victim

Comment on the Strand/Sub-strand:
7.0 OUTDOOR ACTIVITIES
Recreation
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (ART & CRAFT)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
ART & CRAFT
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 PICTURE MAKING
Drawing
Crayon etching
Painting
Montage
Comment on the Strand/Sub-strand:
2.0 INDEGINOUS KENYAN CRAFT
Basketry
Leather work
Pottery
Comment on the Strand/Sub-strand:
3.0 DESIGN, MIXED MEDIA & TECHNOLOGY
Graphic design
Paper craft
Puppetry
Photography
Comment on the Strand/Sub-strand:
4.0 PRESENTATION AND EXHIBITION
Mounting artwork
Exhibition skills
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (MUSIC)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
MUSIC
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 PERFOMING
Songs
Kenyan folk
Musical instruments
Dance
Comment on the Strand/Sub-strand:
2.0 CREATING & COMPOSING MUSIC
Rhythm
Melody
Comment on the Strand/Sub-strand:
3.0 LISTENING, RESPONDING & APPRECIATION
Elements of music
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (INDEGINOUSLANGUAGE)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
INDEGINOUS LANGUAGE
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 LISTENING
Language structure
Responding to instructions
Musical instruments Listening to instructions
Listening to stories and related topics
Comment on the Strand/Sub-strand:
2.0 SPEAKING
Using language
Giving instructions
Giving information
Comment on the Strand/Sub-strand:
3.0 READING

4.0 WRITING

Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (CHRISTIAN RELIGIOUS EDUCATION)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
CRE
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 CREATION
Self-awareness
My family
Attributes of God
Comment on the Strand/Sub-strand:
2.0 THE HOLY BIBLE
Respect for the bible
Bible stories
Comment on the Strand/Sub-strand:
3.0 THE LIFE OF JESUS CHRIST
The birth of Jesus Christ
The miracles of Jesus Christ
Teaching s of Jesus Christ
4.0 CHRISTIAN VALUES
Trust, truthfulness, obedience, responsibility, God’s love, Holiness
Comment on the Strand/Sub-strand:
5.0 THE CHURCH
House of God
The early church
Standing firm in the faith
The Lord’s prayer
Fruits of the Holy spirit

Comment on the Strand/Sub-strand:
6.0 MORALITY & SOCIAL MEDIA
Use of social media
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (HINDU RELIGIOUS EDUCATION)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
HRE
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 NATURE
Panch- mahadhoot
Sacred plants
Comment on the Strand/Sub-strand:
2.0 DIVINITY
Manifestation & enlightened souls
Comment on the Strand/Sub-strand:
3.0 SCRIPTURES
Essence of scriptures
4.0 PRINCIPLES OF DHARMA
Virtue of righteousness
Comment on the Strand/Sub-strand:
5.0 ISHWAR UPAASNAA
Dainik prarthana
Comment on the Strand/Sub-strand:
6.0 UTSAVA
Social & national festivals
Hindu calendar
Comment on the Strand/Sub-strand:
7.0 YOGA
Pranaayam
Aasanas
Comment on the Strand/Sub-strand:
8.0 SADACHAAR
Aspects of integrity
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (ISLAMIC RELIGIOUS EDUCATION)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
IRE
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 QUR’AN
Selected surah’s
Comment on the Strand/Sub-strand:
2.0 HADITH
Prophet Muhammad
Hadith on eating
Hadith on brushing teeth
Hadith on fitness
Comment on the Strand/Sub-strand:
3.0 PILLARS OF IMAN
Attributes of Allah
Angels and their duties
Prophets mentioned in the Qur’an
Comment on the Strand/Sub-strand:
4.0 DEVOTIONAL ACTS
Twahara
Conditions for swalah
Pillars of Swalah
Comment on the Strand/Sub-strand:
5.0 AKHLAQ
Virtues
Vices
Dua
Comment on the Strand/Sub-strand:

6.0 MUAMALAAT
Obligations of parents to children
Obligations of children to parents
Children’s obligations to other family members
Comment on the Strand/Sub-strand:
7.0 HISTORY OF ISLAM
Prophet’s marriage of Khadija
Call to prophet hood
Al- Isra wal miraj
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (FRENCH LANGUAGE)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
FRENCH
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 LISTENING AND SPEAKING
Languages around us
Discovering French
Myself
Comment on the Strand/Sub-strand:
1.1 INTERACTING WITH OTHERS
Etiquette
Giving & responding to instructions
Expressing wishes
Expressing likes & dislikes
Moments of the day
Expressing what one wants
Locating objects in our surrounding
Expressing how one feels
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (GERMAN LANGUAGE)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
GERMAN
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 LISTENIN & SPEAKING
Greetings & introduction
Numbers & days of the week
Phonological awareness
Describing objects & people in the immediate environment
School
Leisure time activities
Foodstuff
Comment on the Strand/Sub-strand:
2.0 REDING
Greetings & introduction
Numbers & days of the week
Phonological awareness
Describing objects & people in the immediate environment
School
Leisure time activities
Foodstuff
Comment on the Strand/Sub-strand:
3.0 WRITING
Greetings & introduction
Numbers & days of the week
Phonological awareness
Describing objects & people in the immediate environment

School
Leisure time activities
Foodstuff
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (CHINESE LANGUAGE)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
CHINESE
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 LISTENIN & SPEAKING
Greetings
Self-introduction
Nationality
My family
My home
School life
Foods & beverages
Time
Colours
Comment on the Strand/Sub-strand:
2.0 REDING
Greetings
Self-introduction
Nationality
My family
My home
School life
Foods & beverages
Time
Colours
Comment on the Strand/Sub-strand:
3.0 WRITING
Greetings
Self-introduction
Nationality

My family
My home
School life
Foods & beverages
Time
Colours
Comment on the Strand/Sub-strand:

LEARNERS ACHIEVEMENT (ARABIC LANGUAGE)

LEARNING AREAS	TERM							COMMENTS/TEACHER STATEMENTS
ARABIC
	TERM 1		TERM 2		TERM 3		AVG	T 1	T 2	T 3
	%	RATE	%	RATE	%	RATE
1.0 LISTENIN & SPEAKING
Introduction of self & others
Reading
Writing
Family
Pre-reading/active reading
Guided writing
My school
In the market
Types of shops
Numbers
Numbers in words
Days of the week
Domestic animals & birds
Animals & birds
Human Body
Foods & meals
Environment
Cleanliness
Comment on the Strand/Sub-strand:

TERM ONE

LEANER’S CONDUCT AND BEHAVIOUR

ATTRIBUTES/AREA	TEACHERS COMMENTS
Classroom conduct
Work completion
Working with others
Time management
Cleanliness/Grooming
Communication

Class teacher’s feedback on learner’s acquisition of core competencies (communication &

collaboration, critical thinking & problem solving, imagination and creativity, citizenship, digital literacy, learning to learn, self-efficacy)

Class Teacher’s Feedback on Learner’s Acquisition Of Values (Responsibility, Respect, Excellence, Care & Compassion, understanding and tolerance, honesty & trustworthy, trust, being ethical)

Evidence of participation in community service learning

Head Teacher’s details
Name	Sign	Date
Parents/ Guardians Details
Name	Sign	Date

TERM TWO

LEANER’S CONDUCT AND BEHAVIOUR

ATTRIBUTES/AREA	TEACHERS COMMENTS
Classroom conduct
Work completion
Working with others
Time management
Cleanliness/Grooming
Communication

Class teacher’s feedback on learner’s acquisition of core competencies (communication &

collaboration, critical thinking & problem solving, imagination and creativity, citizenship, digital literacy, learning to learn, self-efficacy)

Evidence of participation in community service learning

Head Teacher’s details
Name	Sign	Date
Parents/ Guardians Details
Name	Sign	Date

TERM THREE

LEANER’S CONDUCT AND BEHAVIOUR

ATTRIBUTES/AREA	TEACHERS COMMENTS
Classroom conduct
Work completion
Working with others
Time management
Cleanliness/Grooming
Communication

Class teacher’s feedback on learner’s acquisition of core competencies (communication &

collaboration, critical thinking & problem solving, imagination and creativity, citizenship, digital literacy, learning to learn, self-efficacy)

Evidence of participation in community service learning

Head Teacher’s details
Name	Sign	Date
Parents/ Guardians Details
Name	Sign	Date

Teachers' Resources

KCSE 2023 Prediction Exams, Mocks, Replica Exams, Top Student Revision Materials Free Downloads

October 5, 2025 Maverick John Leave a comment

KCSE 2023 Prediction Exams, Mocks, Replica Exams, Top Student Revision Materials Free Downloads

A DOLL’S EXCERPTS S1 Q (5).pdf
A DOLL’S EXCERPTS S1 Q (6).pdf
A DOLL’S HOUSE GUIDE SP (5).pdf
A DOLL’S HOUSE GUIDE SP (6).pdf
A SILENT SONGS KCSE QNS-1 (4).pdf
A SILENT SONGS KCSE QNS-1 (5).pdf
A SILENT SONGS KCSE S2 (3).pdf
A SILENT SONGS KCSE S2 (4).pdf

AGRIC 2023 C-COUNTRY MOCKS (2).pdf
AGRIC 2023 C-COUNTRY MOCKS.pdf
AGRIC 2023 TOP SCH’S MOCKS (2).pdf
AGRIC 2023 TOP SCH’S MOCKS.pdf

AN ARTIST OF FLOATING WORLD GUIDE SP-1 (5).pdf
AN ARTIST OF FLOATING WORLD GUIDE SP-1 (6).pdf
ARTIST OF FLOATING WORLD ESSAYS S1 (3).pdf
ARTIST OF FLOATING WORLD ESSAYS S1 (4).pdf

BEMBEA YA MAISHA REVISION S3 (5).pdf
BEMBEA YA MAISHA REVISION S3 (6).pdf
BEMBEA YA MAISHA S2 Q (5).pdf
BEMBEA YA MAISHA S2 Q (6).pdf

BIOLOGY 2023 TOP SCH’S MOCKS (2).pdf
BIOLOGY 2023 TOP SCH’S MOCKS.pdf

BLOSSOMS ESSAYS S1 Q (5).pdf
BLOSSOMS ESSAYS S1 Q (6).pdf

BUSINESS 2023 C-COUNTRY MOCKS (2).pdf
BUSINESS 2023 C-COUNTRY MOCKS.pdf
BUSINESS 2023 TOP SCH’S MOCKS (2).pdf
BUSINESS 2023 TOP SCH’S MOCKS.pdf

CHEMISTRY 2023 C-COUNTRY MOCKS (2).pdf
CHEMISTRY 2023 C-COUNTRY MOCKS.pdf
CHEMISTRY 2023 TOP SCH’S MOCKS (2).pdf
CHEMISTRY 2023 TOP SCH’S MOCKS.pdf

CHOZI LA HERI GUIDE SP (5).pdf
CHOZI LA HERI GUIDE SP (6).pdf
CHOZI LA HERI KCSE QNS (5).pdf
CHOZI LA HERI KCSE QNS (6).pdf

COMPUTER 2023 C-COUNTRY MOCKS (2).pdf
COMPUTER 2023 C-COUNTRY MOCKS.pdf
COMPUTER 2023 TOP SCH’S MOCKS (2).pdf
COMPUTER 2023 TOP SCH’S MOCKS.pdf

CRE 2023 C-COUNTRY MOCKS (2).pdf
CRE 2023 C-COUNTRY MOCKS.pdf
CRE 2023 TOP SCH’S MOCKS (2).pdf
CRE 2023 TOP SCH’S MOCKS.pdf

ENG KCPE 2023 PREDICTION CYCLES (2).pdf
ENG KCPE 2023 PREDICTION CYCLES.pdf

FATHERS OF NATIONS ESSAYS S1 (5).pdf
FATHERS OF NATIONS ESSAYS S1 (6).pdf
FATHERS OF NATIONS ESSAYS S2 (5).pdf
FATHERS OF NATIONS ESSAYS S2 (6).pdf
FATHERS OF NATIONS EXCERPTS S1 (5).pdf
FATHERS OF NATIONS EXCERPTS S1 (6).pdf
FATHERS OF NATIONS EXCERPTS S2 (2).pdf
FATHERS OF NATIONS EXCERPTS S2 (3).pdf
FATHERS OF NATIONS EXTRACTS S3 (2).pdf
FATHERS OF NATIONS EXTRACTS S3 (3).pdf
FATHERS OF NATIONS GUIDE SAMPLE-1 (4).pdf
FATHERS OF NATIONS GUIDE SAMPLE-1 (5).pdf

FUNCTIONAL WRITING S1 (4).pdf
FUNCTIONAL WRITING S1 (5).pdf

HISTORY 2023 C-COUNTRY MOCKS (2).pdf
HISTORY 2023 C-COUNTRY MOCKS.pdf
HISTORY 2023 TOP SCH’S MOCKS (2).pdf
HISTORY 2023 TOP SCH’S MOCKS.pdf

HOME SCI 2023 TOP SCH’S MOCKS (2).pdf
HOME SCI 2023 TOP SCH’S MOCKS.pdf

ISIMU JAMII REVISION S1 (5).pdf
ISIMU JAMII REVISION S1 (6).pdf

KCSE BEMBEA YA MAISHA QNS-1 (4).pdf
KCSE BEMBEA YA MAISHA QNS-1 (5).pdf

KCSE CLOZE-TEST REVISION S1 (5).pdf
KCSE CLOZE-TEST REVISION S1 (6).pdf

KCSE ENGLISH PASSAGES S1 (5).pdf
KCSE ENGLISH PASSAGES S1 (6).pdf
KCSE ENGLISH PP1 REVISION S1 (5).pdf
KCSE ENGLISH PP1 REVISION S1 (6).pdf
KCSE ENGLISH PP1 REVISION S2 (5).pdf
KCSE ENGLISH PP1 REVISION S2 (6).pdf
KCSE ENGLISH PP2 REVISION S1 (5).pdf
KCSE ENGLISH PP2 REVISION S1 (6).pdf
KCSE ENGLISH PP2 REVISION S2 (5).pdf
KCSE ENGLISH PP2 REVISION S2 (6).pdf

KCSE GRAMMAR REV S1 (5).pdf
KCSE GRAMMAR REV S1 (6).pdf

KCSE INHERITANCE ESSAYS (5).pdf
KCSE INHERITANCE ESSAYS (6).pdf

KCSE ORAL NARRATIVE S1 (4).pdf
KCSE ORAL NARRATIVE S1 (5).pdf

KCSE POETRY REVISION S1 (5).pdf
KCSE POETRY REVISION S1 (6).pdf

KISWAHILI 2023 C-COUNTRY MOCKS (2).pdf
KISWAHILI 2023 C-COUNTRY MOCKS.pdf
KISWAHILI 2023 TOP SCH’ MOCKS. (2).pdf
KISWAHILI 2023 TOP SCH’ MOCKS..pdf

MAPAMBAZUKO YA MACHWEO QNS-1 (5).pdf
MAPAMBAZUKO YA MACHWEO QNS-1 (6).pdf

MWONGOZO WA BEMBEA YA MAISHA SAMPLE-1 (5).pdf
MWONGOZO WA BEMBEA YA MAISHA SAMPLE-1 (6).pdf
MWONGOZO WA MAPAMBAZUKO SAMPLE-1 (5).pdf
MWONGOZO WA MAPAMBAZUKO SAMPLE-1 (6).pdf

NGUU ZA JADI GUIDE SAMPLE-1 (5).pdf
NGUU ZA JADI GUIDE SAMPLE-1 (6).pdf

ORAL LITERATURE S1 (5).pdf
ORAL LITERATURE S1 (6).pdf

PARLIAMENT OF OWLS GUIDE SP-1 (5).pdf
PARLIAMENT OF OWLS GUIDE SP-1 (6).pdf

SILENT SONGS GUIDE SPLE S1-2 (4).pdf
SILENT SONGS GUIDE SPLE S1-2 (5).pdf

THE SAMARITAN GUIDE SP S2 (4).pdf
THE SAMARITAN GUIDE SP S2 (5).pdf
THE SAMARITAN KCSE ESSAYS S1 (5).pdf
THE SAMARITAN KCSE ESSAYS S1 (6).pdf
THE SAMARITAN KCSE ESSAYS S2 (4).pdf
THE SAMARITAN KCSE ESSAYS S2 (5).pdf

TOP STUDENT AGRICULTURE PREDICTIONS .pdf
TOP STUDENT BIO PP3 PREDICTIONS (2).pdf
TOP STUDENT BIOLOGY PREDICTIONS.pdf
TOP STUDENT CHEMISTRY PREDICTIONS.pdf
TOP STUDENT COMPUTER PREDICTIONS QS (2).pdf
TOP STUDENT CRE PREDICTIONS.pdf
TOP STUDENT ENGLISH PP1 PREDICTIONS .pdf
TOP STUDENT GEOGRAPHY PREDICTIONS (2).pdf
TOP STUDENT HISTORY PREDICTIONS (2).pdf
TOP STUDENT MATHEMATICS PREDICTIONS.pdf
TOP STUDENT PHYSICS PREDICTIONS (2).pdf

TPAD_Archived_Reports_How_to_retrieve,_View,_Download_and_Print (2).pdf
TPAD_Archived_Reports_How_to_retrieve,_View,_Download_and_Print.pdf
TSC INTERVIEW QUIZ LATEST (2).pdf
TSC INTERVIEW QUIZ LATEST.pdf

Teachers' Resources

ENGLISH PP3 LANJET CLUSTER EXAMS PLUS ANSWERS IN PDF

October 5, 2025 Maverick John Leave a comment

TRIAL ONE EVALUATION TEST

ENGLISH

PAPER 101/3

Imaginative compositions and Essays based on set texts.

Time: 2hrs 30 Mins

INSTRUCTIONS

Answer Three Questions Only
Question One And Two Are Compulsory
In Question Three Choose Only One Question That You Are Prepared For.
Each Of Your Essays Must Not Exceed 450 Words

IMAGINATIVE COMPOSITIONS
Write a story beginning with the following words:

I knew it was not going to be easy—————————————

Write a story to bring out the meaning of the following saying: “ As you make your bed, so you must lie in it”
COMPULSORY

Blossoms of the Savannah by H. Ole Kulet.

Retrogressive and dehumanizing cultural practices against women are mostly perpetrated by women themselves. Using Blossoms of the Savannah for your illustrations, write an essay in support of the above statement.

OPTIONAL
Memories we lost and other short stories.

Using illustrations from LidudumalinganiMqombothis’ Story “Memories we lost’, discuss the importance of hope even when situations in life seem unbearable.

THE PEARL.

Obsession for wealth can lead to disintegration of people’s lives and character. Discuss this statement referring to the Pearl by John Steinbeck.

101/3

ENGLISH

PAPER 3

(CREATIVE COMPOSITION AND ESSAYS BASED ON SET TEXTS

LANJET CLUSTER EXAMS

Kenya Certificate of Secondary Education

MARKING SCHEME

ENGLISH

PAPER 3

2 ½ HOURS

Paper 101/3 is intended to test the candidates ability to communicate in writing,. Communication is established at different levels of intelligibility, correctness, accuracy, fluency, pleasantness and ability. Within the constraints set by each question, it is the linguistic competence shown the candidate that should carry most of the marks.

Examiner should not hesitate to use the full range of marks for each essay

It is important to determine first how each essay communicates and in which category A,B,C or D as it is(marks indicated below are for question one)

CATEGORIES OF ESSAYS

CLASS D	The candidate either does not communicate at all or his language ability is so minimal that the examiner practically has to guess what the candidate wants to say. The candidate fails to fit the English word into meaningful sentences. The subject is glanced at or distorted. Practically no valid punctuation. All kind of errors “Broken English.”
D- (01-02)		Chaotic, little meaning whatsoever. Question paper or some words from it simply copied.
D (3)		Flow of thought almost impossible to follow. The errors are continuous
D+ (04-05)		Although the English is often broken and the essay is full of errors of all types we can at least guess what the candidate wants to say.
C CLASS (06-10)		The candidate communicates understandably but only more or less clearly. He is not confident with his language. The subject is often undeveloped. There may be some digressions. Unnecessary repetitions are frequent. The arrangement is weak and the flow jerky. There is no economy of language mother tongue influence is felt
C- (06-07)		The candidate obviously finds it difficult to communicate his/her ideas. He/she is seriously hampered by his/her limited knowledge of structure and vocabulary. This results in many errors of agreement, spelling, and misuse of prepositions, tense, verb agreement and sentence construction.
C (08)		The candidate communicates but not with consistent clarity. His/her linguistic abilities being very limited, he/she cannot avoid frequent errors in sentence structure. There is little variety or originality. Very bookish English, links are weak, incorrect, repeated at times.
C+ (09-10)		The candidate communicates clearly but in a flat and uncertain manner. Simple concepts sentence forms are often strained. There may be an overuse of clichés, unsuitable idioms. Proverbs are misquoted or misinterpreted. The flow is still jerky. There are some errors of agreement, tenses and spelling.
B CLASS			This class is characterized by greater fluency and ease of expression. The candidate demonstrates that he/she can use English as a normal way of expressing himself/herself. Sentences are varied and usually well-constructed. Some candidates become ambitious and even over-ambitious. There may be items of merit of the one word or one expression type. Many essays in this category may be just clean and unassuming but they still show that the candidate is at ease with the language. There may be a tendency to under mark such essays. Give credit for tone
B- 11-12			The candidate communicates fairly and with some fluency. There may be little variety in sentence structure. Gross errors are still found occasionally, but this must not be over punished by the examiner.
B 13			The sentences are varied but rather simple and straight forward. The candidate does not strain himself in an effort to impress. There is a fair range of vocabulary and idiom. Natural and effortless. Some items of merit, economy of language
B+ 14-15			The candidate communicates his ideas pleasantly and without strain. There are errors and slips. Tenses, spelling and punctuation are quite good. A number of items of merit of the whole sentence or the whole expression type
A CLASS 16-20			The candidate communicates not only fluently, but attractively with originality and efficiency. He/she has the ability to make us share his deep feelings, emotions, enthusiasms. He/she expresses himself freely and without any visible constraint. The script gives evidence of maturity, good planning and often humour. Many items of merit which indicate that the candidate has complete command of the language. There is no strain just pleasantness, clever arrangement, felicity of expression.
A- 16-17			The candidate shows competence and fluency in using the language. He may lack imagination or originality which usually provides the “spark” in such essays. Vocabulary idiom, sentence structure, links, variety are impressive. Gross errors are very rare
A 18			Positive ability. A few errors that are felt to be slips. The story or argument has a definite impact. No grammar problem. Variety of structures. A definite spark. Many margin ticks
A+ 19-20			The candidate communicated not only information and meaning but also and especially the candidate’s whole self: his /her feelings, tastes, points of view, youth, and culture. This ability to communicate is deep self may express itself in many ways, wide range of effectiveness vocabulary, original approach, vivid and sustained account in the case of narrative, well developed in the case of a debate or discussion. Errors and slips should not deprive the candidate the full marks he deserves. A very definite spark.

TABLE OF CATEGORIES

CLASS MARK CATEGORY

EACH ESSAY

A+ 19-20

A 18

A- 16-17

C+ 09-10

C 08

B- 06-07

B+ 14-15

B 13

C- 11-12

D+ 04-05

D 03

D- 01-02

MARKING SYMBOLS

The main signs indicate three degrees of seriousness of error.

GROSS ERROR OMISSION FOR

CONSTRUCTION

IN MARGIN c

MINOR ERROR OMISSION MINOR CONSTRUCTION

ERROR c

This sign in the margin is used only when a construction error affects more than

One line The following symbols may also be used

FAULTY PARAGRAPHING p

REPETITION ILL (of words) a circle around the word (of ideas) usually in the margin

ILLEGIBILITY Obscure/vague (in margin)

WRONG WORDS ORDER Underline once and write W.O. in margin

ILLOGICAL or CONTRADICTORY ILL (in margin)

VAGUENESS

BROKEN ENGLISH when the candidate fails to communicate BR in margin.

FOR PURPOSES OF IDENTIFICATION

COW to indicate that a candidate has used a pencil to make correction

BRACKETS [ ] indicate a part of a D script that communicates.

*Use as asterisk to indicate an item or a sentence that the rubrics indicate should be used.

II TO INDICATE AN ITEM OF MERIT use a tick (√) either above a word or in the margin for the whole sentence

GROSS ERRORS

Almost any error of agreement
Serious tense error

Error of elementary vocabulary, spelling and misuse

Punctuation errors or missing punctuation which causes serious lack of communication
Elementary errors of sentence construction
Ridiculous use of idioms that affects communication

Misuse of common propositions
Misuse of capital letters

POINTS OF INTERPRETATIONS

a) Points of interpretation

it must be a story if not deduct 2 marks
it must end with the sentence given if not deduct 2 marks (AD)
there must present a credible scenario/ situation of betrayal or one which would lead to the ending of the story, if it is not the case treat it as irrelevant and deduct 2 marks (AD)

b) Points of interpretation

Must be an expository essay. If not deduct 2 marks (AD)
The essay must either be for or against. If not deduct 4 marks (AD)
Expect an introduction and conclusion. However, it is the linguistic ability that should carry the most marks.

BLOSSOMS OF THE SAVANNAH

We would expect that those close to us would be the ones to help us out in our time of need. However, many a time, they are the reason for our suffering. For example, a close friend may spread rumours about you and make people hate you. In Blossoms of the Savannah, various characters have gotten in trouble due to the misdeeds of their relatives, friends or acquaintances.

Accept any other relevant introduction: award 2 marks. (Can be general, contexualized or general-contextualized)

Body

Resian suffers a lot because of her father’s greed. Ole Kaelo seeks to marry off Resian to Oloisudori against her will. He in effect trades her for money given to him by Oloisudori who wants to marry her in exchange for the money he lent Ole Kaelo to establish himself in Nasila. As a result, She runs away from home and even contemplates suicide. She lands in the hands of Olarinkoi who puts her through a lot of physical and emotional pain.
Olarinkoi subjects Resian to a lot of pain. Olarinkoi lies to Resian that he will take her to Emankererei and she feels grateful to him. However, it turns out that he has different plans. He makes her ride on the back of a pickup where she has to deal with the cold and insects. As if that is not enough, he imprisons her in very deplorable conditions. He also attempts to rape her.
Olaisudori makes Ole kaelo suffer due to his demand that he marries Resian. The two had a business arrangement but Oloisudori demands Resian instead of getting money he had loaned him back. This causes Ole Kaelo a lot of sleepless nights and eventually he loses her as she goes to live with Emakererei.
Mama Milanoi hands over Taiyo to the circumcisor. Her mother is expected to safeguard her interests but instead hands her over to be circumcised. This subjects her to physical and emotional pain. Also, Taito loses Joseph as he dies when attempting to rescue her.

Any four well illustrated points 4 *3 =12 (3:3:3:3)

Conclusion

From the above illustrations, it is clear that those close to us can cause us a lot of physical and emotional pain. We should be careful around our friends and relatives.

Any other relevant conclusion, award 2 marks

Introduction: 2 marks

Content: 12 marks

Conclusion: 2 marks

Language: 4 marks

The Optional Set Texts

The Short Stories: The Memories We lost and other stories by Chris Wanjala

There are various challenges faced by African countries many years after they attained their independence. The ‘mzungu’ while taking a ride in a daladala through Dar es Salaam describes some of these challenges as will be illustrated below

Accept any other relevant introduction:award 2 marks. (Can be general, contexualized or general-contextualized)

Body

Lawlessness on the roads. The vehicles should follow traffic laws for safety. However, law and order is not followed as it should be. Passengers are literally packed. A daladala which is the size of a minivan and should therefore carry ten passengers is loaded with 25 passengers.

Poor infrastructure. The roads are in bad condition. We are told that most of the road is a dusty stretch.
People on the buses are said to be in sandals and others are barefoot. This means that they cannot afford better shoes or cannot afford any shoes at all. The narrator describes Kanga as having a trimmed figure ‘molded by beautiful genes and a lifetime of never ending work and deprivation of luxuries’
The police who are supposed to guarantee safety collude with drivers. They solicit bribes to an extent of removing car keys from the ignition.
There is pollution everywhere, air pollution from the dust, noise pollution from conductors advertising their daladalas etc. there is also dirt flying by and people burning rubbish and dead foliage on the sides of the road.

Any four well illustrated points *3=12 (3:3:3:3)

Conclusion

From the above illustrations, it is clear that post independent East African countries still face a lot of challenges.

Any other relevant conclusion, award 2 marks.

Introduction: 2 marks

Content: 12 marks

Conclusion: 2 marks

Language: 4 marks

Drama: Inheritance

Introduction

A bad leader causes a lot of hardships for his or her country. Usually, such a leader is driven by greed. Any decision made is to the detriment of the country. For example, bad leaders give jobs on the basis of tribal affiliation or loyalty. This is bad for a country as such people may not necessary be fit for those jobs. Also, such leaders loot their nation’s economy. In Inheritance, Lacuna Kasoo mismanages Kutula Republic and makes citizens suffer as illustrated below.

Accept any other relevant introduction: award 2 marks. (Can be general, contexualized or general-contextualized)

The citizens are poor. Tamina works for very little pay and what she earns is not enough for the domestic expenses. When she is given eight hundred shillings by her husband, she gets frustrated as the money is not enough to cover all her expenses. Also, from the description of their house, it is clear that the family is poor. This is attributable to the economic mismanagement of the country by Lacuna. For example, he stashes money in foreign countries and lives in luxury, even owning a private jet.
Land is taken away from them. Tamina is forced to sell her land to Chipande. Lacuna is to blame as he favours Chipande in decreeing that coffee can only be grown by Chipande. She is now forced to work for very little pay on a land that used to be hers. Also, Lacuna attempts to displace people from their lands by force as demanded by the colonial powers.
Citizens suffer false imprisonment. Bengo is imprisoned for daring to stand for election against Lacuna Kasoo. Also, Lulu Zen Melo was held at the palace by Lacuna against her will with the intention of deflowering her for the purpose of cementing his position as leader.
There are murders and attempted murders in Kutula. Anyone who is a perceived enemy of Lacuna is killed. Judah Zen Melo is beaten and left for dead for refusing to eliminate his brother Bengo Zen Melo who is perceived as a threat to the leadership of Lacuna. Later, Judah is killed in what is made to look like an accident.

Citizens are disillusioned. Lulu and Judah have gotten so disillusioned that they give up on God. Judah says that he has not looked up since he decided to struggle on his own. Lulu also wonders if God is still there in that valley. All this is attributed to the suffering they have undergone as a result of Lacuna’s misrule. Lulu is sent away from school as her mother cannot raise the exorbitant school fees, Judah is overworked and underpaid and Tamina works for very little pay.

Any four well illustrated points *3 =12 (3:3:3:3)

Conclusion

In conclusion, when a country is mismanaged by a bad leader, the citizens suffer greatly. It is important for leaders to be accountable to their citizens and to run their country in a democratic manner for the good of the citizens.

Any other relevant conclusion, award 2 marks

Introduction: 2 marks

Content: 12 marks

Conclusion: 2 marks

Language: 4 marks

The Novel: The Pearl

Introduction

Wealth and money cannot guarantee happiness. One may be rich but that does not mean he is happy. Juana and Kino have the pearl that if sold will earn them a lot of money thus liberating them from poverty. The Pearl in this case signifies wealth. This new found treasure however robs them of the happiness they had when they were poor.

Accept any other relevant introduction: award 2 marks (Can be general, contextualized or general-contextualized)

Body

The pearl brings opportunists to Kino and Juana’s doorstep. They are only interested in Kino’s new found wealth. The priest, the shopkeeper, the doctor, the beggars outside the church and the pearl buyers scheme to benefit from the rare find.
The Pearl turns Kino’s friends into enemies, they are jealous of Kino. Kino believes his friends will protect him from the evils that might befall him from the pearl but their jealousy is too great that they turn against Kino and his family.

The Pearl turns Juana and Kino against each other. The evil power of the Pearl is strong enough to inspire violence between them. Juana and Kino are so close to one another that conversation isn’t even needed and yet the pearl is able to divide them. It has brought injury and danger and now it pulls Juana and Kino away from each other.

Kino and Juana suffer constant attacks because of the pearl. People are so anxious to get their hands on this jewel that they attackhim, ransack his house leaving Kino’s family in constant fear.
The pearl also brings death to Kino and his family. Coyotito is killed because of the pearl.

Any four well illustrated points*3 =12 (3:3:3:3)

Conclusion

From the above illustrations it is clear that wealth does not bring happiness, and instead has the potential to wreak havoc in the lives of those who posses it.

Any other relevant conclusion, award 2 marks

Introduction: 2 marks

Content: 12 marks

Conclusion: 2 marks

Language: 4 marks

Teachers' Resources

CLASS 8 SOCIAL STUDIES SCHEMES OF WORK TERM 1-3

October 5, 2025 Maverick John Leave a comment

AZIMIO LA KAZI

DARASA LA NANE

MUHULA WA I

ASILIA

KISWAHILI SANIFU
Mwongozo wa Mwalimu
Oxford
Kamusi

JUMA	KIPINDI	FUNZO	MADA	MALENGO	SHUGHULI ZA MWALIMU	SHUGHULI ZA MWANA FUNZI	NYENZO	ASILIA	MAONI
1	MATAYARISHONA KUFUGUA SHULE
2	1	Kusikiliza na kuzungumza/kongea	Maamkizi	Kufikia mwisho wa kipindi mwanafunzi aweze, kutumia baadhi ya msamiati wa maakizi, k.m. hujambo :sijambo. Habari nzuri.	-kusoma -kusikiliza -kutambua -kuzungumza	-kusikiliza -kutambua -kuzungumza	-Picha kiabuni -Kamusi	KS KCM UK 2 MWM UK1
	2	kusoma Ufahamu	Chada chema	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , ufahamu chada chema	-kueleza -kutaja -kuandika -kuiga	-kueleza -kutaja -kuandika -kuiga	-kadi -picha michoro	KS KCM UK 3 MWM UK3
	3	Maombo ya lugha	Shairi ‘saiti kwenda wema’	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kutamka na kukariri shairi ‘saiti kwenda wema,’	kusoma -kusikiliza -kutambua -kuzungumza	-kusoma -kuandika -kutamka -kutumia	-kadi -picha michoro	KS KCM UK 4 MWM UK4
	4	Sarufi	Viambishi ngeli	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kulikariri shairi ‘umuhimu wa kutenda wema’	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK5 MWM UK4
	5	Kuandika (insha)	Heshima	Kufikia mwisho wa kipindi mwanafunzi aweze kuandika na kutumia maneno ya heshima ifaayo katika insha	-kueleza -kutaja -kuandika -kuiga	-kueleza -kutaja -kuandika -kuiga	-Picha kiabuni -Kamusi	KS KCM UK5-7 MWM UK5

3	1	Kuongea/kusikiliza	Akisami	Kufikia mwisho wa kipindi mwanafunzi aweze kubainisha akisami pammoja na maelozo yake, kuandika akisami kwa usahihi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	-kadi -picha michoro	KS KCM UK7 MWM UK7
	2	Ufahamu	Majaaliwa	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kujibu na kuandika maswali yaufahamu	kusoma -kusikiliza -kutambua -kuzungumza	kusoma -kusikiliza -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK8 MWM UK8
	3	Mapambo ya lugha	Misemo na methali	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kutambua na kutumia misemo na methali katika sentensi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK9 MWM UK9
	4	Sarufi	Vivumishi visivyochukua viambishi ngeli	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kubainisha na kutumia vivumishi katika sentensi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-Picha kiabuni -Kamusi	KS KCM UK11 MWM UK10
	5	Kuandika (insha)	Siku ambayo sitaishahau	Kufikia mwisho wa kipindi mwanafunzi aweze kumbuni, na kuandika insha akitumia maneno aliyopewa kwa usahihi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kutumia -kueleza -kuuliza	-kadi -picha michoro	KS KCM UK12 MWM UK10
4	1	Kusikiliza na kuzungumza	tarakimu	Kufikia mwisho wa kipindi mwanafunzi aweze kubainisha tarakimu milion kumi hadi milioni mia moja na kuandika tarakimu kwa usahihi	kusoma -kusikiliza -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 12 MWM UK11
	2	Ufahamu	Sayari	Kufikia mwisho wa kipindi mwanafunzi aweze, kusoma kutaja na kutumia msamiati wa sayari kwa usahihi		kusoma -kusikiliza -kutambua -kuzungumza	-Picha kiabuni -Kamusi	KS KCM UK20 MWM UK12
	3	Mapabo ya lugha	Vitate	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutambua na kutumia vitate katika sentensi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza		-kadi -picha michoro	KS KCM UK 14 MWM UK14
	4	Sarufi	Vihisishi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kueleza, kubainisha na kutumia vihisishi katika sentensi kwa usahihi		-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK22 MWM UK26
	5	Kuandika (insha)	Sayari	Kufikia mwisho wa kipindi mwanafunzi aweze kumbuni, na kuandika isha akitumia maneno aliyopewa kwa usahihi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kutumia -kueleza -kuuliza	-kadi -picha michoro	KS KCM UK 23 MWM UK18
5	1	Kusikiliza na kuzungumza	Dira	Kufikia mwisho wa kipindi mwanafunzi aweze kutambua , kuchora na kutumia msamiati wa dira kwa usahihi	-kusoma -kutumia -kueleza -kuuliza		-Picha kiabuni -Kamusi	KS KCM UK 25 MWM UK20
	2	Ufahamu	Nyota njema	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kubainisha na kujibu maswali ya ufahamu kwa usahihi		-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK 26 MWM UK22
	3	Mapambo ya lugha	Silabi- cha	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutambua na kutumia methali katika sentensi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK28 MWM UK23
	4	Sarufi	Vihisishi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kueleza, kubainisha na kutumia vihisishi katika sentensi kwa usahihi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza		-Picha kiabuni -Kamusi	KS KCM UK29 MWM UK24
	5	Kuandika (insha)	Barua ya kirafiki	Kufikia mwisho wa kipindi mwanafunzi aweze kuandika insha kwa kujaza mapengo ukitumia maneno uliyopewa	-kusikiliza -kutamka -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK30 MWM UK
6	1	Kusikiliza na kuzungumza	Mali ya sili	Kufikia mwisho wa kipindi mwanafunzi aweze kueleza, kuorodhesha na kufafanua faida za maliasilina wajibu wake kuzihusu	-kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 12 MWM UK25
	2	Ufahamu	Maliasili	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutambua na kujibu maswali yaufahamu	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusikiliza -kutamka -kutambua -kuzungumza	-Picha kiabuni -Kamusi	KS KCM UK38
	3	Mapambo ya lugha	Methali zinazopingana kimaana	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutumia na kuandika methali zinazo pingana kimaana	-kusoma -kutumia -kueleza -kuuliza	-kusikiliza -kuandika -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK39 MWM UK
	4	Sarufi	Viunganishi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kueleza, kubainisha na kutumia viunganishi katika sentensi kwa usahihi	-kusoma -kusikiliza -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 40 MWM UK28
	5	Kuandika (insha)	Maliasili	Kufikia mwisho wa kipindi mwanafunzi aweze kubuni kuandika insha kwa kujaza mapengo ukitumia maneno uliyopewa	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	-Picha kiabuni -Kamusi	KS KCM UK 13 MWM UK
7	MTIHANI WA KATI WA MUHULA
8	1	Kusikiliza na kuzungumza	Majina ya wizara mbalimbali	Kufikia mwisho wa kipindi mwanafunzi aweze kutaja na na kueleza shughuli za wizara mbalimbali	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK 40 MWM UK29
	2	Ufahamu	Lau ningekuwa waziri ya elimu	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutambua na kujibu maswali ya ufahamu kwa usahihi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK41 MWM UK31
	3	Mapambo ya lugha	Visawe	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutumia na kuandika visawe huku akieleza maana	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 44 MWM UK33
	4	Sarufi	Viunganishi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutumia na kuandika viunganishi vya chaguo na vya nyongaza kwa usahihi	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-Picha kiabuni	KS KCM UK 45 MWM UK34
	5	Kuandika (insha)	Lau ninekuwa waziri wa elimu	Kufikia mwisho wa kipindi mwanafunzi aweze kubuni na kuandika kwa hati zinazosomeka kulingana na kichwa alichopewa	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunz -Kamusi -Kamusi i	KS KCM UK 46 MWM UK35
9	1	Kusikiliza na kuzungumza	Ngonjera	Kufikia mwisho wa kipindi mwanafunzi aweze kueleza maana ya ngojera, kukariri na kufafanua ujube	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kutambua -kuunganisha	Kitabu cha wanafunzi	KS KCM UK 47 MWM UK37
	2	Ufahamu	Utenzi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kueleza na kujibu maswali ya ufahamu kwa usahihi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	-Picha kiabuni	KS KCM UK 5 6 MWM UK39
	3	Mapambo ya lugha	Nimino za makundi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kueleza na kutumia nomino za makundi katika sentensi kwa usahihi	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK 57 MWM UK40
	4	Sarufi	Viunganishi linganishi	Kufikia mwisho wa kipindi mwanafunzi aweze kueleza kubainisha na kutumia viunganishi linganishi kwa usahihi	-kusoma -kusikiliza -kutambua -kuzungumza	-kusoma -kutumia -kueleza -kuuliza	-Picha kiabuni -Kamusi	KS KCM UK 17 MWM UK
	5	Kuandika (insha)	Utungaji mashairi	Kufikia mwisho wa kipindi mwanafunzi aweze kuakifisha, kutunga shairi kuzingatia arudhi kulingana na kichwa na beti alizopewa	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 58 MWM UK40
10	1	Kusikiliza na kuzungumza	Msamiati wa mahakamani	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma nakutumia baadhi ya msamiati wa maneno wa mahakamani	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 49 MWM UK
	2	Ufahamu	Usipoziba ufa	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kueleza na kujibu maswali ya ufahamu kwa usahihi	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro -Kamusi	KS KCM UK 19 MWM UK42
	3	Mapambo ya lugha	Methali	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kutambua na kutumia methali na maana zake katika sentensi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-Picha kiabuni	KS KCM UK 59 MWM UK43
	4	Sarufi	Manano ya kutiria mkazo(takriri)	Kufikia mwisho wa kipindi mwanafunzi aweze kueleza maana yatakiririna kutumia maneno ya kutilia mkazo katika sentensi kwa usahihi	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	Kitabu cha wanafunzi	KS KCM UK 61 MWM UK45
	5	Kuandika (insha)	kumbumbu	Kufikia mwisho wa kipindi mwanafunzi aweze kubainisha na kuandika insha ya kumbumbu	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK 62 MWM UK45
11	1	Kusikiliza na kuzungumza	Mekoni	Kufikia mwisho wa kipindi mwanafunzi aweze kufasiri maneno ya picha, kujadili nakufafanua baadhi ya msamiati wa mekoni	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-Picha kiabuni	KS KCM UK 63 MWM UK46
	2	Ufahamu	Wageni mekoni	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kuandika nakujibu maswali ya ufahamu	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi -Kamusi	KS KCM UK 64 MWM UK47
	3	Mapambo ya lugha	Methali	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kutambua na kutumia methali na maana zake katika sentensi	-kusikiliza -kutumia -kueleza -kuuliza	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 76 MWM UK51
	4	Sarufi	Matumizi ya ‘si-’	Kufikia mwisho wa kipindi mwanafunzi aweze kutumia na kueleza matumizi sahihi ya ‘si –‘	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 77 MWM UK52
	5	Kusikiliza na kuzungumza	Vipindi vya redio na runinga	Kufikia mwisho wa kipindi mwanafunzi aweze kusikiliza redio narununga nakujibu maswali yatayo ulizwa	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusikiliza -kutumia -kueleza -kuuliza	Redio runinga -Kamusi	KS KCM UK 78 MWM UK 54
12	1	Kuandika insha	Jinsi ya kupika	Kufikia mwisho wa kipindi mwanafunzi aweze kubuni na kuandika insha shahihiya maelezo jinsi ya kupika	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 79 MWM UK55
	2	Ufahamu	Barua rasmi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kueleza na kuandika barua rasmi kwa hati zinazosomeka na nadhifu	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 79 MWM UK56
	3	Mapambo ya lugha	vitawe	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutumia na kuandika vitawe huku akieleza maana	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 78 MWM UK52
	4	Sarufi	Matumizi ya, ‘amba’	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutambua na kuondosha amba’ na kutumia ‘O’ rejeshi mahali pake katika sentensi kwa usahihi	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-Picha kiabuni -Kamusi	KS KCM UK 80 MWM UK58
	5	Kusandika insha	Barua rasmi	Kufikia mwisho wa kipindi mwanafunzi aweze kueleza na kuandika barua rasmi kwa hati zinazosomeka na nadhifu	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 83 MWM UK60
13	MARUNDIO
14	MTIHANI WA MWISHO WA MUHULA

AZIMIO LA KAZI

DARASA LA NANE 2014

MUHULA WA II

ASILIA

KISWAHILI SANIFU
Mwongozo wa Mwalimu
Oxford
Kamusi

JUMA	KIPINDI	FUNZO	MADA	MALENGO	SHUGHULI ZA MWALIMU	SHUGHULI ZA MWANA FUNZI	NYENZO	ASILIA	MAONI
1	KUFUNGUA SHULE NA MATAYARISHO
2	1	Kusikiliza na kuzungumza/kongea	Msamiati wa teknolojia	Kufikia mwisho wa kipindi mwanafunzi aweze, kutumia baadhi ya msamiati wa teknolojia kwa usahihi	-kusoma -kusikiliza -kutambua -kuzungumza	-kusoma -kusikiliza -kutambua -kuzungumza	-Picha kiabuni -Kamusi	KS KCM UK 88 MWM UK61
	2	kusoma Ufahamu	Uchungu wa mwana	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , ufahamu uchungu wa mwana na kujibu maswali ya ufahamu kwa usahihi	-kueleza -kutaja -kuandika -kuiga	-kueleza -kutaja -kuandika -kuiga	-kadi -picha michoro	KS KCM UK 89 MWM UK62
	3	Maombo ya lugha	Misemo	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kutamka na kutumia misemo kwa usahihi	-kusoma -kuandika -kutamka -kutumia	-kusoma -kuandika -kutamka -kutumia	-kadi -picha michoro -Kamusi	KS KCM UK 89 MWM UK63
	4	Sarufi	Matumizi ya ‘na’	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kubainisha na kutumia ‘na’ katika sentensi kwa namna mbalimbali na kwa usahihi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK90 MWM UK62
	5	Kuandika (insha)	Teknolojia	Kufikia mwisho wa kipindi mwanafunzi aweze kuandika, kujadili na kutumia msamiati wa teknolojia kwa usahihi	-kueleza -kutaja -kuandika -kuiga	-kueleza -kutaja -kuandika -kuiga	-Picha kiabuni -Kamusi	KS KCM UK91 MWM UK63

3	1	Kuongea na kusikiliza	Msamiati wa ukoo	Kufikia mwisho wa kipindi mwanafunzi aweze kubainisha baadhi ya misamiatri ya ukoo. Na kuitumia kwa usahihi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	-kadi -picha michoro	KS KCM UK91 MWM UK64
	2	Ufahamu	Sijafisha	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kujibu na kuandika maswali yaufahamu kwa usahihi	kusoma -kusikiliza -kutambua -kuzungumza	kusoma -kusikiliza -kutambua -kuzungumza	-kadi -picha michoro -Kamusi	KS KCM UK92 MWM UK65
	3	Mapambo ya lugha	methali	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kutambua na kutumia metheli zenye mizizi ‘ndi’ katika sentensi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK93 MWM UK66
	4	Sarufi	Matumizi ya ‘ndi’	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kubainisha na kueleza matumizi ya ‘ndi’ katika ngeli zote	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-Picha kiabuni	KS KCM UK95 MWM UK67
	5	Kuandika (insha)	Insha ya maelezo	Kufikia mwisho wa kipindi mwanafunzi aweze kumbuni, na kuandika insha akitumia maneno aliyopewa kwa usahihi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	-kadi -picha michoro	KS KCM UK96 MWM UK68
4	1	Kusikiliza na kuzungumza	Viwanda	Kufikia mwisho wa kipindi mwanafunzi aweze kubainisha kutaja na kueleza aina za bidhaa/ vifaa vinavyo tengezwa katika viwanda	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 96 MWM UK68
	2	Ufahamu	Kazi ya mkono haitupi	Kufikia mwisho wa kipindi mwanafunzi aweze, kusoma kujadili na kujibu maswali ya ufahamu kwa usahihi	kusoma -kusikiliza -kutambua -kuzungumza	kusoma -kusikiliza -kutambua -kuzungumza	-Picha kiabuni -Kamusi	KS KCM UK 104 MWM UK70
	3	Mapabo ya lugha	Methali zinazo fanana ki mawazo	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutambua na kutumia methali zinazo fanana kimawazo			-kadi -picha michoro	KS KCM UK104 MWM UK71
	4	Sarufi	Vielezi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kueleza, kubainisha na kutumia vielezi katika sentensi kwa usahihi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 107 MWM UK72
	5	Kuandika (insha)	Mtungo	Kufikia mwisho wa kipindi mwanafunzi aweze kumbuni, na kuandika isha akitumia maneno aliyopewa kwa usahihi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	-kadi -picha michoro	KS KCM UK 108 MWM UK73
5	1	Kusikiliza na kuzungumza	Matunda, miti na mimea	Kufikia mwisho wa kipindi mwanafunzi aweze kutambua , kuchora na kutumia msamiati wa matunda,miti namimea			-Picha kiabuni	KS KCM UK 109 MWM UK73
	2	Ufahamu	Mwadani wetu	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kubainisha na kujibu maswali ya ufahamu kwa usahihi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kadi -picha michoro -Kamusi	KS KCM UK 9 MWM UK
	3	Mapambo ya lugha	vitawe	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutambua maana na kutumia vitawe katika sentensi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK 110 MWM UK74
	4	Sarufi	Viulizi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kueleza, kubainisha na kutumia viulizi katika sentensi kwa usahihi			-Picha kiabuni -Kamusi	KS KCM UK 11 MWM UK
	5	Kuandika (insha)	Miti	Kufikia mwisho wa kipindi mwanafunzi aweze kuandika insha umuhimu wa miti ukijaza mapengo ukitumia maneno uliyopewa	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK 11 1 MWM UK76
6	1	Kusikiliza na kuzungumza	Vitabu vya maktaba	Kufikia mwisho wa kipindi mwanafunzi aweze kueleza, kuorodhesha na kufafanua na kuchangamkia kusoma vitabu vya maktaba	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha -Kamusi wanafunzi	KS KCM UK 112 MWM UK78
	2	Ufahamu	Tuzungukaje mbuyu?	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutambua na kujibu maswali yaufahamu na kujadili mafunzo katika ngojera hili	-kusikiliza -kutamka -kutambua -kuzungumza	-kusikiliza -kutamka -kutambua -kuzungumza	-Picha kiabuni	KS KCM UK 113 MWM UK79
	3	Mapambo ya lugha	Vitendawili	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutumia nakutega na kutegua vitendawili	-kusikiliza -kuandika -kutambua -kuzungumza	-kusikiliza -kuandika -kutambua -kuzungumza	-kadi -picha michoro -Kamusi	KS KCM UK 114 MWM UK99
	4	Sarufi	Matumizi ya: ‘katika’ kwenye’ na ‘ni’	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kueleza, kubainisha na kutumia ‘katika’ kwenye’ na ‘ni’	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 123 MWM UK81
	5	Kuandika (insha)	Mtungo	Kufikia mwisho wa kipindi mwanafunzi aweze kubuni kuandika insha kwa kujaza mapengo ukitumia maneno uliyopewa	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	-Picha kiabuni -Kamusi	KS KCM UK 122 MWM UK82
7	MTIHANI WA KATI YA MUHULA
8	1	Kusikiliza na kuzungumza	Miti na mimea	Kufikia mwisho wa kipindi mwanafunzi aweze kubainisha, kueleza na kutumia msamiati wa wa miti na mimea kwa usahihi	-kusoma -kusikiliza -kutambua -kuzungumza	-kusoma -kusikiliza -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK 129 MWM UK86
	2	Ufahamu	Mstahimilivu hula mbivu	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kujadili funzo,kutambua na kujibu maswali ya ufahamu kwa usahihi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK 129 MWM UK87
	3	Mapambo ya lugha	Vitate	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutumia na kuandika vitate huku akieleza maana	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 131 MWM UK88
	4	Sarufi	Ukubwa wa nomino	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kueleza, kutumia na kuandika ukumbwa wa nomino	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-Picha kiabuni	KS KCM UK 138 MWM UK90
	5	Kuandika (insha)	Wasifu (mekatilili)	Kufikia mwisho wa kipindi mwanafunzi aweze kubuni na kuandika insha kuhusu mutu mashuhuri kwa hati zinazosomeka kulingana na kichwa alichopewa	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK 138 MWM UK91
9	1	Kusikiliza na kuzungumza	Majina ya kike na kiume	Kufikia mwisho wa kipindi mwanafunzi aweze kueleza kumbainisha na kutumia msamiati wa kike na kiume	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	Kitabu cha wanafunzi	KS KCM UK 139 MWM UK92
	2	Ufahamu	Mjadala: wanafaa kusoma pamoja	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kujadili ,kueleza na kujibu maswali ya ufahamu kwa usahihi	-kujadili -kutumia -kueleza -kuuliza	-kujadili -kutumia -kueleza -kuuliza	-Picha kiabuni	KS KCM UK 143 MWM UK92
	3	Mapambo ya lugha	Visawe	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kueleza maana na kutumia visawe katika sentensi kwa usahihi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK 143 MWM UK93
	4	Sarufi	Hali ya udogo	Kufikia mwisho wa kipindi mwanafunzi aweze kueleza kubainisha na kutumia hali ya udogokutoka hali ya kawaida kwa usahihi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	-Picha kiabuni	KS KCM UK 144 MWM UK96
	5	Kuandika (insha)	mjadala	Kufikia mwisho wa kipindi mwanafunzi aweze kuandika insha ya mjadala kulingana na kichwa ulicho pewa	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 145 MWM UK97
10	1	Kusikiliza na kuzungumza	Majina ya wafanyikazi mbalimbali	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma nakutumia baadhi ya msamiati wa majina ya wafanyi kazi mbalimbali	-kusoma -kusikiliza -kutambua -kuzungumza	-kusoma -kusikiliza -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 146 MWM UK98
	2	Ufahamu	Uhaba wa kazi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kueleza na kujibu maswali ya ufahamu kwa usahihi	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 145 MWM UK97
	3	Mapambo ya lugha	Shairi : ‘nitafanya kazi ngani’	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kukariri na kujadili funzu la shairi hili	-kusoma -kusikiliza -kukariri -kutambua -kuzungumza	-kusoma -kusikiliza -kukariri -kutambua -kuzungumza	-Picha kiabuni	KS KCM UK 146 MWM UK97
	4	Sarufi	Usemi wa taarifa	Kufikia mwisho wa kipindi mwanafunzi aweze kueleza na kubainisha usemi wa taarifa na kubadilisha kwa usemi halisi	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	Kitabu cha wanafunzi	KS KCM UK 147 MWM UK98
	5	Kuandika (insha)	kazi	Kufikia mwisho wa kipindi mwanafunzi aweze kubainisha na kuandika insha akitetea hoja kikamilifu	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK 147 MWM UK99
11	1	Kusikiliza na kuzungumza	Mekoni	Kufikia mwisho wa kipindi mwanafunzi aweze kufasiri maneno ya picha, kujadili nakufafanua baadhi ya msamiati wa mekoni	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-Picha kiabuni	KS KCM UK 21
	2	Ufahamu	Wageni mekoni	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kuandika nakujibu maswali ya ufahamu	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK 22
	3	Mapambo ya lugha	Methali	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kutambua na kutumia methali na maana zake katika sentensi	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 23 MWM UK
	4	Sarufi	Matumizi ya ‘si-’	Kufikia mwisho wa kipindi mwanafunzi aweze kutumia na kueleza matumizi sahihi ya ‘si –‘	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 23 MWM UK
	5	Kusikiliza na kuzungumza	Vipindi vya redio na runinga	Kufikia mwisho wa kipindi mwanafunzi aweze kusikiliza redio narununga nakujibu maswali yatayo ulizwa	-kusikiliza -kutumia -kueleza -kuuliza	-kusikiliza -kutumia -kueleza -kuuliza	Redio runinga	KS KCM UK 24 MWM UK
12	1	Kuandika insha	Jinsi ya kupika	Kufikia mwisho wa kipindi mwanafunzi aweze kubuni na kuandika insha shahihiya maelezo jinsi ya kupika	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 24 MWM UK
	2	Ufahamu	Barua rasmi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kueleza na kuandika barua rasmi kwa hati zinazosomeka na nadhifu	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 25 MWM UK
	3	Mapambo ya lugha	vitawe	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutumia na kuandika vitawe huku akieleza maana	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 23 MWM UK
	4	Sarufi	Matumizi ya, ‘amba’	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutambua na kuondosha amba’ na kutumia ‘O’ rejeshi mahali pake katika sentensi kwa usahihi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-Picha kiabuni	KS KCM UK 25 MWM UK
	5	Kusandika insha	Barua rasmi	Kufikia mwisho wa kipindi mwanafunzi aweze kueleza na kuandika barua rasmi kwa hati zinazosomeka na nadhifu	-kusoma -kusikiliza -kutambua -kuunganisha	-kusoma -kusikiliza -kutambua -kuunganisha	-kadi -picha michoro	KS KCM UK 26 MWM UK
	5
13	JARIBIO LA PILI
14	MTIHANI WA MWISHO WA MUHULA

AZIMIO LA KAZI

DARASA LA NANE 2014

MUHULA WA II

ASILIA

KISWAHILI SANIFU
Mwongozo wa Mwalimu
Oxford
Kamusi

JUMA	KIPINDI	FUNZO	MADA	MALENGO	SHUGHULI ZA MWALIMU	SHUGHULI ZA MWANAFUNZI	NYENZO	ASILIA	MAONI
1	KUFUNGUA NA MATAYARISHO
2	1	Kusikiliza na kuzungumza/kongea	Mihadarati	Kufikia mwisho wa kipindi mwanafunzi aweze, kutumia baadhi ya msamiati wa mihadarati na kufafanua adhari zake.	-kusoma -kusikiliza -kutambua -kuzungumza	-kusoma -kusikiliza -kutambua -kuzungumza	-Picha kiabuni	KS KCM UK 154 MWM UK100
	2	kusoma Ufahamu	Sibaguami	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kujibu na kujadili ujube uliko katika msakala haya	-kueleza -kujadili -kuandika -kuiga	-kueleza -kujadili -kuandika -kuiga	-kadi -picha michoro	KS KCM UK 155 MWM UK101
	3	Maombo ya lugha	Misemo	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kubainisha na kutumia misemo katika sentensi	-kusoma -kuandika -kutamka -kutumia	-kusoma -kuandika -kutamka -kutumia	-kadi -picha michoro	KS KCM UK 156 MWM UK102
	4	Sarufi	Usemi halishi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kubainisha usemi halisi na kubadilisha usemi wa taarifa kuwa usemi halisi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK157 MWM UK103
	5	Kuandika (insha)	Mazungumzo na methali	Kufikia mwisho wa kipindi mwanafunzi aweze kuandika ya mazungumzo kutumia methali kwa ushahihi	-kueleza -kutaja -kuandika -kuiga	-kueleza -kutaja -kuandika -kuiga	-Picha kiabuni	KS KCM UK157 MWM UK104

3	1	Kuongea na kusikiliza	Mazingira	Kufikia mwisho wa kipindi mwanafunzi aweze kujadili namna ya mazingira na njia za kukinga na kuzuia uharubifu	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	-kadi -picha michoro	KS KCM UK4157 MWM UK103
	2	Ufahamu	Hotuba	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kuzingatia na kujibu maswali yaufahamu	kusoma -kusikiliza -kutambua -kuzungumza	kusoma -kusikiliza -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK155 MWM UK104
	3	Mapambo ya lugha	Methali	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma , kutambua na kutumia metheli katika sentensi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK156 MWM UK105
	4	Sarufi	Myambuliko wa vitenzi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kubainisha na kutumia vitenzi katika sentensi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-Picha kiabuni	KS KCM UK154 MWM UK100
	5	Kuandika (insha)	Hotuba	Kufikia mwisho wa kipindi mwanafunzi aweze kumbuni, na kuandika isha akitumia maneno aliyopewa kwa usahihi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	-kadi -picha michoro	KS KCM UK156 MWM UK102
4	1	Kusikiliza na kuzungumza	Ajira ya watoto	Kufikia mwisho wa kipindi mwanafunzi aweze kufasiri ujumbe wa michoro, kueleza na kubainisha ubaya,hasara na madhara ya ajira ya watoto	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 157 MWM UK103
	2	Ufahamu	Krismasi	Kufikia mwisho wa kipindi mwanafunzi aweze, kusoma kutaja na kutumia msamiati mpya kwa usahihi	kusoma -kusikiliza -kutambua -kuzungumza	kusoma -kusikiliza -kutambua -kuzungumza	-Picha kiabuni	KS KCM UK 160 MWM UK105
	3	Mapabo ya lugha	Vitawe	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutambua na kutumia vitawe katika sentensi			-kadi -picha michoro	KS KCM UK 161 MWM UK105
	4	Sarufi	‘a’ unganifu	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kueleza, kubainisha na kutumia vihisishi katika sentensi kwa usahihi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	Kitabu cha wanafunzi	KS KCM UK 162 MWM UK159
	5	Kuandika (insha)	Sherehe	Kufikia mwisho wa kipindi mwanafunzi aweze kumbuni, na kuandika isha akitumia maneno aliyopewa kwa usahihi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	-kadi -picha michoro	KS KCM UK 163 MWM UK 106
5	1	Jaribio la kwanza	Dira	Kufikia mwisho wa kipindi mwanafunzi aweze kutambua , kuchora na kutumia msamiati wa dira kwa usahihi	-kusoma -kuchora -kueleza -kuuliza	-kusoma -kuchora -kueleza -kuuliza	-Picha kiabuni	KS KCM UK 164 MWM UK107
	2	Ufahamu	Nyota njema	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kubainisha na kujibu maswali ya ufahamu kwa usahihi	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK 164-165 MWM UK108
	3	Mapambo ya lugha	Silabi- cha	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma, kutambua na kutumia methali katika sentensi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	Kitabu cha wanafunzi	KS KCM UK 165 MWM UK110
	4	Sarufi	Vihisishi	Kufikia mwisho wa kipindi mwanafunzi aweze kusoma,kueleza, kubainisha na kutumia vihisishi katika sentensi kwa usahihi	-kusoma -kutumia -kueleza -kuuliza	-kusoma -kutumia -kueleza -kuuliza	-Picha kiabuni	KS KCM UK 166 MWM UK112
	5	Kuandika (insha)	Barua ya kirafiki	Kufikia mwisho wa kipindi mwanafunzi aweze kuandika insha kwa kujaza mapengo ukitumia maneno uliyopewa	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kusoma -kusikiliza -kuandika -kutambua -kuzungumza	-kadi -picha michoro	KS KCM UK 167 MWM UK112
6	1-5	Jaribio la kwanza	Marudio	Mwanafunzi aweze: – kujibu maswali aliyoulizwa – kukumbuka yale aliyo funzwa haponawali – kubuni na kuandika kwa hati ilyo someka – kustawisha ukakamavu wa kukabiliana na mtihani	-kueleza -kuongoza kujibu maswali -kusikiliza -kuandika	-kueleza -kuongoza kujibu maswali -kusikiliza -kuandika	-Kitabu cha mwana fuzi -mitihani yajaribio	KS KCM UK32-37 MWM UK115
6
6		Jaribio la pili		Mwanafunzi aweze: – kujibu maswali aliyoulizwa – kukumbuka yale aliyo funzwa haponawali – kubuni na kuandika kwa hati ilyo someka – kustawisha ukakamavu wa kukabiliana na mtihani	-kueleza -kuongoza kujibu maswali -kusikiliza -kuandika	-kueleza -kuongoza kujibu maswali -kusikiliza -kuandika	Kitabu cha mwana fuzi -mitihani yajaribio	KS KCM UK 66-67 MWM UK25
7		Jaribio la tatu		Mwanafunzi aweze: – kujibu maswali aliyoulizwa – kukumbuka yale aliyo funzwa haponawali – kubuni na kuandika kwa hati ilyo someka – kustawisha ukakamavu wa kukabiliana na mtihani	-kueleza -kuongoza kujibu maswali -kusikiliza -kuandika	-kueleza -kuongoza kujibu maswali -kusikiliza -kuandika	Kitabu cha mwana fuzi -mitihani yajaribio	KS KCM UK 98-103 MWM UK48
8		Jaribio la nne		Mwanafunzi aweze: – kujibu maswali aliyoulizwa – kukumbuka yale aliyo funzwa haponawali – kubuni na kuandika kwa hati ilyo someka – kustawisha ukakamavu wa kukabiliana na mtihani	-kueleza -kuongoza kujibu maswali -kusikiliza -kuandika	-kueleza -kuongoza kujibu maswali -kusikiliza -kuandika	Kitabu cha mwana fuzi -mitihani yajaribio	KS KCM UK 132-137 MWM UK60
9	1	Jaribio la tano		Mwanafunzi aweze: – kujibu maswali aliyoulizwa – kukumbuka yale aliyo funzwa haponawali – kustawisha ukakamavu	-kueleza -kuongoza kujibu maswali -kusikiliza -kuandika	-kueleza -kuongoza kujibu maswali -kusikiliza -kuandika	Kitabu cha mwana fuzi -mitihani yajaribio	KS KCM UK 148-153 MWM UK80
10	1	Jaribio la sita		Mwanafunzi aweze: – kujibu maswali aliyoulizwa – kukumbuka yale aliyo funzwa haponawali	-kueleza -kuongoza kujibu maswali	-kueleza -kuongoza kujibu maswali -kusikiliza	Kitabu cha mwana fuzi -mitihani yajaribio	KS KCM UK 168-172 MWM UK99
11	MTIHANI WA KCPE

Teachers' Resources

TOP STUDENT MATHEMATICS REVISION KIT

October 5, 2025 Maverick John Leave a comment

MATHEMATICS 1

PART I

SECTION A:

Use logarithm tables to evaluate (4 mks)

0.0368 x 43.92

361.8

Solve for x by completing the square (3mks)

2x² – 5x + 1 = 0

Shs. 6000 is deposited at compound interest rate of 13%. The same amount is deposited at 15% simple interest. Find which amount is more and by how much after 2 years in the bank (3mks)

The cost of 3 plates and 4 cups is Shs. 380. 4 plates and 5 cups cost Shs. 110 more than this. Find the cost of each item. (3mks)

A glass of juice of 200 ml content is such that the ratio of undiluted juice to water is 1: 7 Find how many diluted glasses can be made from a container with 3 litres undiluted juice (3mks)

Find the value of θ within θ < θ < 360^Oif Cos (2 θ + 120) = γ3 (3mks)

A quantity P varies inversely as Q² Given that P = 4 When Q = 2. , write the equation joining P and Q

hence find P when Q = 4 a (3mks)

A rectangle measures 3.6 cm by 2.8 cm. Find the percentage error in calculating its perimeter. (3mks)

Evaluate: 11/6 x ¾ – 11/12 (3mks)

½ of 5/6

A metal rod, cylindrical in shape has a radius of 4 cm and length of 14 cm. It is melted down and recast into small cubes of 2 cm length. Find how many such cubes are obtained ( 3mks)

A regular octagon has sides of 8 cm. Calculate its area to 3 s.f. (4mks)

Find the values of x and y if ( 2 mks)

3 x 1 = 2

2 1 -1 y

An equation of a circle is given by x² + y² – 6x + 8y – 11 = 0 (3mks)

Find its centre and radius

In the figure given AB is parallel to DE. Find the value of x and y

A line pass through A (4,3) and B(8,13). Find (6 mks)

(i) Gradient of the line

(ii) The magnitude of AB

(iii) The equation of the perpendicular bisector of AB.

A train is moving towards a town with a velocity of 10 m/s. It gains speed and the velocity becomes 34 m/s after 10 minutes . Find its acceleration (2mks)

SECTION B:

Construct without using a protractor the triangle ABC so that BC=10cm, angle ABC = 60⁰ and

BCA = 45⁰

On the diagram , measure length of AC
Draw the circumference of triangle ABC
Construct the locus of a set of points which are equidistant from A and B.
Hence mark a point P such that APB = 45⁰and AP = PB
Mark a point Q such that angle AQB = 45⁰ and AB = AQ

(a) A quadrilateral ABCD has vertices A(0,2) , B(4,0) , C(6,4) and D(2,3). This is given a

transformation by the matrix -2 0 to obtain its image A^I B ^I C^I D^I. under a second transformation

0 – 2

which has a rotation centre (0,0) through –90⁰ , the image A^II B^II C^II D^II of A^I B^I C^I D^I is

obtained. Plot the three figures on a cartesian plane (6mks)

(b) Find the matrix of transformation that maps the triangle ABC where A (2,2) B (3,4) C (5,2)

onto A B C where A( 6,10) B (10,19 ) C ( 12, 13). ( 2mks)

19.

In the triangle OAB, OA = 3a , OB = 4b and OC = 5/3 OA. M divides OB in the ratio 5:3

Express AB and MC in terms of a and b
By writing MN in two ways, find the ratio in which N divides
AB
MC

In the figure below, SP = 13.2 cm, PQ = 12 cm, angle PSR = 80^O and angle PQR = 90⁰. S and Q are the centres (8mks)

Calculate:

The area of the intersection of the two circles

The area of the quadrilateral S P Q R

The area of the shaded region

In an experiment the two quantities x and y were observed and results tabled as below

X	0	4	8	12	16	20
Y	1.0	0.64	0.5	0.42	0.34	0.28

By plotting 1/y against x, confirm that y is related to x by an equation of the form

Y = q

P + x

where p and q are constants. (3mks)

(b) Use your graph to determine p and q (3mks)

(c ) Estimate the value of (i) y when x = 14

(ii) x when y = 0.46 (2mks)

A racing cyclist completes the uphill section of a mountain course of 75 km at an average speed of v km/hr. He then returns downhill along the same route at an average speed of (v + 20) km/hr. Given that the difference between the times is one hour, form and solve an equation in v.

Hence

Find the times taken to complete the uphill and downhill sections of the course.
Calculate the cyclists average speed over the 150km.

In the diagram below, X is the point of intersection of the chords AC and BD of a circle. AX = 8 cm, XC = 4cm and XD = 6 cm
Find the length of XB as a fraction
Show that XAD is similar to XBC
Given that the area of AXD = 6cm², find the area of BXC
Find the value of the ratio

Area of AXB

Area of DXC

A town B is 55 km on a bearing of 050⁰. A third town C lies 75km due south of B. Given that D lies on a bearing of 255⁰from C and 170⁰ from A, make an accurate scale drawing to show the positions of the four towns. (3mks)

(scale 1cm rep 10 km)

From this find,

(a) The distance of AD and DC in km (2mks)

(b) The distance and bearing of B from D (2mks)

MATHEMATICS I

PART 1

MARKING SCHEME (100MKS)

No. Log

= 3.6502

0.3681 2.5660

0.3682 1.6427 + -4 = 1.6502 = 2.8251

0.2087 Logs 2

361.8 2.5585 + – v ans (4) 6.6850 x 10 ^-2

3.6502 = 0.06685

2 x² – 5x + 1 = 0

x²– 5 x + ½ = 0

x² – 5 x = ^– ½

x – 5x + ^–5 ² = ^–½ + ^–5 ² (m)

2 4 4

= x – 5 = ^–½ + 25 = 17 (3)

4 16 16

= x – 5/4 = 17/16 = 1.0625

x – 5/4 ± 1.031

X₁= -1.031 = 1.25 = 0.2192

X₂= 1.031 + 1.25 = 1.281

A₁= P(1 + R/100)²= 6000 x 113/100 x 113/100 = Sh. 7661.40

A₂ = P + PRT/100 = 6000 + 15 X 2 = 6000 + 1800

100

= Shs. 7800

Amount by simple interest is more by Shs. (7800 – 7661. 40)

Shs. 138.60

Let a plate be p and a cup c.

3p + 4c = 380 x 5 15p + 20c = 1900

4p + 5c = 490 x 4 16p + 20c = 1960

-p -60 (m)

p = Shs 60

3(60) + 4 c = 380

4c = 380 –180 = 2000 (3)

c= Shs. 50

Plate = Shs. 60 , Cup = Shs. 50 (A both)

Ratio of juice to water = 1 : 7

In 1 glass = 1/8 x 200 = Sh 25

3 litres = 300 ml (undiluted concentrate) (3)

No. of glasses =v 3000 = 120 glasses

Cos (2 θ + 120) = 3/2 = 0.866

Cos 30 , 330, 390, 690, 750 ….

2 θ + 120 = 330

2 θ = 210 , = 105⁰(3)

2 θ = 390 – 120 = 270⁰ , θ₂ 135⁰

2 θ = 690 – 120 = 570⁰ , θ₃ 285⁰ (for 4 ans)

θ₄= 315^o ( for >2)

2 θ = 750 – 120 = 630⁰,

P = k 4 = K/4 (substitution)

Q² 9

K = 4 X 4 = 16

9 9

P = 16 v when Q = 4

9Q²

P = 16 = 1/9 (A) (3)

9x4x4

The perimeter = (3.6 + 2.8 ) x 2 = 12.8 cm

Max perimeter = (3.65 + 2.85) x 2 = 23 cm Expressions

% error = 13 –12.8 x 100 m = 0.2 x 100 (3)

12.8 12.8

= 1.5620% (A)

1 1/6 x ¾ – 11/12 = (7/6 x ¾ ) -11/12 = 7/8 – 11/12 = 21-22

½ of 5/6 ½ of 5/6 5/12 5/12

= -1/24 = -1 x 12 = -1

5/12 24 5 10 (3)

Volume of rod = П r²h = 22/7 x 4 x 14 = 704cm³ (m)

Volume of each cube = 2x2x2 = 8 cm³ A

No. of cubes = 704 /8 = 88 cm³ A

< AOB = 360 = 45⁰

Tan 67.5 = h

h = 4 x 2.414 A

= 9.650cm

Area of 1 triangle = ½ x 8 x 9.656 x 8 cm = 38.628 x 8 vm

Octagon area = 38.628 x 8 m

= 309.0 cm² (A)

3 2 -1 2

2 1 -1 y

3 – x = 2 (1) x = 1 (2)

2 – 1 = y y = 1 (A)

x ² + y² – 6x + 8y – 11 = 0

x² – 6x + (-3)² + y² + 8y + (4)² = 11 + (-3)² + (4)² (completing the square)

(x – 3)² + (y+4)² = 11 + 9 + 16 = 36

(x – 3)² + (y + 4)² = 6²

Centre is (3, -4)

Radius = 6 units As (3)

14.

Figs A C B and D C E are similar

AB = AC = and AB = BC

DE DC DE CE

10 = 6 + x

3 6

= 10 = 15 + y, m

3 y 60 = 18 + 3x

10y = 15 + 3y 3x = 42

7y = 15 x = 14

y = 15/7 (A) (3)

A (4 , 3) B(8,13)

(i) gdt = change in y = 13-3 = 10 = 5

change in x 8-4 4 2

(ii) Mag AB = 8 -4 4 =

13 -3 10

Length = Ö4²+ 10² = Ö116 = 10.77 units

(iii) Mid point = 4 +8 , 3 + 3

2 2

= (6, 8) (mid point) (5 mks)

gdt of perpendicular to AB = -ve rec. of 5/2

-2/5

Eqn is y = -2/5 x + c

8 = -2/5 x 6 + c = 40 = -12 + 5c

= c = 52/5

y = -2/5 x + 52/5 (A)

Acceleration = Change in velocity

Time

= (34 – 10) m/s = 24 m/s

60 x 10 600

= 0.04m/s_2-(2)

17.

Triangle (8)

AC = 9cm

Circumference Centre

Circle

Perpendicular bisector of AB

(b) a b 2 3 5 6 10 12

c d 2 4 2 10 19 13

2a +2b = 6 x 2 = 49 + 4b = 12

3a + 4b = 10 3a + 4b = 10

a = 2 4 + 2b = b

2c + 2d = 10×2 = 4c + 4d = 20 2 b = 2 b = 1

3c + 4d = 19 3c + 4d = 19

c = 1

2 (1) + 2d = 10

2d = 8 Matrix is 2 1 (A)

d = 4 1 4

OC = 5/3 (31) = 5A

19.

(a) = AO + OB MC = MO + OC

= -3a = 4b = -5/8 (4b) + 5

= 5A – 5/2 b

(b) MN = 5 Mc = 3(5a – 5/2 b)

= 5 s a – 5/2 s b

MN = BN + BN

= 3/8 (4 b) + (1 – t) (-BA)

= 3/8 (4 b) + (1 – t)(3a – 4 b)

= 3/2 b + 3 ta –4b + 4tb

= (3-3t) a (4t – 5/2)b

MN = MN

= 5 s a – 5/2 sb = (3-3t)a + (4t – 5/2 )b

= 5 a = 3 – 3t = 5s + 3t =3

= -5/2 s = 4t –5/2 v 5s + 8t = 5

-5t = -2 t = 2/5

5 s = 3 – 3(2/5)

= 3 – 6/5 = 9/5

s = 9/25

(i) AN : NB = 2 : 3

(ii) MN : 9 : 16

20.

θ x pr²

360

Area of sector SPR = 80/360 x 13.2 x 13.2 x 3.142

= 121.6

Area of triangle SPR ½ x 13.2 x 13.2 x sin 80

= 85.8 cm²

(m of area of ) A (at least one)

(m of area) A(at least one)

Area of segment = 121.6 – 85.8

= 35.8 cm²

Area of sector QPR = 90/360 x 3.142 x 12 x12

Area of PQR = ½ x 12 x 12 = 72²

Area of segment = 113.1 – 72

= 41.1cm²

Area of intersection = (35.8 + 41.1) = 76.9 cm²

b). Area of quadrilateral = Area of PQR + SPR

= 85.8 + 72 = 157.8cm²

Area of shaded region = Area of Quadrilateral – Area of sector SPR

= 157.8 – 121.6

= 36.2 cm²

y = q p + x = q 1 = x + p

p + x y y q q

Gradient = 1/q at (0, 0.95) (8,2.0) (8,2.0) gradient = 2.0 – 0.95 = 1.05

8 8

1 = 0.1312

q = 1 = 7.619

0.1312

q = 7.62.

y(1/y) Intercept p = 0.95 P = 0.95

q 7.62

p = 7.62 x 095 = 7.27

at x = 14, y = 2.7

at y = 0.46, 1/y = 2.174

x = 9.6.

a) Distance = 75km uphill speed = vkm/h

uphill Time = 75/v hrs

Downhill speed = ( + 20) km/h

Downhill Time = 75 hrs.

v + 20

Takes larger uphill

75 – 75 = 1

v v+20

75 (v+20) – 75v = 1

v(v + 20) 1

75v + 1500 – 75v = v(v + 20) = v² + 20v.

v² + 20v – 1500 = 0

v = – 20 + 20² – 4(1) (-1500)

2(1)

v = –20 + 400 + 6000 = –20 + v6400

2 2.

V₁ = –20 + 80 = 30km/hr

V₂ = – 20 – 80 X impossible

speed uphill = 30 km /hr, T = 75 time = 2 ½ hrs

speed downhill = 50 km /hr Time = 75 Time = 2 ½ hr

Average speed = Total distance = 150km = 37.5 km/ hr

Total time 4hrs

X	0	4	8	12	16	20
Y	1.0	0.64	0.5	0.42	0.34	0.28
1/y	1.0	1.56	2.0	2.38	2.94	3.57

D C

A x X x C = BX . XD

8 x 4 = 6BX

BX = 8 x 14² = 16

6 3

X AD = XBC

XA = 8 = 24 = 3

XB 16 16 2

XD = 6 = 3

XC 4 2

< AXD = BXC (vertically opposite <_s))

SAS holds : they are similar.

LSF = 3/2 ASF = (3/2)² = 9/4

Area A x A = 6cm₂ Area B x C = 6 x 9 = 27 = 13.5cm²

24.

a) AD = 50km

DC = 35km

BD = 90km

Bearing is 020⁰

Bearing is 134^o (8mks)

MATHEMATICS I

PART II

SECTION (52 MARKS)

Without using tables, simplify

1.43 x 0.091 x 5.04

2.86 x 2.8 x 11.7 (3mks)

Make x the subject of the formula if

y = a/x + bx (3mks)

Give the combined solution for the range of x values satisfying the inequality

2x + 1< 10 – x < 6x – 1 (3mks)

A man is employed at a KShs. 4000 salary and a 10% annual increment. Find the total amount of money received in the first five years (4mks)

A town A is 56 km from B on a bearing 062⁰. A third town C is 64 km from B on the bearing of 140^o. Find

(i) The distance of A to C (2mks)

(ii) The bearing of A from C (3mks)

Expand (x + y)⁶hence evaluate (1.02) to 3d.p. (3mks)

Rationalise the denominator in (2mks)

Ö 3

1 – v3

The table below shows daily sales of sodas in a canteen for 10 days.

Day	1	2	3	4	5	6	7	8	9	10
No. of	52	41	43	48	40	38	36	40	44	45

Calculate the 4 day moving averages for the data (3mks)

Find the image of the line y = 3x = 4 under the transformation whose matrix is.

3mks

2 1

-1 2

Three points are such that A (4 , 8), B(8,7), C (16, 5). Show that the three points are collinear (3mks)
Write down the inverse of the matrix 2 – 3 hence solve for x and y if

4 3

2x – 3y = 7

4x + 3y +5 (3mks)

Use the table reciprocals to evaluate to 3 s.f. 3mks

1/7 + 3/12 + 7/0.103

Given that O is the centre of the circle and OA is parallel to CB, and that angle

ABC = 107⁰, find

(i) Angles AOC, (ii) OCB (iii) OAB (3mks)

Two points A and B are 1000m apart on level ground, a fixed distance from the foot of a hill. If the angles of elevation of the hill top from A and B are 60^o and 30^o respectively, find the height of the hill (4 mks)
Two matatus on a dual carriageway are moving towards a bus stop and are on level 5 km from the stop. One is travelling 20 km/hr faster than the other, and arrives 30 seconds earlier. Calculate their speeds. (5mks)
If log x = a and log y = b, express in terms of a and b

Log x ³

VY (2mks)

SECTION B:

The table below gives the performance of students in a test in percentage score.

Marks	0-9	10-19	20-29	30-39	40-49	50-59	60-69	70-79
No. of Students	2	4	7	19	26	15	12	5

Using an assumed mean of 44.5, calculate

The mean
The standard deviation
Find the median mark

Draw the graph of y = 2x² – x – 4 for the range of x -3 = x = 3. From your graph

State the minimum co-ordinates

Solve the equations
2x² – x – 4 = 0
2x² – 3x – 4 = 0

Two concentric circles are such that the larger one has a radius of 6cm and the smaller one radius of 4 cm. Find the probability that an item dropped lands on the shaded region 4mks

Two unbiased dice are thrown. Find the probability of obtaining (4mks)
A product of 6
A sum of 8

iii. The same number showing (4mks)

Two pulley wheels centers A and B are joined by a rubber band C D E F G H C round them. Given that larger wheel has radius of 12 cm and AB = 20 cm, CD and GF are tangents common to both wheels and that CBA = 60^o), Find

BD (Length)
CD

iii. Arc length CHG and DEF, hence find the length of the rubber.

V A B C D is a right pyramid with a square base A B C D of side 5 cm. Each of its four triangular

faces is inclined at 75⁰ to the base. Calculate

The perpendicular height of the pyramid
The length of the slant edge VA
The angle between edge VA and base A B C D
The area of the face VAB

Plot the graphs of y = sin x^o and y = cos 2x^o on the same axes for –180 £ x £180^o.

Use your graphs to solve the equation 2 sin x = cos 2x

The depth of the water in a rectangular swimming pool increases uniformly from 1M at the shallow

end to 3.5m at the deep end. The pool is 25m long and 12m wide. Calculate the volume of the pool

in cubic meters.

The pool is emptied by a cylindrical pipe of internal radius 9cm. The water flows through the pipe at speed of 3 metres per second. Calculate the number of litres emptied from the pool in two minutes to the nearest 10 litres. (Take II = 3.142)

A rectangle A B C D is such that A and C lie on the line y = 3x. The images of B and D under a

reflection in the line y = x are B¹ (-1, -3) and D¹ (1,3) respectively.

Draw on a cartesian plane, the line y = x and mark points B¹ and D¹
Mark the points B and D before reflection
Draw the line y = 3x hence mark the points A and C to complete and draw the rectangle ABCD.

State its co-ordinates, and these of A¹ and C¹.

Find the image of D under a rotation, through – 90⁰, Center the origin.

MATHEMATICS I

PART II

MARKING SCHEME.

1.43 X 0.091 X 5.04 X 100000 91 X 504 = 7/10³

2.86 X 2.8 X 11.7 10⁵ 2 x 28 x 117 x 10³

(3)

= 0.007 (A)

y = a/x + bx yx = a + bx²

Either

bx²– yx + a = 0

x = y ± v y² – 4ab

2b (3)

2x + 1£ 10 – x £ bx -1

2x + 1 £ 10 – x 10 –x £ 6x –1

3x £ 9 11£ 7x

x £ 3 x £ 11/7 (3)

11/7 £ x £ 3

a = 4000 r = 110/100 = 1.1 ( 4000, 4000 + 4000, 4400 + 0/100 (4400——)

(a and r)

Sn = a(r ⁿ– 1)

R -1 1.1 Log = 0.04139

X 5

0.20695

0.1 (4)

= 4000 (1.1⁵–1) (any)

1.1 –1 4000 (1.6 – 1)

0.1

A = 4000 ( 0.6105)

0.1

= Sh. 2442 = Sh. 24,420 (A) (4)

0.1

(i) b²= a² + b² – 2ab Cos B

= 64² + 56²– 2(64) (56) cos 78

= 4096 + 3136 – 7168 (0.2079)

= 7232 – km 1490.3

b² = 5741.7 = 5.77 km (5)

(ii) b a

Sin B Sin A

75.77 = 64

Sin 78 sin A Sin A = 64 x 0.9781

75.77

Sin A = 0.08262

A = 55.7⁰ (or B = 46.3⁰)

Bearing = 90 – 28 – 55.7

= 0.06.3⁰ (A)

(x + y) ⁶ = 1 (x) ⁶ (y)⁰ + 6 (x)⁵(y)¹+15(x)⁴ (y)² + 20x³y³ + 15x²y⁴ + 6xy⁵ + y⁶

(1.02)⁶ = (1 +0.02)⁶ x = 1

y = 0.02

(1.02)⁶= 1+6 (0.02) + 15 (0.02)² + 15(0.02) + 20(0.02)³ + 15 (0.02)⁴

= 1 + 0.12 + 0.006 + 0.00016

= 1.12616

= 1.126 (to 3 d.p) (3)

3(1 + 3) = 3 + 3 3 + v3

(1- 3)(1+ 3) 1-3 2

Moving averages of order 4

M₁ = 52 + 41 + 43 + 48 184 = 146

4 4

M₂= 184 – 52 + 40 = 172 = 43 for 7

4 4 for > 4

M₃= 172– 40 + 38 = 170 = 42.5

4 4

M₄= 170 – 38+36 = 168 = 42

4 4

M₅ = 168 – 36 + 40 = 173 = 43 (3)

4 4

M₆= 172 – 40 + 44 = 176 = 44

4 4

M₇= 176 – 44 + 45 = 177 = 44.25

4 4

y = 3x + 4

A(0,4) B (1,7) Object points

A B A B

2 1 0 1 4 9

-1 2 4 7 8 13

Y = Mx + C

M = 13 – 8 = 5 = 1

9-4 5 1

y = x+c y = x + 4

8 = 4 + c c = 4

AB = 8 -4 4 BC = 16 – 8 -8 for either

7 -8 -1 5 – 7 -2

AB = ½ BC and AB and BC share point B.

A,B,C are collinear. (3)

2 -3

4 3 det. = 6 + 12 = 18

Inv.= 1 3 3

-4 2

1 3 3 2 -3 x 1 3 3 7

18 18

-4 2 4 2 y -4 2 5

x 36

y 18 -18 (3)

x = 2, y = -1 (A)

1/7 + 3/12.4 + 7/0.103

1/7 + 3/1.24 x 10^-1 + 7/1.03 x 10^-1

0.1429 + 3(0.8064) + 7 x 10 (0.9709)

= 0.1429 + 0.2419 + 67.96 (3)

=70.52 (A)

(i) ADC = 2×73

= 146⁰

(ii) OCB = x = 180 – 146 = 34

(iii) 360 – 107 – 146 – 34

= 73 ⁰

Tan 30⁰ = y/x y = x tan 30

Tan 60⁰ = 1000 + y ; y = x tan 60 – 1000

X tan 30⁰ = x tan 60 – 1000

0.5773 x = 1.732x – 1000

1.732x – 0.577 = 1000

1.155x = 1000

x = 1000

1.155 = 866.0 m (A) (4)

5 km Slower speed = x km/hr

Time = 5/x

Faster = (x+20) k/h

Time = 5/x=20 T₁ – T₂ = 5/x – 5/x+20 = 30/3600

5 (x+20) –5x 1

x(x+20) 120

120 (5/x + 100 – 5x) = x² + 20x (5)

x² + 20x – 12000

x = –20 400 + 48000

x = -20 ± 220

Spd = 100 km/h

And x = 120 km/h (A)

Log x = a log y = b

Log x³ = Log x³ – log y ^½

= 3 Log x – ½ Log y

= 8a – ½ ab

SECTION B

17.

Marks	Mid point (x)	d = x-44.5	F	E = d/10	Ft	T²	Ft²v
0-9	4.5	-40	2	-4	-8	16	32
10-19	14.5	-30	4	-3	-12	9	36
20-29	24.5	-20	7	-2	-14	4	28
30-39	34.5	-10	19	-1	-19	1	19
40-49	44.5	-0	26	0	0	0	0
50-59	54.5	-10	15	1	15	1	15
60-69	64.5	20	12	2	24	4	48
70-79	74.5	30	5	3	15	9	45

=90 =1 =223

(a) Mean = (1 / 90 x 10) + 44.5 = 44.5 + 0.111

= 44.610

(b) Standard deviation = 10 233/90 – (1/90)²

10 2.478 – 0.0001 (8)

10 2.478

10 x 1.574 = 15. 74 (A)

39.5 + 5.192 (A)

44.69

(a) The probability = Shaded area

Large circle area

Shaded area = ПR² – П r²

= 22/7 (4²– 3²) v = 22/7 x 7 = 22

Large area = 22/7 x4x4 = 352/7 (A)

Probability = 22 = 22 x 7 = 7

352/7 352 16

(b)

	1	2	3	4	5	6
1	1,1	1,2	1,3	1,4	1,5	1,6
2	2,1	2,2	2,3	2,4	2,5	2,6
3	3,1	3,2	3,3	3,4	3,5	3,6
4	4,1	4,2	4,3	4,4	4,5	4,6
5	5,1	5,2	5,3	5,4	5,5	5,6
6	6,1	6,2	6,3	6,4	6,5	6,6

(M)

(i) P(Product of 6) = P((1,6) or (2,3) or (3,2) or (6,1))

= 4/36 = 1/9

(4)

(ii) P (sum of 8) = P( (2,6) or (3,5) or (4,4) or (5,3) or (6,2) )

= 5/36 (A)

(iii) P (same number) = P (1,1) or (2,2) or (3,3) or (4,4) or (5,5) or (6,6)

6/36 = 1/6 (A)

(i) Cos 60 = x/20 x = 20 x 0.5 = 10 cm

BD = 12 – 10 = 2 cm

(ii) CD = y Sin 60 = y/20 y = 20x 0.8666

CD = 17.32 cm

(iii) CHG = 120 reflex = 240⁰

CHG = 240/360 x 2 x p x r

= 50.27

DBF = 120⁰/360 x 2 x П x r = 1/3 x 2 x 3.142 x 2

= 4.189 (A)

Length C D E f G H C = 50.27 + 2(17.32) + 4.189

= 89.189 (A)

(a) From the diagram, XO = 5/2 = 2.5

Tan 75⁰ = VO/2.5 v m

VO = 2.5 x 3.732

Perpendicular height = VO = 9.33 cm

2 (A)

Diagonal of base = 5² + 5² = 50

Length of diag. 50 = 7.071 = 5.536

VA²= AO² + VO² (m)

3.536² + 9.3²

12.50 + 87.05

= 99.55 = 9.98 cm² (A) (8)

(c ) = VAO Tan = 9.33 = 2.639

3.536

VAO = 69.24⁰ (A)

(d) Cos VBA = = 2.5 /9.98 = 0.2505

VBA = 75.49⁰

Area VBA = ½ x 5 x 4.99 x sin 75.45 m ( or other perimeter)

= 5 x 4.99 x 0.9681

= 24.15 cm² (A)

Volume = cross – section Area x L

X-sec Area = (1 x 25) + (½ x 25 x 2.5)

= 25 + 31.25 = 56. M

Volume = 56.25 x 12

= 675 m³

Volume passed / sec = cross section area x speed

= П r²x l = 3.14 x 9/100 x 9/100 x 3 (8)

= 0.07635 m³/sec v (M)

Volume emptied in 2 minutes

= 0.07635 x 60 x 2

= 9.162 m² (A)

1 m³ = 1000 l

= 9.162 litres

= 9160 litres (A)

24.

MATHEMATICS II

PART I

SECTION A (52 MARKS)

Use tables to evaluate

³Ö 0.0912² + Ö 3.152 (5mks)

0.1279 x 25.71

Simplify (a – b)²

a² – b² (2mks)

The gradient function of a curve that passes through point: (-1, -1) is 2x + 3.

Find the equation of the curve. (3mks)

Find the value of k for which the matrix k 3

has no inverse. (2mks) 3 k

Without using tables, evaluate log 128 – log 18

log 16 – log 6 (3mks)

Find the equation of the locus of points equidistant from point L(6,0) and N(-8,4). (3mks)
The value of a machine is shs. 415,000. The machine depreciates at a rate of 15% p.a. Find how many years it will take for the value of the machine to be half of the original value. (4mks)
Use reciprocal tables to evaluate to 3 d.p. 2 – 1

0.321 n2.2 (4mks)

Using the trapezium rule, estimate the area bounded by the curve y = x², the x – axis and the co-ordinates x = 2 and x = 5 using six strips. (4mks)
Solve the equation for 0⁰ £ q £ 360⁰and Cos²q + ½ Cosq = 0 (3mks)
Point P divides line MK in the ratio 4:5. Find the co-ordinates of point P if K is point (-6,10) and M is

point (3,-8) (3mks)

How many multiples of 3 are there between 28 and 300 inclusive. (3mks)
The line y = mx – 1, where m is a constant , passes through point (3,1). Find the angle the line makes with the x – axis. (3mks)
In the figure below, AF is a tangent to the circle at point A. Given that FK = 3cm, AX = 3cm, KX = 1.5cm and AF = 5cm, find CX and XN. (3mks)

Make X the subject of the formula (3mks)

V = ³Ö k + x

sk – x

Write down the inequalities that describe the unshaded region below. (4mks)

0.5 2 x

-1.5

-2

SECTION B (48 MARKS)

Draw the graph of y = -x² + 3x + 2 for –4 £ x £ 4. Use your graph to solve the equations

(i.) 3x + 2 – x² = 0 (ii) –x² – x = -2 (8mks)

The marks obtained by Form 4 students in Examination were as follows:

Marks	0-9		10-19		20-29		30-39		40-49	50-59
No. of students	2		8		6		7		8	10
Marks		60-69		70-79		80-89		90-99
No. of Students		9		6		3

Using 74.5 as the Assumed mean, calculate:

(i) The mean mark

(ii) The standard deviation (8mks)

In the figure below, a and b are the position vectors of points A and B respectively. K is a point on

AB such that the AK:KB = 1:1. The point R divides line OB in the ratio 3:2 and point S divides OK in

the ratio 3:1.

B K

0 a A

(a) Express in terms of a and b

(i) OK (iii) RS

(iii) OS (iv) RA

(b) Hence show that R,S and A are collinear. (8mks)

The figure below is the roof of a building. ABCD is a rectangle and the ridge XY is centrally placed.

Calculate:

(i) The angle between planes BXC and ABCD.

(ii) The angle between planes ABXY and ABCD. (8mks)

On the same axis, draw the graph of y = 2cosx and y = sin ½x for 0⁰ £ x £ 180⁰, taking intervals of 15⁰

(6mks)

From the graph, find:

(a) The value of x for which 2cosx = sin ½ x (1mk)

(b) The range of values of x for which –1.5 £ 2cos x £ 1.5 (1mk)

Two towns T and S are 300km apart. Two buses A and B started from T at the same time travelling towards S. Bus B travelled at an average speed of 10km/hr greater than that of A and reached S 1 ¼ hrs earlier.

(a) Find the average speed of A. (6mks)

(b) How far was A from T when B reached S. (2mks)

P and Q are two ports 200km apart. The bearing of Q from P is 040⁰. A ship leaves port Q on a bearing of 150⁰ at a speed of 40km/hr to arrive at port R 7 ½ hrs later. Calculate:

(a) The distance between ports Q and R. (2mks)

(b) The distance between ports P and R. (3mks)

A farmer has 15 hectares of land on which he can grow maize and beans only. In a year he grows maize on more land than beans. It costs him shs. 4400 to grow maize per hectare and shs 10,800 to grow beans per hectare. He is prepared to spend at most shs 90,000 per year to grow the crops. He makes a profit of shs 2400 from one hectare of maize and shs 3200 from one hectare of beans. If x hectares are planted with maize and y hectares are planted with beans.

(a) Write down all the inequalities describing this information. (13mks)

(b) Graph the inequalities and find the maximum profit he makes from the crops in a year. (5mks)

MATHEMATICS II

PART II

Use logarithm tables to Evaluate

³Ö 36.5 x 0.02573

1.938 (3mks)

The cost of 5 shirts and 3 blouses is sh 1750. Martha bought 3 shirts and one blouse for shillings 850. Find the cost of each shirt and each blouse. (3mks)
If K = ( y-c )^1/2

a) Make y the subject of the formula. (2mks)
b) Evaluate y, when K = 5, p = 2 and c = 2 (2mks)
Factorise the equation:

x + 1/x = 10/3 (3mks)

DA is the tangent to the circle centre O and Radius 10cm. If OD = 16cm, Calculate the area of the shaded Region. (3mks)

Construct the locus of points P such that the points X and Y are fixed points 6cm apart and

ÐXPY = 60⁰. (2mks)

In the figure below, ABCD is cyclic quadrilateral and BD is diagonal. EADF is a straight line,

CDF = 68⁰, BDC = 45⁰and BAE = 98^0.

Calculate the size of: (2mks)

a) ÐABD b) ÐCBD
Otieno bought a shirt and paid sh 320 after getting a discount of 10%. The shopkeeper made a profit of 20% on the sale. Find the percentage profit the shopkeeper would have made if no discount was allowed? (2mks)
Calculate the distance:
i) In nautical miles (nm)
ii) In kilometres (km)

Between the two places along the circle of Latitude:

a) A(30⁰N, 20⁰E) and B(30⁰N, 80⁰E) (Take Radius of Earth = 6371Km). (2mks)
b) X(50⁰S, 60⁰W) and Y(50⁰S, 20⁰E) (Take Radius of Earth = 6371Km). (2mks)
A rectangular tank of base 2.4m by 2.8m and height 3m contains 3,600 litres of water initially. Water flows into the tank at the rate of 0.5m/s. Calculate the time in hours and minutes required to fill the tank. (4mks)
Expand (1 + a)⁵ up to the term of a power 4. Use your expansion to Estimate (0.8)⁵ correct to 4 decimal places. (4mks)
A pipe is made of metal 2cm thick. The external Radius of the pipe is 21cm. What volume of metal is there in a 34m length of pipe (p = 3.14). (4mks)
If two dice are thrown, find the probability of getting: a sum of an odd number and a sum of scoring more than 7 but less than 10. (4mks)
Find the following indefinite integral ò 8x⁵ – 3x dx (4mks)

x³

The figure below represents a circle of radius 14cm with a sector subtending an angle of 60⁰ at the centre.

Find the area of the shaded segment. (3mks)

Use the data below to find the standard deviation of the marks.

Marks (x )

Frequency (f)

(4mks)

SECTION II (48MKS)

The figure below shows a cube of side 5cm.

Calculate:

a) Length FC (1mk)
b) Length HB (1mk)
c) Angle between GB and the plane ABCD. (1mk)
d) Angle between AG and the Base. (1mk)
e) Angle between planes AFC and ABCD. (2mks)
f) If X is mid-point of the face ABCD, Find angle AGX. (2mks)
Draw on the same axes the graphs of y = Sin x⁰ and y = 2Sin (x⁰ + 10⁰) in the domain 0⁰£ x⁰ £ 180⁰
i) Use the graph to find amplitudes of the functions.
ii) What transformation maps the graph of y = Sin x⁰ onto the graph of : y = 2Sin (x⁰ +10⁰).
The table below shows the masses to the nearest gram of 150 eggs produced at a farm in Busiro

country.

Mass(g)	44	45		46		47		48		49		50		51		52		53		54	55
Freq.	1	2		2		1		6		11		9		7		10		12		16	16
Mass(g)	56		57		58	59	60		61		62		63		64		65		70
Freq.	10		11		9	7	5		3		4		3		3		1		1

Make a frequency Table with class-interval of 5g. Using 52g as a working mean, calculate the mean mass. Also calculate the median mass using ogive curve.

A shopkeeper stores two brands of drinks called soft and bitter drinks, both produced in cans of same

size. He wishes to order from supplies and find that he has room for 1000 cans. He knows that bitter

drinks has higher demand and so proposes to order at least twice as many cans of bitter as soft. He

wishes however to have at least 90cans of soft and not more than 720 cans of bitter. Taking x to be

the number of cans of soft and y to be the number of cans of bitter which he orders. Write down the

four inequalities involving x and y which satisfy these conditions. Construct and indicate clearly by

shading the unwanted regions.

Two aeroplanes, A and B leave airport x at the same time. A flies on a bearing 060⁰ at 750km/h and B flies on bearing of 210⁰ at 900km/h:
a) Using a suitable scale draw a diagram to show the positions of Aeroplanes after 2hrs.
b) Use your graph to determine:
i) The actual distance between the two aeroplanes.
ii) The bearing of B from A.

iii) The bearing of A from B.

The Probabilities that it will either rain or not in 30days from now are 0.5 and 0.6 respectively. Find the probability that in 30 days time.
a) it will either rain and not.
b) Neither will not take place.
c) One Event will take place.
Calculate the Area of each of the two segments of y = x(x+1)(x-2) cut off by the x axis. (8mks)
Find the co-ordinates of the turning point on the curve of y = x³ – 3x² and distinguish between them.

MATHEMATICS II

PART I

MARKING SCHEME:

0.0912² = (9.12 x 10^-2)² = 0.008317

Ö 3.152 = 1.776

³Ö 1.776 + 0.008317

0.1279 x 25.91

= ³Ö 1.784317 No. log

0.1279 x 25.91 1.784 0.2514

0.1279 -1.1069

25.71 1.4101 +

0.5170

-1.7344

x 1/3

10^-1 x 8.155(6) 1^-1.9115

Or 0.8155(6)

(a – b)(a – b) = a – b

(a – b)(a + b) a + b

dy = 2x + 3

y = x² + 3x + c

-1 = 1 – 3 + c

c = 1 ; E.g y = x² + 3x + 1

K² – 9 = 0

K = ± 3

log 128 = log 64

18 9

log 16 log 8

6 3

= 2 log (8/3)

log (8/3)

= 2

Midpoint -8 + 6, 4 + 0 (-1, 2)

2 2

Gradient of LN = 4/-14 = -2/7

Gradient of ^ bisector = 7/2

y – 2 = 7/2

x + 1

y = 7/2X + 11/2

207,500 = 415,000(1 – 15 )ⁿ

100

0.5 = ( 85 )ⁿ

100

0.5 = 0.85ⁿ

log 0.5 = n log 0.85

log 0.5 = n

log 0.85

n = –1.6990 = -0.3010 = 4.264yrs

-1.9294 -0.0706

2 x 1 = 1 . x 20 = 0.3115 x 20 = 6.230

3.21 x 10^-1 3.21

1 = 1 = 0.5807 = 0.005807

172.2 1.722 x 10² 100

6.230 – 0.005807 = 6.224193

= 6. 224(3d.p)

X	2	2.5	3	3.5	4	4.5	5
y	4	6.25	9	12.25	16	20.25	25

h = ½

Area= ½ x ½[29+2(6.25+9+12.25+16+20.25+25)]

= ¼ [29 + 127.5]

= ¼ x 156.5 = 39.125 sq. units.

Cos q (cos q + ½ ) = 0

cos q = 0 cos q = -0.5

q = 90⁰, 270⁰ q = 120⁰, 240⁰

\ q = 90⁰, 120⁰, 240⁰, 270⁰

MP = 4 MK MK = -9

9 -18

MP = 4 ( -9 ) = ( -4 )

9 -18 8

\ P is ( -1,0 )

a = 30 d = 3 l = 300

300 = 30 + 3 (n – 1 )

300 = 30 + 3n – 3

300 – 27 = 3n

273 = 3n

91 = n

y = mx – 1

1 = 3m – 1

m = 2/3 = 0.6667

tan q = 0.6667 ; q = 33.69⁰

FK x FC = FA²

FC = 25/3 = 8 ^1/3 cm

CX = 8^1/3 – 9/2 = 23/6 = 3^5/6 cm

CX x XK = XA x XN

3^3/6 x 3/2 = 3 x XN

\ XN = 1^11/12 cm

V³ = k + x

k – x

V³k – V³x = k + x

V³k – k = x + V³x

V³k – k = x( 1 + v³)

V³k – k = x

1 + V³

(i.) x = 2 Þ x £ 2

(ii) y = -2 Þ y > -2

(iii)pts. (0.5,0)

(0,-1.5)

m = -1.5 – 0 = 3

0 – 0.5

Eq. Y = 3x – 1.5 y < 3x – 1.5

SECTION B

X	-4	-3	-2	-1	0	1	2	3	4
Y	-26	-16	-8	-2	2	4	4	2	-2

(i) Roots are x = -0.5 x = 3.6

(ii) y = -x²+ 3x + 2

0 = -x² – x + 2

y = 4x (-2, -8) (1, 4)

Roots are x = -2, x = 1

class x f d=x-74.5 fd d² fd²

0 – 9 4.5 2 – 70 – 140 4900 9800

10 – 19 14.5 8 – 60 – 480 3600 28,800

20 – 29 24.5 6 – 50 – 300 2500 15,000

30 – 39 34.5 7 – 40 – 280 1600 11,200

40 – 49 44.5 8 – 30 – 240 900 7,200

50 – 59 54.5 10 – 20 – 200 400 4,000

60 – 69 64.5 9 – 10 – 90 100 900

70 – 79 74.5 6 0 0 0 0

80 – 89 84.5 3 10 30 100 300

90 – 99 94.5 1 20 20 400 400

Sf = Sfd = Sfd² = 77,600

60 -1680

(i) Mean = 74.5 + -1680

= 74.5 – 28 = 46.5

(ii) Standard deviation = Ö 77600 – ( –1680 )²

60 60

= Ö 1283.3 – 784

= Ö 499.3 = 22.35

a (i.) OK = OA + AK = ½ a + ½ b

(ii) OS = ¾ OK = 3/8 a + 3/8 b

(iii)RS = RO + OS = 3/8 a – 9/40 b

(iv) RA = RO + OA = – 3/5 b + a

RA = a – 3/5 b RS = 3/8 a + 9/40 b

= 3/8( a – 3/5 b)

\ RS = 3/8 RA

The vectors are parallel and they have a common

point R \ point R, S and A are collinear

KB = 3m NK = 1.5m XB = 5m

(i) XK = Ö 5² – 3² = Ö 16 = 4m

let ÐXKN = q

cos q = 1.5 = 0.375

q = 67.97(8)⁰

(ii) In DXNK

XN = Ö 4² – 1.5² = Ö 13.75 = 3.708

In D SMR; MR = KB = 3m

SM = XN = 3.708m

Let ÐSRM = a

tan a = 3.708 =1.236

a = 51.02(3)⁰

21.

21.

	0	15⁰	30⁰	45⁰	60⁰	75⁰	90⁰	105⁰	120⁰	135⁰	150⁰	165⁰	180⁰
Y =2cosX	2.00	1.93	1.73	1.41	1.00	0.52	0.00	-0.52	-1	-1.41	-1.73	-1.93	-2.00
Y = sin ½ X	0.00	0.13	0.26	0.38	0.50	0.61	0.71	0.79	0.87	0.92	0.97	0.99	1.00

(a) X = 73⁰ ± 1⁰

(b) Between 40.5⁰ and 139.5⁰

300km

T S

Let the speed of A be X km/hr

Speed of B = (X + 10) km/hr

Time taken by A = 300 hrs

Time taken by B = 300 hrs

X + 10

300 – 300 = 5

x x + 10 4

300(x + 10) – 300x = 5

x(x + 10) 4

300x + 300 – 300x = 5

x² + 10x

x² + 10x – 2400 = 0.

x = 44.25

X = -54.25 N/A

(b) Distance covered by A in 1 ¼ hrs = 44.25 x 5/4 = 55.3 km

Distance of A from T is 300 – 55.3 = 244.7 km

(a) Distance = 15 x 40 = 300km

(b)

PR² = 200² + 300² –2x 200 x 300 cos70⁰

= 130,000 – 41040 = 88,960

PR = 298.3 km

sin 70⁰ sin a

sin a = 300 sin 70⁰

298.3

= 0.9344

a = 69.1⁰

Bearing of R from P is

40 + 69.1 = 109.1⁰

(i.) X > y

(ii) 4,400X + 10,800Y £ 90,000

Simplifies to 11X + 27y £ 225

(iii) X + y £ 15

X > 0; y > 0

Boundaries

x = y pts (6,6) (12,12)

11x + 27y = 225 pts (13,3) (1,8)

X + y = 15 pts (0,15) (8,7)

Objective function

2400 x 3200y

(pt (2,1)

2400X + 3200y = 8000

Search line ® 3X + 4y = 10

Point that give maximum profit is (12,3)

\ maximum profit

= 2400 x 12 + 3200 x 3 = 38,400 shs.

MATHEMATICS II

PART II

MARKING SCHEME

No log.

36.5 1.5623

0.02573 –2.4104 +

-1.9727

1.938 0.2874 –

-1.6853

-3 + 2.6853

3 3

-1 + 0.8951

1.273(4) ¬ 0.1049

= 1.273(4)

Let shirt be sh x,

let blouse be sh. y.

5x + 3y =1750 (i.)

3x + y = 850 (ii)

mult (ii) by 3

9x + 3y = 2550 (iii)

Subtract (iii) – (i.)

– 4x = -800

Subt for x

= 250

Shirt = sh 200 ; Blouse = sh 250

(a) K²= y – c

y – c = 4pK²

y = 4pK² + c

(b) y = 4 x 2 x 25 + 2 ; y = 202

x² + 1 – 10x = 0

3x²– 10x + 3 = 0

3x (x – 3) – 1(x – 3) = 0

(3x – 1) (x – 3 ) = 0

x = 1/3 or x = 3

Area D OAD pyth theorem AD =12.49cm

½ x 12.49 x 10 = 62.45cm²

Cos q = 10/16 = 0.625

q = 51.3⁰ 62.5

Sector 57.3⁰ x 3.14 x 100 40.2 –

360 = 22.3

ÐXPY = 60⁰

\ÐXC₁Y = 120⁰

B1\ÐC₁XY = ÐC₁YX

= 180⁰ – 120⁰= 30⁰

Construct 30⁰ angles

at XY to get centres

B1 C₁and C₂ mojar arcs drawn

2 on both sides with C₁X and C₂X

as centres.

DAB = 180⁰– 98⁰ = 82⁰

ADB = 180 – (68 + 45 ) = 67⁰

ABD = 180 – (67 + 82)

= 31⁰

(a) 180⁰– (67 + 82)⁰= 31⁰

ÐABD = 31⁰ Opp = 180⁰

(b) (180 – 82)⁰ = 98⁰82 + 98 = 180⁰

180⁰ – (98⁰– 45⁰) =

ÐCBD = 37⁰ 180 – (98 + 45)⁰

= 37⁰

10 x 320

100 Discount = sh 32

Sold at sh 288

If no Discount = ( 320 x 20 ) % = 22.7%

288

(a) Dist along circle of lat.

Long diff x 60 x cos q nm

100 x 60 x Cos 50⁰

100 x 60 x 0.866

5196nm = 100 x 2pR Cos 50⁰

360

100 x 2 x 3.14 x 6371

360 = 5780Km

(b) 80 x 60 Cos 50 = 3895 Km

Vol =2.8 x 2.4 x 3 = 20.16m³

1m³ = 1000 L

20.16m³ = 20160 L

20160

3600

16560 L to fill

0.5 L – 1 sec

16560 L – ?

165600

5 x 3600

33120 hr

3600 @ 9.41 hrs ; @ 564.6 min.

1⁵ + 5.1⁴a + 10.1³.a² + 10.1²a³ + 5.1.a⁴

a = -0.2

1 + 5(-0.2) + 10(-0.2)² + 10(-0.2)³+ 5 (-0.2)⁴

1 – 1.0 + 0.4 – 0.08 + 0.008 = 0.3277 (4d.p)

Area of metal : Material – Cross section.

p(R² – r²)

3.14 (21 –19)

Vol 6.28cm² x 3400cm

= 215.52m³

Possibility space:

. 1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

P(odd) = 3/6 = ½

P(Sum > 7 but < 10) = 9 /36

\ P(odd) and P(sum > 7 but < 10 )

= ½ x 9/36 = 9/72 = 1/8

ò( 8x⁵/x³– 3x/x³) d₄

ò( 8x² – 3x^-2) d₄

16x³/3 + 6x^-3/-3 + C

16x³/3 – 2/x³+ C

Area of DAOB

½ x 14 x 14 x 0.866 = 84.866cm²

Area of sector = 60 x3.14 x 14 x14 = 10.257

360

Shaded Area

84.666 – 10.257 = 74.409cm²

Marks	F	Fx	fx²
5	3	15	75
6	8	48	288
7	9	63	441
8	6	48	384
9	4	36	324

åx = åf=30 åfx=210 1512

S.d = Ö åfx² – ( åfx )²

åf åf

= Ö 1512 – (210)²

30 30

= Ö 50.4 – 49

= Ö 1.4 = 1,183

SECTION II .

(a) FC = Ö 5² + 7.07² = Ö 50 = 7.071

(b) HB = Ö 5² + 7.07²= Ö 75 = 8.660

(d) b = Tan^-1 5/7.071 = Tan^-10.7071 = 35.3⁰

(e) y = Tan^-1 5/3.535 = Tan^-1= 54.7⁰

(f) ÐAGX = 19.4⁰

y = Sin x

x⁰	0⁰	30⁰	60⁰	90⁰	120⁰	150⁰	180⁰
sin x⁰	0	0.50	0.66	1.00	0.866	0.500	0

y = 2 Sin (x⁰+ 10⁰)

X⁰	0⁰	30⁰	60⁰	90⁰	120⁰	150⁰	70⁰
2 Sin(x +10⁰)	0.3472	1.286	1.8794	1.286	0.3472	-0.3472	-1.8794

Amplitudes for y = Sin x⁰ is 1

For

y = Sin(x+10⁰) is 2.

c.f	X	F
61	53	12
16		54
93	55	16
103	56	10
11		57
123	58	9
130	59	7
135	60	5
138	61	3
142	62	4
145	63	3
148	64	3
149	65	1
150	70	1

Mean = x + 52 + -4

150

52 – 0.02

= 51.08

Median = 51.4g.

class interval 59

Class interval	mid point	Freg.	c.f
44-48	46	12	12
49-53	51	49	61
54-58	56	64	125
59-63	69	22	147
64-68	66	3	130
69-73	71	1	150

X + Y £ 1000

X £ 2Y

Y < 720

X > 90

21.(a) 1cm = 200Km/h

A = 200 x 7.5 = 1500 Km

B = 200 x 9 = 1800Km.

(b) (i.) 15.8cm x 200 (ii) Bearing 224⁰

= 3160 Km. (iii) Bearing 049⁰

(a) P(R) x P(R)¹ (b) P(R)¢ x P(R) (c) P(R) x P(R’)

= 0.5 x 0.6 0.5 x 0.4 P(R)’ x P(R)

= 0.3 = 0.2 0.5 x 0.6 = 0.3

0.5 x 0.4 = 0. 2= 0.5

y = x(x + 1)(x – 2)

= x³ – x² – 2x

A₁ = ò(x³ – x² –2x) d₄

^-1[¼ x⁴ – 1/3 x²]_-1

= 0 – ( ¼ + 1/3 – 1) = 5/12

A₂ = ²ò(x³ – x² –2x) d₄

= ⁰ò ¼ x⁴– 1/3 x³ – x²)^-2₀

= ( ¼ .16 – 1/3 .8 – 8 )

= 4^-0– 8/3 – 4 = – 8/3

A₁ = 5/12= A₂ = 2 ²/₃

y = x³ – 3x²

dy = 3x² – 6x

At stationary

Points dy = 0

i.e 3x²– 6x = 0

3x(x – 2) = 0

x = 0 or 2

Distinguish

dy = 3x² – 6x

d²y = 6x – 6

dx²

(i) x = 0 dy² = 6x – 6 = -6 (ii) x = 2

dx² d²y = 6

-6 < 0 – maximum. dx²

\ (0,0) Max Pt. 6 > 0 hence

Minimum Pt.

x = 2, y = 8 – 12 = -4

(2, -4) minimum point.

MATHEMATICS II

PART I

SECTION 1 (52 Marks)

Without using tables evaluate:

Ö7.5625 x ³Ö3.375

15 (5 mks)

Make k the subject of the formula.

y = 1 Ök + y

T² k (3 mks)

If A = (x, 2) and xB = x and if AB = (8), find the possible values of x.

-2 (3 mks)

Simplify completely. (3 mks)

rx⁴ – r

2xr – 2r

Solve the equation. (3 mks)

Log ₃ (8-x) – log ₃ (1+x) = 1

Under an enlargement scale factor -1, A(4,3) maps onto A¹ (4,-5). Find the co-ordinates of the centre of enlargement. (3 mks)

Find the equation of the line perpendicular to the line 4x-y = -5 and passing through the point (-3,-2). (2 mks)
Find the standard deviation of the data below:

3,5,2,1,2,4,6,5 (4 mks)

What is the sum of all multiples of 7 between 200 and 300? (4 mks)

Solve the equation.

½ tan x = sin x for -180⁰ £ x £ 360⁰. (3 mks).

Expand (1-2x)⁴. Hence evaluate (0.82)⁴ correct to 5d.p. (4 mks)

The line y = mx – 3 passes through point (5,2). Find the angle that the line makes with the x-axis. (2 mrks)
A two digit number is such that 3 times the units digit exceed the tens digit by 14. If the digits are reversed, the value of the number increases by 36. Find the number (4 mks)

In the figure below, O is the centre of the circle, OA = 7 cm and minor arc AB is 11 cm long. Taking P = ²²/₇, find the area shaded. (3 mks)

A box contains 36 balls, all identical except for colour. 15 of the balls are black, 15 are brown and the rest are white. Three balls are drawn from the box at random, one at a time, without replacement. Find the probability that the balls picked are white, black and brown in that order. (2 mks)

Find the inequalities that describe the unshaded region R below. (4 mks)

SECTION 2 (48 Marks)

Draw the graph of y = x² + x – 6 for -4 £ x £

Use your graph to solve the equations.

(i) x²+ x – 6 = 0 (ii) x² + 2x – 8 = 0 (8 mks)

The diagram below represents a bucket that has been placed upside down. The radius of the top surface is 15cm and that of the bottom is 40cm. The vertical height of the bucket is 50cm.

Determine:-

The volume of the bucket.
The curved surface area of the bucket. (leave your answers in terms of p)

Draw, on the same axes, the graphs of y = cos q and y = 5 sin q for – 180⁰£ q £ 180⁰

From your graph, determine the amplitude of each wave.
For what value(s) of q is cosq – 5 sin q = 0 (8 mks)

A point P lies on a coast which runs from West to East. A ship sails from P on a bearing of 032⁰. When it reaches Q, 7km from P, a distress signal is observed coming from another ship at R. Given that R is N.E of P and on a bearing of 066⁰ from Q, calculate:

Ð
The distance QR, between the two ships.
The shortest distance from R to the shore. (8 mks)

A bag contains x red balls and y yellow balls. Four times the number of red balls is equal to nine times the number of yellow balls and twice the total number of balls exceeds the number of yellow balls by 44.

How many balls of each colour are three in the bag?
If two balls are drawn out of the bag at random one at a time with replacement what is the probability that the two balls are red? (8 mks)

A Kenyan businessman goes on a trip to West Germany through Italy and back to Kenya. In Kenya he is allowed to take Ksh. 67,000 for sales promotion abroad. He converts the Kenya currency into US dollars. While in Italy, he converts ²/₅ of his dollars into Italian lire, which he spends in Italy. While in West Germany, he converts ⁵/₈ of the remaining dollars into Deutsche marks which he uses up before coming to Kenya. Using the conversion rates 1 US dollar = 1.8 Deutsche marks = 16.75

Ksh = 1340 Italian lire. Answer the following questions:

How many US dollars did he take out of Kenya?
How many Italian lire did he spend in Italy?
How much money, in Deutsche marks did he spend in West Germany?
How much money in Ksh. did he have on his return to Kenya? (8 mks)

PQRS is a parallelogram in which PQ = r and PS = h. Point A is the midpoint of QR and B is a point on PS such that PS : PB = 4:3. PA and QB intersect at M.

Given that PM = kPA and BM = tBQ where k and t are scalars, express PM in two different ways and hence find the values of k and t.

Express PM in terms of r and h only. (8 mks)

Two variables T and X are connected by the equation T = ab^xwhere a and b are constants. The values of T and X are given in the table below:

T	6.56	17.7	47.8	129	349	941	2540	6860
X	2	3	4	5	6	7	8	9

Draw a suitable straight line graph and use it to estimate the values of a and b. (8 mks)

MATHEMATICS III

PART II

Section I: (52 Marks)

Use mathematical tables to evaluate:

8.67 (3 mks)

Ö 0.786 x (21.72)³

Simplify completely. (3 mks)

4 – 1

x² – 4 x-2

An Indian on landing at Wilson Airport changes Re 6000 into Kenya shillings when the exchange rate is Re = Ksh. 1.25. He spent Ksh. 5000 when in Kenya and converted the remaining amount to Rupees at the same rate as before. Find out how much the Indian is left with in Rupees. (3mks)

The last of three consecutive odd numbers is (2x+3). If their sum is 105, find the value of x. (4 mks)

a S b is defined by: a S b = (a + b)

If B S (2 S 3) = 4 S 1, Find B. (3 mks)

Find the value of M. (3 mks)

85⁰

160⁰

(a) Expand (1+2x)⁶ upto the term containing x³ . (2 mks)

(b) By putting x = 0.01, find the approximate value of (1.02)⁶ correct to 4 S.F. (2 mks)

Show that x is the inverse of : Y = 3 -3 1 X = 2 1 (3 mks)

-5 2 5 3

The probabilities of three candidates K, M and N passing an examination is ²/₃, ¾ and ⁴/₅ Find the probability that :

(a) All pass: (1 mk)

(b) At least one fails: (2 mks)

In the figure, PR is tangent to the circle centre O. If ÐBQR=30⁰, ÐQBC=27⁰,and ÐOBA=37⁰, find ÐBAC and Ð

C A

B P R

A frustrum of height 10cm is cut off from a cone of height 30cm. If the volume of the cone before cutting is 270cm³ , find the volume of the frustrum. (3 mks)

Evaluate 0 (2 mks)

( 3x²– 1 ) dx

4 x ²

If one litre of water has a mass of 1000g, calculate the mass of water that can be held in a rectangular tank measuring 2m by 3m by 1.5m. (give your answer in tonnes). (2 mks)
Write down the three inequalities which define the shaded region. (3 mks)

(3,2)

(2,1) (4,1)

The depth of sea in metres was recorded on monthly basis as follows:

Month	March	April	May	June	July
Depth (m)	5.1	4.9	4.7	4.5	4.0

Calculate the three monthly moving averages. (3 mks)

A number of women decided to raise sh. 6300 towards a rural project for bee keeping. Each woman had to contribute the same amount. Before the contribution, seven of them withdrew from the project. This meant the remaining had to pay more. If n stands for original number of women, show that the increase in contribution per woman was: 44100 (3 mks)

n(n-7)

SECTION II: (48 Marks)

Find the distance between points A(50⁰ S, 25⁰ E) and B(50⁰ S, 140⁰ E) in:

(i) Km (ii) nm (8 mks)

(take radius of earth to be 6400km, P = 3.14)

The distance S in metres, covered by a moving particle after time t in seconds, is given by :

S = 2t³ + 4t³– 8t + 3.

Find:

(a) The velocity at : (i) t = 2 (ii) t = 3

The instant at which the particle is at rest. (8 mks)

A car starts from rest and its velocity is measured every second for six seconds. (see table below).

Time (t)	0	1	2	3	4	5	6
Velocity v(ms ^-1)	0	12	24	35	41	45	47

Use trapezium rule to calculate the distance travelled between t = 1 and t = 6. (8 mks)

Using a pair of compass and ruler only, construct triangle ABC such that AB=9cm, BC=14cm and ÐBAC = 120⁰ . Draw a circle such that AB, BC and AC are tangents. What is the radius of this circle? (8 mks)
The marks scored by 100 students in mathematics test is given in the table below:

Marks	10-19	20-29	30-39	40-49	50-59	60-69	70-79
No. of students	8	15	15	20	15	14	13

(a) Estimate the median mark. (2 mks)

(b) Using 44.5 as the assumed mean, calculate:-

(i) The mean mark: (2 mks)

(ii) The variance: (2 mks)

(iii) The standard deviation: (2 mks)

(a) On the same axes, draw the graphs of : y = sin x ; y = cos x

y = cos^x + sin X for 0⁰ Ð X Ð 360⁰.

(b) Use your graph to deduce

(i) The amplitude

(ii) The period of the wave y = cos x + sin x.

Cos x = – sin x for 0⁰ Ð X Ð 360⁰ .

Given a circle of radius 3 units as shown in the diagram below with its centre at O(-1, 6). If BE and DE are tangents to the circle where E (8,2). Given further that Ð DAB = 80⁰.

A E

(a) Write down the equation of the circle in the form ax² + bx + cy² + dy + e = 0 where a, b, c, d, e are constants. (2 mks)

(b) Calculate the length DE. (2 mks)

(d) Calculate the value of angle DCB. (2 mks)

A building contractor has to move 150 tonnes of cement to a site 30km away. He has at his disposal 5 lorries. Two of the lorries have a carrying capacity of 12 tonnes each while each of the remaining can carry 7 tonnes. The cost of operating a 7 tonne lorry is sh. 15 per km and that of operating a 12 tonne lorry is sh. 25 per km. The number of trips by the bigger lorries should be more than twice that made by smaller lorries. (8 mks)

(a) Represent all the information above as inequalities.

How should the contractor deploy his fleet in order to minimise the cost of moving the cement? (8 mks)

MATHEMATICS III

PART I

MARKING SCHEME

	SOLUTION	MRK	AWARDING
1.	Ö7.5625 = 2.75 ³Ö3.375 = ³Ö3375 X ³Ö10^-3 = ³Ö3³x 5³x 10^-1 = 3 x 5 x 10^-1 = 1.5 = 2.75 x 1.5 = 2.75 = 0.275 1.5 x 10 10	1 1 1 1 1	Method for Ö7.5625 Square root Method for ³Ö ³Ö Answer
		5
2.	T²y = Ö k+y K T⁴y²k = k+y T⁴y²k – k = y K(T⁴y²-1) = y K = y T⁴y² – 1	1 1 1	Removal of square root Rearrangement of terms Answer
		3
3.	(x 2) x = (8) -2 x² – 4 = 8 x = +Ö12 = + 2Ö3 = + 3.464	1 1 1	Matrix equation Quadratic equation Answers in any form
		3
4.	r(x² – 1) 2r(x – 1) r(x² – 1)(x² + 1) 2r (x – 1) r(x – 1)(x + 1)( x² + 1) 2r (x – 1) = (x + 1)( x² + 1) 2	1 1 1	Complete factorisation of numerator Factorisation of denominator Answer
		3
5.	1 = log₃3 8 – x = 3 1+x -4x = -5 x = 5 4	1 1 1	Logarithic expression. Equation Answer
		3
6.	Let the centre be (a,b) 4-9 = -1 4-a -5-b 3-b 4-a = -4+9 -5-b = -3+b a = 4 b = -1 centre is (4,-1)	1 1 1	Equation Linear equations Centre
		3
7.	Y = 4x + 5 Gradient = 4 Gradient of ^ line – ¼ y + 2 = – 1 x + 3 4 4y + x = -11	1 1	Gradient of ^ line. Equation.
		2
8.	X = 28 = 3.5 8 standard deviation = Ö 22 = Ö2.75 = 1.658 8	1 1 1 1	Mean d values d² values Answer
		4
9.	a = 203 d = 7 L = 294 294 = 203 + 7(n-1) n = 14 S 14 = 14 (203 + 294) 2 = 7 x 497 = 3479	1 1 1 1	For both a and b Equation For n Sum
		4
10.	Sin x = 2 sin x Cos x Sin x = 2 cosx Sin x 2 cos x = 1 cos x = 0.5 x = 60⁰, 300⁰, -60⁰	1 1 1	Simplification Equation All 3 values
		3
11.	(1 +-2x)⁴ = 1-8x + 24x² – 32x³ + 16x⁴ (0.82)⁴ = (1 + -2 x 0.09)⁴ x = 0.09 (0.82)⁴ = 1 – 0.72 + 0.1944 – 0.023328 + 0.00119376 = 0.35226576 @ 0.35227 (5 d..p)	1 1 1 1	Expansion Value of x All terms Rounded
		4
12.	2 = 5m – 3 m = 1 tan q = 1 q = 45⁰	1 1	Value of m. Angle
		2
13.	Let the number be xy 3y = x + 14 10y + x = 10x + y + 36 = 9y – 9x Þ 36 3y – x = 14 9y – 9x = 36 y = 5 x = 1 the number is 15.	1 1 1 1	1^st equation 2^nd equation method of solving Answer
	S	4
14.	Let ÐAOB = q q x 2 x 22 x 7 = 11 360 7 q = 90⁰ Area shaded = 90 x 22 x 7 x 7 – 1 x 7 x 7 360 7 2 = 77 – 49 2 2 = 28 = 14cm² 2	1 1 1	Value of q Substitution Answer
		3
15.	P(WBb) = 6 x 15 x 15 36 35 34 = 15 476	1 1	Method Answer
		2
16.	Equation inequality L₁ y = x y £ x L₂ y = -2 y ³ -2 L₃ 2y + 5x = 21 2y + 5x < 21	1 1 1 1	1 mark for each inequality. Method for obtaining L³
	(i) roots are x = -3 x = 2 (ii) y = x² + x-6 0 = x² + 2x-8 y = -x + 2 roots are x = -4 x = 2	4	2 1 1 1 1 1	For all correct points. 1 for atleast five correct points. Correct plotting. Scale Smoothness of curve Both roots Linear equation Both roots
			8

18.	h = 15 h+50 40 h = 30cm H = 80cm (a) Volume = ¹/₃ p x 40 x 40 x 80 – ¹/₃ p x 15 x 15 x 30 = 128000 p – 6750 p 3 3 = 121,250p cm³ 3 (b) L² = 80² + 40² L = 15² + 30² = 6400 + 1600 = 225 + 900 = 8000 = 1125 L = 89.44 cm L = 33.54 cm Curved surface area of bucket = p x 40 x 89.44 p x15x33.54 = 3577.6p – 503.1p = 3074.5cm²	1 1 1 1 1 1 1 1	Expression Value of H Substitution Volume L L Substitution Area
		8
19.

20.	(i) ÐRPQ = 13⁰ ÐPQR = 32⁰+90⁰+24⁰ = 146⁰ ÐPRQ = 180⁰– (146⁰+ 13⁰) = 21⁰ (ii) P = 7 sin13⁰ sin 21⁰ P = 7 sin 13⁰ Sin 21⁰ = 4.394km P T (iii) Let PR = q q = 7 sin 146⁰ sin 21⁰ q = 7 sin 146⁰ sin 21⁰ q = 10.92 km sin 45⁰ = RT 10.92 RT = 10.92 sin 45⁰ = 7.72 km (2 d..p)	1 1 1 1 1 1 1 1	Fair sketch ÐPRQ Equation Method Equation Distance PR Equation RT
		8
21.	(a) 4x = 9y 2(x+y) = y+44 Þ 2x + y = 44 4x – 9y = 0 4x + 2y = 88 11y = 88 y = 8 x = 18 (b) P(RR) = 18 x 18 = 81 26 26 169	1 1 2 1 1 1 1	Equation Equation Method of solving Value y Value x Method Answer
		8
22.	(a) 67,000 Ksh = 67,000 US dollars 16.75 = 4,000 dollars (b) 2 x 4,000 = 1600 US dollars 5 1600 US dollars = 1600 x 1340 = 2,144,000 Italian lire (c) Remainder = 2400 US dollars 5 x 2400 = 1500 US dollars 8 1500 US dollars = 1500 x 1.8 = 2700 Deutche marks (d) Remainder = 900 US Dollars 900 US Dollars = 900 x 16.75 Ksh. = 15,075 Ksh.	1 1 1 1 1 1 1 1	Method Answer Method Answer For 1500 Answer Method Ksh.
		8
23.	PM = kPA = k(r + 1h) 2 = kr + 1kh 2 PM = PB + BM 3h + t BQ 4 = 3h + t(-3h + r) 4 4 = 3h – 3t h + tr 4 4 = 3 – 3t h + tr 4 4 t = k 3 – 3t = 1k 4 4 2 3 – 3t = 1 t 4 4 2 5t = 3 4 4 t = 3 + 4 4 5 = 3 5 \ k = 3 5 \ PM = 3r + 3h 5 10	1 1 1 1 1 1 1 1	PM PM PM simplified Both equations method Value of k Value k PM
		8

24.	Y LogT Log T = log a + x log b Log T Þ 0.82, 1.25, 1.68, 2.11, 2.54, 2.97, 3.40, 3.84 y – intercept = log a = 0 a = 1 gradient = 3.84 – 0.82 = 3.02 9 – 2 7 = 0.4315 log b = 0.4315 = 0.4315 b = antilog 0.4315 b = 2.7	1 1 1 2 1 1 1 8	Plotting Labeling of axis Linear All correct logs Value of a Method of gradient Value of b

MATHEMATICS III

PART II

MARKING SCHEME

SOLUTION MARKS AWARDING

1.	No log 8.69 0.9390 0.786 1.8954 21.72 1.3369 1.2323 1.7067 – 2 2 + 1.7067 2 2 – 1 + 0.8533 0.7134 x 10 ^-1 = 0.07134	M1 M1 A1	ü reading to 4 s.f Rearranging
		3
2.	4 – 1 (x-2)(x+2) (x-2) – x+2 (x-2(x+2) – (x-2) (x-2(x+2) -1 x+2	M1 M1 A1
		3
3.	Re6000 = Ksh. 75000 Spent 5000 Rem 2500 Rem 2500 1.25 Re 2000	M1 M1 A1
		3
4.	2x – 1 , 2z + 1 , 2x + 3 6x + 3 = 105 6x = 102 x = 17	M1 M1 A1 A1	Allow M1 for us of different variable.
		4
5.	4 * 1 = 5 4 2 * 3 = 5 6 A * 5 = 5 6 4 A + 5 = 5 x 5A 6 4 6 A + 5 = 25 A 6 24 A = 20	M1 M1 A1 3
6.	180 – M + 20 + 95 = 180 295 – M = 180 – M = – 115 M = 115	B1 B1 A1
		3
7.	1 + 2x + 60x² + 160x³ + 1 + 0.2 + 0.006 + 0.00016 = 1.20616 = 1.206	M1 M1 M1 A1 4	Only upto term in x³. Correct substitution Only 4 s.f.
8.	3 -1 2 1 = I -5 2 5 3 6 -5 3 -3 -10 +10 -5 + 6 1 0 0 1	M1 M1 A1	Matrix multiplication gives : I 1 0 0 1
		3
9.	(a) 2 x 3 x 4 = 2 3 4 5 5 (b) 2 x 3 x 1 + 2 x 1 x 4 + 1 x 3 x 4 3 4 5 3 2 5 3 4 5 1 + 4 + 1 10 15 5 = 17 10	M1 M1 A1
		3
10.	ÐQCB = 30⁰ 180 – (27 + 30) = 123⁰ \ BAC = 57⁰. OBA = 37⁰ OAB = 37⁰ AOB = 106⁰ \ ACB = 53⁰	M1 M1 A1	Isosceles triangle. Angle at centre is twice angle at circumference.
		3
11.	V = 1 x 3.14 x r ² x 10 = 270 L.S.F. 20 = 2 30 3 V.S.F = 2 ³ = 8 3 27 Vol. of cone = 8 x 270 27 = 80cm³ \ Vol. Of frusturm = (270 – 80) = 190cm³	M1 M1 A1
		2
12.	3x ³ – x ^{-1 2} 3 -1 ₁ x ³ + 1 ² x ₁ 8 + 1 – ( 1 – 1) 2 8 1 – 2 = 6 1 2 2	M1 A1 2
13.	(2 x 3 x 1.5) volume 9 m³ 1L º 1000 cm³ 1000 L = 1 m³ 9000 L = 9 m³ 1000 L = 1 tonne 9000 L = 9 tonnes.	M1 A1
		2
14.	y ³ 1 (i) y < x – 1 (ii) y < 5 – x (iii)	B1 B1
		3
15.	M₁ = 5.1 + 4.9 + 4.7 = 4.9 3 M₂ = 4.9 + 4.7 + 4.5 = 4.7 3 M₃ = 4.7 + 4.5 + 4.0 = 4.4 3	M1 M1 M1
		3
16.	Original contribution per woman = 6300 N Contribution when 7 withdraw = 6300 (n-7) Increase – Diff. 6300 – 6300 n-7 n 6300n – 6300(n-7) n(n-7) 6300n – 6300 + 44100 n(n-7) 44100 n(n-7)	M1 M1 1 3
SECTION II (48 Marks)
17.	(i) 115⁰ A B Centre of circles of latitude 50⁰ S. R Cos 50⁰ AB = 115 x 2p R Cos 50^o 115 x 40192 x 0.6428 360 = 8252.98 km (ii) Arc AB 60 x 115 Cos 50 nm 60 x 115 x 0.6428 nm 4435 nm	M1 M1 M1 A1 M1 M1 M1 A1	No. log 60 1.7782 1+5 2.0607 0.6428 1.8080 4435nm 3.6469
		8
18.	(a) V = ds = 6t²+ 8t – 8 dt (i) t = 2 V = 6×4 + 8×2 – 8 = 32 ms^-1 (ii) t = 3 V = 6×9 + 8×3 – 8 = 70ms^-1 (b) Particle is at rest when V = 0 6t² + 8t – 8 = 0 2(3t – 2) (t+2) = 0 t = 2 t = -2 3 particle is at rest at t = 2 seconds 3		Do not accept t = -2. Must be stated.
		8
19.	Area under velocity – time. graph gives distance. A = { h ½ (y₁ + y₆ ) + y₂ + y₃ + y₄ + y₅ )} = 1 { ½ ( 12+47) + 24 + 35 + 41 + 45)} = 29.5 + 14.5 = 174.5m	B1 B1 M1 M1 B1 B1 A1	Trapezium rule only accepted. Formula. Substitution into formular.
		8
20.	Drawing actual Scale 1cm = 2cm Radius 1cm = 2cm	M1 M1 M1 M1 M1 M1 M1 M1	Bisect ÐA Bisect Ð B Intersection at centre of inscribed circle. Draw circle. Measure radius. Arcs must be clearly shown.
		8
21.	mean = 44.5 + 130 100 = 44.5 + 1.3 = 45.8 (b) Variance S (x – A) 2 = 2800 Sf 100 = 28 S.D. = Ö 28 = 5.292	M1 A1 M1 A1 M1 A1
		8
22.	y = sin x x 0 60 120 180 240 30 360 sin x 0 0.866 0.866 0 -0.866 -0.866 0 y = cos x x q 60 120 180 240 300 360 cos x 1 0.5 -0.5 -1.0 -0.5 0.5 1.0 y = cosx + sinx x q 60 120 180 240 30 360 cosx + sinx 1 1.366 0.366 -1 -1.366 -0.366 1.0 (c) Cos x = – sin x x = 45⁰ , 225⁰
23.	(i) amplitude = 1.366 (ii) Period = 300⁰ (a) (x+1) ² + (y-6)² = 3² x² + 2x + 1 + y² – 12y + 36 = 9 x² + 2x + y² – 12y + 28 = 0 (b) cos 10 = OD DE = 3 DE 0.9848 DE = 3.046 (c) Twice ÐOED 10⁰ x 2 = 20⁰ (d) DAB = 80⁰ \ DCB = 100⁰	M1 A1 M1 A1 M1 A1 M1 A1	Formular (x-a)² + (y-b)² = r² Cyclic quad.
		8
24.	Let number of trips by 12 tonne lorry be x. Let number of trips by 7 tonne lorry be y. (a) x > 0 ; y > 0 24x + 21y £ 150 12 x 25 x X + 15 x 7 x y £ 1200 300x + 105y £ 1200 x > 2y (b) Ref. Graph paper. Minimising: 3 – 12 tonne lorry and 2 – 7 tonne lorries should be deployed.	B1 B1 B1

MATHEMATICS IV

PART I

SECTION 1 (52MKS)

Evaluate using logarithms 3Ö7.673 – 15.612

12.3 (4mks)

Solve x – 3x – 7 = x – 2 (3mks)

3 5 5

In the given figure CD is parallel to BAC, calculate the values of x and y. (3mks)

C D

B A

The surface area and volume of a sphere are given by the formulars S = 4pr² and V= ⁴/₃ pr³.

Express V in terms of S only. (3mks)

A line perpendicular to y = 3-4x passes through (5,2) and intercepts y axis at (0,k)

Find the value of K. (3mks)

An alloy is made up of metals P,Q,R, mixed in the ratio 4:1: 5: A blacksmith wants to make 800g of the

alloy. He can only get metal P from a metallic ore which contains 20% of it. How many Kgs of the ore

does he need. (3mks)

The co-ordinate of point A is (2,8) vector AB = 5 and vector BC = 4 Find the

-2 3

co-ordinate of point C. 3mks)

Two buildings are on a flat horizontal ground. The angle of elevation from the top of the shorter building to the top of the taller is 20⁰ and the angle of depression from the top of the top of the shorter building to the bottom of the taller is 30⁰. If the taller building is 80m, how far apart are they

(4mks)

The given figure is a quadrant of a piece of paper from a circle of radius 50cm. It is folded along AB

and AC to form a cone . Calculate the height of the cone formed.

(4mks)

5Ocm

50cm

Express 3.023 as a fraction (2mks)
Point A (1,9), Point B(3,5) and C (7,-3). Prove vectorically that A,B and C are collinear. (4mks)
A salesman gets a commission of 4% on sales of upto shs 200,000 and an additional 2% on

sales above this. If in January he got shs 12,200 as commission, what were his total sales (4mks)

Water flows through a cylindrical pipe of diameter 3.5cm at the rate of 2m/s. How long to the nearest minute does it take to fill a spherical tank of radius 1.4m to the nearest minute? (4mks)
Rationalize the denominator in Ö3

Ö 7 – 2

Leaving your answer in the form Öa + Öb

Where a ,b, and c are integers (3mks)

For positive values of x, write the integral solutions of 3£ x² £ 35 (4mks)
8 girls working 5 hours a day take 12 days to drain a pool. How long will 6 girls working 8 hours a day take to drain the pool?( Rate of work is equal) (2mks)

SECTION II (48 mks)

In the given circle centre O , A,E,F, is target to the circle at E. Angle FED = 30⁰ <DEC = 20⁰ and <BC0 = 15⁰

A F

Calculate (i) <CBE (3mks)

(ii) <BEA (2mks)

(iii) <EAB (3mks)

The sum of the 2^nd and third terms of a G.P is ⁹/₄If the first term is 3,

(a) Write down the first 4 terms of the sequence . (5mks)

(b) Find the sum of the first 5 terms using positive values of the common ratio (r)

(3mks)

E and F are quantities related by a law of the form E = KFⁿWhere k and n are

constants. In an experiment , the following values of E and F were obtained .

E	2	4	6	8
F	16.1	127.8	431.9	1024

Use graphical method to determine the value of k and n (Graph paper provided) (8mks)

In the domain –2 £ x £ 4 draw the graph of y = 3x² + 1 –2x .Use your graph to solve the equation. 6x² 4x + 4 = 0 (graph paper provided) (8mks)
A solid sphere of radius 18cm is to be made from a melted copper wire of radius 0.4mm . Calculate the length of wire in metres required to make the sphere. (5mks)

(b) If the density of the wire is 5g/cm³. Calculate the mass of the sphere in kg. (3mks)

A right cone with slant height of 15cm and base radius 9cm has a smaller cone of height 6cm chopped off to form a frustum. Find the volume of the frustum formed (8mks)

9cm

PQRS are vertices of a rectangle centre. Given that P(5,0) and Q and R lie on the line x+5 = 2y, determine

(a) The co-ordinates of Q,R,S, (6mks)

(b) Find the equation of the diagonal SQ (2mks)

A tap A takes 3 hours to fill a tank. Tap B takes 5 hours to fill the same tank. A drain tap C takes 4 hours to drain the tank. The three taps were turned on when the tank was empty for 1½ hours. Tap A is then closed. Find how long it takes to drain the tank.

(8mks)

MATHEMATICS IV

PART II

SECTION I (52MKS)

Without using mathematical tables, evaluate (3mks)

Ö 0.0784 x 0.27 (leave your answer in standard form)

0.1875

A father is three times as old as his son. In ten years time , the son will be half as old as the father . How

old are they now? (3mks)

A,B,C,D, is a parallelogram diagram. ADE is an equilateral triangle. AB and CD are 3cm apart.

AB = 5cm. Calculate the perimeter of the trapezium ABCE (3mks)

E D C

A B

Given that a = -2, b = 3 and c = -1, Find the value of a³ – b – 2c² (2mks)

2b² – 3a²c

The exchange rate in January 2000 was US $ 1 = Ksh 75.60. and UK £1 = Ksh 115.80. A tourist came to Kenya with US $ 5000 and out of it spent ksh.189,000. He changed the balance in UK £ . How many pounds did he receive? (4mks)

ABC is a cross – section of a metal bar of uniform cross section 3m long. AB = 8cm and AC = 5cm.

Angle BAC = 60⁰ . Calculate the total surface area of the bar in M². (4mks)

The bearing of a school chapel C, from administration block A, is 250⁰ and 200m apart.

School flag F is 150m away from C and on a bearing of 020⁰. Calculate the distance and

bearing of A from F. (5mks)

A box has 9 black balls and some white balls identical except in colour. The probability of picking a white ball is ²/₃

(i) Find the number of red balls (2mks)

(ii) If 2 balls are chosen at random without replacement, find the probability that they are of different colour. (2mks)

Under an enlargement of linear scale factor 7, the area of a circle becomes 441.p

Determine the radius of the original circle. (3mks)

A circle has radius 14cm to the nearest cm . Determine the limits of its area. ( 3mks)
Expand (1 + 2x)⁵ up to the term with x³. Hence evaluate 2.04⁵ to the nearest 3 s.f. (4mks)
The n^th term of a G.P is given by 5 x 2 ^n-2

(i) Write down the first 3 terms of the G.P (1mk)

(ii) Calculate the sum of the first 5 terms (2mks)

3 bells ring at intervals of 12min, 18min and 30min respectively. If they rang together at 11.55am, when will they ring together again. (3mks)
On a map scale 1:20,000 a rectangular piece of land measures 5cm by 8cm. Calculate its actual area in hectares. (3mks)
It costs Maina shs. 13 to buy 3 pencils and 2 rubbers; while Mutiso spent shs.9 to buy one pencil and 2 rubbers. Calculate the cost of a pencil and one rubber (3mks)

Three angles of a pentagon are 110⁰, 100⁰ and 130⁰. The other two are 2x and 3x respectively. Find their values . (2mks)

SECTION II (48MKS)

Members of a youth club decided to contribute shs 180,000 to start a company. Two members withdrew their membership and each of the remaining member had to pay shs. 24,000 more to meet the same expense. How many members remained? (8mks)
A box contains 5 blue and 8 white balls all similar . 3 balls are picked at once. What is the probability that

(a) The three are white (2mks)

(b) At least two are blue (3mks)

A rectangular tennis court is 10.5m long and 6m wide. Square tiles of 30cm are fitted on the floor.

(a) Calculate the number of tiles needed. (2mks)

(b) Tiles needed for 15 such rooms are packed in cartons containing 20 tiles. How many cartons are

there in total? (2mks)

sell each carton to make 20% profit ? (4mks)

The following was Kenya`s income tax table in 1988.

Income in K£ P.a Rate (Ksh) £

1 – 2100 2

2101 – 4200 3

4201 – 6303 5

6301 – 8400 7

(a) Maina earns £ 1800 P.a. How much tax does he pay? (2mks)

(b) Okoth is housed by his employer and therefore 15% is added to salary to make taxable income. He

pays nominal rent of Sh.100 p.m His total tax relief is Shs.450. If he earns K£3600 P.a, how much

tax does he pay? (6mks)

In the given figure, OA = a , OB =b, OP: PA =3:2, OQ:QB = 3:2

B
R

O A

(a) Write in terms of a and b vector PQ (2mks)

(b) Given that AR = hAB where h is a scalar, write OR in terms h, a. and b (2mks)

(d) Calculate the value of k and h (3mks)

A transformation P = and maps A(1,3) B(4,1) and C(3,3) onto A¹B¹C¹. Find the

co-ordinates of A¹B¹C¹ and plot ABC and A¹B¹C¹on the given grid.

Transformation Q maps A¹B¹C¹onto A¹¹(-6,2) B¹¹(-2,3) and C¹¹(-6,6). Find the matrix Q and plot

A¹¹B¹¹C¹¹on the same grid. Describe Q fully. (8mks)

By use of a ruler and pair of compasses only, construct triangle ABC in which AB = 6cm,

BC = 3.5cm and AC = 4.5cm. Escribe circle centre 0 on BC to touch AB and

AC produced at P and Q respectively. Calculate the area of the circle. (8mks)

The following were marks scored by 40 students in an examination

330 334 354 348 337 349 343 335 344 355

392 341 358 375 353 369 353 355 352 362

340 384 316 386 361 323 362 350 390 334

338 355 326 379 349 328 347 321 354 367

(i) Make a frequency table with intervals of 10 with the lowest class starting at 31 (2mks)

(ii) State the modal and median class (2mks)

(iii) Calculate the mean mark using an assumed mean of 355.5 (4mks)

MATHEMATICS IV

PART 1

MARKING SCHEME

Ö – 7.939

12.3

= No log

7.939 0.8998

12.3 1.0899

T.8099 ¹/₃ = 3 + 2.8099 T.9363 3

= -0.8635

A1

Subtraction

Logs

Divide by 3

Ans

5x – 3 (3x –7 ) = 3(x – 2 )

5x – 9x + 21 = 3x – 6

-7x = -27

x = 3⁶/₇

A1

Multiplication

Removal ( )

Ans

3x +5y + x = 180

9x = 180

x = 20

y = 60

B1

Eqn

. r = 3v ¹/₃

. r = S ^½

\ 3V ¹/₃ = S ^½

4P 4P

3V = S ³/₂

4P 4P

V = 4P S ³/₂

3 4P

A1

Value r

Equation

Expression

Grad line = ¼

y – 2 = ¼

x – 5

y = ¼ x + ¾

k = ¾

P in Alloy = ⁴/₁₀ x 800

= 320g

= 100 x 320

= 3.2 kg

M 1

A 1

Equation

P in alloy

Expression

Ans

B (a,b) , C (x ,y)

.a – 2 = 5

.b – 8 -2

.a = 8 b = 6 B(8, 6 )

x – 8 = 3

y – 6 4

x = 11, y = 10 c(11,10)

A1

B conduct

Formular

80 – x

.h = x tan 70

h = (80 – x ) tan 60

\ x tan 70 = 80 tan 60-x tan 60

2.7475x + 1.732x = 138.6

4.4796 x = 138.6

.h = 138.6 x tan 60

4.4796

= 53.59

A1

Expression for h both

Equation

Expression for h

Ans

2pr = 90 x 2p x 50

360

r = 12.5

h = Ö2500 – 156.25

= Ö2343.75

= 48.41 cm

A1

Equation

expression for h

ans

10.

100 n = 302.323

n = 3.023

99n = 299.3

n = 2993

990

= 3²³/₉₉₀

A1

Equation

Ans

11.

AB = 3-1

5-9

= 2

-4

BC = 4

-8

AB = ½ BC

\ AB // BC

But B is common

\ A,B,C are collinear.

B1

A B & BC

Both

12.

4% of 200,000 = 8000/=

balance = 4200/=

6% of x = 4200/=

x = 4200 x 100

= 70,000

sales = sh. 270,000

B1

Both

Expression

Extra sales

Ans

13 .

Time = ²²/₇ x ^3.5/₂x ^3.5/₂ x 200 hrs

²²/₇x 140x140x 140x 3600

= 8960

3600

= 2 hrs 29min

A1

Vol tank

Div x 3600

Tank

14.

Ö3 = Ö3 Ö7 + Ö2

Ö7Ö2 Ö2Ö2 Ö7+ Ö2

= Ö3 Ö7 + Ö2

= Ö21 + Ö6

A1

Multi

Expression

Ans

15.

3 £ x ² x²£ 35

±1.732 £x x £ ± 5.916

1.732 £ x £ 5.916

integral x : 2, 3, 4, 5

B1

Lower limit

Upper limit

Range

Integral values

16.

No of days = ⁸/₆ x ⁵/₈ x 12

= 10 days

A1

Expression

days

17.

(i) ÐCED = ÐECD = 30

Ð CDE = 180 – 60

= 120

Ð CBE = 180-120

=60

(ii) Ð AEC = 90+30

= 120

Ð EAB = 180-(120+45)

= 15⁰

(iii) ÐBEO = 90-45

= 45

B1

ÐA EB = 45⁰

ÐBEO

18.

.ar + ar² = ⁹/₄

3r + 3r² = ⁹/₄

12r² + 12r – 9 = 0

4r² + 3r – 3 = 0

4r² + 6r – 2r –3 = 0

(2r – 1) (2r + 3) = 0

r = ½ or r = -1¹/₂

Ss = 3(1- (1/2 )⁵)

1 – ½

= 3 (1-¹²/_{3 2})

= 6 ( ³¹/₃₂)

= 6 ³¹/₃₂

A1

19.

LOG E. 0.3010 0.6021 0.7782 0.9031

LOG F 1.2068 2.1065 2.6354 3.0103

Log E =n log F + Log K

.n = gradient = 2 2.4 – 1.4 = 12 = 3

Log k. = 0.3 0.7 – 0.3 4

.k = 1.995

¾ 2

E = 2F ³

B1

Log E

Log F

Scale

Plotting

Line

Gradient

.x -2 -1 0 1 2 3 4

.y 17 6 1 6 9 22 41

.y = 3x 2 – 2x + 1 –

0 = 3x 2 – 3x – 2

y = x + 3

B1

All values

At least 5

Line

Scale

Plotting

Smooth curve

Line drawn

Value of r

21.

.h = ¾ p x 18 x 18x 18

p x 0.04 x 0.04

= 24 x 18x 18x 18

0.04 x 0.04 x 100

= 48,600m

density = ⁴/₃ x ²²/₇ x 18 x 18x 18x 15 kg

1000

= 122.2kg

A1

N of wire

¸ to length in cm

¸ for length

conversing to metres

length

expression for density

conversion to kg

ans

22.

H = Ö15² – 9²

= Ö144

= 12

^X/₆ = ⁹/₁₂

X = 4.5

Volume = ¹/₃ x ²²/₇x (81 x 12 –20.25×6 )

= ²²/₂₁ (972 – 121 -5)

= 891 cm³

A1

Method

Radius

Small vd

Large vol

Subtraction of vol.

Ans

23.

R(-a , b) , Q (c,d), S(x , y) ,P (5,0)

PR is diagonal

(a) Mid point PR (0,0)

a + 5 = 0

.a = -5

b- 0 = 0

2
b = 0

R (-5,0)

Grad PQ = -2

Grad RS = -2

.d – 0 = -2

c –5

.d – 0 = ½

c+5

.d+ 2c = 10

2d – c = 5×2 –

4d – 2c = 10

5d = 20

d = 4

c = 3

Q (3, 4)

x + 3 , y+4 = (0,0)

2 2

x = -3 , y = -4 \ s(-3 -4)

(b) y – 4 = 8

x – 3 6

3y = 8x – 12

A1

Ans .

Expression both correct

Equation

Ans

Expression

Equation

MATHEMATICS IV

PART II

MARKING SCHEME

1.	784 X 27 = 187500 Ö 784 x 9 = 4 x 7x 3 62500 250 = 42 125 = 0.336	M1 M1 A1	Factors for Fraction or equivalent C.A.O
		3
2.	Father 3x , r son = x 2(x +10) = 3x + 10 2x +20 = 3x + 10 x = 10 father = 30	M1 A1 B1	Expression
		3
3.	3 = sin 60 AE AE = 3 Sin 60 = 3.464 perimeter = 5×2 + 3.464 x 3 = 10+10.393 = 20.39	M1 A1 B1	Side of a triangle Perimeter
		3
4.	.a³ – b-2c² = (-2)³ – 3 –2(-1)² 2b² – 3a²c 2(3)²–3(-2)²(-1) = -8 –3-2 18 + 12 = -13 30	M1 M1 A1	Substitution Signs C.A.O
		3
5.	Ksh 189,000 = $ 189,000 75.6 = $ 2500 balance = $ 2500 = Kshs. 189,000 Kshs. 189,000 = 189,000 115.8 Uk ₤1632	M1 A1 M1 A1 A1 4	Conversion Conversion
6.	Area of 2 triangles = 2 (½ x 8x 5 sin 60) = 40 sin 60 = 40x 0.8660 = 34.64 cm² Area of rectangle = 300 x 8 + 300 x 5 +300 x BC BC = Ö64 +25 – 2 x 40cos 60 = Ö89 – 80 x 0.5 = Ö89 – 40 = Ö49 = 7 Total S.A. = 300 (8+5+7) + 34.64 cm² = 6000 + 34.64 = 6034.64 cm²	M1 M1 M1 A1	Areas of D B.C. expression Area
		4
7.	AF² = 3²+4²+-2+12x cos 50 = 25 – 24 x 0.6428 = 25-15.43 = 9.57 AF = 3.094 x 50 AF = 154.7m Sin Q = 200 sin 50^o 154.7 = 0.9904 Q = 82.04⁰ Bearing = 117.96⁰	M1 A1 M1 A1 B1	Bearing
		5
8.	(i) No. of white = w w = 2 w+9 3 3w = 2w + 18 w = 18 (ii) p(different colour ) = p(WB N BW) = 2 x 9 + 9 x 18 3 25 27 25 = ¹²/₂₅	M1 A1 M1 A1
		4
9.	A.sf = 1 49 smaller area = 1 x 441 p 49 = 9p pr² = 9p r² = 9 r = 3	M1 M1 A1
		3
10.	Largest area = 22 x (14.5)² 7 = 660.8 cm ² smallest area = ²²/₇ x (13.5)² = 572.8 572.8 £ A £ 660.81	M1 M1 A1
		3
11.	(1 +2 x)⁵ = 1 + 5 (2x) + 10 (2x)² + 10 (2x)³ = 1 + 10x + 40x² + 80x³ 2.045⁵ = 1+2 (0.52)⁵ = 1+10 (0.52)+ 40(0.52)²+80(0.52)³ = 1+5.2 + 10.82 + 11.25 = 28.27	M1 A1 M1 A1
		4
12.	Tn = 5x 2^{n –2} (i) T₁ , T₂, T₃ = 2.5, 5, 10 (ii) S₅ = 2.5(2⁵-1) 2-1 = 2.5 (31) = 77.5	B1 M1 A1	All terms
		3
13.	12 = 2² x 3 18 = 2 x 3² 30 = 2x3x5 Lcm = 22 x 32x 5 = 180 min = 3hrs time they ring together =11.55 +3 = 2.55 p.m	M1 A1 B1
		3
14.	Map area = 40cm ² Actual area = 200x200x40m² = 200x200x40ha 100×100 = 320ha	M1 M1 A1	Area in m² Area in ha CAO
		3
15.	3p + 2r = 13 p + 2r = 9 – 2p = 4 p = sh 2 r = 3.50	M1 A1 B1
		3
16.	110 + 100+130+2x +3x = 540 5x = 200 x = 40⁰ 2x , 3x = 80 and 120⁰ res	M1 A A1 2
17.	Contribution / person = 180,000 X New contribution = 180,000 x – 2 180,000 – 180,000 = 24,000 x –2 x 180,000x – 180,000x +360,000 = 24,000(x-2)x 24,000x² – 48,000x – 360,000 =0 x² – 2x – 15 = 0 x² – 5x + 3x – 15 = 0 x (x – 5)+ 3 (x – 5) = 0 (x + 3 )(x – 5) = 0 x = -3 or = 5 remaining members = 5-2 = 3	B1 B1 M1 M1 A1 M1 A1 B1	‘C’ eqn mult eqn factor both ans remaining members
		8
18.	(a) P (3 white) = 8 x 7 x 6 = 28 13 12 11 143 (b) P(at least 2 blue)=p(WBBorBBWorBWB)orBBB = 8 x 5 x 4 + 5 x 4 x 8 13 12 11 13 12 11 + 5 x 8 x 4 + 8 x 7 x 6 13 12 11 13 12 11 = 204 429 = 68 143 (c) p(2 white and one blue )= p(WWB or WBW or BWW) = 8 x 7 x 5 + 8 x 5 x 7 + 5 x 8 x 7 13 12 11 13 12 11 13 12 11 = 3 x 8 x 7 x 5 13 x 12 x 11 = 70 143	M1 A1 M1 M1 A1 M1 M1 A1
		8
19.	(a) recourt area = 10.5 x 6 m² title area = 0.3 x 0.3 m² No of tiles = 10.5 x 6 0.3 x 0.3 = 700 (b) No of cartons = 700 x 15 20 = 52.5 (c) Cost of 525 cartons = 525 x 100 + 800 x 525 + transport 5 = 10,500+420,000 = 430,500 sale price = 120 x 4.30,500 100 = sh 516,600 s.p of a carton = 516,600 525 = sh. 984	M1 A1 M1 A1 B1 M1 M1 A1
		8
20.	(a) Maina`s tax dues = 1800 x 10 100 = 180 (b) Taxable income = 3600 x 115 – n rent 100 = 36 x 115 – 100 x 12 20 = 4140 – 60 = 4080 Tax dues = 10 x 2100 + 15 x 1980 100 100 = 210 + 297 = 507 Tax relief = 270- Tax paid = 237	M1 A1 M1 A1 M1 M1 A1 B1	1^st slab 2^nd slab
		8
21.	(a) PQ = –³/₅ a + ³/₁b = ³¹/₂ – ³/₅ a (b) OR = h a + h b = a – ha + hb = (1-h) a + h b (c) OR = ³/₅ a + k (³¹/₂ b – ³/₅a) = (³/₅ – ³/₅k)a +3k b (d) 1 – h = ³/₅ – ³/₅k (i) 3k = h (ii) Sub (i) 1 – 3k = ³/₅ – ³/₅k 5- 15k = 3-3k 12k = 2 k = ¹/₆ h = ½	B1 M1 A1 M1 A1 M1 A1 B1
		8
22.	P(ABC) = 0 – 1 1 4 3 = -3 -1 -3 1 0 3 1 3 1 4 3 A¹ (-3,1)B¹ (-1,4)C¹(-3,3) Q(A¹B¹C¹) = a b -3 –1 -3 = -6 –2 –6 c d 1 4 3 2 8 6 => -3a + b = -6 -3c + d = 2 -a + 4b = -2 x 3 -c + 4d = 8 x 3 – 3a + 12b = -6 – 3c + 12d = 24 11b = 0 -11d = -22 b = 0 d = 2 a = 2 d = 2 c = 0 Q = 2 0 0 2	M1 A1 M1 M1 A1 B1 B1 B1	A¹ B¹ C¹ L Q A¹ B¹ C¹ drawn A^ll B^II C^II Ploted Destruction
		8
23. 24.	R = 2.2CM ± 0.1 Area = 22 x 2.2 x 2-2 7 = 15.21cm² Ef =40 efd = -80 (ii) model class = 351- 360 modern class = 341 – 350 (iii) mean = 355.5 – 80 40 = 355.5 – 2 = 353.5	B1 B1 B1 B1 B1 B1 M1 1 1 8 B1 B1 M1 A1 B1 B1 B1 B1
		A1
		8

MATHEMATICS V

PART I

SECTION 1 (52 MARKS)

Use logarithms to evaluate 6 Cos 40 ^0.25
63.4 (4mks)
Solve for x in the equation (x + 3) ²– 5 (x + 3) = 0 (2mks)
In the triangle ABC, AB = C cm. AC = bcm. ÐBAD = 30^o and ÐACD = 25^o. Express BC in terms of b and c. (3mks)
Find the equation of the normal to the curve y = 5 + 3x – x³ when x = 2 in the form
ay + bx = c (4mks)
Quantity P is partly constant and partly varies inversely as the square of q. q= 10 and p = 5 ½ when q =20. Write down the law relating p and q hence find p when qs is 5. (4mks)
Solve the simultaneous equation below in the domain 0 £ x £ 360 and O£ y £ 360
2 Sin x + Cos y = 3
3 Sin x – 2 Cos y = 1 (4mks)
Express as single factor 2 – x + 2 + 1
x + 2 x² + 3x + 2 x + 1 (3mks)
By use of binomial theorem, expand (2 – ½ x )⁵ up to the third term, hence evaluate (1.96)⁵
correct to 4 sf. (4mks)
Points A(1,4) and B (3,0) form the diameter of a circle. Determine the equation of the circle and write it in the form ay² + bx² + cy + dy = p where a, b, c, d and p are constants. (4mks)
The third term of a GP is 2 and the sixth term is 16. Find the sum of the first 5 terms of the GP. (4mks)
Make T the subject of the formulae 1 – 3m + 2
T² R N (3mks)
Vectors, a = 2 b = 2 and c – 6
2 0 4
By expressing a in terms of b and c show that the three vectors are linearly dependent. (3mks)
A cylindrical tank of base radius 2.1 m and height is a quarter full. Water starts flowing into this tank at 8.30 a.m at the rate of 0.5 litres per second. When will the tank fill up? (3mks)
A piece of wood of volume 90cm³ weighs 54g. Calculate the mass in kilograms of 1.2 m³ of the wood. (2mks)
The value of a plot is now Sh 200,000. It has been appreciating at 10% p.a. Find its value 4 years ago.
(3mks)
12 men working 8 hours a day take 10 days to pack 25 cartons. For how many hours should 8 men be

working in a day to pack 20 cartons in 18 days? (2mks)

SECTION II (48MARKS)

The tax slab given below was applicable in Kenya in 1990.
Income in p.a.                           rate in sh
1 – 1980                                  2
1981 – 3960                              3
3961 – 5940                              5
5941 – 7920                              7
Maina earns Sh. 8100 per month and a house allowance of Sh. 2400. He is entitled to a tax relief of Sh.

800 p.m. He pays service charge of Sh 150 and contributes Sh 730 to welfare. Calculate Mwangis net

salary per month. (8mks)

OAB is a triangle with OA = a , OB = b. R is a point of AB. 2AR = RB. P is on OB such that
3OP = 2PB. OR and AP intersect at Y, OY = m OR and AY = nAP. Where m and n are scalars.    Express in terms of a and b.
(i) OR                                                                                                                    (1mk)
(ii)AP                                                                                                                    (1mk)
(b) Find the ratio in which Y divides AP                                                                (6mks)
The table below gives related values of x and y for the equation y = axⁿ where a and n are constants

X	0.5	1	2	3		10
Y	2	8	32		200	800

By plotting a suitable straight line graph on the graph provided, determine the values of a and n.

20. Chalk box x has 2 red and 3 blue chalk pieces. Box Y has same number of red and blue

pieces. A teacher picks 2 pieces from each box. What is the probability that
(a)        They are of the same colour.                                                                            (4mks)
(b)        At least one is blue                                                                                           (2mks)
(c)        At most 2 are red                                                                                              (2mks)

21. Point P(50^oN, 10^oW) are on the earth’s surface. A plane flies from P due east on a parallel of

latitude for 6 hours at 300 knots to port Q.
(a) Determine the position of Q to the nearest degree. (3mks)
(b) If the time at Q when the plane lands is 11.20am what time is it in P. (2mks)
(c) The plane leaves Q at the same speed and flies due north for 9 hours along a longitude to

airport R. Determine the position of R.                                                                       (3mks)
22.       Using a ruler a pair of compasses only, construct :
(a)        Triangle ABC in which AB = 6cm, AC = 4cm and Ð ABC = 37.5^o.                                (3mks)
(b)        Construct a circle which passes through C and has line AB as tangent to the circle at A.             (3mks)
(c)        One side of AB opposite to C, construct the locus of point P such that ÐAPB = 90^o.             (2mks)
23.       A particle moves in a straight line and its distance is given by S = 10t² – t³ + 8t where S is

distance in metres at time t in seconds.
Calculate:
(i) Maximum velocity of the motion.                                                                             (4mks)
(ii) The acceleration when t = 3 sec.                                                                              (2mks)
(iii) The time when acceleration is zero.                                                                                   (2mks)

A rectangle ABCD has vertices A(1,1) B(3,1), C(3,2) and D(1,2). Under transformation

matrix M = 2 2 ABCD is mapped onto A¹B¹C¹D¹

1 3
under transformation M = -1 0 A¹B¹C¹D¹ is mapped onto A¹¹B¹¹C¹¹D¹¹. Draw on the given grid
0 –2

(a)       ABCD, A¹B¹C¹D¹ and A¹¹B¹¹C¹¹D¹¹                                                                  (4mks)
(b)        If area of ABCD is 8 square units, find area of A¹¹B¹¹C¹¹D¹¹.                              (3mks)
(c)        What single transformation matrix maps A¹¹B¹¹C¹¹D¹¹ onto A¹B¹C¹D¹               (1mk)

MATHEMATICS V

PART II

SECTION 1 (52 Marks)

Evaluate without using mathematical tables (2.744 x 15 ⁵/₈)¹/₃ (3mks)
If 4 £ x £ 10 and 6 £ y £5, calculate the difference between highest and least
(i) xy (2mks)
(ii) ^y/_x (2mks)
A 0.21 m pendulum bob swings in such a way that it is 4cm higher at the top of the swing than at the bottom. Find the length of the arc it forms. (4mks)
Matrix 1 2x has on inverse, determine x (3mks)
x +3 x²
The school globe has radius of 28cm. An insect crawls along a latitude towards the east from A(50^o, 155^oE) to a point B 8cm away. Determine the position of B to the nearest degree. (4mks)
The diagonals of triangle ABCD intersect at M. AM = BM and CM = DM. Prove that triangles ABM and CDM are Similar. (3mks)
Given that tan x = ⁵/₁₂, find the value of 1 – sinx
Sin x + 2Cos x, for 0 £ x £ 90 (3mks)

Estimate by MID ORDINATE rule the area bounded by the curve y = x² + 2, the x axis and the lines x = O and x = 5 taking intervals of 1 unit in the x. (3mks)
MTX is tangent to the circle at T. AT is parallel to BC. Ð MTC = 55^o and Ð XTA = 62^o. Calculate Ð (3mks)
Clothing index for the years 1994 to 1998 is given below.

Year	1994	1995	1996	1997	1998
Index	125	150	175	185	200

Calculate clothing index using 1995 as base year. (4mks)

A²digit number is such that the tens digit exceeds the unit by two . If the digits are reversed, the number formed is smaller than the original by 18. Find the original number. (4mks)
Without using logarithm tables, evaluate log₅ (2x-1) –2 + log₅ 4 = log₅ 20 (3mks)
Mumia’s sugar costs Sh 52 per kg while imported sugar costs Sh. 40 per kg. In what ratio should I mix the sugar, so that a kilogram sold at Sh. 49.50 gives a profit of 10%. (4mks)
The interior angles of a regular polygon are each 172^o. Find the number of sides y lie polygon. (2mks)
Evaluate 2x = 2 + 3
341 9.222 (2mks)
A water current of 20 knots is flowing towards 060^o. A ship captain from port A intends to go to port

B at a final speed of 40 knots. If to achieve his own aim, he has to steer his ship at a course of 350^o.

Find the bearing of A from B. (3mks)

SECTION II (48 MARKS)

3 taps, A, B and C can each fill a tank in 50 hrs, 25 hours and 20 hours respectively. The three taps are turned on at 7.30 a.m when the tank is empty for 6 hrs then C is turned off. Tap A is turned off after four hours and 10 minutes, later. When will tap B fill the tank? (8mks)
In the domain –5 £ x £ 4, draw the graph of y = x² + x – 8. On the same axis, draw the graph of y + 2x = -2. Write down the values of x where the two graphs intersect. Write down an equation in x whose roots are the points of intersection of the above graphs. Use your graph to solve. 2x² + 3x – 6 = 0. (8mks)
The average weight of school girls was tabulated as below:

Weight in Kg	30 – 34	35 – 39	40 – 44	45 – 49	50 – 54	55-59	60-64
No. of Girls	4	10	8	11	8	6	3

(a) State the modal class.                                                                                           (1mk)
(b) Using an assumed mean of 47,
(i) Estimate the mean weight                                                                                (3mks)
(ii) Calculate the standard deviation.                                                                      (4mks)

The table below shows values of y = a Cos (x – 15) and y = b sin (x + 30)

X	0	15	30	45	60	75	90	105	120	135	150
a Cos(x-5)	0.97				0.71	0.5				-0.5	-0.71
b sin(x+3)	1.00				2.00				1.00		0.00

(a) Determine the values of a and b                                                                               (2mks)
(b) Complete the table                                                                                                  (2mks)
(c) On the same axes draw the graphs of y = across(x – 15) and y = b sin(x + 30)            (3mks)
(d) Use your graph to solve ½ cos (x – 15) = sin(x + 30)                                                 (1mk)

21. The diagram below is a clothing workshop. Ð ECJ = 30^o AD, BC, HE, GF are vertical

walls. ABHG is horizontal floor. AB = 50m, BH = 20m, AD=3m

(a) Calculate DE                                                                                                           (3mks)
(b) The angle line BF makes with plane ABHG                                                              (2mks)
(c) If one person requires minimum 6m³ of air, how many people can fit in the workshop         (3mks)

To transport 100 people and 3500 kg to a wedding a company has type A vehicles which take 10 people and 200kg each and type B which take 6 people and 300kg each. They must not use more

than 16 vehicles all together.
(a) Write down 3 inequalities in A and B which are the number of vehicles used and plot them

in a graph. (3mks)
(b) What is the smallest number of vehicles he could use. (2mks)

hire charge for the whole function (3mks)

A circle centre A has radius 8cm and circle centre B has radius 3cm. The two centres are

12cm apart. A thin tight string is tied all round the circles to form interior common tangent. The tangents CD and EF intersect at X.

(a) Calculate AX (2mks)
(b) Calculate the length of the string which goes all round the circles and forms the tangent.
(6mks)

Airport A is 600km away form airport B and on a bearing of 330^o. Wind is blowing at a speed of

40km/h from 200^o. A pilot navigates his plane at an air speed of 200km/h from B to A.
(a)     Calculate the actual speed of the plane.                                                                (3mks)
(b)     What course does the pilot take to reach B?                                                          (3mks)
(c)     How long does the whole journey take?                                                                (2mks)

MATHEMATICS V

PART I

MARKING SCHEME

1	SOLUTION	MKS	AWARDING
	No Log 13.6 1.1335 + Cos 40 1.8842 1.0177 – 63.4 1.8021 1. 2156 (4 + 3.2156) ¹/₄ 1.8039 Antilog 0.6366	B1 M1 M1 A1	Log + divide by 4 C.A.O
		4
2.	(x + 3) (x + 3 – 5) = 0 (x +3)b (x – 2) = 0 x = -3 or x = 2	M1 A1	Factors Both answers
3	BD = C Sin 30 = 0.05 CD = b Cos 25 = 0.9063b BC = 0.9063b + 0.5 C	B1 B1 B1	BD in ratio from CD in ratio form Addition
		3
4	Dy = 3 – 3x² dx x = 2, grad = 1 9 Point (2,3) y – 3 = 1 x – 2 9 9y – 27 = x – 2 9y – x = 25	B1 B1 M1 A1	Grad equ Grad of normal Eqn Eqn
		4
5	700 = 100 + n 2200 = 400 + n 1500 = 300m m = 5 n = 200 P = 5 + 200 q2 When q = 5 P = 13	M1 A1 B1 B2	Equan Both ans Eqn (law) Ans (P)
		4
6	4 Sin x + 2 cos y = 6 3 Sin x – 2 Cos y = 1 7 sin x = 7 Sin x = 1 X = 90 Cos y = 1 Y = 0^o	M1 M1 A1 B1	Elim Sub
7	2(x +1) – 1(x + 2) + x + 2 (x+2) (x +1) = 2x +2 – x – 2 + x = 2 (x +2) (x + 1) = 2x + 2 (x + 2) (x + 1) = 2 x + 2	M1 M1 A1	Use of ccm Substitution Ans
8	(-2 – ½ x)5 = 2⁵ – 5 (2)⁴ ( ½ x) + 10(2)³( ½ x)² = 32 – 40x + 20x² = 32 – 4 (0.08) + 20 (0.08)² = 32 – 0.32 + 0.128 = 3	M1 A1 M1 A1
		4
9.	Circle centre C = (3 +1, 0 + 4) 2 2 C( 2, 2) R =Ö (2 – 0)² + (2 – 3)² =Ö 5 (y – 2)² + (x – 2)² = Ö5 y² + x²– 4y – 4x = 8 + Ö5	B1 B1 M1 A1	Centre Radius
		4
10	ar² =2, ar⁵ = 16 a = 2 \ 2 r⁵ = 16 r² r² 2r³ = 16 r³ = 8 r = 2, a = ½ S₅= ½ (1 – ( ½ )⁵) ½ = 1 – ¹/₃₂ = ³¹/₃₂	M1 A1 M1 A1	Both Sub CAO
		4
11	NR – 3MT² = 2RT² T²(2R + 3M) = NR T2 = NR 2R + 3m T = ! Ö NR 2R + 3m	M1 M1 A1	X mult 7² ans
		3
12	2 = m 2 + n 6 2 0 4 2 = 2m + 6n 2 = 0 + 4n n = ½ m = – ½ \a = – ½ b + ½ c \a b c are linearly dep	M1 A1 B1
		3
13	Volume = 22 x 2.1 x 2.1 x 2 x ¾ m³ 7 Time = 11 x 0.3 x 2.1 x 3 x 1,000,000 500 x 3600 = 11.55 = 11.33 hrs time to fill = 8.03 pm	M1 M1 A1
		3
14	Mass = 54 x 1.2 x 1,000,000 90 1000 = 720kg	M1 A1
		2
15	V₃ = P P(0.9)³ = 200,000 P = 200,000 0.9³ = 200,000 0.729 = Sh 274,348	M1 M1 A3
		3
16	No of hours = 8 x 12 x10 x 20 8 x 18 x 25 = 19200 3600 = 5hrs, 20 min	M1 A1
		2
17	Taxable income = 8100 + 2400 = sh. 10,500 = ₤6300 Tax dues = Sh 1980 x 2 + 1980 x 3 + 1980 x 5 + 3670 x 7 12 = 22320 12 = Sh 1860 net tax = 1860 – 800 p.m. = Sh 1060 Total deduction = 1060 + 150 + 730 = 1940 Net salary = 10,500 – 1940 = Sh 8560 p.m.	B1 M1 M1 A1 B1 B1 M1 A1	Tax inc 2 2 net tax total dedu.
		8
18	OR = ²/₃ a + ¹/₃b or (¹/₃ (2a + b) AP = ²/₅ b – a OY = m OR = A + n (²/₅b – a) ²/₅m b + ma = (1 – n)a + ²/₅ n b ²/₅m = ²/₅n m = n \m = 1 – m 2m = 1 m = ½ = n ½ AP = Ay AY:AP = 1:1	B1 B1 B1 M1 M1 A1 A1 B1	EXP, OY Eqn M = n Sub CAO Ratio
		8
19	Log y = n log x + log a Log a = 0.9031 A = 8 Grad = 1.75 – 0.5 0.4 + 0.2 = 1.25 0.6 = 2.08 n = 2 \y = 8x² x = 3 y = 8 x 3² = 72 y = 200 x = 5	B1 B1 B1 B1 B1 S1 P1 L1	Log x Log y A N Missing x and y Scale Points Line
		8
20	P (same colour) = P (XRRrr orXBB or YXX or YBB) = ½ (²/₅ x ¼ + ³/₅ x ²/₄) x 2 = 2 + 6 20 20 = 8 20 = ²/₅ (b) P(at least 1B) = 1 – P(non blue) = 1 – P (XRR or YRR) = 1 – ½ (²/₅ x ^¼) x 2 = 1 – ¹/₁₀ = ⁹/₁₀ (c) P(at most 2 Red) = 1 – P (BB) = 1 – ½ (³/₅ x ²/₄)² = 1 – ⁶/₂₀ = ¹⁴/₂₀ or ⁷/₁₀	M1 M1 M1 A1 M1 A1 M1 A1	Any 2 Any 2 Fraction
		8
21	(a) PQ = 1800nm q = 1800 60 x 0.6428 = 46.67 = 47^o Q (50^oN, 37^oE) (b) Time diff = 47 x 4 60 = 3.08 Time at P = 9.12am (c) QR = 2700 nm x ^o = 2700 60 = 45^o R (85^oN, 133^oW)	M1 A1 M1 A1 M1 A1 B1
		8
22		B1 B1 B1 B1 B1 B1 B1 B1	Bisector of 150 Bisector 75 AB AC ^ at A Bisector AC Circle Ð AB Locus P with A B excluded
		8
24	A¹B¹ C¹D¹ 2 2 1 3 3 1 = 4 8 10 6 1 3 1 1 2 2 4 6 9 7 A¹¹ B¹¹ C¹¹ D¹¹ -1 0 4 8 10 6 = -4 –8 -10 -6 0 –2 4 6 9 7 -8 -12 -18 -14 NM = -1 0 2 2 0 –2 1 3 = -2 -2 -2 -6 (b) det = Asf = 12 – 4 = 8 Area A¹¹ B¹¹ C¹¹ D¹¹ = 8 x 8 = 64 U² (c) Single matrix = Inv N = ½ -2 – 0 0 –1 = -1 0 0 – ½	B1 B1 B1 M1 A1 B1	Product Product Det Inverse
		6
23	Ds = 20t – 3t² + 8 =0 Dt 3t²– 20t – 8 = 0 T = 20 ! Ö400 + 4 x 3 x 8 6 t = 7.045 sec max vel = 148.9 – 140.9 – 8 = 0.9 m/s d² s = 6t – 20 dt² when t = 3 a = -2m/s² 6t – 20 = 0 6t = 20 t = 3 ²/₃ sec	M1 A1 M1 A1 M1 A1 M1 A1
		8

MATHEMATICS V

PART II

MARKING SCHEME

No	Solution	Mks	Awarding
1	2744 x 125 ¹/₃ 1000 8 2744 ¹/₃ x 5^{3 1}/₃ 1000 2³ 2³ x 7³ ¹/₃ x 5 103 2 2 x 7 x 5 = 3.5 10 2	M1 M1 A1	Factor Cube root
		3
2	(i) Highest – 10 x 7.5 = 75 Lowest – 6 x 4 = 24 – 51 (ii) Highest = 7.5 = 1.875 4 Lowest = 6 = 0.600 10 1.275	M1 A1 M1 A1	Highest Fraction
		4
3	Cos q = 17 = 0.8095 21 q = Cos 0.8095 = 36.03^o Arc length = 72. 06 x 2 x 22 x 21 360 7 = 26.422cm	M1 A1 M1 A1	q
		4
4	x² – 2x(x +3) = 0 x² – 2x² – 6x = 0 -x² – 6x = 0 either x = 0 or x = 6	M1 M1 A1	Equ Factor Both A
		3
5	8 = x x 2 x 22 x 28 Cos 60^o 360 7 8 = x x 44 x 28 x 0.5 360 7 x = 8 x 360 x 7 44 x 28 x 0.5 = 32.73^o = 33^o	M1 M1 A1 B1	x exp
6	ÐDMC = Ð AMB vert. Opp = q ÐMAB = Ð MDC = 180 – q BASE Ls of an isosc. < 2 Ð MBA = Ð MAC 180 – q base angles of isos < 2 <’s AMC and < CDM are equiangle \ Similar proved	B1 B1 B1
		3
7	Tan x = ⁵/₁₂ h = Ö b² + 12² = Ö25 + 144 = Ö169 = 13 1 – Sinx = 1 – 5 sin x + 2 Cos x ⁵/₁₃ + 2 x ¹²/₁₃ ¹²/₁₃ = 12 x 13 = 12 ²⁹/₁₃ 13 29 29	M1 M1 A1	Hypo Sub
		3
8	Y = x ² + 2 Area = h (y₁, = y₂ +……..y_n) = 1(2.225 + 4.25 + 8.25 +14.25 + 22.25) = 51.25 sq units	B1 M1 A1	Ordinals
		3
9	ÐCBA = 117^o Ð ACD = 55 Ð BAC = 180 – (117 + 55) = 8^o	B1 B1 B1 3
10		B1 B1 B1 B1	1994 1996 1997 1998
		4
11.	Xy = 35 y = ³⁵/_x 9x – 9y = -18 Sub x² + 2x – 35 = 0 x² + 7x – 5x – 35 = 0 x (x + 7) – 5(x + 7) = 0 (x – 5) (x + 7) = 0 x = -7 x = +5 y = 7 Smaller No. = 57 = 75	B1 M1 A1 B1
		3
12	Log₅ (2x – 1 )4 = log₅5² 20 4(2x – 1) = 5² 20 2x – 1 = 25 5 2x – 1 = 125 2x = 126 x = 63	M1 M1 A1
		3
13	C.P = 100 x 49.50 110 = 45/- 52x + 40y = 45 x + y 45x + 45y = 52x + 40 -7x = -54 ^x/_y = ⁵/₇ x : y = 5 : 7	B1 M1 M1 A1
		4
14	2n – 4 it angle = 172 n (2n – 4) x 90 = 172n n 90 (2n – 4) x 90 = 172 n 180 n – 360 = 172n 180n – 172n = 360 8n = 360 n = 45	M1 A1 M1
		2
15	2 x = 2. 1 + 3. 1 6.341 9.22 2x = 2 x 0. 1578 + 3 x 0.1085 = 0.3154 + 0.3254 = 0.6408 x = 0.3204	B1 A1	Tables
		2
16	Bearing 140^o Sin q = 20 Sin 110 40 = 0.4698 = 228.02 Bearing of A from B = 198.42	M1 A1 B1
		3
17	Points that each tap fills in one hour A = 1 B = 1 C – 1 50 25 20 In one hour all taps can fill = 1 + 1 + 1 = 11 50 25 20 100 In 6hrs all can fill = 11 x 6 = 33 parts 100 50 taps A and B can fill = = 1 + 1 = 3 part in 1 hr 50 25 50 In 4 1 hrs, A and B = 25 x 3 + 1 6 6 50 4 Parts remaining for B to fill = 1 – 33 + 1 = 1 – 91 = 9 parts 50 4 100 100 Time taken = 9 x 25 hrs = 2 ¼ hrs 100 1 7.30 am 6. hrs 13.30 4.10 5.40pm 2.15 7.55 pm	M1 B1 B1 B1 M1 A1
18	x² + x – 8 = -2 – 2x y = x² + 3x – 6 Points of intersection (-4, 1.4) y = x² + x – 8 = 2x² + 3x – 6 x² + 2x + 2 y = x² + x – 8 x 2 2y = 2x² + 2x – 16 0 = 2x² + 3x – 6 2y = -x – 10 y = – 2.6 Ny = 1.2	8 B1 B1 B1 B1	Eqn Point of inter Line eqn Both
19	(a) Modal class = 45 – 49 (i) Mean = 47 + -55 50 = 47 – 1.1 = 45.9 (ii) Standard deviation = Ö 3575 – –55 ² 50 50 = Ö71.5 – 1.21 =Ö 70.29 = 8.3839	4 B1 B1 M1 A1 B1	fd fd²
		8
20	(a) a = 1 b = 2 ½ cos (x – 15) = Sin (x + 30) has no solution in the domain	B1 B1 B1 B1	All All A & b
		8
21	(a) O Cos 30 = 20 X X = 20 0.866 = 23.09 DE = Ö 50² + 23.09² = Ö 2500 + 533.36 = Ö 3033.36 = 55.076m (b) GB = Ö 20² + 50² = 53.85 Tan q = 14.55 53.85 = 0.27019 q = 15.12^o	B1 M1 A1 M1 A1
		8
	(c) Volume of air = 50 x 20 x 3 + ½ x 20 x 11.55 x 50 = 3000 + 5775 = 8775 No. of people = 8775 6 = 1462.5 j 1462	M1 M1 A1
		8
22	(a) A + B [ 16 5A + 3B ³ 50 2A + 3B [ 35 (b) 14 vehicles (c) A – 6 vehicles B – 8 Cost = 6 x 1000 + 8 x 1200 = 6000 + 9600 = 15,600/=	B1 B1 B1 M1 A1	In equation 3 Vehicles
		8
23	x = 8 12 – x 3 = 8.727 FBX = 3 = 0.9166 = 23.57 3.273 3FBX = 47.13 Reflex Ð FBD = 312.87 Reflex arc FD = 312.87 x 22 x 6 360 7 = 16.39cm Reflex Arc CE = 312.87 x 22 x 16 360 7 = 43.7cm FE (tangent) = Ö144 – 121 = Ö 23 = 4.796cm 2 FE = 9.592 Total length = 9.592 + 4.796 + 43.7 + 16.39 = 74.48 cm²	M1 A1 M1 A1 M1 A1 M1 A1
		8
24	(a) 200 = 40 Sin 50 Sin q Sin q = 40Sin 50 200 = 0.7660 5 =0.1532 q = 8.81^o Ð ACB = 180 – (50 + 8.81)^o = 121.19^o x = 200 Sin 121.19 Sin 50 x = 200 x Sin 121.19 Sin 50 = 200 x 0.855645 0.7660 = 223.36Km/h (b) Course = 330^o – 8.81^o = 321.19^o (c) Time = 600 321.19^o = 2.686 hrs	M1 A1 M1 M1 A1 B1 M1 A1 8

MATHEMATICS VI

PART I

SECTION I (52 MARKS)

Evaluate without mathematical tables leaving your answer in standard form

0.0171² X 3

855 X 0.531 (2 Mks)

Six men take 14 days working 8 hours a day to pack 2240 parcels. How many more men working

5 hours a day will be required to pack 2500 parcels in 2 days (3 Mks)

M In quadrilateral OABC, OA = 4i – 3j. OC = 2i + 7j

AB = 3OC. cm: mB = 2:3. Find in terms of i and j

C vector Om (3 Mks)

O A

By matrix method, solve the equations

5x + 5y = 1

4y + 3x = 5 (3 Mks)

In the given circle centre O, ÐABC = 126⁰.

Calculate ÐOAC (3 Mks)

A C

Solve the equation

2(3x – 1)²_– 9 (3x – 1) + 7 = 0 (4 Mks)

Maina, Kamau and Omondi share Shs.180 such that for every one shilling Maina gets, Kamau gets 50

Cts and for every two shillings Kamau gets, Omondi gets three shillings. By how much does Maina’s

share exceed Omondi’s (3 Mks)

Expand (2 + ¹/₂x)⁶ to the third term. Use your expression to evaluate 2.4⁶ correct to 3 s.f (3 Mks)
The probability of failing an examination is 0.35 at any attempt. Find the probability that

(i) You will fail in two attempts (1 Mk)

(ii) In three attempts, you will at least fail once (3 Mks)

Line y = mx + c makes an angle of 135⁰with the x axis and cuts the y axis at y = 5. Calculate the

equation of the line (2 Mks)

During a rainfall of 25mm, how many litres collect on 2 hectares? (3 Mks)
Solve the equation a – 3a – 7 = a – 2 (3 Mks)

3 5 6

The sum of the first 13 terms of an arithmetic progression is 13 and the sum of the first 5 terms is

–25. Find the sum of the first 21 terms (5 Mks)

The curved surface of a core is made from the shaded sector on the circle. Calculate the height of

the cone. (4 Mks)

20cm 125⁰ 20 cm

Simplify (wx – xy – wz + yz) (w + z) (3 Mks)

z² – w²

The bearing of Q from P is North and they are 4 km apart. R is on a bearing of 030 from P and on

a bearing of 055 from Q. Calculate the distance between P and R. (3 Mks)

SECTION II (48 MARKS)

In the given circle centre O, ÐQTP = 46⁰, ÐRQT = 74⁰ and ÐURT = 39⁰

U T P

S 39⁰

Calculate R

(a) ÐRST (1 Mk)

(b) ÐSUT (3 Mks)

(d) ÐPST (2 Mks)

The exchange rate on March 17th 2000, was as follows: –

1 US$ = Kshs.74.75

1 French Franc (Fr) = Kshs.11.04

A Kenyan tourist had Kshs.350,000 and decided to proceed to America

(a) How much in dollars did he receive from his Kshs.350,000 in 4 s.f? (2 Mks)

(b) The tourist spend ¼ of the amount in America and proceeded to France where he spend Fr

16,200. Calculate his balance in French Francs to 4 s.f (3 Mks)

Kshs. does he receive for his balance than he would have got the day he left? (3 Mks)

On the provided grid, draw the graph of y = 5 + 2x – 3x² in the domain -2 £ x £ 3 (4 Mks)

(a) Draw a line through points (0,2) and (1,0) and extend it to intersect with curve y = 5 + 2x – 3 x 2

read the values of x where the curve intersects with the line (2 Mks)

(b) Find the equation whose solution is the values of x in (a) above (2 Mks)

(a) Using a ruler and compass only, construct triangle PQR in which PQ = 3.5 cm, QR = 7 cm

and angle PQR = 30⁰ (2 Mks)

(b) Construct a circle passing through points P, Q and R (2 Mks)

The given Region below (unshaded R) is defined by a set of inequalities. Determine the inequalities (8 Mks)

2 R (3,3)

-3 5

The table below shows the mass of 60 women working in hotels

Mass (Kg)	60 – 64	65 – 69	70 – 74	75 – 79	80 – 84	85 – 89
No. of women	8	14	18	15	3	2

(a) State (i) The modal class (1 Mk)

(ii) The median class (1 Mk)

(b) Estimate the mean mark (4 Mks)

XY, YZ and XZ are tangents to the circle centre O

at points A, B, C respectively. XY = 10 cm,

YZ = 8 cm and XZ = 12 cm. (2 MKS)

.. B

A Y

(a) Calculate, length XA (2 Mks)

(b) The shaded area (6 Mks)

Maina bought a car at Kshs.650,000. The value depreciated annually at 15%

(a) After how long to the nearest 1 decimal place will the value of the car be Kshs.130,000 (4 Mks)

(b) Calculate the rate of depreciation to the nearest one decimal place which would make the value of

the car be half of its original value in 5 years (4 Mks)

MATHEMATICS VI

PART II

SECTION 1 (52 MARKS)

Simplify 32a¹⁰ ^-2/₅ ÷ 9b⁴ ^11/₂

b¹⁵ 4a⁶ (2 Mks)

Use logarithm tables to evaluate

Ö0.375 cos 75

tan 85.6 (4 Mks)

The marked price of a shirt is Shs.600. If the shopkeeper gives a discount of 20% off the marked price, he makes a loss of 4%. What was the cost of the shirt? (3 Mks)
The surface area (A) of a closed cylinder is given by A = 2pr² + 2prh where r is radius and h is height of the cylinder. Make r the subject. (4 mks)
In the circle centre O, chords AB and CD intersect at X. XD = 5 cm

XC = 1/4 r where r is radius. AX:XO = 1:2 Calculate radius of the circle. (3 mks)

A 5cm D

C O

Simplify 2 – 1 (3 mks)

5 – 2Ö3 5 + 2Ö3

P is partly constant and partly varies as q2. When q = 2, P = 6 and when q = 3, P = 16. Find q when P = 64 (4 mks)
The figure on the side is a tent of uniform cross-section A F

ABC. AC = 8m, BC = 8m, BD = 10m and (ACB = 120⁰. 8m

If a scout needs 2.5 m³ of air, how many scouts can fit 120^o C E

in the tent. 8m (4 mks)

B D

10m

The length of a rectangle is given as 8 cm and its width given as 5 cm. Calculate its maximum % error in its perimeter (3 mks)
ABCD is a rectangle with AB = 6 cm, BC = 4 cm AE = DH = 4 cm BF = CG = 12 cm. Draw a

labelled net of the figure and show the dimensions of the net

Expand (1 + 2x)⁶ to the 3rd term hence evaluate (1.04)⁶ (4 mks)
The eye of a scout is 1.5m above a horizontal ground. He observes the top of a flag post at an

angle of elevation of 20⁰. After walking 10m towards the bottom of the flag post, the top is observed at angle of elevation of 40⁰. Calculate the height of the flag post (4 mks)

A bottle of juice contains 405ml while a similar one contains 960ml. If the base area of the

larger Container is 120 cm². Calculate base area of the smaller container. (3 mks)

It takes a 900m long train 2 minutes to completely overtake an 1100m long train travelling at

30km per hour. Calculate the speed of the overtaking train (3 mks)

Okoth traveled 22 km in 2³/₄ hours. Part of the journey was at 16 km/h and the rest at 5 km/h.

Determine the distance at the faster speed (3 mks)

P and Q are points on AB such that AP:PB = 2:7 and AQ:QB = 5:4 If AB = 12 cm, find PQ

(2 Mks)

SECTION B (48 MARKS)

The income tax in 1995 was collected as follows:

Income in Kshs. p.a rate of tax %

1 – 39,600 10

39,601 – 79,200 15

79,201 – 118,800 25

118,801 – 158,400 35

158,401 – 198,000 45

Mutua earns a salary of Kshs.8,000. He is housed by the employer and therefore 15% is added to his salary to arrive at its taxable income. He gets a tax relief of Shs.400 and pay Shs.130 service charge. Calculate his net income (8 Mks)

The probability Kioko solves correctly the first sum in a quiz is ²/₅ Solving the second correct

is ³/₅ if the first is correct and it is ⁴/₅ if the first was wrong. The chance of the third correct is

²/₅ if the second was correct and it is ¹/₅ if the second was wrong. Find the probability that

(a) All the three are correct (2 Mks)

(b) Two out of three are correct (3 Mks)

A businessman bought pens at Shs.440. The following day he bought 3 pens at Shs.54. This

purchase reduced his average cost per pen by Sh.1.50. Calculate the number of pens bought earlier and the difference in cost of the total purchase at the two prices (8 mks)

In D OAB, OA = a, OB = b

OPAQ is a parallelogram.

ON:NB = 5:-2, AP:PB = 1:3

Determine in terms of a and b vectors

(a) OP (2 Mks)

(b) PQ (2 Mks)

(d) PN (2 mks)

A cylindrical tank connected to a cylindrical pipe of diameter 3.5cm has water flowing at 150

cm per second. If the water flows for 10 hours a day

(a) Calculate the volume in M³ added in 2 days (4 ms)

(b) If the tank has a height of 8 m and it takes 15 days to fill the tank, calculate the base radius

of the tank (4 mks)

A joint harambee was held for two schools that share a sponsor. School A needed Shs.15 million while

School B needed 24 million to complete their projects. The sponsor raised Shs.16.9 million while other

guest raised Shs.13.5 million.

(a) If it was decided that the sponsor’s money be shared according to the needs of the school

with the rest equally, how much does each school get (5 mks)

(b) If the sponsor’s money was shared according to the schools needs while the rest was in the ratio of

students, how much does each school get if school A has 780 students and school B 220

students (3 mks)

Voltage V and resistance E of an electric current are said to be related by a law of the form

V = KEⁿ where k and n are constants. The table below shows values of V and E

V	0.35	0.49	0.72	0.98	1.11
E	0.45	0.61	0.89	1.17	1.35

By drawing a suitable linear graph, determine values of k and n hence V when E = 0.75(8mks)

The vertices of triangle P,Q,R are P(-3,1), Q (-1,-2), R (-2,-4)

(a) Draw triangle PQR and its image P^IQ^IR^I of PQR under translation T = 3 on the provided grid 4 (2 Mks)

(b) Under transformation matrix m = 4 3 , P^IQ^IR^I is mapped on to P^IIQ^IIR^II. Find the

co-ordinates of P^IIQ^IIR^II and plot it 1 2 on the given grid (4 Mks)

MATHEMATICS VI

PART 1

MARKING SCHEME

171 X 171 X 3 X 10^-5 M1

855 X 531

= 2 X 10^-6 A1

No. of men = 6 X 14 X 8 X 2500 M1

2 X 5 X 2240

= 75 A1

Extra men = 75 – 6 = 69 B1

OM = 2i + 7j + 2/5 (4i – 3j + 6i + 21j – 2i – 7j) M1

= 2i + 7j + 2/5 (8i + 11j) M1

= 26 i + 57 j

5 5 A1

2 5 x = 1

3 4 y 5 M1

x ^-1/₇ ⁵/₇ 1

y = ³/₇ ^-2/₇ 5 M1

x = 3

y -1

x, 3, y = -1 A1

Reflex ÐAOC = 126 x 2 = 252⁰ B1

Obtuse ÐAOC = 360 – 252 = 108⁰ B1

= ¹/₂ (180 – 108)⁰

= 36⁰ B1

18x² – 39x + 18 = 0

6x² – 13x + 6 = 0 B1Ö equation

6x² – 9x – 4x + 6 = 0

3x(2x – 3) (3x – 2) = 0 M1

x = ²/₃ or A1

x =1 ½ B1

M : K : O = 4 : 2 : 3 B1Ö ratio

Maina’s = 4/9 X 180

= 80/- B1Ö Omondi’s

Omondi’s = 60/- and Maina’s

Difference = Shs.20/- B1 difference

(2 + ¹/₂x)⁶ = 2⁶ + 6(2⁵) (¹/₂x + 15 (2⁴) (¹/₂ x)² M1

= 64 + 96x + 60x² A1

2.4⁶ = (2 + ¹/₂ (0.8))⁶

= 64 + 96 (0.8) + 60 (0.64) M1

= 179.2

@179 to 3 s.f A1

P (FF) = ⁷/₂₀ X ⁷/₂₀

= ⁴⁹/₁₀₀ B1

P (at least one fail) = 1 – P (F^IF^I F^I)

= 1- ¹³/₂₀³ M1

= 1 – 2197 M1

8000

= 5803

8000 A1

grad = term 135

= -1 B1

y = mx + c

y = -x + 5 B1

Volume = 2 x 10,000 x 10,000 x 25 M1Ö x section area

1000 10 M1Ö conv. to litres

= 500,000 Lts A1

10a – 6(3a – 7) = 5(a -2) M1

10a – 18a + 42 = 5a – 10

– 13a = -52 M1

a = 4 A1

2a + 12d = 2

2a + 4d = -10 M1

8d = 12

d = 1¹/₂ A1

a = -8 B1

S₂₁ = ²¹/₂ (-16 + 20 X 3/2) M1

= 147 A1

2 p r = 120 x p x 40 M1

360

r = 6.667 cm A1

h = Ö 400 – 44.44 M1

= 18.86 cm A1

= (w (x – z) – y (x – z)) (w + z) M1Ö factor

(z – w) (z + w)

= (w – y) (x – z) (w + z) M1Ö grouping

(z – w) (z + w)

= (w – y) (x – z)

z – w A1

25⁰ B1Ö sketch

55⁰

Q 125 PR = 4 sin 125 M1

Sin 25

P 3

(a) <RST = 180⁰ – 74⁰ = 106⁰ B1

(b) < RTQ = 90⁰– 74⁰ = 16⁰ B1

< PTR = 46⁰ + 16⁰ = 62⁰ B1

< SUT = 62⁰ – 39⁰ = 23⁰ B1

= 180 – 32 = 148⁰ B1

Obtuse ROT = 360 – 148 = 212⁰ B1

(d) < PTS = 46 + 180 – 129 = 97⁰ B1

< PST = 180 – (97 + 39) = 44⁰ B1

(a) Kshs.350,000 = $ 350,000 M1

74.75

= $ 4682 A1

(b) Balance = ³/₄ x 4682

= $ 3511.5 B1

$3511.5 = Fr 3511.5 x 74.75 M1

11.04

= Fr 23780 A1

Expenditure = Fr 16 200

Balance = Fr 7580

= Kshs.97,024

Value on departure = Kshs.7580 X 11.04 B1 bothÖ

= Kshs.83 683.2

Difference = Kshs.97,024 – 83683.2 M1

= Kshs.13,340.80 A1

X	-2	-1	0	1	2	3
Y	-11	0	5	4	-3	-16

B1Övalues

S1Ö scale

8 — P1Ö plotting

6 — C1 Ö curve

4 —

-2 — 1 2 3 x

-4 —

-6 —

-8 — y=2x=2

-10 —

-12 —

-14 — x =-0.53 + 0.1 BI

-16 — Nx = 1.87+ 0.1

y = 5+2x-3x²=2-2x MI for equation

3x²-4x-4x-3=0 AI equation

x = -0.53 ± 0.1 B1

mx = 1.87 ± 0.1

y = 5 + 2x – 3x² = 2 – 2x M1 Ö for equation

\ 3×2 – 4x – 3 = 0 MA1 Ö equation

20.

B1 Ö 30⁰

R B1 Ö 2 ^ PQ, QR

B1 Ö 2 ^ bisectors

B1 Ö circle

9 Q

Radius = 4.2 ± 0.1 B1Ö radius

Area of circle = ²²/₇ x 4.22

= 55.44 ± 3 cm2

Area of D PQR = ¹/₂ x 3.5 x 7.5 sin 30 M1Ö D and circle

= 6.5625 cm²

Difference = 55.44 – 6.5625 M1Ö sub

= 48.88 cm² A1

Line (i) ^y/₂ + ^x/₅ = 1

5y + 2x = 10 B1Öequation

5y + 2x = 10 B1Ö inequality

Line (ii) ^y/₄ + ^x_/-3 = 1

3y = 4x + 12 B1Ö equation

3y < 4x + 12 or 3y – 4x < 12 B1Ö inequality

Line (iii) grad = ^-1/₃ y inter = 4

3y + x = 12 or 3y = -x + 12 B1Ö equation

3y + x < 12 B1Ö inequality

Line (iv) y – 3 = -3

x – 3 2

2y + 3x = 15 B1Ö equation

\ 2y + 3x £ 15 B1Ö equation

CLASS

60 – 64

65 – 69

70 – 79

75 – 79

80 – 84

85 – 89

496

938

1296

1155

246

174

Sf = 60

Sfx 3809

B1Ö x column

B1Ö f column

(a) (i) Modal class = 70 – 74 B1Ö model class

(ii) Median class = 70 – 74 B1Ö median

(b) Mean = 3809

60 M1

= 63.48 A1

S1Ö scale

B1 Ö blocks

59.5 – 64.5

64.5 – 69.5 e.t.c.

(c)

Histogram

20 —

15 —

10 – –

5 —

55 60 65 70 75 80 85 90

(a) XA = a, YA = 10 – a, YB = 10 – a, CZ = 10 – a = ZB

YZ = 10 – a + 12 – a = 8 M1

2a = 14

a = 7 cm A1

Cos X = 100 + 144 – 64

240 M1Ö any angle of the D

= 0.75

X = 41.41⁰

¹/₂ X = 20.70⁰ A1Ö ¹/₂ of the angle

r = OA = 7tan 20.7 B1 Ö radius

= 2.645 cm

Shaded area = ¹/₂X 10 X 12 sin 41.41 – ²²/₇ X 2.645² M1 Ö D & circle

= 39.69 – 21.99

= 17.7 cm² A1Ö

(a) 650,000 (0.85)ⁿ = 130,000 M1Ö formula

1.15n = 0.2

n = log 0.2 M1Ö

log 0.85

= 1.3010

1.9294

= – 0.6990 M1

– 0.0706

= 9.9 years A1

(b) 650,000 (1 – ^r/₁₀₀)⁵ = 325,000 M1

(1 – ^r/₁₀₀)⁵ = 0.5

1 – ^r/₁₀₀ = 0.5 ^1/5 M1

= 0.8706

^r/₁₀₀ = 0.1294 A1

r = 12.9 % B1

MATHEMATICS VI

PART II

MARKING SCHEME

SECTION I (52 MARKS)

= b¹⁵ ²_/5 X 4a⁶ ³_/2

32a¹⁰ 9b⁴ M1Ö reciprocal

= 2a⁵ A1

27 2

No. Log.

0.375 1.5740 +

cos 75 1.4130

2.9870 _

tan 85.6 1.1138

3.8732 = 4 + 1.8732

2 2

2.9366

0.0864

S. Price = 80 X 600

100

= Shs.480 B1

Cost Price = x

96x = 480 M1

100

x = Shs.500 A1

r² + hr = ^A/₂_p M1

r² + hr + (^h/₂)² = ^A/_2A + ^h/₄ M1

(r + ^h/₂)² = Ö 2A + h²

4p M1

r = ^-h/₂ ± Ö2A + h² A1

4p 4

(1²/₃r) (¹/₃ r) = (¹/₄ r) (5) M1

4r² – qr = 0

r(4r – q) = 0 M1

r = 0

or r = 2.25 A1

= 2 (5 + 2Ö3) – 1 (5 – 2Ö3) M1

(5 – 2Ö3) (5 + 2Ö3)

= 10 + 4Ö3 – 5 +2Ö3 M1

= 5 + 6Ö3 A1

13 3

P = Kq² + c

6 = 4k + c

16 = 9k + c M1 Ö subtraction

5k = 10

k = 2

c = -2 A1 Ö k and c

P = 64 2q² = 66

q = Ö33

= ± 5.745 A1

Volume = ¹/₂X 8 X 8 sin 120 X 10 M1 Ö area of x-section

No. of scouts = 32 sin 60 X 10 M1 Ö volume

2.5 M1

= 110.8

= 110 A1

Max. error = 2(8.5 + 5.5) – 2(7.5 + 4.5)

= 2 B1

% error = ²/₂₆X 100 M1

= 7.692% A1

G 3

B1 Ö net

H D G H B1 Ö dimen. FE must be 10cm

4cm 4cm

B1 Ö labelling

E 4cm A 12cm F 10cm E 3

4cm 12cm

(1 + 2x)⁶= 1 + 6(2x) + 15 (2x)² M1

= 1 + 12x + 60x² A1

(1.04)⁶= (1 + 2(0.02))⁶

= 1 + 12 (0.02) + 60(0.02)² M1

= 1.264 A1

BT = 10 cm B1

CT = 10 sin 40 M1

= 6.428 m A1

A₁ 10cm B C h = 6.428 + 1.5

1-5 = 7.928 B1

A.S.F = 405 ²_/3 = 27 ²_/3 = 9 B1

960 64 10

smaller area = 29 X 120 M1

164

= 67.5 cm² A1

Relative speed = (x – 30)km/h B1

2 km = 2 hrs

(x – 30)km/h 60 M1

2x – 60 = 120

x = 90 km/h A1

16 Km/h 5 Km/hr

x Km (22 – x) Km

x + 22 – x = 11

16 5 4 M1

5x + 352 – 16x = 220 M1Ö x-multiplication

11x = 132

x = 12 km A1

AP = ²/₉ x 12 = 2²/₃ cm B1 Ö both AP & AQ

AQ = ⁵/₉ x 12 = 6²/₃ cm

\ PQ = 6²/₃ – 2²/₃ = 4 cm B1 Ö C.A.O

Taxable income = ¹¹⁵/₁₀₀ x 8000 M1

= Shs.9200 p. m

= Shs.110,400 p.a A1

Tax dues = ¹⁰/₁₀₀ x 39600 + ¹⁵/₁₀₀ x 39600 + ²⁵/₁₀₀ x 31200 M1 Ö first 2 slabs

= 3960 + 5940 + 7800 M1 Ö last slab

= Shs.17,700 p.a

= 1475 p.m A1

net tax = 1475 – 400

= Shs.1075 B1 Ö net tax

Total deductions = 1075 + 130

= Shs.1205

net income = 8000 – 1205 M1

= Shs.6795 A1

(a) P (all correct) = ²/₃ x ³/₅ x ²/₅ M1

= ¹²/₁₂₅ A1

(b) P (2 correct) = ²/₅ x ³/₅ x ³/₅ + ²/₅ x ²/₅ X ¹/₅ + ³/₅ x ⁴/₅ x ²/₅

M1

= ¹⁸/₁₂₅ + ⁴/₁₂₅ + ²⁴/₁₂₅ M1

= ⁴⁶/₁₂₅ A1

= P(2 correct or 3 correct)

= ⁴⁶/₁₂₅ + ¹²/₁₂₅ M1

= 46 + 12 M1

125

= 58

125 A1

Old price/pen = 440

New price/pen = 494 B1Öboth expressions

x + 3

440 – 494 = 1.50

x x + 3 M1 Ö expression

440(x + 3) – 494x = 1.5x² + 4.5x M1Ö x-multiplication

x² + 39x – 880 = 0 A1 Ö solvable quad. Eqn

x² + 55x – 16x – 880 = 0 M1 Ö factors or equivalent

(x – 16) (x + 55) = 0

x = -55

or x = 16 A1 Ö both values

\ x = 16

difference in purchase = 19 X 1.50 M1

= Shs.28.50 A1

(a) OP = a + ¹/₄ (b – a) M1

= ³/₄ a + ¹/₄ b A1

(b) PQ = PO + OQ

= –³/₄ a – ¹/₄ b + ¹/₄ (a – b) M1

= –¹/₂ a – ¹/₂ b A1

= ¹/₄ (b – a) + ⁵/₃ b M1

= ²³/₁₂ b – ¹/₄ a A1

(d) PN = PB + BN

= ³/₄ (b – a) + ²/₃ b M1

= ¹⁷/₁₂ b – ³/₄ a A1

(a) Volume in 2 days = 22 x 3.5 x 3.5 x 150 x 20 x 3600 M1 Ö area of x-section

7 2 2 1,000,000 M1 Ö volume in cm³

= 103.95 m³ M1 Ö volume in m³

(b) 22 X r² x 8 = 103.95 x 15 x 7 M1

7 2

r² = 103.95 x 15 x 7 M1

2 x 2 2x 8

= 31.01 M1

r = 5.568 m A1

(a) Ration of needs for A:B = 5:8

A’s share = ⁵/₁₃ x 16.9 + ¹/₂ x 13.5 M1

= 13.25 Million A1

B’s share = (13.5 + 16.9) – 13.25 M1

= 13.25 M1

A’s share ⁵/₁₃ x 16.9 + ^39/₅₀ x 13.5

6.5 + 10.53

= 17.03 m A1

B’s share = 30.4 – 17.03 M1

= 13.37 Million A1

Log V = n Log E = log k

Log V	-0.46	-0.13	-0.14	-0.01	0.05
Log E	-0.35	-0.21	-0.05	0.07	0.13

B1Ö log V all points

B1Ö log E all points

S1 Ö scale

P1Ö plotting

Log V = n log E + log K L1 Ö line

Log K = 0.08

K = 1.2 ± 0.01 B1 Ö K

N = ^0.06/_0.06 B1 Ö n

= 1 ± 0.1

\ v = 1.2E B1Ö v

when E = 0.75, V = 0.9 ± 0.1 8

(a) T 3 PQR ® P^IQ^IR^I

4 P^I (0,5), Q^I (2,2) R^I (1,0)

P^I Q^I R^I P^II Q^II R^II

(b) 4 3 0 2 1 = 15 14 4 M1 Ö

1 2 5 2 0 10 6 1 A1 Ö

P^II (15,10), Q^II (14,6), R^II (4,1) B1Ö

= 5

area of P^II Q^II R^II = 5 (area P^IQ^IR^I)

= 5 X 3.5 M1Ö

= 16.5 cm² A1

Teachers' Resources

CBC Grade 7 Social Studies Schemes of Work Free Editable Word, PDF Downloads

October 5, 2025 Maverick John Leave a comment

CBC Grade 7 Social Studies Schemes of Work Free Editable Word, PDF Downloads

GRADE 7 SOCIAL STUDIES SCHEME OF WORKTERM 3

TEACHERS NAME……………………………………..SCHOOL……………………………….TERM THREE YEAR

Week	Lesson	Strand	Sub-strand	Specific-Learning outcomes	Learning Experience	Key Inquiry Question(S)	Learning Resources	Assessment Methods	Reflection
1	1	Sustainable Use of Resources in Society	Sustainable Use of Resources in Society	By the end of the lesson, the learner should be able to: a) Explain the meaning of sustainable use of resources. b) Demonstrate sustainable ways of using resources available in their community. c) Appreciate the resources available in their community.	Learners are guided to explain the meaning of sustainable use of resources. In groups or in pairs, learners to demonstrate sustainable ways of using resources available in their community.	What are resources?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 156-157 Pictures Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Sustainable Use of Resources in Society	Applying Sustainable use of resources available in the community	By the end of the lesson, the learner should be able to: a) Identify a resource that can be sustainably used in their community. b) Discuss the uses of the resource identified. c) Design sustainable ways of using the resource identified in the community. d) Engage in activities that ensure sustainable use of the resource.	Learners to identify a resource that can be sustainably used in their community. In groups, learners to discuss the uses of the resource identified. In groups, learners are guided to design sustainable ways of using the resource identified in the community	Which type of resources are found in your community?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 158-159 Photographs Pictures Video clips Realia Computing devices	Oral questions Oral Report Observation
	3	Sustainable Use of Resources in Society	Appreciating sustainable use of resources for sustenance of life	By the end of the lesson, the learner should be able to: a) Identify ways of appreciating sustainable use of resources for sustenance of life. b) Design posters with communication messages on sustainable use of resources for sustenance of life. c) Appreciate sustainable use of resources for sustenance of life.	Learners are guided to identify ways of appreciating sustainable use of resources for sustenance of life. In groups, learners are guided to design posters with communication messages on sustainable use of resources for sustenance of life	How will you appreciate sustainable use of resources for sustenance of life?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 160-161 Pictures Video clips Realia Computing devices	Oral questions Oral Report Observation
2	1	Political development and Governance	Political development in Africa up to 1900	By the end of the lesson, the learner should be able to: a) Describe the political setup of Ogiek community up to 1900 b) Discuss the role of the Ogiek political setup. c) Draw the governance structure of the Ogiek. d) Appreciate the Ogiek community.	Learners are guided to describe the political setup of Ogiek community up to 1900 In groups, learners to discuss the role of the Ogiek political setup. Learners are guided to draw the governance structure of the Ogiek	Where did the Ogiek community lived?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 162-164 Atlas Photographs Pictures Video clips Maps Charts Computing devices	Oral questions Oral Report Observation
	2	Political development and Governance	Political Organization of the Zulu	By the end of the lesson, the learner should be able to: a) Describe the political setup of Zulu community up to 1900 b) Discuss the role of the Zulu political setup. c) Draw the governance structure of the Zulu. d) Appreciate the Zulu community.	Learners are guided to describe the political setup of Zulu community up to 1900 In groups, learners to discuss the role of the Zulu political setup. Learners are guided to draw the governance structure of the Zulu	Where did the Zulu community lived?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 164-166 Atlas Photographs Pictures Maps Realia Computing devices	Oral questions Oral Report Observation
	3	Political development and Governance	Political Organization of the Asante	By the end of the lesson, the learner should be able to: a) Describe the political setup of Asante community up to 1900 b) Discuss the role of the Asante political setup. c) Draw the governance structure of the Asante. d) Appreciate the Asante community.	Learners are guided to describe the political setup of Asante community up to 1900 In groups, learners to discuss the role of the Asante political setup. Learners are guided to draw the governance structure of the Asante	Where did the Asante community lived?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 166-167 Atlas Photographs Pictures Video clips Realia Computing devices	Oral questions Oral Report Observation
3	1	Political development and Governance	The concepts “Scramble for and Partition” of Africa	By the end of the lesson, the learner should be able to: a) Define the concept of scramble and partition of Africa. b) Discuss the various European groups that came to Africa. c) Name the European explorers who came to Kenya. d) Have a desire to learn more about explorers.	Learners to define the concept of scramble and partition of Africa. In groups, learners to discuss the various European groups that came to Africa. Learners are guided to name the European explorers who came to Kenya	What is the meaning of scramble? What is the meaning of partition?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 168-170 Atlas Pictures Video clips Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Political development and Governance	European Traders	By the end of the lesson, the learner should be able to: a) Name various traders that came to Africa up to 1900. b) Identify the factors that led to the presence of Europeans in Africa. c) Discuss the role of various traders that came to Africa. d) Have a desire to learn more about European Traders.	Learners are guided to name various traders that came to Africa up to 1900 Learners to identify the factors that led to the presence of Europeans in Africa. In groups, learners are guided to discuss the role of various traders that came to Africa	Which factors led to the presence of Europeans in Africa?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 170-171 Photographs Pictures Video clips Maps Computing devices	Oral questions Oral Report Observation
	3	Political development and Governance	Matching the Countries in Africa with their Colonial Masters	By the end of the lesson, the learner should be able to: a) Identify the countries of Africa and their colonial masters from the map. b) Match the colonial masters with the countries they colonized in Africa. c) Enjoy using the map of Africa.	Learners are guided to identify the countries of Africa and their colonial masters from the map. Learners are guided to match the colonial masters with the countries they colonized in Africa	Who were colonial masters of Kenya?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 172 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
4	1	Political development and Governance	Terms of the Berlin Conference of 1884-1885 on the Partition of Africa	By the end of the lesson, the learner should be able to: a) Identify the meaning and implication of the terms of the Berlin Conference of 1884-1885 on partition of Africa from the plaque. b) Discuss the terms of the Berlin Conference. c) Create posters on the terms of the Berlin Conference of 1884-1885 d) Acknowledged the Political Organisation of Selected Communities in Africa.	Learners to identify the meaning and implication of the terms of the Berlin Conference of 1884-1885 on partition of Africa from the plaque. In groups, learners to discuss the terms of the Berlin Conference. In groups, learners to create posters on the terms of the Berlin Conference of 1884-1885	What are the terms of the Berlin Conference of 1884-1885 on partition of Africa?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 173-175 Atlas Photographs Pictures Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	2	The Constitution of Kenya	The Constitution of Kenya	By the end of the lesson, the learner should be able to: a) Define the term constitution. b) Identify the importance of the constitution of Kenya. c) Compose a song on any eight national values enshrined in the Constitution of Kenya. d) Appreciate the importance of the constitution of Kenya.	Learners to define the term constitution. Learners to identify the importance of the constitution of Kenya. In groups, learners to compose a song on any eight national values enshrined in the Constitution of Kenya.	What is a constitution? What is the importance of Constitution of Kenya?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 176-178 Atlas Photographs Pictures Maps Charts Computing devices	Oral questions Oral Report Observation
	3	The Constitution of Kenya	Ways of Upholding and Protecting the Constitution of Kenya for Social Cohesion	By the end of the lesson, the learner should be able to: a) Search for ways of upholding and protecting the Constitution of Kenya. b) Discuss the importance of upholding and protecting the constitution. c) Uphold and protect the constitution of Kenya.	Learners to search for ways of upholding and protecting the Constitution of Kenya. In groups, learners to discuss the importance of upholding and protecting the constitution.	Why do you think it’s important for Kenyans to uphold and protect the constitution?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 179-181 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
5	1	Democracy	Types of Democracy practiced in Africa	By the end of the lesson, the learner should be able to: a) Define democracy. b) Identify types of democracy. c) Role play different types of democracy. d) Appreciate the use of democracy.	Learners to define democracy. Learners are guided to identify types of democracy. In groups, learners are guided to role play different types of democracy.	What is democracy?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 182-184 Photographs Pictures Video clips Computing devices	Oral questions Oral Report Observation
	2	Democracy	Importance of Democracy in Society	By the end of the lesson, the learner should be able to: a) State the importance of democracy in society. b) Discuss the role of citizens in democratic representation. c) Draw the picture in learner’s book 7 d) Appreciate the importance of democracy in society.	Learners to state the importance of democracy in society. In groups, learners to discuss the role of citizens in democratic representation. Learners to draw the picture in learner’s book 7 pg. 186	How can we ensure that democracy is practiced in our society? What are democratic values?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 185-187 Photographs Pictures Maps Charts Computing devices	Oral questions Oral Report Observation
	3	Democracy	Characteristics of Various Types of Democracy in Governance	By the end of the lesson, the learner should be able to: a) Identify the characteristics of Various Types of Democracy in Governance. b) Recite the poem in learner’s book 7 c) Apply democratic values in interactions with others in the community. d) Promote democratic values in the community.	Learners to identify the characteristics of Various Types of Democracy in Governance. Learners to recite the poem in learner’s book 7 pg. 189	Why should we Practise democracy?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 187-190 Pictures Charts Realia Computing devices	Oral questions Oral Report Observation
6	1	Human Rights	Evolution of Human Rights as practiced in society	By the end of the lesson, the learner should be able to: a) Define Human rights. b) Identify the characteristics of Human Rights in society. c) Classify human rights as stipulated in the Human Rights as Stipulated in the human rights instruments. d) Appreciate the evolution of human rights.	Learners to define human rights. Learners to identify the characteristics of Human Rights in society. Learners are guided to classify human rights as stipulated in the Human Rights as Stipulated in the human rights instruments	What are human rights? Why is it important to know our rights?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 191-196 Pictures Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Human Rights	The concept of Equity and Non-Discrimination in Fostering Solidarity	By the end of the lesson, the learner should be able to: a) Brainstorm on how equity and non-discrimination foster solidarity in the society. b) Explain how to promote equity and non-discrimination in society. c) Respect, adhere to and promote of human rights for sanctity of life.	Learners to brainstorm on how equity and non-discrimination foster solidarity in the society. Learners to explain how to promote equity and non-discrimination in society.	How can we promote equity and non- discrimination in society?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 196-199 Pictures Computing devices	Oral questions Oral Report Observation
	3	African Diasporas	African Diasporas	By the end of the lesson, the learner should be able to: a) Define diaspora. b) Indicate on the map they have drawn countries inhabited by African diasporas by mid 1960s c) Examine the role of diasporas in the political development in Africa. d) Acknowledged African diasporas for promotion of African Unity in society today.	Learners to define diaspora. Learners are guided to indicate on the map they have drawn countries inhabited by African diasporas by mid 1960s Learners are guided to examine the role of diasporas in the political development in Africa.	What is the role of industrial revolution in Europe in the development of African diasporas? How can we promote African unity in the society today?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 200-204 Video clips Charts Computing devices	Oral questions Oral Report Observation
7	1	Global Citizenship	Global Citizenship	By the end of the lesson, the learner should be able to: a) Define global interconnectedness and interdependence. b) Identify positive and negative effects of globalization at local and national levels. c) Discuss the qualities of a global citizen. d) Appreciate the qualities of a global citizen.	Learners to define global interconnectedness and interdependence. Learners to identify positive and negative effects of globalization at local and national levels. In groups, learners to discuss the qualities of a global citizen.	What is global interconnectedness? What is interdependence? What are the qualities of a global citizen in the modern society?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 205-208 Pictures Video clips Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Global Citizenship	Contribution to the Wellbeing of the international community	By the end of the lesson, the learner should be able to: a) Explain what they understand by the term ‘common humanity’ b) Identify how they can develop a sense of belonging to a common humanity for harmonious living. c) Develop a sense of belonging to a common humanity for harmonious living.	Learners to explain what they understand by the term ‘common humanity’ Learners to identify how they can develop a sense of belonging to a common humanity for harmonious living	Which are the common concerns in the world today?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 209-211 Pictures Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	3	Global Governance	Organisation of African Unity (OAU)	By the end of the lesson, the learner should be able to: a) Identify the founding member countries of OAU. b) Discuss the achievements of OAU. c) State the challenges affected by OAU d) Draw the organizational structure of the OAU. e) Appreciate the importance of OAU.	Learners to identify the founding member countries of OAU. In groups, learners to discuss the achievements of OAU. Learners to state the challenges affected by OAU Learners are guided to draw the organizational structure of the OAU	Why was the OAU formed?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 213-217 Photographs Pictures Video clips Realia Computing devices	Oral questions Oral Report Observation
8	1	Global Governance	African Union (AU)	By the end of the lesson, the learner should be able to: a) Describe the formation of African Union (AU) b) Discuss the achievements of AU. c) State the challenges affected by AU d) Sing the African Union Anthem. e) Appreciate the importance of AU	Learners to describe the formation of African Union (AU) In groups, learners to discuss the achievements of AU. Learners to state the challenges affected by AU the challenges affected by AU Learners are guided to sing the African Union Anthem.	What are the achievements of African Union (AU)?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 217-220 Photographs Pictures Video clips Computing devices	Oral questions Oral Report Observation
	2	Global Governance	Member countries of the African Union	By the end of the lesson, the learner should be able to: a) Identify the AU member states from an atlas. b) Draw a map of Africa showing member countries of African Union (AU) c) Appreciate the importance of AU	Learners are guided to identify the AU member states from an atlas. Learners are guided to draw a map of Africa showing member countries of African Union (AU)	How should leadership and integrity be promoted in the society today?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 221-223 Photographs Pictures Video clips Realia Computing devices	Oral questions Oral Report Observation
	3	Global Governance	Organizational structures of the African Union	By the end of the lesson, the learner should be able to: a) Identify various organs that run the AU. b) Identify the factors which can promote continental interconnectedness and interdependence. c) Draw the organizational structure of African Union (AU) d) Appreciate the importance of AU	Learners to identify various organs that run the AU. Learners are guided to identify the factors which can promote continental interconnectedness and interdependence. Learners are guided to draw the organizational structure of African Union (AU)	How can we promote continental interconnectedness and interdependence in Africa?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 223-226 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
9				ASSESSMENT

2023 SCHEME OF WORK

SOCIAL STUDIES

GRADE SEVEN

TERM 3

SCHOOL	GRADE	LEARNING AREA	TERM	YEAR
	GRADE 7	SOCIAL STUDIES	3	2023

Week	Lesson	Strand	Sub-strand	Specific-Learning outcomes	Learning Experience	Key Inquiry Question(S)	Learning Resources	Assessment Methods	Reflection
1	1	Sustainable Use of Resources in Society	Sustainable Use of Resources in Society	By the end of the lesson, the learner should be able to: d) Explain the meaning of sustainable use of resources. e) Demonstrate sustainable ways of using resources available in their community. f) Appreciate the resources available in their community.	Learners are guided to explain the meaning of sustainable use of resources. In groups or in pairs, learners to demonstrate sustainable ways of using resources available in their community.	What are resources?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 156-157 Pictures Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Sustainable Use of Resources in Society	Applying Sustainable use of resources available in the community	By the end of the lesson, the learner should be able to: e) Identify a resource that can be sustainably used in their community. f) Discuss the uses of the resource identified. g) Design sustainable ways of using the resource identified in the community. h) Engage in activities that ensure sustainable use of the resource.	Learners to identify a resource that can be sustainably used in their community. In groups, learners to discuss the uses of the resource identified. In groups, learners are guided to design sustainable ways of using the resource identified in the community	Which type of resources are found in your community?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 158-159 Photographs Pictures Video clips Realia Computing devices	Oral questions Oral Report Observation
	3	Sustainable Use of Resources in Society	Appreciating sustainable use of resources for sustenance of life	By the end of the lesson, the learner should be able to: d) Identify ways of appreciating sustainable use of resources for sustenance of life. e) Design posters with communication messages on sustainable use of resources for sustenance of life. f) Appreciate sustainable use of resources for sustenance of life.	Learners are guided to identify ways of appreciating sustainable use of resources for sustenance of life. In groups, learners are guided to design posters with communication messages on sustainable use of resources for sustenance of life	How will you appreciate sustainable use of resources for sustenance of life?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 160-161 Pictures Video clips Realia Computing devices	Oral questions Oral Report Observation
2	1	Political development and Governance	Political development in Africa up to 1900	By the end of the lesson, the learner should be able to: e) Describe the political setup of Ogiek community up to 1900 f) Discuss the role of the Ogiek political setup. g) Draw the governance structure of the Ogiek. h) Appreciate the Ogiek community.	Learners are guided to describe the political setup of Ogiek community up to 1900 In groups, learners to discuss the role of the Ogiek political setup. Learners are guided to draw the governance structure of the Ogiek	Where did the Ogiek community lived?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 162-164 Atlas Photographs Pictures Video clips Maps Charts Computing devices	Oral questions Oral Report Observation
	2	Political development and Governance	Political Organization of the Zulu	By the end of the lesson, the learner should be able to: e) Describe the political setup of Zulu community up to 1900 f) Discuss the role of the Zulu political setup. g) Draw the governance structure of the Zulu. h) Appreciate the Zulu community.	Learners are guided to describe the political setup of Zulu community up to 1900 In groups, learners to discuss the role of the Zulu political setup. Learners are guided to draw the governance structure of the Zulu	Where did the Zulu community lived?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 164-166 Atlas Photographs Pictures Maps Realia Computing devices	Oral questions Oral Report Observation
	3	Political development and Governance	Political Organization of the Asante	By the end of the lesson, the learner should be able to: e) Describe the political setup of Asante community up to 1900 f) Discuss the role of the Asante political setup. g) Draw the governance structure of the Asante. h) Appreciate the Asante community.	Learners are guided to describe the political setup of Asante community up to 1900 In groups, learners to discuss the role of the Asante political setup. Learners are guided to draw the governance structure of the Asante	Where did the Asante community lived?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 166-167 Atlas Photographs Pictures Video clips Realia Computing devices	Oral questions Oral Report Observation
3	1	Political development and Governance	The concepts “Scramble for and Partition” of Africa	By the end of the lesson, the learner should be able to: e) Define the concept of scramble and partition of Africa. f) Discuss the various European groups that came to Africa. g) Name the European explorers who came to Kenya. h) Have a desire to learn more about explorers.	Learners to define the concept of scramble and partition of Africa. In groups, learners to discuss the various European groups that came to Africa. Learners are guided to name the European explorers who came to Kenya	What is the meaning of scramble? What is the meaning of partition?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 168-170 Atlas Pictures Video clips Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Political development and Governance	European Traders	By the end of the lesson, the learner should be able to: e) Name various traders that came to Africa up to 1900. f) Identify the factors that led to the presence of Europeans in Africa. g) Discuss the role of various traders that came to Africa. h) Have a desire to learn more about European Traders.	Learners are guided to name various traders that came to Africa up to 1900 Learners to identify the factors that led to the presence of Europeans in Africa. In groups, learners are guided to discuss the role of various traders that came to Africa	Which factors led to the presence of Europeans in Africa?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 170-171 Photographs Pictures Video clips Maps Computing devices	Oral questions Oral Report Observation
	3	Political development and Governance	Matching the Countries in Africa with their Colonial Masters	By the end of the lesson, the learner should be able to: d) Identify the countries of Africa and their colonial masters from the map. e) Match the colonial masters with the countries they colonized in Africa. f) Enjoy using the map of Africa.	Learners are guided to identify the countries of Africa and their colonial masters from the map. Learners are guided to match the colonial masters with the countries they colonized in Africa	Who were colonial masters of Kenya?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 172 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
4	1	Political development and Governance	Terms of the Berlin Conference of 1884-1885 on the Partition of Africa	By the end of the lesson, the learner should be able to: e) Identify the meaning and implication of the terms of the Berlin Conference of 1884-1885 on partition of Africa from the plaque. f) Discuss the terms of the Berlin Conference. g) Create posters on the terms of the Berlin Conference of 1884-1885 h) Acknowledged the Political Organisation of Selected Communities in Africa.	Learners to identify the meaning and implication of the terms of the Berlin Conference of 1884-1885 on partition of Africa from the plaque. In groups, learners to discuss the terms of the Berlin Conference. In groups, learners to create posters on the terms of the Berlin Conference of 1884-1885	What are the terms of the Berlin Conference of 1884-1885 on partition of Africa?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 173-175 Atlas Photographs Pictures Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	2	The Constitution of Kenya	The Constitution of Kenya	By the end of the lesson, the learner should be able to: e) Define the term constitution. f) Identify the importance of the constitution of Kenya. g) Compose a song on any eight national values enshrined in the Constitution of Kenya. h) Appreciate the importance of the constitution of Kenya.	Learners to define the term constitution. Learners to identify the importance of the constitution of Kenya. In groups, learners to compose a song on any eight national values enshrined in the Constitution of Kenya.	What is a constitution? What is the importance of Constitution of Kenya?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 176-178 Atlas Photographs Pictures Maps Charts Computing devices	Oral questions Oral Report Observation
	3	The Constitution of Kenya	Ways of Upholding and Protecting the Constitution of Kenya for Social Cohesion	By the end of the lesson, the learner should be able to: d) Search for ways of upholding and protecting the Constitution of Kenya. e) Discuss the importance of upholding and protecting the constitution. f) Uphold and protect the constitution of Kenya.	Learners to search for ways of upholding and protecting the Constitution of Kenya. In groups, learners to discuss the importance of upholding and protecting the constitution.	Why do you think it’s important for Kenyans to uphold and protect the constitution?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 179-181 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
5	1	Democracy	Types of Democracy practiced in Africa	By the end of the lesson, the learner should be able to: e) Define democracy. f) Identify types of democracy. g) Role play different types of democracy. h) Appreciate the use of democracy.	Learners to define democracy. Learners are guided to identify types of democracy. In groups, learners are guided to role play different types of democracy.	What is democracy?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 182-184 Photographs Pictures Video clips Computing devices	Oral questions Oral Report Observation
	2	Democracy	Importance of Democracy in Society	By the end of the lesson, the learner should be able to: e) State the importance of democracy in society. f) Discuss the role of citizens in democratic representation. g) Draw the picture in learner’s book 7 h) Appreciate the importance of democracy in society.	Learners to state the importance of democracy in society. In groups, learners to discuss the role of citizens in democratic representation. Learners to draw the picture in learner’s book 7 pg. 186	How can we ensure that democracy is practiced in our society? What are democratic values?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 185-187 Photographs Pictures Maps Charts Computing devices	Oral questions Oral Report Observation
	3	Democracy	Characteristics of Various Types of Democracy in Governance	By the end of the lesson, the learner should be able to: e) Identify the characteristics of Various Types of Democracy in Governance. f) Recite the poem in learner’s book 7 g) Apply democratic values in interactions with others in the community. h) Promote democratic values in the community.	Learners to identify the characteristics of Various Types of Democracy in Governance. Learners to recite the poem in learner’s book 7 pg. 189	Why should we Practise democracy?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 187-190 Pictures Charts Realia Computing devices	Oral questions Oral Report Observation
6	1	Human Rights	Evolution of Human Rights as practiced in society	By the end of the lesson, the learner should be able to: e) Define Human rights. f) Identify the characteristics of Human Rights in society. g) Classify human rights as stipulated in the Human Rights as Stipulated in the human rights instruments. h) Appreciate the evolution of human rights.	Learners to define human rights. Learners to identify the characteristics of Human Rights in society. Learners are guided to classify human rights as stipulated in the Human Rights as Stipulated in the human rights instruments	What are human rights? Why is it important to know our rights?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 191-196 Pictures Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Human Rights	The concept of Equity and Non-Discrimination in Fostering Solidarity	By the end of the lesson, the learner should be able to: d) Brainstorm on how equity and non-discrimination foster solidarity in the society. e) Explain how to promote equity and non-discrimination in society. f) Respect, adhere to and promote of human rights for sanctity of life.	Learners to brainstorm on how equity and non-discrimination foster solidarity in the society. Learners to explain how to promote equity and non-discrimination in society.	How can we promote equity and non- discrimination in society?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 196-199 Pictures Computing devices	Oral questions Oral Report Observation
	3	African Diasporas	African Diasporas	By the end of the lesson, the learner should be able to: e) Define diaspora. f) Indicate on the map they have drawn countries inhabited by African diasporas by mid 1960s g) Examine the role of diasporas in the political development in Africa. h) Acknowledged African diasporas for promotion of African Unity in society today.	Learners to define diaspora. Learners are guided to indicate on the map they have drawn countries inhabited by African diasporas by mid 1960s Learners are guided to examine the role of diasporas in the political development in Africa.	What is the role of industrial revolution in Europe in the development of African diasporas? How can we promote African unity in the society today?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 200-204 Video clips Charts Computing devices	Oral questions Oral Report Observation
7	1	Global Citizenship	Global Citizenship	By the end of the lesson, the learner should be able to: e) Define global interconnectedness and interdependence. f) Identify positive and negative effects of globalization at local and national levels. g) Discuss the qualities of a global citizen. h) Appreciate the qualities of a global citizen.	Learners to define global interconnectedness and interdependence. Learners to identify positive and negative effects of globalization at local and national levels. In groups, learners to discuss the qualities of a global citizen.	What is global interconnectedness? What is interdependence? What are the qualities of a global citizen in the modern society?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 205-208 Pictures Video clips Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Global Citizenship	Contribution to the Wellbeing of the international community	By the end of the lesson, the learner should be able to: d) Explain what they understand by the term ‘common humanity’ e) Identify how they can develop a sense of belonging to a common humanity for harmonious living. f) Develop a sense of belonging to a common humanity for harmonious living.	Learners to explain what they understand by the term ‘common humanity’ Learners to identify how they can develop a sense of belonging to a common humanity for harmonious living	Which are the common concerns in the world today?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 209-211 Pictures Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	3	Global Governance	Organisation of African Unity (OAU)	By the end of the lesson, the learner should be able to: f) Identify the founding member countries of OAU. g) Discuss the achievements of OAU. h) State the challenges affected by OAU i) Draw the organizational structure of the OAU. j) Appreciate the importance of OAU.	Learners to identify the founding member countries of OAU. In groups, learners to discuss the achievements of OAU. Learners to state the challenges affected by OAU Learners are guided to draw the organizational structure of the OAU	Why was the OAU formed?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 213-217 Photographs Pictures Video clips Realia Computing devices	Oral questions Oral Report Observation
8	1	Global Governance	African Union (AU)	By the end of the lesson, the learner should be able to: f) Describe the formation of African Union (AU) g) Discuss the achievements of AU. h) State the challenges affected by AU i) Sing the African Union Anthem. j) Appreciate the importance of AU	Learners to describe the formation of African Union (AU) In groups, learners to discuss the achievements of AU. Learners to state the challenges affected by AU the challenges affected by AU Learners are guided to sing the African Union Anthem.	What are the achievements of African Union (AU)?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 217-220 Photographs Pictures Video clips Computing devices	Oral questions Oral Report Observation
	2	Global Governance	Member countries of the African Union	By the end of the lesson, the learner should be able to: d) Identify the AU member states from an atlas. e) Draw a map of Africa showing member countries of African Union (AU) f) Appreciate the importance of AU	Learners are guided to identify the AU member states from an atlas. Learners are guided to draw a map of Africa showing member countries of African Union (AU)	How should leadership and integrity be promoted in the society today?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 221-223 Photographs Pictures Video clips Realia Computing devices	Oral questions Oral Report Observation
	3	Global Governance	Organizational structures of the African Union	By the end of the lesson, the learner should be able to: e) Identify various organs that run the AU. f) Identify the factors which can promote continental interconnectedness and interdependence. g) Draw the organizational structure of African Union (AU) h) Appreciate the importance of AU	Learners to identify various organs that run the AU. Learners are guided to identify the factors which can promote continental interconnectedness and interdependence. Learners are guided to draw the organizational structure of African Union (AU)	How can we promote continental interconnectedness and interdependence in Africa?	KLB: Top Scholar; Social Studies Learner’s Book Grade 7 pg. 223-226 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
9	ASSESSMENT

Teachers' Resources

Secondary school exams 2021-2022

October 5, 2025 Maverick John Leave a comment

Are you looking for Free form 1, 2, 3, and 4 High School revision materials and marking schemes (Topic by topic questions and answers for all subjects)? All these and many more updates notes, examinations, schemes of work, lesson plans and many more resources are available here.

Please note that all the notes, exams, revision documents, schemes of work and other resources are available here at no cost; they are free for all. Try the resources today and share freely with others.

FORM 1-4 TOPICAL REVISION RESOURCES, KCSE MOCKS, KCSE PREDICTOR EXAMS, MADE FAMILIAR AND OTHER RESOURCES.

Scroll through the resources below and select that which you may be interested in. Remember, the documents below are completely free of charge.

TUMBO LISILOSHIBA

PHYSICS MADE FAMILIAR

PEARL ESSAYS

MEMORIES WE LOST

MATHS PREDICTOR SET 1

MATHS MADE FAMILIAR

MADE FAMILIAR HOME SCIENCE

MADE FAMILIAR CRE KIT

ENGLISH MADE FAMILIAR

KISWAHILI MADE FAMILIAR

KISWAHILI PREDICTOR SET 1

KIGOGO KCSE QUESTIONS

KCSE PHYSICS MOCKS SET 2

KCSE PHYSICS MOCKS SET 1

KCSE PHY PREDICTOR SET 1

KCSE MOCKS SET 2.

KCSE MOCKS SET 1

KCSE MATHS MOCKS SET 2

KCSE MATHS MOCKS SET 1

KCSE KISW MOCKS SET 2

KCSE KISW MOCKS SET 1

KCSE INHERITANCE ESSAYS

KCSE HISTORY MOCKS SET 1-1

KCSE HIST MOCKS SET 2

KCSE GEOGRAPHY MOCKS SET 1

KCSE GEO MOCKS SET 2

KCSE ENGLISH MOCKS SET 2

KCSE ENGLISH MOCKS SET 1-1

KCSE ENG PREDICTOR SET 1

KCSE CRE MOCKS SET 2

KCSE CRE MOCKS SET 1-1

KCSE CHEM MOCKS SET 2

KCSE CHEM MOCKS SET 1

KCSE BUSINESS MOCKS SET 2

KCSE BUSINESS MOCKS SET 1-1

KCSE BLOSSOMS ESSAYS

KCSE BIOLOGY MOCKS SET 1

KCSE BIO MOCKS SET 2

KCSE AGRIC MOCKS SET 2

KCSE AGRIC MOCKS SET 1

KCSE 2021 PREDICTION SET 2

KCSE 2021 PREDICTION SET 1

HOME-SCIENCE MOCKS SET 2

HISTORY PREDICTOR SET 1

GEOGRAPHY MADE FAMILIAR

GEOOGRAPHY PREDICTOR SET 1

FRENCH TOPICAL QUESTIONS

CROSS COUNTRY MOCKS SET 1

CRE PREDICTOR SET 1

COMPUTER STUDIES PREDICTOR SET 1

CHOZI LA HERI KCSE

CHEMISTRY PREDICTOR SET 1

CHEMISTRY MADE FAMILIAR

BUSINESS PREDICTOR SET 1

BUSINESS MADE FAMILIAR

BLOSSOMS EXCERPTS

BIOLOGY PREDICTOR SET 1

BIOLOGY MADE FAMILIAR

AGRICULTURE MADE FAMILIAR

AGRICULTURE PREDICTOR SET 1

A DOLL’S HOUSE KCSE

A DOLL’S HOUSE EXCERPTS

FORM 4 EXAMS

FORM 4 TERM 2 OPENER

FORM 3 EXAMS

FORM 3 TERM 3 OPENER.

FORM 3 TERM 2 OPENER

FORM 3 SET 2 ASSIGNMENT.

FORM 3 SET 1 ASSIGNMENT

FORM 3 MIDTERM 3 EXAMS

FORM 3 ENDTERM 3 EXAMS

DOWNLOAD FREE HIGH SCHOOL MATERIALS

FREE UPDATED NOTES

FORM ONE NOTES

FORM TWO NOTES

FORM THREE NOTES

FORM FOUR NOTES

FREE LATEST EXAMS WITH MARKING SCHEMES

FORM ONE EXAMS

FORM TWO EXAMS

FORM THREE EXAMS

FORM FOUR EXAMS

FORM 1-4 FREE EXAMS

SCHEMES OF WORK

KCSE REVISION MATERIALS

Search more free materials here: [ivory-search id=”16550″ title=”Get Free Primary and Secondary: Notes, Exams, KCSE, KCPE papers, Schemes of work and more”]

FREE PRIMARY SCHOOL RESOURCES

FREE CLASS 8 RESOURCES

LOWER PRIMARY (PP1 & 2)

LOWER PRIMARY (GRADE 1-6)

FORM 2 EXAMS

FORM 2 TERM 3 OPENER

FORM 2 TERM 2 OPENER

FORM 2 MIDTERM 3 EXAMS

FORM 2 ENDTERM 3 EXAMS

FORM 1 EXAMS, TOPICAL RESOURCES & OTHER REVISION MATERIALS

FORM 1 TERM 3 OPENER

FORM 1 TERM 2 OPENER

F1 TERM 1 SET 3 EXAMS

F1 TERM 2 MIDTERM EXAMS

F1 TERM 2 ENDTERM EXAMS

F1 TERM 1 SET 2 ASSIGNMENT

F1 TERM 1 SET 1 ASSIGNMENT

F1 PHYSICS TOPICALS

F1 MATHS TOPICALS

F1 KISWAHILI TOPICALS

F1 HISTORY TOPICALS

F1 GEOGRAPHY TOPICALS

F1 ENGLISH TOPICALS

F1 CRE TOPICALS REVISION

F1 CHEMISTRY TOPICALS

F1 BUSINESS TOPICALS

F1 BIOLOGY TOPICALS

F1 AGRIC TOPICALS

secondary school exams 2021,

free revision papers,

primary school exams 2021,

form 1 exams 2021,

kenya high school past papers form 1,

free exams with marking schemes,

alliance high school past papers,

teachers arena exams 2021,

Teachers' Resources

FORM 4 KCSE MOCK JOINT EXAMS PLUS MARKING SCHEMES NEW

October 5, 2025 Maverick John Leave a comment

DOWNLOAD FREE FORM 4 POST MOCK JOINT EXAMS WITH MARKING SCHOOLS.

KISWAHILI JOINT EXAMS PAPER 2 MARKING SCHEMES

KISWAHILI JOINT EXAMS PAPER 2

KISWAHILI JOINT EXAMS PAPER 3

PHYSICS KISWAHILI JOINT EXAMS PAPER 1

JOINT EXAMS PAPER 3 KISWAHILI MARKING SCHEME

JOINT EXAMS PAPER 1 KISWAHILI

MATHS JOINT EXAMS PAPER 2

JOINT EXAMS PAPER 2 HISTORY

JOINT EXAMS PAPER 2 HISTORY MARKING SCHEME

JOINT EXAMS PAPER 1 HISTORY MARKING SCHEME

JOINT EXAMS PAPER 1 HISTORY

JOINT EXAMS PAPER 2 GEOGRAPHY

JOINT EXAMS PAPER 2 MARKING SCHEME

JOINT EXAMS PAPER 1 GEOGRAPHY

JOINT EXAMS PAPER 1 GEOGRAPHY MARKING SCHEME

JOINT EXAMS GEOGRAPHY CONFIDENTIAL

JOINT EXAMS PAPER 1 ENGLISH MARKING SCHEME

JOINT EXAMS PAPER 1 ENGLISH

JOINT EXAMS PAPER 2 ENGLISH

JOINT EXAMS PAPER 1 ENGLISH

JOINT EXAMS PAPER 2 MARKING SCHEME

JOINT EXAMS PAPER 3 QUESTIONS & MARKING SCHEMES

JOINT EXAMS PAPER 1 COMPUTER STUDIES

JOINT EXAMS PAPER 2 COMPUTER STUDIES

JOINT EXAMS PAPER 2 COMPUTER MARKING SCHEME

JOINT EXAMS PAPER 1 COMPUTER STUDIES MARKING SCHEME

JOINT EXAMS PAPER 3 CHEMISTRY CONFIDENTIAL

JOINT EXAMS PAPER 3 CHEMISTRY MARKING SCHEMES

JOINT EXAMS PAPER 3 CHEMISTRY

JOINT EXAMS PAPER 1 CHEMISTRY

JOINT EXAMS PAPER 2 CHEMISTRY

JOINT EXAMS PAPER 2 CHEMISTRY MARKING SCHEME

JOINT EXAMS PAPER 1 CHEMISTRY MARKING SCHEMES

JOINT EXAMS PAPER 2 BIOLOGY

JOINT EXAMS PAPER 1 BIOLOGY QUESTIONS & ANSWERS

JOINT EXAMS PAPER 3 BIOLOGY MARKING SCHEME

JOINT EXAMS PAPER 1 BIOLOGY MARKING SCHEME

JOINT EXAMS PAPER 3 CONFIDENTIAL

JOINT EXAMS PAPER 3 BIOLOGY

JOINT EXAMS PAPER 3 PHYSICS CONFIDENTIAL

JOINT EXAMS PAPER 3 PHYSICS

JOINT EXAMS PAPER 3 PHYSICS MARKING SCHEME

JOINT EXAMS PAPER 2 PHYSICS

JOINT EXAMS PAPER 2 PHYSICS MARKING SCHEME

JOINT EXAMS PAPER 1 PHYSICS MARKING SCHEME

JOINT EXAMS PAPER 2 MATHS MARKING SCHEME

JOINT EXAMS PAPER 1 MATHS MARKING SCHEME

JOINT EXAMS PAPER 1 MATHS

JOINT EXAMS PAPER 2 CRE

JOINT EXAMS PAPER 2 CRE MARKING SCHEME

JOINT EXAMS PAPER 1 MARKING SCHEME

JOINT EXAMS PAPER 1 CRE

JOINT EXAMS PAPER 1 AGRICULTURE

JOINT EXAMS PAPER 2 AGRICULTURE

JOINT EXAMS PAPER 2 MARKING SCHEME

JOINT EXAMS PAPER 1 AGRICULTURE MARKING SCHEME

JOINT EXAMS PAPER 2 BUSINESS STUDIES

JOINT EXAMS PAPER 2 BUSINESS STUDIES MARKING SCHEMES

JOINT EXAMS PAPER 1 BUSINESS STUDIES MARKING SCHEME

JOINT EXAMS PAPER 1 BUSINESS STUDIES

Teachers' Resources

Grade 9 KJSEA exams and answers

October 5, 2025 Maverick John Leave a comment

Download free Grade 9 KJSEA exams and answers below:

G9-ENGLISH.docx
G9-KISWAHILI.docx
G9-INTEGRATED.docx
G9-PRETECHNICAL.docx
G9-CAS.docx
G9-SOCIAL.docx
G9-CRE-1.docx
GRADE 9 KJSEA MAT KEY AREAS.pdf
GRADE 9 KJSEA SST KEY AREAS.pdf
G9 KJSEA MAT BLUE PRINT PREDICTION.pdf
GRADE 9 KJEA PRE TECH KEY AREAS.pdf
GRADE 9 KJSEA INT SCI KEY AREAS.pdf
GRADE 9 KJSEA CAS KEY AREAS.pdf
GRADE 9 KJSEA AGRIC KEY AREAS.pdf
G9 KJSEA AGRIC BLUE PRINT PREDICTION.pdf
GRADE 9 KJSEA IRE KEY AREAS.pdf
G9 KJSEA ENG BLUE PRINT PREDICTION.pdf
G9 KJSEA CAS BLUE PRINT PREDICTION.pdf
G9 KJSEA CRE BLUE PRINT PREDICTION.pdf
AGRI 9.pdf
KISW 1 9.pdf
KISW 29.pdf
SST 9.pdf
ENG P 1 9.pdf
PRE TECH 9.pdf
CREATIVE 9.pdf
MATH 9.pdf
SUCCESS GRADE 9 MATHS T1 -1.pdf
G9 ENG PP1.pdf
SUCCESS GRADE 9 INTERGRATED SCIENCE PP1 T1 .pdf
G9-MATHEMATICS-2.docx
G9 KJSEA IRE BLUE PRINT PREDICTION.pdf
G9 KJSEA KISW BLUE PRINT PREDICTION.pdf
GRADE 9 KJSEA KIS KEY AREAS.pdf
GRADE 9 KJSEA ENG KEY AREAS.pdf
GRADE 9 KJSEA CRE KEY AREAS.pdf
G9-MATHEMATICS-2 (2).docx
G9-IRE-1 (2).docx
GRADE-9-TERM-2-PRETECHNICAL-LESSON-PLANS-1.docx
grade-9-rationalized-cre-lesson-plans-term-2.docx

Teachers' Resources

Education Hub Form 3 Exams with Answers {Latest}

October 5, 2025 Maverick John Leave a comment

Education Hub Form 3 Exams with Answers {Latest}:

Form 3 Exams & Answers For all subjects

Download term 1, 2 and 3 free Form 3 Exams & Answers For all subjects below. Continue downloading more free Exams below: Form 2 Examinations with…

Latest English Form 3 Exams and Marking Schemes Free Downloads

Latest English Form 3 Exams and Marking Schemes Free Downloads Set 1 paper 3 eng.docx paper 2 eng.docx ms paper 1eng.docx paper 1eng.docx ENGLISH PP3 MS.docx eng p2 ms.docx Set 2 SET 5 SET…

CHEMISTRY FORM 3 EXAMS WITH MARKING SCHEMES

FORM 3 CHEMISTRY EXAMS DOWNLOADS. CHEMISTRY FORM 3 P2 EXAM QUESTIONS CHEMISTRY FORM 3 P2 EXAM MARKING SCHEME CHEMISTRY FORM 3 P1 EXAM QUESTIONS CHEMISTRY FORM 3 P2…

Latest Chemistry Form 3 Exams and Marking Schemes Free

Latest Chemistry Form 3 Exams and Marking Schemes Free Set 1 CHEM P2 SET 1.doc CHEM P1 SET 1.doc CHEM P2 MS SET1.doc CHEM P1 MS SET1.doc CHEM P3 SET…

Latest Physics Form 3 Exams and Marking Schemes Free Downloads

Latest Physics Form 3 Exams and Marking Schemes Free Downloads Latest Exams Set Series MATHS P1 Q MS SET 10.docx MATHS P2 Q MS SET 10.docx Maths P2…

Latest Physics Form 3 Exams and Marking Schemes Free Downloads

Latest Physics Form 3 Exams and Marking Schemes Free Downloads Latest Exams Set Series PHY P2 SET 1.docx PHY P3 MS SET 1.docx PHY P3 SET 1.docx PHY P2…

Latest Business Studies Form 3 Exams and Marking Schemes Free Downloads

Latest Business Studies Form 3 Exams and Marking Schemes Free Downloads Set 1 B STUDIES P1 SET 1.doc B STUDIES P1 MS SET 1.docx ~$STUDIES P1 SET 1.doc B…

Latest History and Government Form 3 Exams and Marking Schemes Free Downloads

Latest History and Government Form 3 Exams and Marking Schemes Free Downloads Latest Exams Set Series PAPER 2 QSTS.docx FORM3 PAPER 1 MARKING SCHEME.docx PEPR 2 MRK.docx FORM3 PAPER…

Form 3 exams with marking scheme (Comprehensive papers)

Educationnewshub.co.ke –

Looking for Form three (3) comprehensive exams? look no further. Download all the updated Form 3 exams with marking schemes here. Check the TEACHERS’…

Latest Kiswahili Form 3 Exams and Marking Schemes Free Downloads

Latest Kiswahili Form 3 Exams and Marking Schemes Free Downloads Set 1 KIDATO 3-P3-MS.xml KIDATO 3-P3-QUESTIONS.doc KIDATO 3-P2-MS.xml KIDATO 3-P2-QSTIONS.xml KIDATO 3-P1-MS.xml KIDATO 3-P1-QSTIONS.xml Set 2 kiswahili 2.doc Kiswahili PP3.docx kiswahili 3.docx Kiswahili BMT.doc Kiswahili PP1.docx kis1.docx Set 3 Kiswahili…

Best Biology Form 3 Exams and Marking Schemes Free Downloads

Educationnewshub.co.ke

Latest Biology Form 3 Exams and Marking Schemes Free Downloads Set 1 ~$O P1 SET 1.docx ~WRL0003.tmp ~$O P1 MS SET 1.docx ~$O P3 SET 1.rtf ~$O P3 MS SET…

Complete Form 3 Exams & Answers

Educationnewshub.co.ke

Comprehensive Form 3 Exams and answers for all subjects Posted on June 6, 2024 by News Blaze Digital Team Complete Form 3 Exams & Answers – Boost Your Knowledge…

Form 3 exams with marking scheme

Educationnewshub.co.ke

In need of free Form 3 revision papers with answers pdf download? Well. Download free exams with marking schemes below; FREE FORM 3 EXAMS PLUS…

Form 3 Exams- Full papers & Answers

Educationnewshub.co.ke

Download free Form 3 Exams- Full papers & Answers here.

Form 3 Examinations with marking scheme (All High School Subjects)

MwalimuOnline.com

Get unlimited free downloads of all the Form 3 Examinations with marking scheme (All High School Subjects) Continue downloading more free Secondary School Exam Papers…

Latest CRE Form 3 Exams and Marking Schemes Free

Educationnewshub.co.ke

Latest CRE Form 3 Exams and Marking Schemes Free Set 1 CRE P2 QS.docx ~$E P1QS.docx CRE P1QS.docx CRE P2 MRK.docx CRE P1 MRK.docx Set 2 C.R.E P1 MRK.docx CRE 1 QST.docx CRE 2…

Latest Geography Form 3 Exams and Marking Schemes Free Downloads

Educationnewshub.co.ke

Latest Geography Form 3 Exams and Marking Schemes Free Downloads Latest Exams Set Series Geography P2 QS.docx Geography P2 MRK.docx Geography P1QS.docx ~$ography P1 MRK.docx ~$ography P1QS.docx Geography P1 MRK.docx SET 10 SET…

Latest Agriculture Form 3 Exams and Marking Schemes Free

Educationnewshub.co.ke

Latest Agriculture Form 3 Exams and Marking Schemes Free Set 1 AGRIC P2 SET 1.docx AGRI P1 MS SET 1.docx AGRIC P1 SET 1.docx AGRIC P2 MS SET 1.docx Set…

Form 3 Exams for all subjects- Question Papers & Answers

Educationnewshub.co.ke

Download free Form 3 Exams for all subjects- Question Papers & Answers. All these resources are available at no cost. Form 3 Set 1 Exams Form…

Free Form 3 Term 2 Exams {Comprehensive}

Educationnewshub.co.ke

Free Form 3 Term 2 Exams 2025 {Comprehensive} available below: CRE MS ENGLISH PP1 Q (1) PHYSICS PP1 F3 MS GEOGRAPHY PHY F3 P3 KISWAHILI…

Form 4 Term 1, 2 & 3 Exams {Latest & Past Mocks, KCSE}

Educationnewshub.co.ke

Download free Form 4 Term 1, 2 & 3 Exams {Latest}: One click free downloads. Click on any link for automatic and absolutely free…

Form 3 Term 1, 2 & 3 Exams {Latest}

Educationnewshub.co.ke

Get free Form 3 Term 1, 2 & 3 Exams {Latest} by clicking on the links below: FORM 3 SUNRISE EXAMS 101 F3 ENGLISH MS 101 F3…

Form 2 Term 1, 2 & 3 Exams {Latest}

Educationnewshub.co.ke

Download free Form 2 Term 1, 2 & 3 Exams {Latest}. Achievers and Sunrise Exams available too at no extra cost: FORM 2 SUNRISE EXAMS 101…

Form 1,2 & 3 Term 1-3 Exams (All subjects)

MwalimuOnline.com

Download free Form 1,2 & 3 Term 1-3 Exams (All subjects) here. Continue downloading more free Exams below: Form 2 Examinations with marking scheme (All High…

ENGLISH PP3 FORM 4 KASSU JOINT EXAMINATION TEST PLUS ANSWERS

Educationnewshub.co.ke

Name……………………………………………………Index Number………………………………Class…………… Adm. No……………………….Date……………………………. 101/3 ENGLISH PAPER 3 (Creative Writing and Essay based on Set Texts) TIME: 2 ½ HOURS SUNSHINE SECONDARY SCHOOL (Kenya Certificate of Secondary Education) Instructions to candidates: …

Best online courses

Education resources

Form 3 Termly Exams Full Papers & Marking Schemes- All subjects

MwalimuOnline.com

Download the latest Form 3 Termly Exams Full Papers & Marking Schemes- All subjects at no cost at all. Continue downloading more free Exams below: Form…

Form 1 Exams Term 1-3 Full Papers & Marking Schemes- All subjects

MwalimuOnline.com

Looking for free secondary school exams and marking schemes? Look no further. Download free Form 1 Exams Term 1-3 Full Papers & Marking Schemes-…

History & Govt Notes, Exams, KCSE Past Papers and Revision Exams- Form 1,2,3 & 4

MwalimuOnline.com

Get free History & Govt Notes, Exams, KCSE Past Papers and Revision Exams for Forms 1,2,3 & 4. Get more KCSE Revision Materials at no…

FORM 1 ALL SUBJECTS EXAMS: TERM 1-3 FREE EXAMS & ANSWERS

Educationnewshub.co.ke

Looking for form one examinations in all subjects? You can now download form one termly exams, assignments, home works, revision papers and marking schemes…

Free End of Term 1-3 Exams and Marking Schemes Form 3 & 4

Educationnewshub.co.ke

End of Term 1-3 Exams & Marking Schemes for Form 3 & 4 Download thousands of official marking schemes and exam updates for Form 3…

Teachers' Resources

KCSE Mokasa Maths Joint Exams Free

October 5, 2025 Maverick John Leave a comment

School:………………………………………………………………………………………………
Name: ………………………………………………Adm No…………….Class:……….………
Candidate’s Signature:……………………………….. Date: …………………………………
121/2
MATHEMATICS M O K A S A 2 J O I N T E X A M I N A T I O N –
PAPER 2 Kenya Certificate to Secondary Education
MATHEMATICS PAPER 2- ALT A TIME: 2 ½ HOURS TIME: 2 ½ HOUR

Instructions to candidates
• Write your name and admission number in the spaces provided above
• Sign and write the date of examination in the spaces provided.
• This paper consists of two sections: Section I and Section II.
• Answer all questions in section I and only five questions from section II.
• Show all the steps in your calculations, giving the answers at each stage in the spaces provided below each question.
• Marks may be given for correct working even if the answer is wrong.
• Non-programmable silent electronic calculators and KNEC mathematical tables may be used, except where stated otherwise.
• This paper consists of 17 printed pages.
• Candidates should check the question paper to ascertain that all the pages are printed as indicated and that no questions are missing.
• Candidates should answer the questions in English.
For Examiner’s Use Only
SECTION I

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total

SECTION II

17 18 19 20 21 22 23 24 Total

GRAND TOTAL

SECTION I (50 Marks)
1. Solve the following equations (3mks)

2. Find the percentage error in the volume of a cone whose radius is 7.0 cm and has an exactverticalheightof18cm. (3mks)

3. Solve the equation, 2cos2x=3sinx for (3mks)

4. Simplify without using tables or calculator (3mks)

5. Withoutusingmathematicaltablesoracalculator,solvetheequation. (3marks)
2log10x – 3log102 =1-log105

6. A businessman invested ksh 1,000,000 in a fixed deposit account that pays 12% per annum compound interest, every 2 month. Calculate the number of years his amount will be Ksh 1,126,162.42(3marks)

7. Using the properties of chords and tangents, construct a tangent touching point P on the circumference of the circle below showing clearly the centre of the circle. (3marks)

8. In a soccer competition, the number of goals (G) scored in penalty kicks ispartly constant and partly varies as the skill (S) of the player. Given that G = 8 when S=2 and G =12 when S =4, find thevalue of G whenS =6. (3marks)

9. The position vector of A is OA= i-3j-3k and that of B is OB= 3i-j+2k. A point N divides AB externally in the ratio 3:1. Find the magnitude of ON. (3marks)

10. .a) Expand up to the fourth term. (2marks)

b) Use the expansion to evaluate (2marks)

11. The figure below shows a circle Centre O, radius 7cm. Angle AOB= . If a point is selected at random inside the circle, find the probability that it lies in the shaded region. (3marks)

12. The mass of a mixture P of beans and maize is 72kgs. The ratio of beans to maize is 3:5. A second mixture R of maize and beans of mass 98kg is mixed with P. The final ratio of beans to maize is 8:9 respectively. Find the ratio of beans to maize in R. (3marks)

13. A curve has a turning point at the point (1,1). Given that the gradient function of the curve is , find the value of a and the equation of the curve. (3 marks)

14. Find the area bounded by the curve , x =-3 x = 2 and the x-axis (4marks)

15. Study the figure below hence describe transformation mapping the wave y = sinx to
y = 1/2 sin2x (2mks)

16. In the figure below, ST is a tangent to the circle at S. AXBT and CXS are straight lines.

Find;
(a) The length of XB. (2 marks)

(b) The size of angle STX. (2 marks)

SECTION B – 50MARKS
17. X and Yare two points on the earth’s surface and on latitude 300 N. The two points are on the longitude 40 W and 140 E respectively(Takeπ = 22/7 and radius of the earth R =6370km) Calculate:
i) The distance from X to Y along a parallel of latitude in kilometres. (3marks)

ii) The shortest distance from X to Y along a great circle in kilometres (4mks)

iii) If the local time at Y is 8.00am on Wednesday, What is the day and the local time at X in 24
hours system.(3mks)

18. The table below shows the masses measured to the nearest Kg of 200 people.
Mass kg 40-49 50-59 60-69 70-79 80-89 90-99 100-109
No of people 9 27 70 50 26 12 6
(b) Draw a cumulative frequency curve for the data above. (4 marks)

ii) The number of people whose mass lies between 70.5 kg and 75.5 kg (1 mark)

(d) From your graph find
i) The lower quartile (1 mark)

ii) The upper quartile (1 mark)

iii) The interquartile range (2 marks)

19.

Thefigureaboveshowsthemodelofa roofwithrectangularbasePQRS.PQ=40cmandPS= 24 cm. The ridge XY = 30 cm and is centrally placed. The faces PSX and QRY areequilateraltriangles. Misthe midpoint ofQR.
Calculate correctto2decimalplacesthe:
a) PerpendiculardistanceofXYfromtheplanePQRS (3 marks)

b) AnglebetweenSXandPQRS (4marks)

c) AnglebetweenplanesRSXYandQPXY (4 marks)

20. The principal of mazuri high school intends to spend not more than ksh 18,000 to transport minimum of 70 students to the county games using two matatus A and B. Matatu A has a passenger capacity of 10 and B a capacity of 30.The cost per trip for matatu A is ksh 2000 and that of matatu B is ksh 3000. Given that A makes less than 5 trips.Taking trips made by matatu A be x while trips made by matatu B be y
a) Write down all the inequalities to represent the above information. (4marks)

b) Use the grid below to represent the above information. (4mks)

c)Find the number of trips that each matatu should make to minimize the amount of money the school will spend. (2mks)

21. (a) A quantity p varies directly as the square of q and inversely as the square root of r. If q increases by 20% and r decreases by 36%, find the percentage change in p. (3 marks)

(b) The velocity of water flowing through a pipe is inversely proportional to the square of the radius of the pipe. If the velocity of the water is 30cm/s when the radius of the pipe is 2cm. Find the velocity of water when the radius of the pipe is 4cm. (3 marks)

(c) Three quantities X and Y and Z are such that X varies partly as Y and partly as the inverse of the square ofZ. When X= 6,Y= 3 and Z = 2.When X = 8,Y=5 and Z = 1.Find the value of X when Y = 10 and Z = 8 (4mks)

22. (a) Complete the table below for the function . (2 marks)

(b) On the grid provided, draw the graph of . for . (3 marks)

(d) By drawing a suitable line, use the graph in (b) to solve the equation . (3 marks)

23. A triangle with vertices A(1,1),B(3,1) and C(2,3) undergoes a transformation represented by the matrix to A’B’C’.
(i) Draw the triangle ABC on the grid provided. (1mk)

(ii) Calculate the coordinates of A’B’C’ and draw it on the grid hence describe the transformation that maps ABC to A’B’C’. (3mks)

(iii) The triangle A’’B’’C’’ A’’(2,0) ,B’’(6,-2) and C’’(4,1) is the image of triangle ABC.
i) Draw triangle A’’B’’C’’ on the grid provided. (1mark)
ii) Find the matrix of transformation that maps A’’B’’C’’ to ABC. (3marks)

(iv) Triangle DEF area 60cm2 undergoes transformation represented by the transformation matrix . Find area of the image of triangle DEF. (2marks)

24 .(a) (i)Using a ruler and a pair of compass only, construct a triangle ABC in which AB=6cm,
BC = 7cm and angle ABC = 75o (3mks)

Measure:
(i) Length of AC (1mark)
(ii) Angle ACB (1mark)
(b) Locus of P is such that BP = PC. Construct P (2marks)

Teachers' Resources

CRE FORM 3 WORK (SIMPLIFIED NOTES)

October 5, 2025 Maverick John Leave a comment

FORM THREE

SELECTED TEACHINGS FROM THE NEW AND THE OLD TESTAMENTS

TOPIC ONE: GIFTS OF THE HOLY SPIRIT

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

a) Discuss what Jesus taught about the role and gifts of the Holy Spirit.
b) Describe the manifestations of the Holy Spirit in Christianity today.
c) Identify the fruits of the Holy Spirit
d) Interpret the message of Peter on the day of Pentecost.

LESSON ONE: TEACHINGS OF JESUS ON THE ROLE OF THE HOLY SPIRIT. Read JOHN 14:15-26, 16: 5-15,

and ACTS 1: 7- 8

Introduction

The Holy Spirit is the third person in the trinity. There is the power of Christ, the power of God, and the

Holy Spirit who gives gifts such as prophecy and healing. The Holy Spirit is mentioned several times in

the Bible; (1) during creation in Genesis, (2) at the annunciation of the birth of Jesus, (3) at the beginning

of the ministry of Jesus, (4) during baptism, (5) revelation of Jesus in the temple (6) Jesus spoke of the

Holy Spirit during his mission or ministry, after resurrection and before ascension

Learning outcomes. By the end of this lesson:

State the role of Holy Spirit in the church and in Christian lives today
Enumerate the gifts of the Holy Spirit
Analyse the Manifestation of the Holy Spirit in the church and Christians today
Give the role of love in church and in Christian lives today
The role of Holy Spirit in Church and in Christian lives today.

Read JOHN 14:15-26 and JOHN 16: 5-15, ACTS 1: 7- 8

The Holy Spirit has many roles in the church and in Christian lives today. These roles are to:

 Teach Christians on a daily basis messages of Jesus

 Live in the hearts of believers of Christ

 Be an advocate, a counselor, helper and a comforter to those who love Jesus Christ and obey God’s

commandments.

 He would remind the disciples the words said by Jesus Christ and introduce them to their deeper

meanings.

 Interpret the deeper meaning of the messages of Jesus Christ.

 Reveal the truth and mysteries of and about God.

 Affirm the right of Jesus as the Son of God.

 Reveal the glory of Jesus death.

 Reveal what is right and wrong

 Give the disciples of Jesus power to become witnesses of Christ.

 Give courage to the disciples of Jesus and modern Christians to face prosecution on the account of

following Jesus.

 Enable the disciples to expose the secret lives and heart of sinful people.

 Guide Christians; help believers to cast away evils spirits, to heal, to preach the word of God, to

encourage, and to condemn evil in the society.

Paul teaching about the Gifts of the Holy Spirit.

Read 1 Corinthians chapters 12, 13, and 14.

Spiritual gifts are extra-ordinary favors, talents, abilities, and dispositions given to Christians by God for

the benefit of all believers. The gifts are used for the service of others and not for self-glorification and

gratification.

The message of Peter on the day of the Pentecost

Peter told the disciple that what was happening was the fulfillment of Jesus’ prophecy.

– He said that Jesus of Nazareth was the Son of God.

– He said that the suffering and death of Jesus was according to God’s plans.

Death was the fulfillment of the Old Testament prophecy.

Gifts of the Holy Spirit

Gift of wisdom: – having deep understanding of issues- ‘seeing far’, being perceptive.
Gift of knowledge: – ability to understand the basic facts about Jesus, His mission and knowledge

about spiritual issues.

The gift of faith: – refers to the confidence in God’s help. It is deep trust in God.
The Gift of healing: – ability, and power to heal all forms of sickness by calling upon the name of Jesus

Christ.

The gift of performing miracles: – gift of healing miracles, creative miracles for example, dead legs

becoming alive.

The gift of preaching
The gift of prophecy: – the ability to interpret God’s word. The ability to foresee what will happen in

the future as revealed by God.

The gift of distinguishing spirits or discernment: – the ability to know whether a spiritual gift is from

God, the Holy Spirit or from the evil spirit

The gift of speaking in tongues. The ability to utter, speak in a tongue, language unknown to the

believer. Tongues are used when addressing God for self-edifications. It is personal growth.

The gift of interpretation of tongues: – the ability to understand and interpret the messages of those

speaking in tongues.

The gift of love. (Read 1 Corinthians 13)

Paul stressed that all the gifts of the Holy Spirit are to be demonstrated with love. He stressed that love,

a fruit of the Holy Spirit is supreme over other spiritual gifts possessed by Christians. It’s the greatest of

all. Speaking in tongues, preaching, and martyrdom without love is useless.

Components of Love

Love is patient, kind, not jealous or boastful, not arrogant or rude, is not ill mannered or selfish, and

does not insist on its own way. It is not disrespectful. It is not irritable or resentful. It does not rejoice at

wrong but rejoices in truth. It bears all things.

Love believes all things, hopes all things, and endures all things. Love is eternal. Love never fails. The

other gifts are temporary but love, faith and hope are eternal.

Manifestation of the Holy Spirit in the church and Christians today

Gifts of the Holy Spirit have been manifested in churches today. We see this manifestation through

people possessing the gifts of the Holy Spirit. For example, leaders in church have displayed the gift of

wisdom. Preachers, and Christian’s ministers have been casting out demons and performing healing.

There are reported cases of interpretation of tongues and gift of prophecy in churches today.

When Christians display the gifts of the Holy Spirit such as speaking in tongues the Holy Spirit is

manifested. Other manifestations of the Holy Spirit are:

 Through healing, prophecy, gifts of discernment, boldness in preaching, and casting out demons

among others

 Christians helping the poor by giving generosity and in kindness.

 Through singing, dancing, shouting (fruit of joy)

 Through unity of believes and fellowships.

 Through praying,

 Christian’s persecutions/temptations.

Criteria for Discerning the Gifts of the Holy Spirit.

Christians who have the Holy Spirit and are guided by Jesus have certain characteristics. These are:

 They will confess that Jesus is Lord

 They cannot say a curse.

 They speak the truth. They worship God and behave in accordance with Jesus teaching.

 They led by the Holy Spirit and are known by the fruits of the Holy Spirit. These fruits are love, joy,

peace, and patience.

 Such persons serve all Christians without discrimination and strife.

 They do not do sinful acts such as sexual immorality. They do not practice idolatry, and sorcery. They

do not have in their hearts and minds hatred, and jealously or any other negative feelings and actions.

The fruits of the HOLY SPIRIT (GALATIANS 5:16-26)

Paul taught that the fruit of the spirit are: Love, Joy, Patience, Long suffering, Goodness or Generosity,

Faith and faithfulness, Peace, Meekness and kindness, gentleness, self- control and temperance.

Answer these questions after reading – JOHN 14:15-26 and JOHN 16: 5-15, ACTS 1: 7- 8 and 1

Corinthians chapters 12, 13, and 14.

What is the role of the Holy Spirit among Christians? (Read a)
Discuss the gifts of the Holy Spirit
Write a talk about the Holy Spirit
Define love?
Describe the different types of love
Why do Christians need the Holy Spirit today?
State the role of love in church and in Christian lives today.
How has the gift of the Holy Spirit been manifested in Christian lives?
Which activities show that the Holy Spirit is working among Christian in Kenya.
How have the gifts of the Holy Spirit been misused in the church today?

Answers are also in the text. Read sections with answers

The role of the holy spirit

An advocate, a counsellor and a comforter.

He would remind and introduce the disciples to the deeper meaning of the word of Jesus Christ.

To reveal the myth and mysteries of God.

He would affirm the right of Jesus as the Son of God.

He would reveal the glory of Jesus’ death.

He would enable the disciples to discern and expose the secret heart of sinful men.

The gift of the Holy Spirit has been misused today by pride and public manifestation of the gift as a

way of show off. Some Christians have misused the gift of Holy Sprit of prophecy by prophesying for

money.

LESSON TWO. PETER’S MESSAGE ON THE DAY OF PENTECOST. Read ACTS 2: 14-41

Introduction

Jews commemorate Pentecost day. This is the day that God gave Moses his laws on mount Sinai. It is

also referred to as the festival of weeks. Pentecost day was celebrated 50 days after the Passover. It was

compulsory for all Jews. On this day, Jews brought offering, the first fruits of harvest, to the temple in

Jerusalem.

Learning outcomes. By the end of this lesson You should be able: –

Describe Pentecost day
Narrate Peters’ Message.
Explain the relevance of the Pentecostal Experience
Pentecost a day

On the Pentecostal day, the disciples were gathered in Jerusalem awaiting the promise of the Holy

Spirit. And as promised, the Holy Spirit came in the form of a strong wind, and tongues of fire. The Holy

Spirit rested on the head of each disciple. The disciples received the gift of the Holy Spirit. They spoke in

new tongues. Some of the observers mistook this experience. They thought that the disciples were

drunk with wine.

Peter stood up to explain what was happening and defend the disciples. He told those who saw the

experience that the disciples were not drunk. It was in the morning.

Peter’s Message. Read Joel 2: 28 – 32

Peter told the onlookers that; what was happening is fulfillment of Joel’s prophesies about the

outpouring of Gods spirit. He said that Jesus of Nazareth was the Son of God. This was proved by the

miracles that Jesus performed. He emphasized that the suffering and death of Jesus was according to

God’s plans. Jesus is a descendant of David. Death and the resurrection of Jesus fulfilled prophesies in

the Old Testament.

God raised Jesus from the dead. He taught that Jesus had both the nature of God and Man. The apostles

are the living witnesses of the resurrection of Jesus. Jesus has been exalted and sits on the right hand of

God where He is Lord and Judge. They holy Spirit is a gift from Jesus

Peter then invited the listeners to repentance so that they could be forgiven and receive the gift of the

Holy Spirit. Three thousand souls accepted salvation message and were added to the fellowship of the

disciples.

After the Holy Spirit infilling.

The disciples sold their possessions and goods and assisted the needy. They did many wonders and

signs. They continued to live in unity, worshiping God, fellowshipping together, and breaking the bread.

Lessons Christians learn from Leadership of Peter.

Christians should be:

Courageous and stand up for Jesus Christ all the times.
Ready to spread the Gospel of Christ.
Win new converts to Jesus by inviting them to repentance.
Have faith in the risen Christ.
Pray to be filled with the Holy Spirit like Peter and those in church leadership should take their roles

seriously.

Relevance of the Pentecostal Experience

Speaking in diverse tongues signified that Christianity is a universal religion. It pointed out the

importance of all languages when communicating to God. There were no specific languages for speaking

with God, as it was when Latin was the language of literacy and Christianity.

Christians should be bold in their preaching. They should not be afraid as they have the counsel and

helper, the Holy Spirit. Christians should understand that God chooses anyone as a leader, preacher, and

witness of Christ.

Pentecostal experience signifies that Christians need to receive and be filled with the Holy Spirit

Revision questions

a) Explain the meaning of the Pentecost
b) Describe the manifestations of the holy spirit on the day of the Pentecost (Acts 2: 1-40)(or narrate the

events that took place on the day of the Pentecost)

c) Write down five teachings about Jesus from Peter’s speech on the day of the Pentecost
d) What were the qualities of peter that made him a successful leader of the apostolic church?
e) What lessons can Christians learn from the events of the day of the Pentecost?
f) State the teachings of Jesus on the holy spirit (John 14:14-26) (acts 1:7-8)
g) What is the role of the holy spirit according to Jesus?
h) What is the role of the holy spirit in the believers or the church or Christians?
i) Outline the fruits of the holy spirit
j) State the criteria for discerning the spiritual gifts
k) List down the gifts of the holy spirit
l) Explain why Paul taught that love is the greatest of all spiritual gifts
m) Explain how the Holy spirit is manifested in the church today
n) State ways in which the gifts of the holy spirit are being abused in the church today

TOPIC TWO: THE UNITY OF BELIEVERS

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

a) Explain teaching in selected New Testament texts of the unity of believers.
b) Identify the metaphors used to describe unity of believers.
c) Identify the causes of disunity in the early and modern church

LESSON ONE: TEACHINGS OF THE UNITY OF BELIEVERS IN SELECTED NEW TESTAMENT TEXTS

Unity of believers refers to oneness of those who have faith in Jesus Christ.

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

Describe activities of early Christians
Describe characteristics of the people of God

iii. Explain the meanings of these symbolic expressions

– The body of Christ

– The Vine and the Branches

– The Church / Assembly of God

– The Bride

Early Christians

The early Christians in Jerusalem demonstrated their unity by.

 Holding joint prayer sessions

 Sharing the Lords supper, that is Eucharist.

 Sharing their possessions with the poor.

The showed oneness and unity as believers. They expressed their oneness using various terms, images,

metaphors and symbols. They regarded themselves as the people of God, the church and an Assembly

of God. When they celebrated the last supper, eating of bread was a symbol of the body of Christ. They

saw themselves as belonging to one tree with the vine and branches. As followers of Christ, the early

Church saw itself as the Bride of Christ.

Discussion of Symbolic Expressions
The people of God

Read 1 PETER 2: 9-10. Peter has outlined the characteristics of the people of God. He says that the

people of God are

Believers in God: through faith in Jesus Christ.

The ‘Chosen race’, ‘a royal priesthood’, a holy nation’ ‘a chosen people’

Those who stand out from the rest because they live a holy and righteous life.

Form a Holy nation chosen to proclaim the works of God.

Not just the descendants of Abraham but people who follow Jesus Christ and His teachings.

The body of Christ

Read 1 Corinthians 12:12-27, and Ephesians’ 4:1-12.

The Holy Spirit is the one who brings Christians together as one body of Christ to serve the church.

Christians are given gifts for the purpose of sharing the body of Christ.

Jesus Christ is the head of the church. And just as the body has many parts, playing different roles, so

has the Church. Every member of the church plays a vital role because different members have different

spiritual gifts and callings. Some are Apostles, Teachers, Prophets, Evangelists, Pastors and Miracle

performers, Administrators and those who show mercy to others and encourage (exhort) others.

All church activities should be directed to the welfare of the church, just as the function of each part of

the body is necessary for the well being of the whole body. To have a united body, members should be

meek, and patient in order to bear the fruit of the Holy Spirit. For a church to be united, or to be

considered as one body, Christians should have faith in God the father, one Lord Jesus Christ, one Holy

Spirit and have faith in God through Jesus Christ.

iii. The Vine and the Branches

Read John 15:1-10

The vine represents Jesus. Vine tree was a tree that bore grapes. The vine tree was a symbol of

prosperity and peace. Jesus is the vine and the Father is the vinedresser. Christians/ believers are the

branches. They are expected to produce good fruits by remaining faithful and united in Christ. Faithful

branches bear fruit like good Christians while unfruitful branches are like unfruitful Christians.

Christians should remain united to Christ who is the vine so as to bear fruits. The teachings of Jesus

purify the Christians. The dead branches of the Vine trees are cut off and the livings ones are trimmed or

pruned. This is done so that the vines may produce high yields. Likewise unfaithful Christians, believers

are rebuked and corrected so as to bear high yields.

The Church or Assembly of God. Read Ephesians 5: 21 – 32

Church is a Greek word “““ekklesia””, which means people. People who belong to the Lord. Assembly of

God is the coming together of people of diverse social and cultural backgrounds who recognize lordship

of Jesus. The church is likened to the relationship between a husband and a wife. Christians (the church)

are expected to be united with Christ just as a husband and wife are united in marriage. Just as

husbands and wives are expected to love one another, so too, are Christians called upon to express love

to one another and to love God.

A husband is the head of a family; Jesus is also the head of the church.

The Bride. Read 2 Corinthian 11: 2, and Revelations 21: 1 – 12

In the Old Testament, God calls Israel a bride. In the New Testament, Christians are referred to as “a

bride’ in the New Jerusalem’. God or Jesus Christ is the bridegroom. Christians are reminded that the life

on earth is a temporary home. Their real home is in heaven, the Holy city of God. Just as a bride is

expected to be faithful to her husband, so are Christians expected to be faithful to God by observing the

covenant way of life. Deviation from the covenant was portrayed as adultery.

John, who wrote the book of revelations, sees a vision of a new heaven and a new earth in which faithful

Christians will be rewarded. Christ will come to take His bride to eternity to live there forever. The

relationship between Christians and Jesus/ God is like a marriage. It is a covenant. It is a relationship

where the church (bride) is expected to submit to God. Jesus died for the church, a show of His or God’s

love. Likewise Christians should be committed in their relationship to God.

SAQ. 1. Discuss in twos who is a bride and what takes place in a wedding.

Discuss the significance of the symbols used to express the unity of the believers. These are “The

people of God”, “The body of Christ”, “The vine and the branches” “The church or assembly of God” and

“The bride”.

LESSON TWO: CAUSES OF DISUNITY IN THE EARLY CHURCH

The early church experienced some challenges, which led to divisions among the early disciples and

Christians.

Learning Outcomes. After reading this lesson,

i Identify causes of disunity in the early church

ii State causes of disunity in the modern church

iii Compare the causes of disunity in the early and modern church

iv Suggest possible solutions to disunity in modern church

Causes of Disunity in the Early Church

After Jesus ascended to his Father and left the Holy Spirit to look after his followers, the disciples

established congregations or communities to spread the Word of God. As believers of Christ met and

prayed together, there were disagreements and divisions brought about by several factors and issues.

These were:

Disputes, among early Christians; concerning leadership of the Church. Christians wanted different

leaders: Paul, Apollos, Cephas or Christ. Paul told them that Christ couldn’t be divided (1 Corinthians

1:10 -21).

Sexual immorality was another cause of disunity in the early church. Some Christians were doing or

having irresponsible sexual behaviours. These were incest, fornication, and prostitution. Paul

condemned such behaviours and told Christians to stop sinning and honor God with their bodies. The

body of a Christian is the temple of the Holy Ghost (1 Corinthian 5: 1-13, 6:12 – 20).

Christians settling disputes in civil courts. Paul advised they ought to talk over issues among themselves

and agree to solve problems on their own (1 Corinthians 6).

Dispute over marriage and divorce. Some Christians were opposed to marriage. Others were

encouraging divorce. Paul addressed these issues in 1 Corinthian, chapter 71-16. Paul advised Christians

that it was okay to marry or not to marry. But marriage was needed to stop immorality.

Eating of meat offered to idols. Some Christians were eating meat offered to idols while others were

against it. Paul advised Christians not to eat anything that will cause their faith to weaken or fail. (1

Corinthians 8 and10: 14 – 20.

There were disputes about dressing during worship. Should women cover their head during worship?

Should women shave hair? Should men wear long hair? (1 Corinthian 11:1-16).

Some Christians were overeating and over drinking during the Holy Communion – misuse of the Lord’s

Supper, (1 Corinthians 11:17 – 33).

Misuses of spiritual gift especially the gift of speaking in tongues. Paul taught that all gifts are equal (1

Corinthians 12).

There was a misunderstanding about the resurrection of the body and the dead. Some were saying

there is no resurrection. Paul preached that if there is no resurrection then their preaching was in vain

as they were witnesses to the resurrection of Jesus Christ (1 Corinthians 15).

Causes of disunity among believers and church in Kenya today

Leadership differences. Some Christians are struggling for power. This has led to formation of splinter

groups, divisions and enmity between these groups.

Cultural differences. Christians are divided by their African cultural beliefs from their backgrounds. This

culture is merged with Christianity and Western cultural practices forming a unique mixture of beliefs.

Some Christians are permissive, while others are conservative. This has led to disunity, for example in

the areas of dressing.

Discrimination. There is inequality within the church between the rich and the poor, the whites and

blacks. Some Christians are viewed as more spiritual than others, on basis of the tribe, gender, wealth

and social status among others.

Misuse of freedom of worship. Christians are starting sprinter churches, probably because they want to

control church finances without supervision by the wider church. To justify their departure, they spread

propaganda against the ‘mother’ church, and other churches in order to attract followers. The more

followers a church has the more tithe it collects.

Misuse of church funds. Some church leaders and followers misuse church funds

Differences in the practice of baptism

Arrogance and pride by some Christians.

Sins: sexual immorality in the church, divorce and marriage issues.

Some Christian denominations reject the human nature of the person of Jesus Christ; that Christ had

both a human and divine nature e.g. Nomiya church.

SAQ. Can you think of factors that led to disunity among Christians in the early church that you have

noted in the Kenyan church?

Reasons why Christians should work in Unity.

Christians face many problems and they therefore need to work together in unity to:

Promote oneness of Christians in Jesus Christ.

Promote the teachings of Jesus Christ.

Achieve effective evangelism or ministry.

Adopt a common attitude to the integration of African culture in worship.

Prevent the formation of sprinter groups and cults.

Reduce the internal wrangling.

Have a common stand in dealing with issues affecting the society.

Possible Solutions to disunity

The church should settle issues that divide its members by Christians:

Learning to appreciate and respect the practices and belief of other Christian’s denominations.

Having or forming a common goal

Striving to be guided by the principle of love in solving problems facing them.

Observing the teachings of disciples, prophets, apostles, God, laws of Moses, Jesus and the Bible.

Avoiding doing anything to their fellow Christians that would cause suffering and disharmony.

Activities that the early church did in order to remain united were that they:

Ate bread together.

Held fellowships together.

Shared with the needy.

Prayed together for each other

In the current worldwide Church, there is disunity amongst believers or Christians. The most common

ones are due.

Leadership differences and wrangles for power.

Cultural differences amongst Christians.

Some Christians are permissive while others are conservative.

Differences in the interpretation of the Bible.

Misuse of church funds

Pride and arrogance.

Revision questions

Write down terms used in the new testament to refer to believers in Christ
Identify five causes of disunity in the church today
Identify factors which cause disunity among the Christians today
Discuss reasons why members of Christian families in Kenya find it difficult to harmoniously live

together

Explain how the church strengthens family relationships today

TOPIC THREE. TEACHINGS FROM SELECTED OLD TESTAMENT

PROPHETS

INTRODUCTION

This chapter introduces one to the work of prophets in the Old Testament. In Form One, some prophets

were taught e.g. Moses, Elijah, Nathan and Samuel. Traditional African prophets were also taught.

In Form Three, we compare true and false prophets and the Traditional African prophets.

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

Define a prophet, and prophecy
Identify categories of prophets
Explain the importance of prophets in Israel.
Describe the characteristics of prophets.
Explain how prophetic messages were written.
Compare the relationship between prophesies in the Old Testament and the New Testament

LESSON ONE: PROPHETS

Learning outcomes. After reading this lesson, you should be able to: –

Give a correct definition of a prophet, and prophecy
List prophets in categories
Definitions of a prophet, and prophecy

The word prophet comes from a Hebrew word “Rabii’ meaning ‘one who is called or one who

announces God’s message. A prophet is also referred to as a seer. A prophet is a person sent by God to

teach and give people messages about things to come in future from God. Prophets received divine

messages from God and communicated them to the people.

A prophet is therefore a person who foretells events as revealed to him or her by God. Examples of

prophets include Samuel, Elijah, Jeremiah and prophetesses (female prophet) Deborah, and Huidah.

Prophecy is a statement, a message of something that is going to happen in the future. The action of

giving future messages is called prophecy.

Categories of prophets

There were many categories of prophets. These were:

a) Major Prophets. These were Prophet’s whose messages covered a long period of time. Their

messages were long and detailed. For example Prophet Jeremiah, Ezekiel, and Daniel.

b) Minor prophets. There are 12 books of the Minor Prophets examples They are called minor because

their messages are short, brief and do not contain detailed information. The Minor Prophets are Amos,

and Hosea, Joel, Obadiah, Jonah, Micah, Nahum, Habakkuk, Zephaniah, Haggai, Zechariah, Malachi.

c) Canonical prophets the term canon means law. Canonical prophets are law prophets. The individual

utterances of these prophets are laws. Both minor and major prophets are canonical prophets,

d) The early prophets are Moses, Nathan Elijah, and Elisha. These prophets belonged to guilds schools.

Their prophecies are not recorded under their names. Their prophecies are written in books, which do

not bear their names.

e) Cultic prophets like Hannah (N.T.) served in the places of worship. They assisted the priest officiating

worship

f) Professional / court prophets like Samuel, Micah, and Gad lived together in the temple and in groups.

They earned their living through their work. They did not work elsewhere

g) False prophets are pretenders to speak in the name of Yahweh but God did not call them. They spoke

lies in accordance with the messages people wanted to hear.

Characteristics of true prophets

There were two (2) major categories of prophets in the Old Testament, (1) true prophets and (2) false

prophets. True prophets are those whose prophecies occurred and were fulfilled. Prophesies of false

prophets did not occur. True prophets distinguished themselves from false prophets and ordinary

people.

They experienced God dramatically when He called them and in their ministry. They were God’s

spokesmen and women. They responded in faith to their call.

God gave them specific tasks in their commission and God’s assurance and support in their ministry.

They urged people to repent and turn back to God.

In their messages, they taught that God demands sincere worship and not elaborate rituals. They

understood God and taught about God righteousness, goodness, mercifulness, and loving care. They

condemned evil in the society and proclaimed God’s judgment and punishment to those who failed to

keep the covenant. They spoke with authority and acted with courage. They upheld God as a universal

God for all nations. They talked of a remnant that shall remain after punishment or those that have

continued to worship God sincerely. Their utterances were true because they were fulfilled

They spent a lot of their time in prayers. They prayed regularly. At such times they withdrew from

people in order to have a quiet time to seek God.

All the true prophets received opposition from their audiences and they were ready to suffer for telling

God’s word.

The Characteristics of false prophets.

Some of the prophecy of false prophets contradicted prophesies of the true prophets. False prophets

followed their own imaginations, and gave false hopes. They told people what they wanted to hear.

They had no personal knowledge of God. Hence, their prophecies were not in line with the divine

revelations.

They used evil forces such as magic, and divinations to call upon the spirits of the dead. They were paid

for prophesy and benefits materially from their clients. They served Baal and were mainly immoral. They

committed crime.

Review questions

How can we know true and false prophets today?

LESSON TWO: IMPORTANCE OF PROPHETS IN ISRAEL

Introduction

Learning outcomes. After reading this lesson, you should:

Describe the work of prophets in Israel
Explain how God communicated with prophets and Israelites
Analyse the content of the Prophetic messages
Work of prophets in Israel

Prophets kept Israelites in communication with God. They communicated God’s will to the people of

Israel. They foretold God’s judgments and punishment for sinners. They condemned the behaviour of

the rich towards the poor. Through their messages, people reformed their lives since they condemned

all forms of social evils and ritual sins.

They contributed to the writing of their messages leading to the compilation of the Bible.

Prophets guided and gave people hope. They taught people the laws of God. They warned people of

dangers to come. They condemned idolatry and stressed the worship of one true God, Yahweh.

They anointed the Kings in Israel. Kings consulted the prophets before any major undertaking such as

war among others.

They acted as conscience of kings. They advised them and challenged Kings when they went wrong.

God’s communication with prophets and Israelites

God communicated to Prophets through visions, voices that were audible and clear, events, prayers,

dreams, signs, ordinary things, and words which came to their minds with great power.

Writing messages of the prophets

The canonical prophets as mentioned earlier had their works and prophecies recorded under their

names. Canonical prophets are referred to as writing prophets. It’s possible that some prophets wrote

down their own prophecies. They wrote what God spoke to them as He dictated. An example is

Jeremiah who wrote what he was told …’Get a scroll and write on it everything that I have told you

about Israel, Judah and all nations. (Jeremiah 36:2, Isaiah 30:8).

Two, the prophet’s message were probably written by other people. These were their assistant,

secretary, scribe, and disciples or followers as the prophet prophesied.

Thirdly some of the prophetic messages could have been preserved as oral traditions and later written

as books. A good example is 2 Kings.

Content of the Prophetic messages

Prophetic messages contained lessons from God to Israel. For example, the:

Prophetic sayings were and still are oracles or poetic passages spoken by God himself through

prophets. The prophecies were addressed to different nations. They carried specific teachings to the

people, for example predicting future occurrences

Narratives in the first person give an account of the prophet’s testimony. They spoke of their

experiences with God, and responses to the call of God. They tell us about prophet’s impelling

compulsion to speak God’s word. The narratives are written in the first person. They have a format ‘ The

Lord said to me… The year that King Uzziah died, I was the Lord…”

iii. Narratives in the third 3rd person have messages written by a third party, i.e. not the prophet but

another person. For example, “Isaiah said to them, “Thus you shall say to your master, thus says the

Lord: “Do not be afraid of the words.” (Isaiah 37:6). The message recounts the prophets’ personal life,

and political background.

LESSON THREE: PROPHESIES IN THE OLD TESTAMENT, NEW TESTAMENT AND AFRICAN TRADITIONAL

SOCIETY

Introduction

The Israelites and the African traditional societies as well as other world communities had prophets who

foretold the future. Among the Israelites, there were prophets chosen by God and false prophets who

told messages which communities wanted to hear. Among the African traditional communities, there

were wise men and women who prophesied about the future.

In this lesson, we shall compare these prophecies and learn what was similar and different about these

them. The Old Testament prophecies are compared with those from the African traditional society and

the New Testament

Learning outcomes. After studying this lesson, you should be able to:

State relationships between Prophesies in the Old Testament New Testament and the African

Traditional Society

Discuss the similarities between prophets in the African traditional society and the Old Testament
Identify differences between prophets in the African traditional society and the Old Testament
Relationships between Prophesies

Several Old Testament (O.T.) prophecies were and are fulfilled in both the old and New Testament (N.T)

in the life and ministry of Jesus Christ. The Law of Moses is used in both the Old Testament and the New

Testament. However Jesus gave the law a deeper meaning.

The teachings and prophecies of the prophets provided the foundation for the message in the New

Testament. The prophecies of Prophet Nathan to King David that God would raise up an offspring from

the lineage of David was fulfilled in Jesus Christ, the expected messiah.

Jesus disciples in the New Testament referred a lot to messages in the Old Testament. The teachings of

Jesus in the New Testament are based in the Old Testament prophecies. They are therefore similar to

each other because New Testament is a continuation of the Old Testament.

The New Testament is the new covenant spoken of by Prophet Jeremiah and other Prophets like Isaiah,

Micah, and Nathan. Their prophecies about Messiah are fulfilled in the New Testament.

Similarities between prophets in the African traditional society and the Old Testament. In both

traditions, prophets:

 Were endowed with divine powers and they dealt with religious matters.

 Acted as intermediaries between God and people

 Warned people of impending dangers and disasters due to disobedience

 Had supernatural experiences

 Encouraged morality and discouraged evil ways

 In some cases, could heal

 Withstood oppression and opposition by the political rulers

 Encouraged people to fight injustices in society

 Foretold future disasters such as drought and wars. They explained why they were going to occur.

 Were consulted when things were not well in the society.

 Received revelations through dreams, visions and thoughts

 Were gender sensitive male prophets and female prophetesses.

Differences (O.T.) between prophets in the African traditional society and the Old Testament.

The Old Testament prophets had a personal relationship with God. They communicated God’s messages

to Israelites.

The prophets in the African traditional society communicated and received messages from the ancestor

spirits

Old Testament prophets were God’s mouthpieces. They began their prophesy with ‘thus saith the

lord’…. While the prophets in the African traditional society predicted what would happen to individuals,

and communities.

The authority of prophets in the Old Testament came from God while the authority of prophets in the

African traditional society came from their ancestors’ spirits.

In the Old Testament prophets were called directly by God while in some African traditional

communities the prophetic office was hereditary. The African traditional prophets dealt with family and

local community issues while Old Testament prophets dealt with national issues, and crises. African

traditional prophets were diviners while Old Testament prophets consulted God.

Relevance of Old Testament prophets to Christians today

Christian should be ready to be messengers of God. The call to be a Christian has a prophetic role. Some

Christians are called to the office of a prophet and should prophecy for the glory of God and for the

common good of the people. As God’s spokes person one should always stand for the truth. Christian

should proclaim God’s will even if the message is not pleasant to the people.

Once appointed as a prophet, one should pass the messages to who ever they are sent to without fear

or favour. God’s messengers should always condemn the social political economic evils in the society.

As God’s messengers Christians should live exemplary lives. They should stand for what they preach and

should expect persecutions because of their works as God’s messengers. They should be ready to suffer

for the sake of the gospel.

Christians should pray to God to give them guidance, wisdom, and inspiration to be able to handle

hardships in their lives. They should provide hope for the people in times of suffering.

Christians should realize that God calls both men and women to His service. They should be ready to

obey Gods’ prophetic call and not run away e.g. Jonah. They should be concerned and take care of the

welfare of the poor community members.

Revision questions

Define the terms prophet and prophecy
List five categories of true prophets
State the difference between true and false prophets
In what ways were God’s prophets called?
Outline the similarities and differences between the old testament prophets and the traditional

African ones.

What is the relevance of prophets to Christians today?

TOPIC FOUR: PROPHET AMOS

Introduction

Amos is one of the prophets God sent to Israel to warn the people because of their evil life.

Politically, the Nation of Israel had become rich. There grew classer, the rich and the poor. The rich

started oppressing the poor.

Socially, there was still the rich – poor gap. The rich exploited the poor. Merchants sold bad food,

expensive and used false measurer.

Religiously, the Israelites had turned away from God and were worshiping false gods. Syncretism was

practiced. Priests were paid and God’s prophets were rejected.

It is in this situation that Amos was called.

He is called through visions.

Amos is one of the canonical or writing prophets. The book of Amos is a temptation of oracles spoken by

the prophet on different occasions. Note that after the death of King Solomon, the kingdom of Israel

was split into two and rules by Rehoboam and Jeroboam. The northern Kingdom; called Judah was ruled

by Rehoboam and was inhabited by two tribes. The southern kingdom called Israel was ruled by

Jeroboam and was inhabited by 10 tribes. Amos came from Judah and prophesied in Israel.

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

a) Analyse Prophet Amos work in Israel
b) Describe the call of Amos
c) Explain the teaching of Amos
d) Relate relevance of Amos teaching to Christianity today

LESSON ONE: Prophet Amos work in Israel

Read Amos 1:1

Learning outcomes. After reading this lesson, you should:

Describe the call of Amos
Describe the socio, political and economic situation in Israel during the time of Prophet Amos
Explain religious situation in Israel
The call of Amos (AMOS 1:1,3:8,7:10 – 15)

Prophet Amos was born in a village called Tekoa in Judah, the southern kingdom. Before his call, Amos

was a shepherd and a dresser of sycamore trees. He was not a professional prophet. But God called him

to be a prophet. He received his call in form of a vision around 758 BC. Amos responded to God’s call

with obedience. He felt a deep compulsion to prophesy (Amos 3:8). God directed him to give his

message to the people of Israel, the northern kingdom (Amos 7:15). He was asked to speak the will of

Yahweh. He was also to fore tell punishment if Israelites did not repent their sins. His message was

opposed, and challenged by Amaziah the priest of Bethel.

Religion. Israelites worshipped Yahweh and other gods. Idolatry was also present. This form of

worship is called Syncretism . There was religious hypocrisy. Like today, there was an emphasis on

external observances of religious practices and less concern for internal observances. The priests were

paid for religious work. Those who couldn’t pay did not have religious ceremonies. They were offered at

the expense of the poor. The prophets of God were rejected.

Social – economic – political situation. When Amos prophesied, King Jeroboam ruled Israel, the

northern kingdom while King Uzziah ruled Judah. Amos was sent to prophesy to the people of Israel in

the northern kingdom. He concentrated his work mainly in Bethel and Samaria – the capital city of Israel

and the main centres of worship.

When Amos started his prophesy, there was peace and prosper in Israel and Judah. Both kingdoms were

wealthy. However, the wealth did not reach the poor. This was because the wealth and power were in

the hands of the king, his family, his officials, and wealthy merchants. As a result, Israel citizens were

divided into two classes; the rich and the poor.

Unfortunately, the rich people owned big luxurious houses. They drunk wine, and used the most

expensive perfumes. They acquired their wealth at the expense of the poor. They oppressed and

exploited the poor. The merchants of trade for example, were dishonest in their trade businesses. They

sold bad wheat to unsuspecting customers and overcharged customers by measuring with false scales.

Because of the inflated prices, the poor borrowed money from the rich at high interest rates to buy

basic things like food. Hence, there was massive bribery and corruption in society and law courts.

As a result the poor lacked basic necessities or needs like food, shelter, and clothing. It was at this time

when God sent Amos to give prophesy to Israel.

SAQ. How did the rich oppress the poor in Israel?

LESSON TWO: VISIONS OF AMOS

Read AMOS 7: 1 – 9, 8:1 – 3. 9:1 – 4)

Vision is a picture we have in our mind. It is a future to come. Amos was shown many visions by God.

Lesson outcomes. After reading these verses in Amos you should be able to: –

Analyse all the visions and
State the message of each vision
Summaries things that God condemned through Amos
The vision of the locusts (Amos 7:1 – 3 )

Amos saw a swarm of locusts being sent by God to destroy all plants and food crops in the land. The

locusts were, a sign of disaster, which God was going to send to Israel as a punishment for their

disobedience. Amos cried to God to forgive the people. God heard and changed his mind.

The vision of a great fire (Amos 7:4 – 6)

Amos saw a vision of a supernatural fire that burnt up the land. He asked God to forgive the people and

God listened. The punishment was stopped.

The vision of a crooked wall/ the plumb line (Amos 7:7 – 9)

Amos saw the Lord standing beside the wall checked it with a plumb line. The wall represented the

Israelites. They stopped observing the laws of their covenant with God. God found Israelites disobeying

the covenant. God promised to destroy holy places of Israel..

The vision of a basket of ripe fruits (Amos 8:1 – 3)

In this vision, Amos saw a basket of ripe fruits. Fruits are harvested at the end of the summer. This

meant that Israel was ripe for punishment for her refusal to turn to God. Amos did not pray for

forgiveness. God would no longer withhold His judgment. Time for repentance was over.

The vision of the destruction of the altar. Read Amos 9:1 – 4.

Amos saw the Lord standing by the altar. The Lord ordered the destruction of the temple. The shrines of

Dan and Bethel were destroyed because they were the centres of idolatry. No one would escape

punishment no matter where they hide.

Summary of issues that God pointed out to Israel through Prophet Amos

Lack of social justice

There was lack of social justice and responsibility by the king of Israel. Social justice means dealing with

other people fairly. It implies showing concern for the needs of others.

Lack of responsibility. This refers to the rulers and people of Israel being accountable for their actions.

In modern life, it is doing ones duty and fulfilling ones obligation to God and others.

Practice of hypocritical religion in Israel. The Israelites were insincere in their worship. They made

empty sacrifices. They worshipped idols as well as God. They profaned the name of God (Yahweh). They

made idols of Baal and offered sacrifices to them. They worshipped other gods. This is syncretism and

God does not allow worship of any other God but himself.

God’s judgment against Israel and other nations. God promised to destroy Israel and leave a remnant

of them for restoration.

Oppressions of the poor by the rich

God condemned King Jeroboam rule of Israel because of the oppression of the poor, government

corruption and bribery of king’s officials. These officials sold the righteous for silver and the needy for a

pair of sandals (shoes) i.e. its like practising slavery. The rich trampled on the poor, despised them and

placed no value on the poor. The poor gave their garments as security for loan. This was contrary to

God’s commandments. The garment was supposed to be returned back to the owner before sunset. The

Samaritan women were ‘fat like the well fed cows of Bashan’ led luxurious lives and were very unkind to

the poor. The rich took an excessive share of the harvest from the farmers. Rulers loved luxury and were

arrogant. They loved material things and showed pride in material possessions. They used expensive

perfumes.

Corruption and bribery. The judges were corrupt. They accepted bribes. There was a conspiracy

between the rich and the judges against the poor

Pride in materials possessions

The capital city of Israel was Samaria. It was built on a mountain called Bethel, which was also a place of

worship. There was prosperity in the land. The Israelites prided themselves in their riches and materials

possessions. Amos told them God would destroy their wealth.

Dishonesty. This is telling lies, cheating or using unjust means to get certain things. The wealthy

merchants waited impatiently for the end of the holy days so that they could engage in lucrative

businesses. They cheated the poor by using false scales. They sold bad wheat to the poor. They mixed

good and bad grains and sold them to unsuspecting people.

Sexual immorality

Sexual immorality was prevalent or common in Israel. For example a father and son would have sex with

the same girl. There was temple (cultic) prostitution. There was dishonesty; sexual immorality. This

sexual behaviour made the temple unholy.

Drunkenness

They Israelites spent time drinking when the poor lacked the basic needs. They engaged in excessive

drinking of wine. They even forced the Nazarites to drink wine. They accepted drunkenness.

Profaning the name of the God

Israelites did not respect the name of God. They committed sin. They forced Nazirites to drink wine;

forcing it down their throats yet they knew that Nazirites were people set aside and chosen by God to

serve God. This act showed contempt of God’s commands. Nazirites were not supposed to drink wine or

cut their hair. Israelites did this to show their contempt of the Lord,

Hypocritical Religion and Idolatry in Israel

Hypocrisy is pretending to be something different from the person one is. It is also saying one thing, and

doing another thing. For example, Israelites did a lot of religious rites according to the laws of Moses

and yet majority of them were unjust, corrupt and oppressed the poor. They observed the external

religious activities while their hearts were corrupt and insincere. Amos condemned Israelites for this

hypocrisy, characterized by insincere worship, and mixture of religious beliefs leading to diverse

practices of religion i.e. syncretism. This is a combination or mixture of Israelites’ monotheism

(Yahwehism) and worship of idols and other gods especially Baal, the gods of their neighbours.

Empty sacrifices

The Israelites made elaborative offerings and sacrifices. Yet God was interested only in sincere worship

and free will offerings and not mere sacrifices, and tithes. ‘Take away from me the noise of your songs’

(Amos 5:21 – 23).

LESSON THREE. GOD’S JUDGMENT AGAINST ISRAEL AND OTHER NATIONS

Read Amos chapter 1 and 2

Learning outcomes. After studying this lesson, you should be able to:

State the sins committed by Israel and other nations
Identify how God punished Israel and other nations
i) Israel. She committed several crimes, which were condemned by Prophet Amos. Read lesson two

again before you go on and list down crimes that were pointed out by Amos. Okay, you have seen that

Israel committed crimes of injustice, disobedience to God, breaking their covenant with God, idolatry,

hypocrisy among other sins mentioned above. Israel was punished for these crimes.

Punishments were severe. Israelites would be exiled forcibly and painfully. Earthquakes, famines, fires,

oppression from foreign kings, epidemics and divine silence, would destroy their kingdom and holy

places.

ii) Syria. Its capital was Damascus. Syria committed war crimes. The soldiers were excessively cruel in

times of war. They murdered their prisoners brutally. For this cruelty, their punishment was to be

severe. Their palaces would be destroyed by fire and the people would be exiled in Kir.

iii) Gaza and philistines. Their crime was capturing other people and selling them into slavery. For this

sin, God’s punishment was destruction of their city by divine fire. It would burn down the wall of Gaza

city and destroy it. God would have no more association with them.

iv) Tyre. Their Crime was violation of a treaty of friendship they had made. They broke it by capturing a

“whole nation into exile in the land of Edom”. The punishment was …God would send fire to destroy city

of Tyre and its fortress (Amos 1:9-10).

Edom. Her people were descendants of Esau. Yet Edom was ruthless to the Israelite to whom they

were closely related. For this crime of ruthlessness, the punishment was … God would destroy them by

fire

vi) Ammon committed crime of brutal killings. The people of Ammon attacked and killed their

neighbours. They “ripped open pregnant woman in Gilead” (vs. 13). God’s punishment was destruction

of the fortress and wall of the city of Rabbah by fire. “Their king and his officers will go into exile: (vs.

15).

vii) Moab. The people of Moab; their crime was mishandling the body of the king of Edom. They burned

his bones to ashes. God’s punishment was destruction of the city of Kerioth by divine fire. The people,

their rulers and leaders would be killed in battle.

viii) Judah. Their crimes were (1) failure to obey God’s commands and (2) despising god’s teaching.

ix) Samaria, Egypt and Ashdod. Their crime was dishonesty and “filling their mansions with things taken

by crime and violence” (Amos 3:10). Women of Samaria committed the crime of drunkenness,

oppressing the weak and poor. The punishment for all these countries is destruction of their land,

mansions and army. But a remnant will not go to captivity, and shall not be destroyed. Amos said the

remnants are like … 2 legs, or a piece of an ear of a sheep rescued from the mouth of a lion (Amos 3:12)

x) Amaziah the priest of Bethel. He strongly opposed Amos and told him to go back and prophesy in

Judah. Amos told Amaziah God sent him to Israel. His punishment for opposing God’s messenger was..

Amaziah’s wife would be a harlot, his children will die in the war, his land will be given to others, and

Amaziah will die in a foreign land (Amos 7: 14-17).

Lessons to learn from God’s judgment of Israel and other nations

The Assyrians attacked Israel, occupied their land and exiled others. God is (a) universal, (b) God hates

sin (c) God is concerned about the welfare of his people

(d) God is merciful and spares a remnant

Israel’s election (Amos 2:9 – 11, 3:1 – 2, 9:7

Election: is an act of choosing a person or group of people for a purpose or action. Israel’s election refers

to God’s choice of the Israelites out of the entire human kind to be his people. God chose them to serve

him, be a Holy nation and to be the light of the world. God made a covenant with the Israelites. In the

covenant they agreed to live a holy life. In return, God looked after them. He led them out of Egypt to

the wilderness and finally to Canaan. God chose His prophets from the Israelites and raised Nazirites.

Despite God’s favour, the Israelites rebelled and sinned against God. And although Israelites were

reminded that God cared for other nations equally and are to be punished if they disobeyed God; and

that they were neither superior, nor better than other nations, they disobeyed God several times.

xii. The day of the lord Amos taught that the day of the lord would be a day of severe judgment for sins.

. It is not a time of happiness, joy or victory. It is a day of darkness, terror, disaster, gloom, wailing,

flooding, mourning, defeat, punishment, famine for food and God’s word.

xiii. The Remnant and Restoration. Remnant means a small number of survivors. These are the Israelites

who will remain after the entire nation is punished. They are also those who returned to Jerusalem after

the exile.

Restoration is an act of reinstating things / persons to their former state or position. Amos informed the

Israelites that God was still looking after them, and waiting for their repentance. The nation of Israel

would not be destroyed completely. God would preserve the few righteous ones. He would raise the

fallen dynasty of David. People would be restored back to their land to rebuild their cities. There was to

be a great harvest and grapes shall overflow.

xiv. Duty of Christians. Christians are the selected people of God. As the chosen ones, they should one,

live holy lives and two, use their position to serve God and others. Three, Christians have a moral

responsibility to spread God’s word, four, care for the needy and five, be the light of the world.

The Day of the lord. Read Amos 5:18-20, 6:3-5, 8:7-13. in the Old Testament, the day of the Lord is

the day that Yahweh would make Israel victorious against other nations. On this day the Israelite

believed that God would establish his rule over and with Israel. The day of the Lord was also believed to

be the day when Israel would be prosperous, would have favour with God, and the just would triumph

over the wicked.

In the New Testament, the day of the lord is also the Day of Judgment (Parousia). It is the day of the

second coming of Christ. On that day, everyone will be judged. Christians believe that it is the day that

Christ will come for His bride (the church). Those who had obeyed the laws of God shall be received by

Christ and given the reward of the eternal life. On that day, God’s kingdom shall be established and

Christ will reign forever.

xvi. Relevance of Amos teachings to Christians today. The messages of the prophecy of Amos are

relevant to Christians today. This is because God is universal. He chose Israel but still punished her for

her disobedience, and sins just as He punished other nations like Syria and Gaza.

The message that God hates hypocrisy is very clear. Thus Christians should truthful and practice what

they preach. They must worship God in sincerity. Other messages are:

Justice. Christians should be just / fair in dealing with others.

Self – Indulgence. Christians should not pursue luxury and self-indulgence when others lack the basic

needs.

Bribery. Christians should condemn bribery and corruption, and uphold justice.

Punishment. Christians should bear in mind that God will punish every evil.

Wealth. When Israel became wealthy, they departed from the covenant with God. Christians should

share their wealth with the needy and acquire their wealth justly

Hypocritical religion. Amos taught about hypocrisy in religion. This was for example offering empty

sacrifices. Christians have to learn to be sincere, to be concerned about their internal well being and soul

more than outward observances of religion.

Drunkenness. Christians should not engage in activities that can divert their faith from God. If that

happens, they should learn to be Repentant.

Revision exercise

List the visions that Amos saw
Explain the evils that Amos condemned in his teachings
Give reasons why prophet Amos condemned idol worship in Israel
List evils in the society today that Amos would condemn

TOPIC FIVE. PROPHET JEREMIAH

Introduction.

Israel had not taken heed to Amos’ prophecies. This was especially on idolatry. So, God sent another

prophet to continue with the same work. Jeremiah was therefore appointed as a prophet.

Jeremiah is one of the Old Testament Major Prophets. He was called to a prophet at around 627 B.C. He

was called as a young man, probably 20 years old. He prophesied in the southern kingdom- Judah, for a

period of 40 years. His prophetic ministry took place before and during the exile of Judah.

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

a Describe the political, Social, and religious background of prophet Jeremiah.

b Describe the personal life and call of Jeremiah.

c Explain the evils condemned by Jeremiah.

d Explain the contents of the temple sermon.

e Highlight the relevance of Jeremiah’s teaching on evils, false prophets and Christians today.

LESSON ONE: THE CALL JEREMIAH

Learning outcomes. After reading this lesson, you should be able to: –

Describe the situation of the people of Judah
Identify religious, political and socio classes of Judah

iii. Describe the call of Jeremiah

Explain lessons that modern Christians can learn from the call of Jeremiah
The Kingdom of Judah

Social background

The people of Judah were divided into three social classes. At the top were the (i) Aristocrats. These

were the ruling class, which consisted of the king, his family, royal officials, princesses, priests, and

professional prophets. This class of the rich oppressed the poor.

Below them was the class (ii) of technical professional such as stonecutters, carpenters, builders,

masons, blacksmiths, masons, and others craftsmen (2 Kings 12:12). Below them was class (iii) made up

of poor people such as slaves, widows, orphans, and foreigners. All these poor people were mistreated.

In terms of ethics, there was moral degradation. They committed adultery, prostitution, murder, false

witness, and corruption.

Religions background.

The Kings and people of Judah worshipped idols. They practiced human sacrifice, divination and magic,

and listened to false prophecies. They abandoned their covenant with God and their way of life and

practiced syncretism, which is worshipping God and other false gods like Baal.

King Josiah tried to restore true worship by carrying out several reforms. Prophetess Huldah prophesied

that Judah would be punished after Josiah’s death since he humbled before Yahweh.

Political Background.

Prophet Jeremiah lived in the 7th century BC and prophesied when Judah was ruled by King Josiah, and

later his sons Jehoiakim, and Zedekiah; and king Jehoiachin. Judah was conquered and ruled by

Assyrians who were conquered by Egyptians who ruled Judah up to 605 BC. Egyptians; were conquered

by Babylonians under King Nebuchadnezzar. This was according to the prophecies of Jeremiah.

The Call of Jeremiah. Read Jer 1: 19.

Jeremiah’s father was a priest called Hilkiah. He was born in the territory of Benjamin; at a place called

Anathoth, He was well educated.

Jeremiah was called to be a prophet in 627 B.C during the reign of King Josiah. He received his call in

form of a dialogue with Yahweh. God told him that he had appointed him to be his messenger; even

before he was formed in his mother’s womb, God had selected him to be a prophet. Jeremiah said he

was too young and did not know how to speak. Jeremiah was forewarned of the hostility he would

encounter in his prophetic career. God told him that He would protect him and not to fear.

God touched Jeremiah’s mouth. This symbolized that God is the one who shall put words in his mouth.

Jeremiah responded to God’s call in faith and obedience. He was given a message that God was going to

bring judgment upon the Kingdom of Judah. God promised to make him a fortified city, an iron pillar and

bronze wall for protection. He was commanded by God not to marry, neither have children and not to

attend social gatherings, weddings, and funerals. His mission made him isolated and lonely.

As a result, his own family and relatives rejected him and plotted to kill him. But he had few friends like

Ebed- melech, Ahikam who helped him to get out of a pit.

Jeremiah was persecuted by; the kings of Judah. Priests including priest Pashhur opposed him, and false

prophets like Hannaniah. He prophesied that God shall punish wicked Kings, priests, and ordinary

people. He suffered spiritually and emotionally.

At the fall of Jerusalem in 587 B.C, the army officers of Nebuchadnezzar released him from prison. He

went to Egypt where he died at an old age and as a faithful servant of God. His life was symbolic to the

people of Judah. During his call, Jeremiah saw two visions.

Vision one was the vision of a “branch of an almond tree”.

The tree seemed dead, bare, yet life was in it. This vision was telling Judah that although God seemed to

be ‘sleeping’, He was watching over them if they obey Him.

Vision two was “a pot boiling in the north, and it is about to tip over this way” (1:13). The boiling pot

tilted away from the north signified that the destroyers of Judah would come from the north. The pot

was ready to boil over and spill its contents. This meant that Judah was soon going to have trouble.

Babylon would pour horrifying disasters on Judah.

Lessons from the call of Jeremiah

God has a purpose for each person and He can call anybody to do His work. He calls the unborn, the

young, old, rich, and poor. God prepares people for His work, through specific experiences at family

level, in school, and church.

A person who is called to serve God should be ready to meet opposition. God protects His servants and

promises to be with them. Jeremiah felt inadequate to speak. Christians should not let their human

weakness hinder them from performing their tasks. Christians should respond to God’s call in

obedience.

LESSON TWO. EVILS ADDRESSED BY JEREMIAH. Read Jeremiah 2, 3, 4, 5,7, 9, 10, 23, and 28.

Learning outcomes. After reading this lesson,

Name the evil practices that Jeremiah condemned
Explain why Jeremiah condemned these evil practices

There were many evils in Judah and Israel. We have mentioned some of them. These were: necromancy,

dishonesty, deception, false prophecy, human sacrifice, and idolatry

Necromancy. Words related to necromancy are divinations, magic, sorcery, and playing tricks on

people’s minds. Necromancy is the art of seeking hidden knowledge from the mysterious world of

spirits: using magic, and divination, which is invoking the dead. Divination was condemned in the

Hebrew language. Diviners, magicians, sooth sayers and fortunetellers used necromancy. Prophet

Jeremiah condemned necromancy.

Reasons why Jeremiah condemned necromancy

Necromancy was a deception and therefore an evil practice. The diviners gave false information from

their own imagination. This practice polluted the true worship of Yahweh and indicated Israelites lack of

faith in the one true God. Two, by trusting in divination, and magic, the Israelites showed their lack of

knowledge of the one true God. Three, by consulting the mediums, the Israelites disobeyed God (Jer

27:8-10).

ii) Deception and Dishonesty

Dishonesty is lack of moral integrity or moral uprightness. Deception is cheating, and telling lies

intentionally. It is also giving false and misleading information.

The Israelites were dishonest because they worshiped God and at the same time committed social

injustices against their brothers and sisters. Their repentance was insincere. There was treachery, and

greed. They laid traps for each other. People pretended to be friendly and at the same time conspired to

kill. Jeremiah challenged the Israelites people to ‘circumcise their hearts which were deceitful. Their

tongues were ‘deadly arrows’ and they listened to false prophesies like that of Hannaniah

Jeremiah condemned deception. This was because it led to syncretism, and hypocrisy in worship; and

breaking down of the covenant way of life. Jeremiah warned the Israelites and asked them to repent

iii. False prophesy by Hannaniah. Jer 28

During the reign of king Zedekiah, Hannaniah broke the yoke that Jeremiah was wearing. Hannaniah

spoke in the name of Yahweh. He lied to the people as he spoke from his imagination and dreams.

Jeremiah denounced Hannaniah. He predicted and prophesied the death of Hannaniah in the same year.

And it came to pass. Jeremiah had also prophesied that the captivity of Judah should be long contrary to

Hannaniah who said Judah will be exiled for 2 years.

Reasons for condemning false prophets

Prophets of Baal were still in existence. False prophets like Hannaniah had filled the people of Israel with

unrealistic hopes of peace yet Judah was to be destroyed. Recall the characteristics of true and false

prophets. False prophets did not condemn sin. They prophesied for money and in the process misled

people away from Yahweh. False prophets prophesied from their dreams, imaginations and not from

God. They gave people false hopes. They intended to make themselves popular, with the King and the

people.

iv) Human sacrifice. The people offered human sacrifice to idols and oppressed each other. Human

sacrifice is the act of killing human beings for a religious or spiritual purpose. The Israelites copied this

activity from the Canaanites. Children were believed to be the best sacrifice since people believed they

would get great favors from the deities. Some kings such as Ahaz and Manasseh sacrificed their sons to

idols. Jeremiah condemned human sacrifice.

Reasons for condemning human sacrifice

Human sacrifice was an act of idolatry. It indicated infidelity of the Israelites to the one true God. It

demonstrated Israel’s disrespect for the sacred gift of life. It showed their lack of knowledge of the true

nature of Yahweh. Human sacrifice defiled the land for life is in the blood. Blood speaks hence the land

was crying at this vengeance. God did not ask for human sacrifices. Human sacrifice was a sign of lack of

love of God and love for one another. It is a demonstration of disregard for human life. Only God has the

right to take away life. In our country people kill each other every day especially on the road. Why do we

do this?

Idolatry

Idolatry is the worship of many gods. Idols are images made by people for worship. The Israelites

practiced syncretism, which we said was the worship of Yahweh and idols. The people of Israel were

worshipping Baal the Queen of heaven, sun, moon, stars, and also Yahweh (Jer 8:2).

Idols were placed even in Yahweh’s sacred places. The temple was defiled by idols. This the temple

unclean. Jeremiah condemned it. He told the people of Israel that “{they have forsaken the fountain of

living waters (GOD) and hewn out for themselves broken cisterns (IDOLs) that can hold no water” (Jer 2:

11-13).

Why did Jeremiah condemn idolatry? Read Jer 2: 20, 2:1- 3, 5: 7- 8.

Idolatry is like adultery and prostitution. It defiled people and was a sign of lack of faith in Yahweh. It

defiled the land. Idolatry led to divine judgment and punishment.

People of Judah abandoned Yahweh the ‘Husband’ and chased “lovers” the idols and deities The

Israelites (Northern kingdom) had been punished before and yet Judah did not learn from them. By

worshipping idols Judah broke the covenant and their relationship with God. And unless the people of

Judah repented, they would be punished; as there is only one true living God to be worshipped and

obeyed. Is there idolatry among Christians today’s

Other evils condemned by Jeremiah

People of Judah trusted that the temple was secure, holy and cannot be destroyed. Jeremiah denounced

this false belief about the temple. He warned them that God would destroy the temple because of the

many evils committed in it. The temple of God had become a ‘den of robbers’ and human sacrifices.

People of Judah committed other evils such as hypocrisy (Jer 7; 9-10); social injustice (adultery, murder),

stubbornness, and rebellion.

The temple

Temple is a place of worship. The temple of Israelites was in Jerusalem. It signified the presence of God

among his people. The Israelites believed God could never destroy or allow destruction of the temple.

Jeremiah stood at the gates of the temple court during Jehuiakim’s reign, and Judah that God would

destroy the temple and send them to exile. He urged them to repent and turn back to God. King Josiah

heard the message of Jeremiah and he reformed religious practices in Judah.

vii. Religions reforms carried out by King Josiah

This topic is not clearly spelt out in the syllabus. It is based on the book of Deuteronomy. The scroll was

discovered in the temple during repairs.

Josiah ordered the repair of the temple of God. He led a national ceremony to review the covenant. He

destroyed idols and altars associated with the worship of foreign deities throughout Judah. He

eliminated all the priests associated with the worship of false deities. He celebrated Passover in

Jerusalem. The successors of King Josiah did not follow his example. They became corrupt. They

persecuted the prophets of God. They listened to false prophets. They promoted idolatry and child

sacrifice.

viii. The Relevance of Jeremiah’s teachings to Christians today.

Christians should denounce hypocrisy in the society today. They should not result to witchcraft,

divination and sorcery. They should be upright, and worship God in sincerity. They are to proclaim divine

judgment upon those who refuse to obey God’s will, just like Jeremiah declared God’s judgment upon

Judah due to the sins of the people.

Like Jeremiah, Christians should speak out against modern idols like love of money, power, obsession

with sports, sex, and drugs among other evils. Christians should condemn destruction of human life,

violence; murder, abortion, parents killing their own children, genocide and exploitation of the poor.

Christians should be aware of the existence of false teachings and prophecies. They should pray for

God’s guidance and wisdom to be able to distinguish truth from false teaching. Christians have a

responsibility to correct one another and call on sinners to repent.

Christians are to be trustworthy, upright, and merciful to the poor and condemn dishonesty. They

should practice justice in their relationship with others; preach against disobedience, stubbornness and

pray to God to help them overcome these vices.

Read these review questions and answer before reading answers>

Why was Jeremiah reluctant to accept the call?
Which evils / sins did Jeremiah Condemn?.
Give examples of idol worship in Kenya.
Describe Jeremiahs temple sermon

SAQ answer.

Jeremiah felt inadequate because he was too young to work for God. He argued that he did not know

how to speak. He was afraid. He knew he would face stiff opposition from the people of Judah. The

message of God’s judgments is difficult to deliver.

Read text again and look for evils and sins that Jeremiah condemned.
Examples of idol worship in Kenya are many. Some people including Christians practice witchcraft,

sorcery, personality cults and hero worship of religions and political leaders. Other people, worship

money, materialism, media, and sports obsession with power / status Sexual immorality – devil worship

Jeremiahs temple sermon. Read text again.

LESSON THREE. JEREMIAH’S TEACHINGS ON JUDGMENT AND PUNISHMENT

Read Jeremiah 5:12-18, 6;1-30, 7:30, 8:1-17, 10: 17-25, 15;1-9, 17:1-13, 25: 1-38

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

a Summarize in two paragraphs Jeremiah key teachings.

b Explain the significance of symbolic acts related to judgement and punishment.

c Describe suffering and lamentations of Jeremiah

d Explain the teachings of Jeremiah on the new covenant.

Jeremiah teachings. Sin was internalise in the hearts of the people of Judah. God punished them. God

punishes people because of their unfaithfulness. Punishment is a penalty, for an offence or a crime

committed.

But in punishing people, God is a just judge. He does not punish people without a reason irrespective of

their status.

God judges people by looking into their hearts. Divine judgment is for a group. For example, the people

of Judah were punished as a group. However God searches each person’s heart and judges accordingly.

God executes His judgment by means of political and historical events. Divine punishments are in forms

of natural disasters like drought, famine, and epidemics. God’s punishment is unavoidable, and

inescapable. Judah took the best option by surrendering to the Babylonians.

The purpose for God’s judgement is to correct the sinner. God gave his people a chance to repent before

he punished them. God’s judgment is universal. It is not limited to one nation. God punished the

neighbours of Judah who at that time were Egypt, Moab, Ammon, and Babylon. God’s punishment is

severe compared to that of venomous snakes that bite the people of Judah. God’s judgement is not

necessarily a punishment from God for one’s sins. It is symbolic. The sufferings of Jeremiah were

symbolic of the life of the people of Judah.

What can we learn about God’s punishments? Are modern disasters such as cyclones, floods,

earthquakes, landslides, epidemics, bomb blasts, civil wars, forest fires, rebellions in schools a sign of

God’s judgment and punishment? What do you think?

Symbolic acts related to judgement and punishment

People use several methods to convey messages to each other. We use songs, advertisements, dramas,

and stories by the fireside, in novels, the Internet, and magazines to communicate messages about

children, adults, society, political leaders, poverty and many others. The prophets used: (1). Oracles;

‘Thus says the Lord’; (2) Allegories (3) Parables (4) Songs (5) Symbolic Visions (6) Symbolic actions and (7)

dramatized messages

Symbolic acts of Jeremiah

i The linen waist cloth (Jer.13)

ii Jeremiah’s personal life (Jer.16)

iii Jeremiah’s visit to a potter (Jer.18)

iv The broken earthen flask (Jer.19)

v The symbolic vision of 2 baskets of figs (Jer.24)

vi The wearing of the yoke

The Linen Waist Cloth. Read Jer.13

Jeremiah was instructed by God to buy a linen waistcloth and wear it around his waist without dipping it

in water. He was told to hide the cloth in a hole near river Euphrates. Afterwards he was told to take the

cloth. He found it spoilt for wearing.

Significance. The liner material was for priestly garments in Israel. It symbolized Israel’s holiness. The

unwashed cloth represented Judah’s sinful pride. Israel used to cling close to God but now Israel / Judah

were spoilt, rebellious, arrogant and pursued foreign gods. God was going to destroy them if they did

not repent. The spoilt linen waistcloth was a symbol for future God’s action.

Jeremiah’s personal Life. Read Jer 16. His life was a symbolic act. He was told not to marry, have

children, and nor attend funerals, social gatherings, feasts and wedding parties.

Significance. The personal life of Jeremiah was one of suffering. This signified the suffering that the

people of Judah would be subjected to. Judah was punished because of their wickedness and rebellion.

Jeremiah’s loneliness signified the perishing of families through the sword, famine and disease. It would

be a time of terror for the families of Judah. Their normal social life of feasting, merry making would

come to an end. There would be no weddings and no one to bury the dead. Hence Jeremiah was

forbidden from mourning for the dead.

iii. Jeremiah’s at the potter’s house (Jer.18)

Jeremiah was told to go to a potter’s house. He found the potter making a clay vessel. “ Whenever a

piece of pottery turned out imperfect, he would take the clay and make it into something else (18: 4).

The potter made a better pot, more perfect vessel than the spoilt one.

Significance. God is the potter. People of Judah are the clay. As the potter destroyed to vessel, God

intended to destroy Judah because of their wickedness and mould those who repented into better

people. God was going to shape them into faithful people. God’s judgement was to be a corrective

punishment.

The broken clay Jar. Read Jer.19. God told Jeremiah to buy a clay flask

He then took some elders and priests to the valley of Valley of Hinnon. He delivered a sermon

condemning the people of Judah for their idolatry and other evils. Jeremiah then broke the clay jar in

their presence and announced to them that Yahweh would destroy Jerusalem and Judah as Jeremiah

had destroyed the jar.

Significance. The kings, priests and prophets of Judah would be shattered like the clay flask because of

their sins. Sine, they brutally sacrificed their children; they are to suffer horrifying experiences at the

hand of their enemies. They shall suffer starvation and turn into cannibals; eating their own children and

neighbours (v.9).

Broken pieces of a clay pot cannot be moulded. No one was to escape judgment. However there is hope

after punishment.

Two Baskets of Figs (Jer.24). Jeremiah received the visions, after the deportation and exile of leading

citizens of Judah and Israel to Babylon. Two baskets of figs were placed in front of the temple. One

basket had very good figs, which had ripened. The other basket had bad figs unfit for human

consumption.

Significance. The basket of good figs signified the first exile. God would renew their hearts; use them to

fulfil his promises to the Israelites. He would recreate them to a new people. The basket of the bad figs

represented people living in Jerusalem and Egypt. Since they were not exiled they had a self-righteous

attitude. They thought that God spared them because they were truthful but it was not so. They shall

also be destroyed through famine, and diseases. This vision signifies hope and restoration of the

Israelites.

Jeremiah Wears an Ox Yoke. Read Jer. 27. When Zedekiah son of Josiah became the ruler of Judah,

Jeremiah was instructed by God “to make” for himself “ a yoke out of leather straps and wooden

crossbars” and to wear it around his neck (27: 2). Jeremiah moved around in the yoke for quite

sometime in public.

He was also given a message for ambassadors of kings of Edom, Moab, Ammon, Tyre, and Sidon, who

were coming to see King Zedekiah in Jerusalem. They were to give God’s message to their kings. The

message was to “submit to King Nebuchadnezzar of Babylonia; his son, and his grandson. Any nation

that accepted this message shall not suffer; but if any nation ..will no submit to King Nebuchadnezzar of

Babylonia rule, God will punish that nation by war, starvation and disease” Read Jer 27:6-8. The message

for king Zedekiah was to surrender to the Babylonian rule and live, if he resists he would perish.

The message for priests and people of Judah was not to be misled by the false prophets. The temple

would be destroyed. Its treasures looted by the Babylonians.

Significance. The yoke represented the Babylonians rule. Nebuchadnezzar was used by God to bring

judgment to all nations. Yahweh is a universal God and his judgment is universal. Sinners are punished

regardless of their origin or nation. Those who repent are spared.

Reflection questions

Why did God inspire Jeremiah to use symbolic acts to convey his message?

Answer

Israelites were stubborn. Jeremiah acts were reminders to Judah to turn to God and stop idolatry and all

the sins they were committing. They had drifted too far from God. False prophets were prophesying lies

to them. The people of Judah were expected to meditate on these acts and understand God’s will for

them and see the seriousness of the matter. This was also to imprint a lasting impression in their minds.

SAQ. Which methods do pastors / priests use to communicate God’s message to Christians today?

The sufferings and lamentations of Jeremiah

Read Jer 11, 12, 17:14 – 18, 18:18- 23 , 20: 1 – 6, 27, 37, and 38.

Jeremiah sufferings were experiences that were painful; physically and emotionally. In suffering there is

loss and grief. Lamentations are strong emotional expressions of pain and grief. Jeremiah suffered in the

following ways

Rejection by his own family and relatives. They plotted to kill him. This grieved Jeremiah.
Anathoth planned to kill him but God protected Jeremiah. He pronounced God’s judgment upon them

III. Jeremiah suffered when he was accused falsely. He was accused of blasphemy after the temple

sermon. He foretold the destruction of the temple, just like Jesus Christ in the New Testament did.

He was accused of treachery. That he was planning to leave Jerusalem and join the Babylonians. This

led to Jeremiah being arrested and put in an underground jail.

Jeremiah received death threats because of speaking for God. King Jehoiakim plotted to kill prophet

Uriah. The prophet escaped to Egypt but he was followed to Egypt, arrested and killed by king

Jehoiakim. The king had planned to accuse Jeremiah of Uriah death. Ahikam and other elders defended

Jeremiah. (Jeremiah 26)

Jeremiah suffered loneliness and solitude. He felt emotional anguish and complained to God of his

orders not to marry, neither attend social gathering and celebrations. This made Jeremiah lonely since

he did not participate in the family life, political life, community activities and religious life.

VII. Jeremiah experienced inner personal struggle due to his love for his own people He did not want to

see them suffer but the people were stubborn Read Jer. 12:1 – 6, 15:10 – 21, and 27.

VIII. Jeremiah’s prophesying judgment caused him emotional pain and agony. His messages were mainly

of severe judgment and punishment.

He went through a spiritual struggle in his relationship with God. He felt frustrations, doubts, self-pity

and despair. He wondered why God made him suffer. Why do the wicked prosper? He also wondered

why God was taking too long to fulfil his prophecies. God assured him that Judah would be punished and

promised to give Jeremiah victory against his enemies.

Jeremiah suffered physical assault, imprisonment and an attempt on his life. Pashhur, the chief

temple priest ordered beating and chaining of Jeremiah to the temple gate. Jeremiah prophesied that

Pashshur’s name would change to ‘terror everywhere’.

King Zedekiah released Jeremiah from the cell to his court. Jeremiah continued to prophecy and was

thrown in a muddy cistern. Here he was rescued by Ebed- melech an Ethiopian Eunuch. The court

officials had accused him of not being patriotic. Jeremiah remained in jail until the Babylonians

overthrew Jerusalem. He did not change his prophecies. Read Jer. 10:1 – 6, 27, 37, and 38.

Is there relevance of the sufferings and lamentations of Jeremiah to Christians today? From his suffering

Christians learn to be ready to face opposition and rejection from their own family members and

relatives for the sake of the gospel. Christians should be prepared to suffer persecution for the Lord.

Christians should be ready to make sacrifices for the sake of God. Be ready to lead humble lives.

Jeremiah’s open confessions to God encourage Christians to be open to God. Christians should let God

avenge for them just like Jeremiah prayed to God to revenge his enemies. Christians should not lose

hope in times of difficulty. Christians learn that tribulations strengthen their faith. Christians should

learn to deal with negative emotions such as self – pity, grief and trust God. Jeremiah was told by God to

repent of his negative utterances. Christians should do the same as they are assured of divine security

and protection against their persecutors.

LESSON FOUR. JEREMIAH’S TEACHING ABOUT THE NEW COVENANT

A covenant is an agreement. Another word for covenant is testament. Jeremiah taught that there would

be a new covenant between God and Israel. This new covenant would be different from the Old (Sinai)

covenant. The new covenant would renew the broken relationship between God and his people.

Lesson outcomes. After reading Jeremiah’s teaching:

State the terms of the new covenant.
Identify the differences between the old covenant and the new covenant
Summarize the similarities between the old covenant and the new covenant
The New Covenant. In the new covenant, the law would be written in the hearts of the people unlike

the old covenant where the law was written on stone tablets. Every individual would know God

personally and not through prophets as it was during times of Jeremiah and previous one. Each person

would be responsible for his/her sins. God would forgive sins and remember them no more. The new

covenant would be established after God’s punishment of Israel and establishing a’ new Israel’, a ‘new

people’ of God.

The new covenant would establish a new beginning. People would forget the first Exodus. The second

Exodus would be deliverance and restoration from Babylon. God would initiate the new covenant as he

did with the first. It would be a new covenant of peace, unity, prosperity, Joy and gladness. In the new

covenant a ‘righteous branch’ would be established. The new covenant would be everlasting. It would

not be broken again.

Differences between the old covenant and the new covenant

Old Covenant New Covenant

Based on law Based on faith
Word written on stone tablets Word written in peoples hearts
God known personally by a few priests prophets and prophets Each to person to know God personally
Covenant broken when people sinned Everlasting covenant
Sins punished collectively Sins punished individually
1st Exodus from Egypt 2nd Exodus from Babylon
Sealed by animal sacrifice Sealed by Jesus sacrifice (blood)

What are the similarities between the old and the new covenant? Jesus fulfilled the new covenant. Jesus

is the ‘righteous branch’ from the lineage of David. In the last supper, before his death, Jesus said ‘this

cup which is poured out for you is the new covenant in my blood. Read Luke, 22:20. The death and

resurrection of Jesus marks the new covenant. Jesus spoke of forgiveness of sins of humanity Jesus

forgave people’s sins, for example, the sinful woman in Simon’s house (Luke7: 36 – 50). In the new

covenant the law would be written in people’s hearts. Jesus summarized the Mosaic Law into ‘love God

with all your heart, mind, strength and love your neighbour as you love yourself. Jesus established the

kingdom of God as a new community of God’s people based on faith (the Christians).

Jesus fulfilled the new covenant prophecies The teachings of Jeremiah new covenant of hope and

restoration is fulfilled in Jesus Christ and the new testament church (Christians) Heb.8:7 – 12.

LESSON FIVE. JEREMIAH’S TEACHINGS ON HOPE AND RESTORATION

Learning Outcomes

(a) Explain the symbolic acts related to hope and restoration

(b) Describe the fall of Jerusalem and the exile of the Israelites

Symbolic acts related to hope and restoration.

The symbolic acts were one hope and restore. Hope is to expect something that is desired; while to

restore is to bring back as nearly as possible the former or original state or condition. The symbolic acts

were 5 in number.

The first symbolic act was a vision of 2 baskets of figs. We have discussed it. Refer to the symbolic act

related to judgment.

The second symbolic act was Jeremiah buying a field. God instructed Jeremiah to buy a field from his

cousin Hanamel of Anathoth. Jeremiah bought the field for 17 cents of silver. He then handed the title

deed and open copy to Baruch. Baruch was told to keep the title deed and the copy in an earthen vessel

for preservation for a long time. Jeremiah prophesied the restoration of the exiles to their homeland.

The significance of this symbolic act is the assurance of restoration of Judah and Israel after suffering.

People will be restored to their homeland. After 70 years people of Judah would reconstruct their

homes, cultivate their land, and own property (Jer 32; 1 -15).

The third symbolic act was Jeremiah’ letter to the Jews in Babylonia. Jeremiah wrote to the people of

Judah a letter of encouragement while in exile. They were to settle down, build houses, marry and have

children, live in peace with the Babylonians. They were to pray for the welfare of their masters and to

ignore false prophets who lied to them about the safety of Jerusalem and a quick return. God would

restore them back to their land after 70 years of exile were over. The exiles were to trust in God and not

give up (Jer.29).

The four symbolic act was a wooden ox yoke. The yoke represented captivity and suffering of Jews in

exile. It was also a sign of hope if the people of Judah were willing to submit to the Babylonian rule. God

would restore them back to their land. Their yoke would be broken and they would be set free.

The fifth symbolic act was the visit to the porter’s house

The fall of Jerusalem and the exile of the Israelites (Jer.39)

Jeremiah’s prophecy came to pass. Jerusalem fell to the Babylonians in the ninth year of king Zedekiah

in 587BC. The Babylonians conquered Jerusalem and seized it. King Zedekiah fled but; he was captured

by the Babylonians army. He witnessed the execution of his sons. His eyes were gauged out. He was

then taken in chains to captivity in Babylon. Solomon’s temple was looted and destroyed. Villages,

Jerusalem and the palace were destroyed and burnt down. The priests, court officials, army officials,

people in the upper class, craftsmen were executed. City people were taken to Babylon as captives. The

poor, aged and a few people were left behind and given vineyards to farm.

Nebuchadnezzar’s army was brutal to the Israelites. Many were killed. A few like Ebed – Melech were

spared as prophesied by Jeremiah (he had rescued him from the well). Nebuchadnezzar ordered the

release of Jeremiah. He was treated well

Judah became a province of Babylon. Gedaliah was appointed governor of Judah. He stayed at Mizpah,

the headquarters of Judah. Ishmael killed Gedaliah. Later Jeremiah was forced to go to Egypt by the

Israelites. Jeremiah died in Egypt, an old man, and still faithful to his call.

LESSON SIX. RELATING THE TEACHINGS OF JEREMIAH TO THE NEW TESTAMENT AND CHRISTIAN LIFE

TODAY

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

1.Describe the teachings of Jeremiah in relation to Christian life today

Describe the teachings of Jeremiah in relation to the new testament

Jeremiah was rejected by his; relatives, friends and the Israelites. In the New Testament, Jesus was

rejected in his hometown of Nazareth: and by the religious leaders of Israel. Jeremiah compared himself

to a lamb being led to the slaughter. Jesus in the New Testament is referred to as a lamb led to the

slaughter. Jeremiah’s suffering symbolizes divine judgment over Judah. However Jesus sufferings was to

bring salvation to all mankind. Both Jeremiah and Jesus experienced spiritual agony. Jeremiah

experience agony and felt left alone by God. Jesus too felt agony when praying in the garden of

Gethsemane and when on the cross.

Jeremiah taught that God is universal and a just judge. The gospel of Jesus is universal and everybody is

judged according to his or her faith in God. Jeremiah and Jesus accused the Israelites of turning the

temple into a “den of robbers”. Jeremiah and Jesus were both accused of blasphemy. Both challenged

false beliefs about the temple. Both Jeremiah and Jesus spoke of the coming judgment of God.

The new covenant was fulfilled in the life and ministry of Jesus Christ Jeremiah spoke of hope and

restoration. Jesus gives hope of eternal life in the New Testament.

Relationship of Jeremiah’s teaching to Christian today.

Christians are to preach the gospel of Jesus Christ. They are empowered by the Holy Spirit to endure

suffering and to grow spiritually. Christians like Jeremiah face false prophets who speak in Jesus name.

Christians are to be watchful and obey Yahweh

Like Jeremiah Christians should call people to repentance. The new covenant is fulfilled in Christian’s

individual relationship with God. Christians are the new people, the new Israel as prophesied by

Jeremiah. His teachings reveal that God is universal. Christians are from all corners of the earth.

Christians should prepare for divine judgment by practicing love, righteousness, self-denial, and faith in

God.

Revision exercise

List the evils that Jeremiah condemned

2.What are some of the evils that church leaders condemn today?

Explain the symbolism used during the call of prophet Jeremiah
What did Jeremiah teach about the new covenant?
Why did prophet Jeremiah condemn the way the Israelites worshipped?
Explain Jeremiah’s temple sermon as recorded in jeremiah7: 1-15
What forms of punishment did Jeremiah prophesy that God would use on Judah?
Outline the content of Jeremiah’s letter to exiles in Babylon
Explain four symbolic acts related to judgement and punishment as demonstrated by prophet

Jeremiah

Identify the relevance of Jeremiah’s teaching to Christians today
In what ways is the prophetic mission of Jeremiah similar to that of Jesus?

TOPIC SIX. NEHEMIAH

Introduction

The book of Nehemiah is a historical writing. Nehemiah is a record of his deep dependence on God and

his frequent prayer to God. Nehemiah means “Yahweh has comforted. Nehemiah was the son of

Hacaliah of Judah. He was not a prophet. He was exiled to Babylon. Persians captured Babylon and

improved the living condition of the Israelites. They were allowed religious freedom but had to pay

tributes.

Learning outcomes. By the end of this topic you should be able to;

Describe the historical, religious and social background to Nehemiah
Identify occasions when Nehemiah prayed
Explain the importance of prayer in Christian life

D .Describe leadership qualities of Nehemiah and relevance to Christians today.

LESSON ONE. BACKGROUND TO NEHEMIAH

Learning outcomes. After reading this lesson,

Describe how the people of Judah lived and worshipped.
Explain the conquest of Israel and Judah by foreign forces

iii. Give reasons why God allowed Judah and Israel to be conquered and exiled.

Political and historical background. From 587 BC to 538 BC, Israelites were in exile. In 538 B.C., the

first group of Israelites was set free and returned to Judah. Cyrus the Great, of Persia ruled his subjects

through governors. They were led out of Babylon by Joshua the high priest and Zerubbabel who became

the first governor of Judah.

Some Jews remained in Babylon. They were referred to as Jews in Diaspora or dispersion. Other Jews

remained in other lands including Egypt, and Mediterranean lands

Nehemiah. He was a cupbearer in the palace of the Persian king Artaxerxes I. He later became a

governor of Judah. Even after the rebuilding of the wall of Jerusalem, Israelites remained subjects of the

Persian king.

The Wall of Jerusalem was important to Israel and Judah. The Wall represented a sense of pride,

ownership, privacy, independence and

Security. The Greeks conquered the Persians; who were later conquered by Romans.

Social background

The Jews in foreign lands retained their Jewish way of life. The land of Israel was partly occupied by

foreigners. The foreign cultures of neighboring rulers influenced Israelites who returned. They for

example, intermarried with foreigners, a custom that God did not allow. Israelites were not to

intermarry with other people according to the Mosaic Law. In spite of this however, Jews maintained

their separated identity. Some of the foreigners despised Jews. The wealthy Jews oppressed the poor

Jews. In Jerusalem there was starvation. Nehemiah condemned oppression of the poor.

Religious background

Jews returned to rebuild the temple of Jerusalem and the altar of God for sacrifices. While in exile, Jews

were allowed by the Babylonian king to practice their religion. They worshipped Yahweh, practiced

circumcision, obeyed dietary laws and observed the Sabbath. The exiles could not however observe all

the religious practices for example offering animal sacrifices.

Nehemiah returned to Jerusalem to rebuild it’s the wall. The temple of Jerusalem was rebuilt, cleared

and dedicated to God.

LESSON TWO. Prayers by Nehemiah and modern Christians

Learning outcomes. After reading this lesson the learner should be able to:

Outline occasions when Nehemiah prayed to the Lord.
Discuss the importance of prayer

Nehemiah prayed, mourned, and fasted. He prayed often and for all actions, keeping God’s law,

forgiveness, punishments, human relations, Jerusalem, good works, contributions and offerings,

observance of Sabbath day, and preparing duty allocations for priests and Levites. .

When he learnt about the suffering of Jews who remained in Judah and the ruined state of Jerusalem;

He prayed for forgiveness on behalf of his people (Neh.4: 1 – 11).

Making a request to King Artaxerxes to be permitted to return to Judah (Neh.2: 4 –

iii. When his enemies ridiculed the Jews and planned to discourage them from rebuilding the wall of

Jerusalem. Tobiah in particular said that the wall was poorly constructed and it could be brought down

by; a fox jumping on it. Nehemiah requested God to punish the enemies who were mocking temple

builders (Neh.4: 4 – 5).

When he learnt that his enemies were conspiring to attack Jerusalem to stop the construction work,

he prayed and organised people to provide a 24-hour guard of the wall (Neh.4: 7 – 9).

.v. For his good work, he prayed for his works (Neh 5:19).

When his enemies plotted to destroy him, he prayed God for strength and courage to overcome his

enemies (Neh 6: 19).

vii. When Shemaih attempted to frighten him to hide in the temple claiming that there was a plot to kill

him, Nehemiah prayed and asked God to punish his enemies (Neh 6:14).

viii. When he organized contributions for Levites and musicians; and people to distribute them. He asked

God to remember his work for the house of God (Neh 13:14).

He stopped trade on the Sabbath day, and organised rest on the Sabbath day. He warned traders

against violating the Sabbath law. He asked Lord to remember him for these actions (Neh.13: 22).

Nehemiah prayed for punishment of the son of Joiada. The son of Joiada had brought disgrace to the

priest hood by marrying a foreigner, the daughter of Sanballat from the town of Beth Horon, (Neh

13:29). After cleansing the Israelites of foreign influence, he forbade mixed marriages

He prepared duty regulations for priests and Levites. He allocated them duties. He then organised

Jews to bring offerings for maintaining priests and Levites. He prayed God to remember his work for the

temple, priests and Levites (Neh 13:31).

Importance of prayer in Christian life

Through prayers, Christians express their faith in God and praise God for his greatness, goodness,

holiness, and majesty. Prayer brings Christians closer to God; it strengthens their relationship with God.

Through prayer Christians request for their needs, blessings, success, good health, and protection

among other requests.

Prayers help Christians to listen to God and to seek his will. Prayer is a source of strength. It gives

Christians courage to face and overcome life’s challenges. Christians seek guidance, comfort and support

in times of trials. In prayer, Christians intercede for the sick, poor, hungry, prisoners, friends, family and

community. The communal / public prayers unite Christians together. Through prayers, Christians ask

for forgiveness and the ability to forgive others. In prayers, Christians trust that God listens and answers

their prayers.

LESSON THREE: LEADERSHIP QUALITIES OF NEHEMIAH

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

State the leadership qualities of Nehemiah
Explain the relevance of Nehemiah’s leadership qualities to Christians today

Introduction. A leader is someone charged with the responsibility of guiding, controlling, directing and

leading others. Nehemiah had many leadership qualities. These were: –

1) God fearing man. Nehemiah feared God, relied and depended on God.

2) Prayerfulness – he prayed constantly before and after making decisions.

3) Courageous – He displayed courage even when his life was in danger

4) Hard work and commitment. He was dedicated to the rebuilding of the wall of the temple and

Jerusalem.

5) Team spirit – he was a team leader, motivating people to work.

6) He had planning and organizational skills

7) He was visionary

He had compassion for the needy especially the poor, Levites and priests

9) He was patriotic loved his country

10) Wisdom. He made wise decisions at the right time.

11) He led by example, a role model

12) He was honest and sincere in his prayers

13) He was shrewd and impartial

14) His trusted God absolutely.

15) He was decisive. He told God about decisions he had made and asked for their recognition.

16) He was humble. He asked to be allowed to return to Jerusalem and oversee the repair of its wall and

temple.

16) He believed in law and punishment of wrong doers. He asked God to punish lawbreakers especially

Jews who married foreigners.

Relevance of Nehemiah’s leadership to Christians today

Christians should copy all the leadership qualities of Nehemiah. They should trust in God and seek his

guidance in all their activities and needs.

Christians should live a life of prayer
Christians should be courageous, be ready to defend the gospel of Jesus Christ.
Christians should be dedicated to their work. Work diligently and honestly
Christians should set realistic goals and organize their activities.
Christians should seek wisdom from God to be able to choose appropriate activities to attain their

visions.

Christians should care for the needy and be compassionate to all
Christians should be patriotic and ready to defend their country against internal / external threats.
Christians should need to fight for the rights of the helpless children, widows, orphans, and aged.
Christians should seek God first, view themselves as servants of God and be good role models.

LESSON FOUR. BUILDING THE WALL OF JERUSALEM

The wall of Jerusalem was destroyed when Babylonians conquered Judah. After finishing the wall, he

dedicated it to the Lord. Dedication is to devote something in honor of a person held dear or to set aside

something for some special purpose.

Learning Outcomes. After reading this lesson, you should be able to: –

Describe the problems that Nehemiah faced when building the wall of Jerusalem
Describe the dedication of the wall of Jerusalem
Identify lessons, which Christians can learn from Nehemiah.
Nehemiah rebuilt the wall of Jerusalem. The rebuilt wall had several gates with different names. The

gates were the entrances to Jerusalem. Their names were Dung gate, Potsherd gate, Fountain gate,

Water gate, Horse gate, East gate, Sheep gate, Fish gate, Watch gate and Ephraim gate. Knowing the

names of the gates may not be necessary but its good information.

Problems faced by Nehemiah. When Nehemiah was building the wall of Jerusalem, he faced many

challenges. There was lack of cooperation by the nobles of Tekoa. They did not want to do manual work

at first but they later repented. Nehemiah faced opposition from enemies such as. Sanballat, and

Tobiah, the Arab who tried to thwart the progress of Nehemiah’s work.

As he built Jerusalem, the rich oppressed the poor. This was worsened by famine

The priests misused the temple and the offerings. For example, temple duties had been abandoned. The

Levites were not getting their share of the offerings and the Sabbath was violated. There was laxity in

observance of the Sabbath. This was a challenge to Nehemiah because Sabbath day should be kept holy.

There was a lot of foreign influence because of the conquests by several foreign armies, intermarriages

and interactions between Jews, neighboring people and foreigners. Marriages in particular threatened

the identity of the Israelites as a nation. Worse still Priests married to foreign women defiled the

priesthood according to Nehemiah. Because of these assimilations of Jews through marriages,

Nehemiah knew that Israel and Judah would eventually be lost as God’s nation. Because of his

opposition to these interactions, Nehemiah received death threats.

Dedication of the wall of Jerusalem (NEH. 12:27 – 47)

The rebuilt wall was dedicated to God. The wall restored security and prestige of God’s people. The wall

of Jerusalem was set-aside for God in a solemn ceremony. There was a dedication ceremony in which

people sung with symbols, harps, lyres, trumpets and other instruments. The priests, and Levites

purified themselves.

The people led by Ezra, Nehemiah, the priests and other leaders of Judah walked around the wall. They

divided themselves into two groups. One group walked from the right side and the other group from the

left side and converged at the temple. Sacrifices were offered and people rejoiced. Some men were

appointed to be in charge of the storehouses; where tithes, and first fruits of harvest were kept.

Relevance of Nehemiah’s experience to Christians today

Christians should expect opposition, as did Nehemiah. They should not be afraid of being ridiculed,

mocked and despised. If it happens, Christians should persevere in God’s work. They should put their

trust in God like Nehemiah did.

They should also fight for the welfare of the disadvantaged groups and not exploit them. They have a

moral obligation to condemn injustice and take practical steps to help solve problems that afflict

individuals, groups, nations, and society. They should be in the forefront fighting HIV/ AIDS and drug

abuse.

Christians should be on the look out for external influence that may corrupt morals of the society and

the church. They should learn that leadership involves suffering, persecution, and sacrifices. This is

foregoing personal interests for the sake of the kingdom of God.

LESSON FIVE: RENEWAL OF THE COVENANT

Learning outcomes. After reading this lesson, you should be able to: –

List the stages followed to renew the covenant.
Identify issues that Ezra mentioned in his prayer

iii. List the vows that were made by the Israelites during renewal of the covenant

Stages of the renewal of the covenant. Israelites were the chosen people of God. They had suffered

many hardships. There was therefore a need for the renewal of the covenant between God and

Israelites. The ceremony to renewal the covenant was held in Jerusalem and was led by Ezra, the Levites

and other religious leaders. The renewal of the covenant can be discussed in 3 main stages:

Stage 1. A great public assembly was held in the square of Jerusalem inside the water gate. God’s law

was read and expounded to the people. The people of Israel praised and worshipped God. They cried

and grieved. They were sad because they realized that they had failed to observe the Mosaic Law. They

were instructed to go and celebrate, as it was a holy day of God and an occasion for joy not sorrows.

State 2. The feast of booths/tabernacle was celebrated for 7 days. It was a reminder of the days in the

wilderness when the Israelites dwelt in tents. The Law of Moses was read each day during the

celebrations.

Stage 3. There was a public confession of sin. People fasted, prayed and praised God. The public

confession was followed by the renewal of the covenant vows and a promise to keep God’s law in

future.

Ezra’s prayer closed the celebrations. In his prayer, he recalled God’s acts of creation. He then recounted

the history of the Israelites. He mentioned the previous acts of God; where the Lord had demonstrated

His love and mercy for the Israelites. He then confessed the sins of their ancestors and the present

Israelites. These were the sins of rebellion and disobedience.

Promises and vows made by Israelites during the renewal of the covenant. Israelites promised God

that they would

 Live according to God’s law, by obeying all his commands and requirements.

 Stop intermarrying with foreigners living in their land.

 Cancel debts every 7th year

 Contribute annually towards the temple expenses to ensure that the house of God was not neglected.

 Provide sacrifices and offerings for the temple and arrange for provision of wood for burnt sacrifices

according to the law.

 Offer first fruits of their harvest and dedicate the first born and flocks as required by the law.

 Pay for their tithes as required by the law.

Which lessons can we learn from the renewal of the covenant? God is good, loving, merciful, and faithful

to his promises. God forgives all people and we are all sinners. We fail in our moral obligation to God

and to one another.

Since we are sinners, we should repent our sins and strive to live according to God’s law. Christians are

to encourage one another as well as others to repent as it brings about reconciliation with God and with

one another.

Christians should be forgiving and avoid situations that lead them to sin

SAQ. Check from form 1 work, this information.

Outline Nehemiah’s final reforms
What is a covenant?
What are the components of a covenant?
Discuss how the covenant was renewed
List examples of covenants in the Old Testament and modern life.
Explain what Christians can learn from the experiences of Nehemiah
Compare or relate the teachings from Nehemiah’s exemplary life to the teaching of St. Luke’s Gospel

and Christian life today.

LESSON SIX: FINAL REFORMS OF NEHEMIAH

Introduction. Changes for improvement are known as reforms, which are either political, economical,

social, religious or a combination of any of them. Examples of reformers are King David, Prophet Elijah,

and Martin Luther King among others.

Nehemiah. After building the wall, Nehemiah went back to King Artaxerxes II who if you remember had

given permission to go to Jerusalem and build its destroyed perimeter wall. Later he returned to

Jerusalem and carried out these reforms.

Lesson outcomes. After reading this lesson, you should be able to:

List reforms of Nehemiah
Suggest what we can learn from the teachings of Nehemiah and that of St. Luke’s Gospel
Reforms by Nehemiah. We have discussed reforms, which Nehemiah carried out during his stay in

Judah, where he was the governor (Neh 5:14). The major reforms were

i Rebuilding the wall of Jerusalem as well as its gates.

ii Cleansing of the temple: Nehemiah threw him out Tobiah a foreigner who was living in the temple

quarters.

iii Reinstatement of the Levites and other temple workers. Levites, and musicians had left the temple

duties to work in their farms to earn a livelihood. They were supposed to work in the temple and be

supported by member contributions. Nehemiah organised Jews to make offerings and tithes to support

temple workers. With these contributions, Nehemiah reinstated and redeployed Levites, priests,

musicians and other temple workers.

iv Reform of the Sabbath observance. The Israelites were told by the Lord to work for 6 days and rest on

the Sabbath day. The Jews started working on the Sabbath day. The merchants camped outside waiting

for the reopening of the gates of the temple to do business. When Nehemiah started rebuilding

Jerusalem, he ordered closure of the gates of Jerusalem from the eve of Sabbath to the end of the

Sabbath.

v Separations from foreigners (Neh.13: 23 – 30). It was against God’s law to marry foreigners. Nehemiah

cursed the men who had married foreign wives. He beat Jews, pulled their hair and forced them to take

oaths that neither they, nor their sons nor daughters shall intermarry.

vi Purification of priesthood and the office of the Levites. Nehemiah cleansed the priesthood. He sent

away Eliashib, a grandson of the High Priest Joshua, because he had given Tobiah a foreigner, a room in

the temple.

Comparing teachings of Nehemiah and St. Luke’s Gospel

i Nehemiah lived a prayerful life while St. Luke’s gospel emphasizes importance of prayer. Jesus taught

the role of prayer in Christianity.

ii Nehemiah fasted, St. Luke’s gospel records that Jesus fasted.

iii Nehemiah prayed for forgiveness of sinful Jews. We see Jesus in St. Luke’s gospel being a leader who

prayed for the forgiveness of his enemies.

iv Nehemiah cared for the needy. Jesus showed compassion to the needy and taught his followers to

follow His example.

v Nehemiah condemned evil so did Jesus

vi Nehemiah is seen as a reformer of the Mosaic Law. In St Luke Gospel, Jesus was also a reformer. He

insisted on inner holiness.

vii Nehemiah cleansed the temple of traders so did Jesus.

viii Nehemiah was very strict on the Sabbath observance. St. Luke’s gospel teaches that Jesus is lord over

Sabbath. He healed and “Worked” on Sabbath.

ix Nehemiah was opposed to racial intermarriages, St. Luke Gospel was dedicated to Theophilus, a

gentile convert

x Christianity kingdom of God in St. Luke’s gospel is for all, not just the Jews.

Nehemiah had good leadership skills and wisdom. These are demonstrated in St Luke Gospel.
Relating Nehemiah’s teachings to Christian life today

i Prayers and fasting are fundamental to Christians just like they were to Nehemiah who led a prayerful

life.

ii Nehemiah’s example teaches Christians to face all forms of opposition with courage, wisdom, and

firmness

iii The good leadership qualities of Nehemiah are relevant to Christians and they are to be emulated.

iv Nehemiah cared for the needy. Christians should learn to give spiritual food, physical food and

clothing to the needy, orphans, widows.

v As Nehemiah renewed the covenant, Christians should seek spiritual renewal publicly and privately.

They should seek for communal as well as individual forgiveness.

vi Nehemiah cleansing the temple and organised an inventory for temple contributions, offerings and

tithes. He also appointed key people to look after temple contributions and pay Levites and priests.

Christians should learn to use the church buildings and contributions rightly

vii Nehemiah was guided by the Law of Moses and land just like Christians are guided by the scriptures

(Bible) and the law of the nation. The Bible is the source and basis of Christian principles.

Revision questions

Describe the political background of Nehemiah
Describe the social background to the vocation of Nehemiah
Describe the religious background to the vocation of Nehemiah
Describe occasions when Nehemiah prayed
State occasions when Christians pray
What is the importance of prayer in Christian life?
Identify the leadership of Nehemiah’s patriotism
Explain the relevance of Nehemiah’s leadership to a Christian today
Explain the relevance of Nehemiah’s experience to Christians today
explain the problems that Nehemiah encountered in his vocation
Explain the steps taken by Nehemiah to renew the covenant
State the promises the Israelites made during the renewal of the covenant

Study activities. Visit a church or your church and observe the display of the gifts of the Holy Spirit by the

members. Study the books of Amos, Jeremiah and Nehemiah before hand.

Form three answers.

TOPIC ONE: THE GIFTS OF THE HOLY SPIRIT.

Qn a. Explain the meaning of the Pentecost.

 Pentecost means fifty days after the harvest.

 It was one of the religious festivals celebrated by Israelites annually.

 In the Old Testament, the day of the Pentecost was celebrated during the wheat harvest in order to

thank god for the blessing of the harvest.

 Israelites came from all over the world and gathered in Jerusalem for this celebration.

 In the New Testament, the meaning of the festival changed. It was celebrated to commemorate the

coming of the Holy Spirit upon God’s people as they gathered in the upper room.

Qn b. Describe the manifestations of the Holy Spirit on the day of Pentecost. (Acts 2: 1-40) OR (narrate

the events that took place on the day of Pentecost).

 Disciples gathered in a room.

 Sounds came from heaven like a rush of mighty wind and filled the house.

 There appeared tongues of fire.

 The tongues of fire were distributed on each one of them.

 They were filled with the Holy Spirit.

 They were speaking in foreign languages and tongues.

 Those who were observing them were amazed, as they could not understand what they were saying.

 They accused them of being drunk

 Peter stood up and explained that they were not drunk as it was too early in the day to get drunk.

 He explained how they were filled with the Holy Spirit as prophesied by prophet Joel.

 He told them that it was Jesus whom they had rejected and crucified who had sent them the Holy

Spirit.

 The people asked peter what they could do.

 Peter told them to repent and be baptized.

 On that day about 3000 people were added to the church.

Qn c. write down five teachings we learn about Jesus from Peter’s speech on the day of Pentecost.

 Jesus was from Nazareth

 He had a divine nature or was son of God

 He had a human nature

 He was attested by God to work miracles and wonders through Jesus.

 Jesus’ death/ crucifixion was according to God’s plan

 God raised Jesus from the dead

 Jesus conquered death

 The death and resurrection of Jesus fulfils the prophecy of David

 Jesus was a descendant of David

 The Holy Spirit was from Jesus Christ as he had promised.

 God has made Jesus Christ both lord and Christ/ messiah

 Jesus ascended into heaven. He is exalted at the right hand of God

 The risen Christ is a source if hope or salvation to many sinners/crippled/the dead

Qn d. What were the qualities of peter that made him a successful leader for the apostolic church?

 He was a man of great faith

 He was a good orator

 He dedicated his life to Jesus

 He was filled with the holy spirit

 He could perform miracles or wonders

 He was an eye- witness of the ministry of Jesus Christ.

 He was full of wisdom and knowledge i.e. Anania’s and Saphira’s case

Qn e. what lessons can Christians learn fro the events of the day of Pentecost

 They learn that Jesus always honors and keeps his promises e.g. he promised to send the Holy spirit

and did it

 Baptism in the holy spirit is very important for every believer

 That obedience yields immediate results i.e. the disciples obeyed Jesus by testifying in Jerusalem and

they received the Holy Spirit.

 It is important for believers to meet for fellowship. The disciples did this and they received the Holy

Spirit

 That the Holy Spirit enables Christians to declare the gospel with boldness

 It was the plan of God that Jesus was crucified

 Jesus indeed rose from the dead as peter witnessed

 Jesus was the son of God

Qn f. state the teachings of Jesus on the Holy Spirit

 The Holy Spirit comes from the father

 The Holy Spirit will comfort disciples

 The Holy Spirit will abide with believers forever. He was to teach the world and reveal the truth about

God

 The Holy Spirit would guide them into all truth and make them understand or know more about Jesus

 The percolate i.e. comforter/make strong/counselor who give advice

 He was to help them attain eternal life. If it was necessary for him to die and return to the father so

that Holy Spirit will be sent to them. It was to replace Jesus as a counselor and an advocate

 He was to give the disciples authority to forgive or not to forgive

 The spirit would remind them all that Jesus had taught them

 The holy spirit will reprove the world of sin, righteousness and judgement

 He would glorify Jesus amongst the believers

 He will enable believers to be witnesses of Jesus in the whole world

 He was to strengthen disciples as a wonderful counselor

 He was to continue with the work of Jesus as a witness

Qn g. what is the role if the holy spirit according to Jesus?

 He comforts believers

 He teaches believers all things

 He bring into remembrance all that Jesus taught his disciples

 The holy spirit would convict the world of their sins and lead them to righteousness

 He will guide the believers in all the truth

 He will glorify Christ and teach about him

 He will tell of the things to come in the future

 He would not speak on his own authority but would speak only what he hears from the father

 He will enable believers to be witnesses of Jesus in the world

 He will counsel believers because he knows the mind of God

 He will enable believers know the perfect will of God

Qn h. what is the role of the Holy Spirit in the believers (or Christians or the church)

 He enables believers to preach with power

 He comforts believers

 He guides believers in all truth

 He gives believers boldness to witness about Jesus

 He enables Christians to produce the fruit of the spirit

 He washes sacrifices and justifies the believer in the name of Jesus

 He teaches believers all things

 He enables Christians to access God the father and son in prayer

 He enables Christians talk in tongues in worship

 He enables Christians to perform miracles in the name of Jesus

 He enables Christians to declare sins and transgressions of others

Qn i. Outline the fruits of the Holy Spirit (Galatians 5:6-26)

 Love  showing compassion to one another

 Joy  deep happiness when one has a good relationship with God

 Peace  being at peace with all people

 Patience  being to wait in difficulties

 Kindness  being caring and helpful towards others

 Goodness  seeking to do best in their lives

 Faithfulness  having confidence in God

 Gentleness  being calm and avoiding violence

 Self-control  have strong control over their emotions

Qn j. state the criteria for discerning of the spiritual gifts

 The gift must glorify Jesus so that one who is under the influence of th Holy Spirit will be able to

recognize Jesus as lord and savior

 The gifts must not call Jesus accursed

 The test of love. The gift must be accompanied with a good or true frit. To discover whether or not

the person who has the holy spirit must bear the fruits of the spirit

 One who is user the influence if the Holy Spirit is known by his or her way of life. He/she will act and

behave in accordance with the teachings of Jesus.

 Doctrinal test for example, prophecy should always in agreement with the scripture because the Holy

Spirit cannot contradict what is written

 Loyalty or conformity to Jesus. The gift doesn’t envy other believers

 The gift must be subject to the word of God

 The true gift will be guided by principles of sincerity and honesty

 The true gift will humbly submit to God

 The gift should encourage the growth of the church and edify her

Qn k. List down the gifts of the Holy Spirit.

 The gift of wisdom (a deep understanding of who God is an his purpose for human life)

 The gift of knowledge that is the basic understanding of the truth about Jesus Christ

 The gift of faith that refers to the confidence or truth in God’s inspiration and help in undertaking

difficult tasks

 The gift of healing: the power to heal all types of sicknesses

 The gift to perform all types of miracles including healing

 The gift of prophecy: that is the ability to expound on the scriptures and foretell its future

implications

 The gift of distinguishing gifts: the ability to tell the difference between gifts that come from the spirit

and those that are not

 The gift of speaking in tongues: the ability to understand and interpret tongues

 Lastly the gift of love, which is the greatest of all the spiritual gifts.

Qn l. Explain why Paul taught that love is the greatest of all spiritual gifts.

 Paul taught that love is the greatest of all spiritual gifts. He said that love is patient and kind

 It’s not jealous or boastful. It is not arrogant or rude or conceited. It does not hold grudges or ill

mannered or selfish

 It does not insist on its own way. It is not irritable or resentful

 It does not rejoice at wrong doings but rejoices in the truth

 Love bears, believes, hopes and endures all things

 It is ready to deep firm its faith, hope and its patience

 Love does not succumb to pressure but always perseveres

 He justified that love is the greatest gift of the spiritual gifts because in prayer, the gift of tongues

becomes nothing but meaningful when accompanied by love (charity)

 On faith, Paul says that even if one has faith that can move mountains but has no love, he is nothing

 Charity or generosity including sacrificing own life is nothing without love

Qn m. Explain how the Holy Spirit is manifested in the church today

 Through dynamic, power, bold and vigorous teaching of the gospel

 Through speaking in tongues in many evangelical churches

 Through the gift of healing many people are healed as they are prayed for

 Through the gift of love, Christians show mercy to all members of the society regardless of their race,

sex or age (helping the poor in the society)

 Through the gift of prophecy some believers give proper guidance to the church

 Through the gift of discernment of spirits believers are able to tell the type of spirit that is in

operation

 Through the gift of faith, believers have been able to accomplish tasks that seem rather impossible

 Some Christians through the holy spirit are able to withstand a persecution to the point of death

 The holy spirit convicts sinners and makes them confess their sins

 Through the holy spirit many Christians see heavenly visions and dreams

 The fear of the lord is upon many evangelical groups through the Holy Spirit

 In some evangelical gatherings, there are many supernatural things during worship e.g. shaking and

swaying

 It is also manifested through prayer at individual or congregational levels

 Through decision making in church i.e. solving problems and issues in church

 Through singing and dancing or music

 Through offertory and alms or sadaka

 Holding fellowship meetings, bible study and reading the bible

 Celebration of sacraments e.g. Eucharist and lord’s supper

 Bringing new converts to the church

 Pastoral cave and counseling It is manifested in Ecumenism: working together of the churches

 Writing Christian literature e. g. books, pamphlets and magazines

 Enabling Christians to confess their sins and reconciliation meetings

 Education and giving instructions

Qn n: State ways in which the gifts of the Holy Spirit have been abused in the church today.

 Cheating that one has a certain gift of the Holy Spirit

 Commercialization of the gifts. People are asked to pay money before being prayed for or being

healed

 False interpretation of the bible, prophecy or predicting the future

 Unscrupulous Christians may impart demoniac powers or innocent faithful

 Some Christians who possess the gifts of the Holy Spirit develop pride or selfishness or superiority

complex

 Wrong use of the gifts of the Holy Spirit where faithful get into ecstasy or trance which may lead to

injuries

 Distinguishing oneself as a person with a special call e.g. preacher with intention of exploiting others

or situations

TOPIC TWO: UNITY OF BELIEVERS

Qn a. Write down the terms used in the New Testament to refer to believers in Christ

 The people of God

 The body of Christ

 The bride of Christ

 The vine and the branches

 The assembly of God

 Christians

 The people of the way (followers of the way) other terms

 Followers of Christ

 New Israel

 Church

 The sheep

 The royal church

 Brethren

 Royal race

 Royal priest hood

 Holy nation

 The children of light

 Saints

 Brothers and sisters in Christ

Qn b. identify five causes of disunity in the early church

 The question on the inclusion of the gentiles in the church. Some Jewish Christians were not ready to

accept gentile Christians in the church unless they underwent circumcision

 There was negligence of the widows in the distribution of food

 Disagreement between and among leaders e.g. Paul and Barnabas, Peter and Paul

 Groupings in the church where some Christians owed loyalty to individuals. They said that they

belonged to individuals like Apollo others Peter and others Paul

 Question of immorality, where some Christians did not live according to the teachings of Christ

 The problem of the gifts of the Holy Spirit. Some Christians became arrogant because they were more

gifted than others

 Different interpretations of the doctrines e.g. resurrection, sin, salvation, Christology, Holy Spirit,

dressing

 Behaviour during the lord’s supper

 Christians took others to a pagan rule of law

 Question of the resurrection of the body

 Question of celibacy

 Question of incest sexual immorality

 Different approaches to common life between Christians communities in Jerusalem and Antioch

Qn c. identify factors, which cause disunity among Christians today

 Selfishness or greed for money by some Christians

 Rivalry or competition for leadership positions or greed for power

 Misinterpretation by some Christians of the work of the holy spirit

 Arrogance or pride by some Christians

 Corruption in the church

 Failure by some Christians to live according to the law of God or their failure to live exemplary

 Lack of concern by some Christians about the plight of others

 Misinterpretation of the bible or doctrinal differences

 Misuse of church funds or power by some leaders

 Lack of transparency and accountability in running church affairs

 The emergence of charismatic movements in the church creates a situation where some Christians

think that they are more spiritual or holier l than others

 Political interference where Christians find themselves in different political camps

 Sexism where women are not involved in decision-making. Women are under represented

 Discrimination against the youth or churches ignoring the youth in running the church

 Tribalism where Christians are divided along tribal lines

 International differences

Qn d. Discuss reasons why members of Christian families in Kenya find it difficult to harmoniously live

together

 Unfaithfulness or promiscuity

 Misuse of family resources or lack of resources

 Child abuse e.g. beating, raping, incest or favourism

 Alcoholism or drug use and abuse

 Separation of family members e.g. due to wage labour or education

 Denial of conjugal rights

 Sickness e.g. HIV/AIDs, impotence, barrenness or cancer

 Child delinquency

 Lack of tolerance or forgiveness or presence of cruelty

 Greed for wealth or self esteemed prestige or professionalism

 Religious fanaticism or denominational differences

 Traditional or cultural inhabitation or western cultural influences or permissive

 Generation gap

Qn e. explain how the church strengthen family relationships today

 Through guidance and counseling and mediation

 Hold seminars, conferences for couples, children the youth through publications on Christian living

e.g. magazines, books or pamphlets

 Use of mass media e.g. televisions. Radios or videos

 Through offering pastoral care in homes or house to house visits

 Giving financial support to the needy families

 Praying for families

 Through preaching, teaching and condemning vices

 Offering employment to the jobless

 Providing vocational training skills

SELECTED OLD PROPHETS AND THEIR TEACHINGS.

Q1. Define the terms prophet and prophecy

Prophet: Refers to one who speaks God’s message. He is God’s spokesman. His message includes

predictions of the future.

Prophecy: Is the message spoken by a prophet. Oracles spoken by prophets.

Q2. List the five categories of true prophets

i) Major prophets

These include Isaiah, Jeremiah, Ezekiel and Daniel.
They are called Major Prophets because the books are long and contain clearly written messages.
They bear the names of the writers.

ii) Minor prophets

These refer to 12 books that are short and contain less important than those in major books e.g. Amos,

Hosea, Joel, Obadiah through to Malachi.

iii) Canonical prophets

Both the major and minor prophets are together referred to as canonical prophets.

iv) The early prophets

They belonged to guilds or schools.
They lived together in communities under a chief prophet. Elijah and Elisha are examples.
These are those who served in places of worship e.g. at Dan, Bethuel)
They were called cultic prophets because they were associated with religious activities in shrines.
They traveled around together delivering oracles.

v) Cultic prophets

They worked side by side with priests and said prayers especially people’s petition to Yahweh.

Q3. State the difference between true and false prophets

True prophets False prophets

 They were called by God to be His spokesmen  Not called by God.

 Were obedient to God.  Not obedient to Him.

 Believed in one God.  Could worship other gods and led people into immorality.

 They were prayerful.  Not.

 Spoke and acted with authority from God.  No authority from God.

 They led holy lives.  Were immoral e.g. believed in false gods.

 Spoke God’s word.  Spoke their opinion.

 Suffered physically and psychologically because of speaking the truth.  Run away suffering.

 Spoke the truth.  False

 Did not ask for pay.  Asked for pay.

 Spoke form a common tradition based on the Mosaic Law.  Did not have any reference.

Q4. In what ways were God’s prophets called?

 Some were called through visions or dreams e.g. Amos and Samuel.

 Others were called through other prophets e.g. Elisha.

 Words or message came into their minds.

 Through prophetic symbolic actions e.g. Jeremiah

 Through common objects – an object becoming a significant sign of God’s power and activities Jer.

1:11-13.

 Through prayers.

Q5. Outline the similarities and differences between the Old Testament prophets and the Traditional

African Ones

a) Similarities:

 Both possessed spiritual powers.

 Both were mediators between people and a Supreme Being.

 Both performed the role of healing people physically and spiritually (miracle).

 They received calls mainly through visions/dreams, which were considered supernatural.

 Were both expected to be people of integrity and obedient to religious codes.

 Gave warnings and solutions to their people in case they offended the Supreme Being.

 Foretold the future.

b) Differences:

Old Testament Tradition African

 Received their message from God  Received their message from spirits and ancestors.

 Appointed by God.  Inherited

 Rejected by people  Respected and feared in society

 Prophecy went to other nations  Confined in tribal community

 Prophecies preserved in writing  Passed on orally

 Believe and worship of one God  Believe in god spirits

 Performed miracles  Did not

Q6. What is the relevant of prophets to Christians today?

 Through reading their prophecies, Christians get to know the will of God.

 Jesus who is the cornerstone of Christianity is stressed throughout prophecy – since Abraham.

 Prophecy has helped many to be preachers (i.e. prophecy = preaching).

 Christians learn to be faithful to Yahweh just like the Old Testament prophets.

 They too learn to be holy and prayerful like them e.g. Jeremiah.

 Prophets encouraged justice e.g. Elijah, Christians should do the same.

 As prophets, Christians should provide hope to the people in times of suffering.

 They learn that they can face suffering just like the prophets did e.g. Jeremiah e.g. persecution,

rejection etc.

 They should condemn sin like the prophets.

 The writings of the prophets strengthen their faith when they need them.

PROPHET AMOS

Q1. List the visions that Amos saw

 He saw a swarm of locusts. Amos 7:1-3

 He saw a great fire. Amos 7:4-6

 The plumb line/crooked wall. Amos 7:7-8

 Basket of ripe fruits. Amos 8:1-3

 The destruction of the temple. Amos 9:1-4

Q2. Explain the evils that Amos condemned in his teachings

 Sexual immorality (Amos 2:17)

Amos condemned temple prostitution – 23:17.
Father and son were going to the same woman.
They copied these from the Canaanite pagans, which was wrong and unfaithful to Yahweh.

 Slavery: (Amos 2:6)

The righteous, the rich made the poor slaves. This is because they borrowed from the rich and could not

repay so they made them work like slaves and treated them harshly. Some sold them for a paid of

sandals. This was breaking God’s laws, which guided them on how to treat their poor fellow Israelites.

 Idolatry: Amos 5:26

Amos accused them for breaking God’s covenant by worshipping other gods.

 Cheating in Business: He condemned the following:

Merchants used false measures
They overcharged the poor
Sold goods of low quality
They sold poor people for not paying debts
They too charged high interest rates

 Bribery and Corruption Ex. 23:8

He condemned elders who were unjust and corrupt.
They took bribes and grew rich from heavy levies from innocent people in law courts.

 Greed and excessive luxury

He condemned women of Samaria who drink and lived in luxury when there were poor needy people.

 Breaking God’s law on garments secured for pledges

God gave Israelites items that were to be given out to the creditors as a guarantees for the goods

borrowed e.g. Millstones for grinding, were to be taken and returned in the evening because they were

used daily.

 Robbery and Violence

Poor were being oppressed and violated.

 Self – Indulgence and false sense of security

Leaders thought God could not punish them because they were a chosen race.
But Amos told them they would be attacked.

Q3. Give reasons why Prophet Amos condemned idol worship in Israel

 It broke the covenant way of life.

 __________It was against the 10 commandments, which directed the Israelites to worship one God.

 It was a sign of disobedience to God.

 It promoted immorality e.g. temple prostitution.

 The worship of God belittled and degraded God.

 It promoted falsehood in the society.

 Religion became commercialized.

 Led to false prophecy.

 People got concerned with external behavior and not internal.

Q4. List evils in society today that Amos would condemn

 Tribalism

 Bribery and corruption

 Robbery with violence

 Dishonesty in business

 Grabbing of public land and property

 Stealing

 Oppression of the poor e.g. underpayment

 Immorality e.g. prostitution

PROPHET JEREMIAH

Q1. List evils that Jeremiah condemned

Human sacrifice
Hypocrisy in worship
Dishonesty in business
Defilement of the temple – temple prostitution
Social injustice
Idolatry
False prophecy
Necromancy
Exploitation of the poor

Q2. What are some of the evils that the church leaders condemn today?

Hypocrisy/pretence in worship
Murder/suicide/abortion/genocide
Exploitation of the poor/robbery
Dishonesty
False prophets
Human sacrifices among devil worshippers
Sexual immorality e.g. adultery

Q3. Explain the symbolisms used during the call of Prophet Jeremiah

 God touched Jeremiah’s mouth. This was to symbolize that God was the source of the message.

Jeremiah was to deliver.

 A branch of an almond tree that was base – God was watching to see the fulfillment of the message

he gave to Jeremiah.

 A pot of boiling facing away from the North and about to tilt toward Judah. God would use a nation

from the North to bring judgement on the people of Judah because of their wickedness.

 A fortified city. A bronze wall and an iron pillar. God was going to protect him even though he was

going to meet opposition.

 To uproot and pull down, to destroy and overthrow. God would pass judgement on the nation of

Judah and other nations.

 To build and to plant. There was still hope of the restoration of people of Judah after exile.

Q4. What did Jeremiah teach about t the New Covenant?

 The new covenant was to be written in people’s hearts.

 The covenant was to be made between God and the remnant community after exile.

 The people were to have a personal knowledge of God in the new covenant.

 God was to forgive their sin and remember them no more.

 Each individual was responsible for his won sins.

 The new covenant was to be initiated by God.

 The new covenant was to last forever.

 It was as a result in the emergence of a new people of God or new Israel.

Q5. Why did Prophet Jeremiah condemn the way the Israelites worshipped?

 They broke God’s commands e.g. the 1st and do not worship other gods – they worshipped idols.

 They practiced hypocrisy i.e. they were concerned with external religious observance while their

hearts were far from God.

 They forgot the saving history of God and worshipped other gods e.g. Asherah.

 They practiced syncretism i.e. they worshipped both Yahweh and foreign Gods.

 They listened to false prophets and rejected God’s prophets e.g. Jeremiah. They even killed some.

 They dishonored the sanctity of human life by offering human sacrifice.

 They neglected the disadvantaged (widows & orphans).

 They were dishonest in business and deceitful to one another.

 They narrowed themselves in necromancy, divination and magic.

 They rebelled against God by breaking the covenant relationship.

Q6. Explain Jeremiah’s temple sermon as recorded in Jeremiah 7:1-15

 God commanded prophet Jeremiah to speak in the temple.

 It was a response to the people of Israel to stop understanding religion through the practice of

syncretism and immorality.

 At the gate to the temple, Jeremiah proclaimed that the people of Judah had to change their way of

life and stick to the covenant they made with God.

 They had to stop defiling the temple of placing idols in it.

 They had to stop committing social injustices and as murderer/exploitation of the weak, orphans

widows and foreigners.

 The practice of human sacrifice was murder and displeasing to God.

 Hypocrisy was bad.

 The Israelites believed that the temple was secure from destruction because of its holiness was not

true.

 God would destroy Israelites/Jerusalem through invasion of a foreign nation.

 If the people stopped their evil ways, God would not bring judgement upon them.

 God would destroy the temple of Jerusalem and send the people to exile.

Q7. What forms of punishment did Jeremiah prophesy that God would use on Judah?

 The punishment would be in form of a foreign body that God use to conquer Judah.

 They would be attacked and their city destroyed.

 People would suffer and die due to their sins.

 The punishment would in form of drought. This would affect people and animals.

 God’s punishment would come through death, diseases and sword.

 Their punishment would be a defeat inflicted to them by Babylonian.

 The punishment would be the loss of their land to a foreign nation and their enslavement.

 God would allow the enemy to destroy Jerusalem and take survivors to captivity.

Q8. Outline the content of Jeremiah’s letter to exiles in Babylon (Jer. 29)

 He encouraged the Israelites in Babylon to build houses and live in them.

 Plant gardens and eat their produce.

 Marry and increase.

 Pray for their rulers.

 Not to worship false gods.

 Not to be cheated by false prophets.

 To obey their masters.

 Worship one God.

Q9. Explain four symbolic acts related to judgement and punishment as demonstrated by Prophet

Jeremiah

 Linen waist cloth – the rotten/useless linen cloth that had been hidden in the caves and lift to rot

stood for Israel’s state of being useless before the eyes of God. A sign that they had soiled their

priesthood.

 Jeremiah was asked not to marry the solitary life symbolized solitude in exile.

 Two baskets of fig fruits – the bad fruits signified that the bad people would be punished.

 Wooden yoke – he was asked to carry a wooden yoke and work around with it signifying suffering in

Babylon – exile.

 Breaking an earthly flask – destruction of the temple.

 Visit to a potter – whereby the potter destroyed a pot due to poor shape and remolded it. God would

remold Israel to a shape befitting them.

 Not to comfort anybody – these would be sorrow and suffering, no help while in exile.

Q10. Identify the relevance of Jeremiah’s teaching to Christians life today

 Christians are called to preach God’s gospel as Jeremiah did.

 Christians should accept suffering like Jeremiah did.

 They should learn to distinguish between false and true prophets.

 Like Jeremiah, they should condemn evil in society.

 They have a duty to call people to repentance as Jeremiah did.

 Christians should be good examples to the people by living, holy and upright lives as Jeremiah did.

 People should be able to know the nature of God through the lives of Christians.

 They should believe they are the new community as prophesied by Jeremiah in the new covenant.

Q11. In what ways is the prophetic mission of Jeremiah similar to that of Jesus?

 Both were rejected by their own relatives and communities.

 Both experienced opposition from political and religious authorities.

 Both prophesied the destruction of the temple.

 Both lamented over the stubbornness of the people of Jerusalem.

 Both predicted divine judgement and punishment in Israel.

Jeremiah predicted the new covenant that is fulfilled by Jesus.

Prophet Nehemiah

Qn 1. Describe the political background of Nehemiah

 He worked during the Babylonian exile which lasted between 589- 538 BC

 During his vacation, Israelites were oppressed politically

 The Israelites hoped that God would soon liberate them fro this bondage

 In 538 BC the Babylonians were conquered by Cyrus the great king of Persia

 In 538 BC king Cyrus allowed Israelites to return to Judah

 King Cyrus gave the Israelites a decree to rebuild the temple of Jerusalem

 In 538BC the first exile under Zebu Babel

 Joshua the priest departed from Babylon and started to rebuild alters of God

 Under the guidance of prophets Haggai and Zachariah the temple was rebuilt and dedicated

 The second exile arrived under prophet Ezra; after king Artaxerxes authorized Ezra to re establish

Israelites religious and moral expectations of the Mosaic Law.

 Nehemiah was a servant the king Artaxerxes palace. The king authorized him to go and rebuild the

walls of Jerusalem

 Amidst all opposition from Samaritan, Nehemiah accomplished the reconstruction of the walls of

Jerusalem in 52 days. He then dedicated the walls to God.

 This restored the sense of political pride in Israel. However the Israelites remained subjected to the

Persians and continued to pay tribute. The Persians were later overthrown by Romans who ruled the

entire region until the time of the birth of Jesus

Qn 2. Describe the social background to the vacation of Nehemiah

 Israelites men married foreign women

 Children spoke different languages from their mothers

 Hebrew language almost became extinct

 Nehemiah condemned mixed marriages and even banned them

 Exiles who returned home were humiliated by foreigners who partially occupied their land

 The Samaritans threatened Nehemiah’s life as the rebuilt walls of Jerusalem

 Rich Jews oppressed the poor e.g. they would confiscate their property for failure to repay debts

Qn 3. Describe the religious background to the vocation of Nehemiah

 While in exile the Babylonians allowed the Jews to continue with their religious lives

 The exiles became the period of purification

 They returned with a new zeal to worship God; they rebuilt the altar under Zerubbabel for offering

burnt offerings to God

 The returnees built the temple of Jerusalem under Haggai and Zachariah and dedicated to god by Ezra

 Nehemiah embarked on rebuilding the walls of Jerusalem amidst opposition in 52 days the wall was

complete. Consequently, Jerusalem once more became the centre of worship for Israel. Idolatry was not

allowed again in Israel after the exile.

 The temple of Jerusalem was dedicated to Yahweh. The Israelites renewed their covenant with God

under prophet and priest Ezra. Nehemiah carried out various religious reforms

Qn 4. Describe occasions when Nehemiah prayed

 When he heard about the suffering of his fellow Jews back in Judah

 When he learned about the state of ruin of Jerusalem and king Atarterxes to request him to allow him

go back to Judah

 When his enemies e.g. Tobiah and Samballat ridiculed him as he reconstructed the walls of Jerusalem

 When he learned of his enemies conspiracy to attack Jerusalem

 When his enemies conspired to destroy his life/ kill him

 When Shemiah attempted to frighten him to hide in the temple as hi life was in danger

 When he cleansed and arranged the temple as a house of God

 When he warned the people of Judah against violating the Sabbath law

 After chasing away the son in law of Samballat from the temple

 After cleansing the Israelites of foreign influence

Qn 5. State occasions when Christians pray

 When they are faced with diverse persecutions. They ask God to protect them

 When they don’t understand certain scriptures. They ask God to give them revelation

 When they are faced with certain difficulties of life. They ask God to help them

 When the nation is facing political crisis. They pray for peace

 When they feel inadequate and sinful. They ask God to perform certain miracles for them e.g. healing

Qn 6. What is the importance of prayer in Christian life?

 Prayer helps Christians to praise God, give thanks to him and to repent

 It helps Christians to pour out their hearts to God

 It helps Christians to rely to God for emotional and mental stability. It helps put our problems to God

 It strengthens Christians. It gives them determination and character to remain steadfast in their

responsibilities despite the challenges

 Through prayer a Christian can request to stand against personal attacks and temptations

 Prayer is the source of courage and strength in times of tribulations

 It brings one closer to God, we use it to praise God, use it to ask for God’s supply of their needs, used

to ask for forgiveness and promotes important virtues e.g. persistence and patience and promotes unity

among different communities

Qn 6. Identify the leadership of Nehemiah’s patriotism

 He was a tune patriot i.e. after talking to the Jews and getting the news of distribution of Jerusalem,

he was forced to go back home.

 Reliance to God. He totally relied on God and to his call i.e. in most cases he prayed before carrying

out an activity

 Devoted/ talented. As a cupbearer to the emperor he was an educated, talented and trustworthy

young man

 Visionary. He had a vision and he shared it with enthusiasm to inspire Jerusalem leaders to rebuild

the wall

 Initiative.

 He took the initiative to persuade the emperor to put things right

 Exceller organizer. He carefully organized the rebuilding process. He organized how the wall of

Jerusalem was to be built in steps

 Careful planner. He carefully examined and inspected the wall before starting the work

 People’s representative. He was a proper representative of his people in Israel. he had a sense of

responsibility to his community

 Shrewd. He avoided the meetings organized by his opposer and overlooked the abuses placed on him

 Impartial. He appointed men of integrity and God fearing to keep guard over Jerusalem

 Selfless and kind. He had the skill of solving problems. He hence cancelled all debts that people had

 Homogenous. He employed different strategies to counteract his opposer

Qn7. explain the relevance of Nehemiah’s leadership to a Christian today

 A Christian should use his/her present position to serve God

 Christians should acknowledge God as their source of power and giver of gifts

 A leader should appoint people who are trustworthy and honest to help him/ her in ruling the

country

 God answers our prayers as a result of asking others for help

 A Christian leader should keep his /her plans a secret until it matures to make an announcement

 Christians should share their visions with others the way Nehemiah did

 Leaders should take care of the needy in the society

 As a Christian one could be lured to temptations; the way Nehemiah was opposed we should be

ready to resist temptations

 Christians should be ready to help in solving problems in the society Christians should act as role

models by carrying out spiritual activities with the truth and helping in work after starting projects.

Qn 8. Explain the relevance of Nehemiah’s experience to Christians

 They should not exploit the needy and disadvantaged

 They should defend the rights of the weak and use their work place, family and friends

 They should ask God to protect them from the mischief of their enemies

 That they should pray to God to give them guidance in their endeavors

 That they should persevere in all difficulties as Nehemiah did

 The should condemn the injustices in the society

 They should know that leadership involves challenges and difficulties

 They should be practically involved in problem solving e.g. HIV/AIDs scourge

Qn 9. Explain the problems that Nehemiah encountered in his vocation

 Oppression of the poor Jews by the rich Jews e.g. demanded high interests on borrowed money

 Great opposition from the enemies they tried to frustrate his/her efforts to build the walls of

Jerusalem

 Threat to his own life. His adversaries wanted to kill him

 Lack of co-operation and support from the Jews. They refused to work with him on the wall project

 Excessive foreign influence in Israel. Intermarriage brought about foreign influence which threatened

to extinct the Jew culture and language

 Violation of the Sabbath laws. Israelites went on to do their daily chores on the Sabbath day

 Abuse of the temple. Eliaship housed Tobias the heathen and God’s enemies

 Misuse of offerings. The levies were denied their share of sacrificial offerings as required by the law

Qn 10. Describe the steps taken by Nehemiah to renew the covenant

 Ezra the priest read the book of the covenant and explained the meaning of the Law of Moses. The

Israelites listened carefully and their lives changed. They responded Amen, amen

 Celebration of the feast of shelters. After reading the scriptures, they realized that they had not been

celebrating the feast of shelters. This was to remember their deliverance from Egypt. They were also to

think about God’s protection and guidance

 The Israelites confessed of their sins as they learnt that they had not been following God’s

commandments. Nehemiah was devoted to confession of national sin and prayers to God’s grace

 Recital of God’s dealings with Israel. They recital of God’s mighty acts is done in this. They

remembered their history and this renewed God’s grace and power in them

 A renewed covenant sealed. The covenant was renewed in writing and the leaders put seals

 The binding agreement that people and God was done by the Israelites joining hands

Qn 11. State the promises that Israelites made during the renewal of the covenant

 That every seventh year, they would cancel debts according to the Mosaic Laws

 That they should observe God’s commandments and live according to his laws

 That they would offer the first of their harvests as required by Torah

 That they would dedicate their first-born sons to God

 That they will not intermarry with foreigners at all

 That they will not buy corn or anything else on the Sabbath day

 That they will remit their arrival temple expenses to ensure that God’s house was okay

 That they will provide sacrifices and offerings at the temple

 That they will pay their tithes according to the law

Group study activities

Read and study the book of Luke by
Dividing up the chapters in the book of Luke among the members of the class and let every group

present a summary of the chapters allocated to them.

Check out movies about the life, death and resurrection of Jesus Christ but note that your study

according to the syllabus is based on St. Luke’s gospel.

Teachers' Resources

Grade 7 CBC Free Schemes of Work

October 5, 2025 Maverick John Leave a comment

GRADE 7 KLB TOP SCHOLAR PRE- TECHNICAL SCHEMES OF WORK TERM

SCHOOL…………………………… TEACHER’S NAME………………………………………. TERM 3 YEAR 2023

WEEK	LESSON	STRAND	SUB-STRAND	SPECIFIC LEARNING OUTCOMES	· LEARNING EXPERIENCES	KEY INQUIRY QUESTIONS	LEARNING RESOURCES	ASSESSMENT METHODS	REFLECTION
1	1	Drawing.	Geometrical Construction.	By the end of the lesson, the learner should be able to; (a). Identify different career fields where the knowledge of geometrical construction could be applied in the locality. (b). Discuss the different career fields where knowledge of geometrical construction could be applied in the locality. (c). Construct objects found at school, at home and in the community using geometric construction knowledge. (d). Appreciate the career fields that regularly use geometry.	· In groups, pairs, individually, learners are guided to: · identify the different career fields where knowledge of geometrical construction could be applied in the community. · Search and discuss the different career fields where knowledge of geometrical construction could be applied in the locality. · apply geometry in different career fields · Visit a workplace to learn about the people they employ to use geometrical construction skills.	Where can geometrical construction be applied?	Top Scholar Pre-Technical pg 152-153. Digital devices Charts. Realia	Observation schedule. Written test Assessment rubric. Oral questions.
	2	Drawing.	Geometrical Construction – Importance of Geometrical Construction.	By the end of the lesson, the learner should be able to: (a).State the importance of geometrical construction in everyday life. (b). Discuss the importance of geometrical construction in everyday life. (c). Summarize and present points on the importance of geometrical construction in everyday life. (d). Appreciate the importance of geometrical construction in everyday life.	· In groups,pairs,learners are guided to: · brainstorm the importance of geometrical construction in everyday life. · discuss the importance of geometrical construction in everyday life. · Summarize and present points on the importance of geometrical construction in everyday life. · Use digital devices to search the internet for the importance of geometrical construction in everyday life.	How is geometrical construction important in our everyday life?	Top Scholar Pre-Technical Studies pg 153-154. Digital devices.	Oral questions. Written test. Assessment rubric.
	3	Drawing.	Project Activity 3-Task 3.1.	By the end of the lesson, the learner should be able to: (a). Suggest the materials for making an item designed in project activity 2.	· In groups,learners are guided to: · use visual aids to observe and pick out the materials used to make the item designed in project activity 2. · discuss the materials that can be used to make the item. · state and discuss the advantages and disadvantages of each material. · identify the most suitable material to use.	Which materials are suitable for making items to solve the problems in your community?	Top-Scholar Pre-Technical Studies pg 154-155. Digital devices. Photos.	Observation. Checklists. Oral questions.
	4	Drawing.	Project Activity 3-Task 3.2.	By the end of the lesson, the learner should be able to; (a). Gather the materials for making the item designed in project activity 2.	· In groups,learners are guided to; · refer to the materials identified in Task 3.1. · find and collect the materials chosen in the school or community.	Which materials are suitable for making item to solve the identified problem in the community? How do you collect the materials?	Top Scholar Pre-Technical Studies pg 155. Environment.	Observation. Checklists.
	5	Drawing.	Project Activity 3- Task 3.3.	By the end of the lesson, the learner should be able to; (a). Store the prepared materials for making the item designed in project activity 2.	· In groups,learners are guided to; · discuss how to keep the materials safe, secure and not damaged. · keep/store the materials collected safely.	How do you keep the collected materials safe,secure and not damaged?	Top Scholar Pre-Technical Studies pg 155. Collected materials. Digital devices.	Oral questions. Observation.
2	1	Energy Resources.	Sources of Energy.	By the end of the lesson, the learner should be able to: (a). Identify the sources of energy within the locality. (b). Discuss the sources of energy in the locality (c). Use digital devices to explore other sources of energy. (d).Make charts & flashcards showing the sources of energy. (e).. Appreciate the different sources of energy used in the locality.	· In groups,pairs ,learners are guided to: · discuss the concept of energy. · observe pictures in learner’s book and identify the sources of energy within the locality. · Search the internet on videos of sources of energy. · discuss the different sources of energy.	What is energy? Where does energy come from?	Top Scholar Pre-Technical Studies pg 156-157. Digital devices. Pictures. Realia.	Oral questions. Written tests. Checklists. Assessment rubric.
	2	Energy Sources.	Sources of Energy -Renewable and Non-renewable sources of energy.	By the end of the lesson, the learner should be able to: (a). Define and differentiate between renewable and non-renewable sources of energy. (b). Identify and discuss the sources of energy as either renewable or non-renewable from pictures. (c).Make flashcards showing the renewable and non-renewable sources of energy in the locality. (d).Classify the sources of energy in the locality as either renewable or non-renewable. (e). Appreciate the renewable and non-renewable sources of energy used in the locality.	· In groups,pairs, learners are guided to; · use dictionaries or digital devices to search the meaning of renewable and non-renewable sources of i. · Identify the sources of energy in pictures that are non-renewable and renewable. · Search the internet for examples of renewable and non-renewable sources of energy. · Make flashcards showing the renewable and non-renewable sources of energy. · use the flashcards to group various sources of energy as renewable and non-renewable.	What is the difference between renewable and non-renewable sources of energy? What is renewable and non-renewable source of energy?	Top Scholar Pre-Technical Studies pg 158-159. Pictures. Flashcards. Digital devices.	Assessment rubric. Written test. Checklists. Oral questions.
	3	Energy Resources.	Sources of Energy -Advantages and disadvantages of sources of energy.	By the end of the lesson, the learner should be able to: (a). Identify the advantages and disadvantages of renewable sources of energy. (b). Discuss the advantages and disadvantages of renewable sources of energy. (c). Search the internet for advantages and disadvantages of renewable sources of energy. (d). Summarize the advantages and disadvantages of renewable sources of energy on charts/exercise books. (e). Acknowledge the advantages and disadvantages of renewable sources of energy.	· In groups,learners are guided to: · identify and discuss the advantages and disadvantages of renewable sources of energy in the locality. · Search the internet for more points on advantages and disadvantages of renewable sources of energy. · Summarize the advantages and disadvantages of renewable sources of energy on charts/exercise books.	What are the advantages of renewable sources of energy? What are the disadvantages of renewable sources of energy?	Top Scholar Pre-Technical Studies pg 160-161. Pictures. Digital devices. Charts.	Assessment rubrics. Written tests. Checklists. Oral questions.
	4	Energy Resources.	Sources of Energy – Advantages and disadvantages of sources of energy.	By the end of the lesson, the learner should be able to: (a). Identify the advantages and disadvantages of non-renewable sources of energy. (b). Discuss the advantages and disadvantages of non-renewable sources of energy. (c). Summarize the advantages and disadvantages of non-renewable sources of energy on charts & exercise books. (d). Acknowledge the advantages and disadvantages of non-renewable sources of energy.	· In groups,learners are guided to: · identify and discuss the advantages and disadvantages of non-renewable sources of energy. · Summarize the advantages and disadvantages of non-renewable sources of energy on charts. · Use digital devices to search for other advantages and disadvantages of non-renewable sources of energy.	What are the advantages of non-renewable sources of energy? What are the disadvantages of non-renewable sources of energy?	Top Scholar Pre-Technical Studies pg 161. Charts. Digital devices. Pictures.	Assessment rubrics. Checklists. Written tests. Oral questions.
	5	Energy Resources.	Sources of Energy – Careers related to sources of energy.	By the end of the lesson, the learner should be able to: (a). Identify the different careers which are related to energy in the locality. (b). Discuss the roles of different careers related to energy in the locality. (c). Make flashcards showing the different careers related to energy. (d). Appreciate the different careers related to energy in the locality.	· In groups,pairs,learners are guided to: · Study the pictures in learner’s book and identify the different careers related to energy in the locality.. · discuss the careers related to energy. · Search the internet for more careers related to energy in the community. · Make flashcards showing the different careers related to energy.	Which careers are related to energy in the locality?	Top Scholar Pre-Technical Studies pg 162-163. Pictures. Flashcards. Digital devices.	Assessment rubric. Checklists. Written tests. Oral questions.
3	1	Energy Resources.	Sources of Energy -Importance of Energy.	By the end of the lesson, the learner should be able to: (a). State the importance of Energy in our lives. (b). Discuss the importance of energy in our lives. (c). Search the internet for more points on importance of energy in our lives. (d). Appreciate the importance of energy in our lives.	· In groups,learners are guided to: · Study the pictures in learner’s book and identify the activities in the pictures. · state the importance of energy in our lives. · discuss the importance of energy in our lives. · Use digital devices to search for more points on the importance of energy in our lives.	Why is energy important to our daily lives?	Top Scholar Pre-Technical Studies pg 164-165. Digital Devices. Pictures.	Assessment rubrics. Written tests. Oral questions.
	2	Energy Resources.	Uses of Energy-Forms of Energy.	By the end of the lesson, the learner should be able to: (a). Identify the different forms of energy in the locality. (b). Discuss the different forms of energy in the locality. (c).Draw charts showing the forms of energy in the locality. (d). Appreciate the different forms of energy in the locality.	· In groups,learners are guided to; · study the pictures in learner’s book and identify the different forms of energy. · discuss the different forms of energy in the locality. · Search the internet for more information on the forms of energy. · Draw charts showing the forms of energy in the locality and display them.	What are different forms of energy in the locality?	Top Scholar Pre-Technical Studies pg 165-167. Pictures. Digital devices.	Assessment rubric. Oral questions. Written tests. Checklists.
	3	Energy Resources.	Uses of Energy – Kinetic and Potential Energy.	By the end of the lesson, the learner should be able to: (a).Define and differentiate between kinetic and potential energy. (b).Classify the different forms of energy into either kinetic or potential energy. (c). Search the internet for videos about kinetic and potential energy. (d). Appreciate the kinetic and potential energy.	· In groups,learners are guided to: · Search the meaning of kinetic and potential energy from the internet or dictionary. · differentiate between kinetic and potential energy. · study pictures in learners book and classify the different forms of energy into either kinetic or potential energy. · search the internet for videos about kinetic and potential energy.	What is the difference between kinetic and potential energy?	Top Scholar Pre-Technical pg 168-170. Pictures. Digital devices.	Written tests. Oral questions. Assessment rubric.
	4			By the end of the lesson, the learner should be able to:	·
	5	Energy Resources.	Uses of Energy.	By the end of the lesson, the learner should be able to: (a). Identify the uses of different forms of energy in the locality. (b). Discuss the uses of different forms of energy in the locality. (c). Make charts showing the uses of the different forms of energy in different sectors. (d). Appreciate the uses of the different forms of energy in the locality.	· In groups,learners are guided to; · identify and discuss the uses of different forms of energy within the locality. · Use digital devices to explore the different uses of energy. · walk around the locality to observe and record the different energy uses.	What ways can energy be useful to our lives?	Top Scholar Pre-Technical Studies pg 171-172. Pictures. Digital devices. Charts.	Assessment rubrics. Written tests. Oral questions. Checklists.
4	1	Energy Resources.	Uses of Energy- Careers that require the use of energy.	By the end of the lesson, the learner should be able to: (a). Identify the careers that require the use of energy within the locality. (b). Discuss the careers that require the use of energy within the locality. (c).Make flashcards to show the different careers related to use of energy. (d). Recognize the different types of careers which require the use of energy within the locality.	· In groups,learners are guided to; · study the pictures in learner’s book and identify the different types of careers that require the use of energy within the locality. · discuss the different types of careers that require the use of energy within the locality. · make flashcards showing the different types of careers that require use of energy.	Which types of careers require the use of energy within the locality?	Top Scholar Pre-Technical Studies pg 173-174. Pictures. Flashcards.	Assessment rubrics. Written tests. Oral questions. Checklists.
	2			By the end of the lesson, the learner should be able to: By the end of the lesson, the learner should be able to: (a). State the roles of energy in the day to day life. (b). Discuss the roles of energy in the day to day life. (c). Search the internet for other roles of energy. (d). Appreciate the role of energy in the day to day life.	· In groups,learners are guided to; · study the pictures in learner’s book and identify the different types of careers that require the use of energy within the locality. · discuss the different types of careers that require the use of energy within the locality. · make flashcards showing the different types of careers that require use of energy.	What ways can energy be useful to our lives? Which types of careers require the use of energy within the locality?	Top Scholar Pre-Technical Studies pg 173-174. Pictures. Flashcards. .	Assessment rubrics. Written tests. Oral questions. Checklists
	3	Energy Resources.	Uses of Energy-The role of energy.	By the end of the lesson, the learner should be able to: (a). State the roles of energy in the day to day life. (b). Discuss the roles of energy in the day to day life. (c). Search the internet for other roles of energy. (d). Appreciate the role of energy in the day to day life.	· In groups,learners are guided to; · state the role of energy in our day to day life. · discuss the role of energy in our day to day life. · summarize their points and present in class. · use digital devices to search for other roles of energy.	How does energy affect our daily life? How does energy help us in carrying out tasks at home?	Top Scholar Pre-Technical Studies pg 175. Digital devices. Pictures.	Oral questions. Written tests.
	4	Energy Resources.	Self-Assessment	By the end of the lesson, the learner should be able to: (a). Attempt questions on the sub-strand :Sources of Energy.	· Individually, learner is guided to: · answer the questions on the sub-strand.		Top-Scholar Learner’s Book pg 156-164. Assessment books.	Written tests. Checklists. Assessment rubrics.
	5	Energy Resources.	Project Activity 4-Making the items.	By the end of the lesson, the learner should be able to: (a). Identify the safety precautions to observe when working with tools to make the item designed in project activity 2. (b). Discuss the safety precautions to observe when handling the materials and tools making the item. (c).Make charts showing the safety precautions to adhere to when working tools to make item designed in project activity 2.	· In groups, learners are guided to: · Familiarize with the safety rules and precautions in the workplaces. · Discuss the safety precautions to observe when handling the materials and tools making the item. · Make charts showing the safety precautions to adhere to when working.	Why is it important to observe safety precautions when working?	Top Scholar Pre-Technical Studies pg 176. Charts.	Practical work. Observation.
5	1	Energy Resources.	Project Activity 4: Making the item.	By the end of the lesson, the learner should be able to: (a). Identify the tools you will need to prepare the materials collected in project activity 3. (b). Discuss the tools you will need to prepare the materials collected in project activity 3. (c).Use appropriate tools to prepare the materials collected in project activity 3.	· In groups, learners are guided to; · select and use appropriate tools to prepare the materials collected in project activity 3. · Assemble the required tools.		Top Scholar Pre-Technical Studies pg 176.	Practical work. Observation.
	2	Energy Resources.	Project Activity 4: Making the item.	By the end of the lesson, the learner should be able to: (a).Use appropriate tools to make the item designed in project activity 2.	· In groups, learners are guided to: · Outline and discuss the steps to follow when assembling the prepared pieces of materials to the item. · Summarize the procedure. · follow the procedure to make the item by joining the prepared pieces of material.	Which procedure will you use to assemble the prepared pieces of materials to make the item?	Top Scholar Pre-Technical Studies pg 177. Materials.	Practical Work.
	3	Energy Resources.	Project Activity 4: Making the item.	By the end of the lesson, the learner should be able to: (a). Display the item made for others to see and appreciate.	· In groups,learners are guided to; · display the item made for others to see and appreciate.		Item made. Top Scholar Pre-Technical pg 177.	observation. Checklists.
	4	Energy Resources.	Project Activity 4.	By the end of the lesson, the learner should be able to: (a). Take pictures of the item made and print the pictures.	· In groups,learners are guided to; · Use digital devices to take pictures of the item made and print them.		Digital devices. Item made	Practical Work.
	5	Energy Resources.	Project Activity 4.	By the end of the lesson, the learner should be able to: (a).Draw pictures of the item made.	· Individually,learner to; · draw the pictures of the item made by classmates.		Pencils and papers. Item made.	Practical work. Observation.
6-8	· Complection of Projects and Creation of Portfolios. · Community Service Learning Class Activity.
9	ASSESSMENT

GRADE 4 REPORT CARD

MARKING SCHEME

2 θ + 120 = 330

P = 16 = 1/9 (A) (3)

DE DC DE CE

v + 20

SECTION B:

MATHEMATICS I

MARKING SCHEME.

R -1 1.1 Log = 0.04139

Sin B Sin A

A B A B

2 1 0 1 4 9

Large circle area

Large area = 22/7 x4x4 = 352/7 (A)

Length of diag. 50 = 7.071 = 5.536

Volume passed / sec = cross section area x speed

MATHEMATICS II

Using 74.5 as the Assumed mean, calculate:

MATHEMATICS II

MATHEMATICS IV

A1

A1

B1

A1

A 1

A 1

A1

A1

A1

A1

B1

B1

A1

A1

B1

A1

B1

A1

LOG E. 0.3010 0.6021 0.7782 0.9031

B1

B1

A1

A1

A1

MATHEMATICS IV

PART II

MARKING SCHEME

A1

A A1

1

MATHEMATICS V

MARKING SCHEME