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MICROSOFT EXCEL, SPREADSHEETS, TEACHER NOTES FREE

October 5, 2025 Maverick John Leave a comment

SPREADSHEETS.

Definition of a Spreadsheet.

A Spreadsheet is a ledger sheet that lets the user enter, edit, and manipulate numerical data.

A Spreadsheet usually consists of a series of rows & columns in which data entries can be made.

Types of Spreadsheets:

There are 2 types of spreadsheets:

Manual spreadsheet:

A Manual spreadsheet is ledger book with many sheets of papers divided into rows and columns for entering/writing data.

The data is entered manually using a pen or pencil.

Electronic Spreadsheet:

A computer program that looks like the manual ledger sheet with rows & columns for entering data that can be manipulated mathematically using of formulae.

Advantages of Electronic Spreadsheets over Manual Worksheets.

An electronic spreadsheet:

Has a large worksheet for data entry & manipulation as compared to manual worksheet.

Has inbuilt formulae called Functions that are non-existent in manual worksheets. These functions enable the user to quickly manipulate mathematical data.

Uses the power of the computer to quickly carry out operations.

Has better formatting & editing qualities than the manual worksheet.

Utilizes the large storage space available on computer storage devices to save & retrieve documents.

Can easily be modified in its form, while a manual spreadsheet involves a lot of manual calculations & are very difficult to amend.

The user can very quickly & efficiently perform complicated computations using the information stored in an electronic spreadsheet.

It is accurate in its calculations & allows automatic recalculation on formulae.

I.e., when one value/figure is changed, the result of the formula is automatically adjusted by the computer so as to correspond with the different input. For a manual spreadsheet, changing one value means rubbing the result & writing the correct one again.

It offers graphical representation of data leading to comprehensive decisions.

Replaces the pencil & paper approach of the manual operations of the worksheet.

I.e., it enables the user to produce neat work because; all the work is edited on the screen and a final copy is printed. With a manual spreadsheet, neatness & legibility of the work depends on the writer’s hand-writing skills.

It improves on the capabilities & speed of the Calculator.

Examples of the commonly used Spreadsheet packages

VisiCalc – this was the 1^st type of spreadsheet to be developed for PCs.
Lotus 123 – this is an integrated software with spreadsheet module, graphs, and database.
Microsoft Excel.
Corel Quattro-Pro
Microsoft Works Excel
Super calculators.
Vp-Planner.

Review Questions.

Define a Spreadsheet.
Differentiate between the traditional analysis ledger sheet and an electronic spreadsheet.
Name three commonly spreadsheet packages.

COMPONENTS OF A SPREADSHEET

A spreadsheet has 3 main components, namely;

Graphs / Charts.

Workbook:

When working in any spreadsheet program, you use workbook files to hold your information.

A Workbook is a file in a spreadsheet package that contains one or more worksheets. The worksheets are made up of rows & columns in which you work and store your data.

A Workbook allows the user to organize various kinds of related information in a single file.

Database:

Spreadsheet programs such as Excel have special features, which can be used to manage data values entered in the cells of the spreadsheet.

These features, which are found on the Data menu, were incorporated in Excel but they belong to Database Management System software.

Examples of such features include: Filtering of records, use of Forms, calculating of Subtotals, data validation, Pivot tables and Pivot chart reports.

Example:

If related data values are entered on the same row, they form a Record. Hence, a worksheet can be manipulated as a database that has data records entered in it.

Graphs/Charts:

A Chart is a graphical/pictorial representation of data in a worksheet. Charts are used to summarize data in a worksheet in a pictorial form.

They enable the users to present complex data elements from a worksheet in a simple format that they can understand.

Charts make it easy for users to see comparisons, patterns, and trends in data, e.g., instead of having to analyse several columns of a worksheet, one can see at a glance whether sales are falling or rising.

Examples of charts are: Pie charts, Line graphs, Bar charts, Histograms, Column charts, etc.

Review Questions.

Name and describe the three components of a spreadsheet.
Explain the following terms as used in spreadsheets.

Application areas of spreadsheets (Areas where Spreadsheets are used)

Spreadsheets provide an easy & streamlined means of financial management. They are mostly used by Accountants to record their daily transactions & also keep financial records.

For example; a spreadsheet can be used to do the following:

Record sales & purchases.
Calculate profits.
Produce Invoices, and also compile financial statements.
Prepare budgets.

Assist the management of an organization to monitor the current state of payments from customers in relation to goods delivered.

Detect aged debtors (i.e., those people who have owed you money for more than the period allowed in your terms of business.

Track the value of assets over time (i.e., Appreciation and Depreciation).

Note. Most spreadsheet programs come with inbuilt functions such as SUM, AVERAGE, PRODUCT, etc, which enable the Accountant to carry out his/her daily accounting tasks easily.

Data management.

A spreadsheet enables information to be produced easily and kept up-to-date.

For example;

It enables the user to create, edit, save, retrieve and print worksheet data & records.
It enables data to be arranged neatly in tabular structure.
Related data can be typed on the same worksheet. If the data is on different worksheets, the worksheets can be linked so that the data can be accessed easily.

Some of the data management functions include:

Sorting (i.e., arranging worksheet records in a particular order so as to easily access the data items).

Filtering (i.e., displaying only the records that meet a given condition).
Use of Forms to enter & view records.
Use of Total/Subtotal

Scientific Applications.

Spreadsheet programs can be used by Scientists & Researchers to compile & analyse their results.

Statistical analysis / Mathematical operations.

Spreadsheets provide a set of data analysis tools that can be used to develop complex statistical analyses. In addition, some of the tools generate charts.

Examples of statistical functions include:

AVERAGE – used to calculate the mean of a set of values.
MEDIAN – used to give the value in the middle of a set of values.

Such mathematical operations can be used by:

Teachers to compile their students’ marks and produce results.

Clerks & Secretaries to enable them easily create tables of figures and manipulate them quickly as required.

Forecasting (What if analysis).

The automatic recalculation feature makes it possible to use the “What if” analysis technique.

What if analysis is a feature in a spreadsheet that is used to find out the effect of changing certain values in a worksheet on other cells.

It involves changing the value of one of the arguments in a formula in order to see the difference the change would make on the result of the calculation.

This method can be used for financial forecasting, budgeting, cost analysis, etc.

Review Questions.

Explain five application areas where spreadsheet software can be used.
Explain the concept of “What if” analysis.

Common features of Electronic spreadsheets.

The following are the typical facilities provided by electronic spreadsheets:

Have the ability to create, edit, save & retrieve worksheets.

Have inbuilt functions & formulae which can be used to perform calculations.

Allows Automatic recalculation, i.e., when you change one value, the rest of the values in the spreadsheet are automatically recalculated by the computer to correspond with the different input. This enables you to play “what if” games with your system.

Have the ability to Sort and filter data (i.e., arrange data in a predefined order).

Have a Data validation facility, which ensures that the correct data is entered into the Spreadsheet.

Have a Chart facility that can be used to draw line graphs, Bar charts, histograms, etc.

Have the ability to format data (both text & numeric data) using predefined formats.

Some Spreadsheets have a SOLVER facility that is used to uncover the best uses of scarce resources so that desired goals can be achieved.

Have the ability to adjust Column widths & Row heights automatically.

Have the ability to hide and unhide rows & columns, and also freeze panes.

They enable printing of worksheets within the shortest time possible.

They have pre-designed Templates for automating tasks.

A Template is a document that acts as a blueprint or outline for other documents of the same type. It contains the standard text, graphics & formatting that will be used in all documents of this type.

This means that, all formulas and formatting for similar workbooks such as Invoices can be saved as templates and then be used to automate the task without having to create the workbook again.

Have the ability to summarize data using Consolidation and Pivot tables.

Consolidation allows the merging of several worksheets into a summary sheet, while still keeping the original worksheets intact. Consolidation adds together cells with the same co-ordinates in the various worksheets.

Pivot tables can be used to cross-tabulate large amounts of data.

Differences between an Electronic Spreadsheet and a Calculator

An electronic spreadsheet: –

Has more memory than calculator.
Is able to perform complex logical operations, but a calculator cannot.
Uses the large storage capacity of the computer that a calculator does not have.
Has a large working area that a calculator does not have.

Review Questions.

Describe any five features of a spreadsheet program.
State five features of spreadsheets that are useful in financial modelling.
How does a spreadsheet differ from a Calculator?

MICROSOFT EXCEL

This is a Spreadsheet program that enables users to create electronic worksheets that can be used to perform simple & complex calculations using a computer.

Ms-Excel has inbuilt functions that are used as shortcuts for performing mathematical, financial and statistical calculations.

Starting Microsoft Excel.

Click Start, point to Programs, then click Microsoft Excel.

–OR–

Click the Microsoft Excel icon, if it is displayed on the desktop.

WORKSHEET LAYOUT (Features/ Parts/ Elements of the Ms-Excel Screen).

At the top of the window,
- Title bar. It has the System /Control menu button on the left & the Resizing buttons on the right.
- Menu bar.
- Toolbars, e.g., Standard & Formatting toolbars. They contain the Toolbar buttons.
- Name box – displays the active cell, e.g., A1.
- Formula bar: A bar at the top of the Ms-Excel window that is used to enter or edit values or formulas in cells or charts. It also displays the constant value or formula stored in the active cell.

To display or hide the formula bar, click Formula bar on the View menu.

Column Identifiers (or Column headers) – Letters that identify the columns.
Row Identifiers (or Row headers) – numbers that identify the rows.

A Worksheet has a total of 256 columns & 65,536 rows.

Active (Current) cell – the cell in which the selection box (Cell pointer) is placed.
Cell Pointer.
Gridlines – the thin lines that indicate the cell boundaries in a worksheet.

At the bottom of the window,
- Status bar – displays different indicators about the current working environment.

To display or hide the Status bar, click Status bar on the View menu.

Sheet tabs – these are names of the sheets that appear at the bottom of the workbook window.
Tab scrolling buttons – They enable the user to select and use a different sheet.

Scroll bar, scroll box & the scroll arrows.

Scroll bars are the shaded bars along the right side and bottom of a window. To scroll to another part of the file, click the arrows in the scroll bar or drag the scroll box.

THE WORKSHEET:

This is the primary document in a Spreadsheet program that is used to store & work with data.

A Worksheet is a tool that is used for maintaining numeric data in a tabular form, simplifying numerous calculations and presenting numerical data graphically.

A worksheet is basically a page stored in a workbook, and acts as the working area.

A Worksheet consists of cells that are organized into columns & rows in which data entries are made.

Columns: – These are fields that make up the worksheet of a Spreadsheet. A Column is a vertical arrangement of cells.

Rows: – These are records that form a worksheet. A Row is usually a horizontal arrangement of cells.

Cell:

A box formed when a row & a column intersect in a worksheet or a table, where the data is entered.

A cell is referred to or identified by use of the column letter heading & the row number heading (e.g., A1 refers to the first cell).

A Worksheet can be used in:

A Company Sales Report to show the sales for each item over the year.
An Employees’ Payroll to calculate the employee’s salaries for each month.
A Students Progress record to store information on student’s marks and monitor their progress.
Personal Expenses to maintain a budget of your monthly expenses.
Mortgage Repayment Calculations to calculate the monthly repayment amount on a mortgage loan.

To Insert a single new worksheet.

On the Insert menu, click Worksheet.

Selecting worksheets.

To select Do this

A single sheet Click the tab for the sheet.

Two or more adjacent sheets Click the tab for the first sheet, hold down the SHIFT key, then click the tab for the last sheet.

When you select a sheet, the color of its tab will change to white.

Two or more nonadjacent sheets Click the tab for the first sheet, hold down CTRL key, then click the tabs for the other sheets.

All sheets in a workbook Right-click a sheet tab, then click Select All Sheets on the shortcut menu.

Note. To deselect the sheets, click inside any of the worksheets.

To Rename a worksheet (Giving meaningful names to sheets).

Click the tab for the sheet you want to rename.
On the Format menu, point to Sheet, then click Rename.

The current name for that sheet will be selected.

Press Backspace or Delete, type a new name, then press ENTER.

To Delete worksheets.

Select the worksheet(s) you want to delete.
On the Edit menu, click Delete Sheet.

To Hide a worksheet.

Select the sheet(s) you want to hide.
On the Format menu, point to Sheet, then click Hide.

To Display a hidden worksheet.

On the Format menu, point to Sheet, then click Unhide.
In the Unhide sheet box, double-click the name of the hidden sheet you want to display.

Ms-Excel add-ins – Components that can be installed on your computer to add commands and functions to Excel. These add-in programs are specific to Excel.

CREATING A NEW WORKBOOK.

To create a new, blank workbook.

On the File menu, click New, then click Blank Workbook on the New Workbook task pane.

To create a new workbook based on the default workbook template.

Click on the New workbook icon on the Standard

TYPES OF DATA IN SPREADSHHETS.

Labels (Text).

Labels are texts consisting of alphanumeric characters that can be entered into a cell.

E.g., Item codes such as Salary, Names such as John.

Labels are made up of alphanumeric character strings.

In Excel, Text is any combination of numbers, spaces, & nonnumeric characters.

E.g., 10A19, 27AXY, 12-976, 208 4675.

Values (Numbers).

Values consist of numerals & mathematical formulas entered into a cell.

In Excel, a number can contain only the following characters: digits 0 to 9 + – ( ) / $ %.

Formulas.

A Formula is a sequence of values, cell references, functions & arithmetic operators whose calculation results to a numeric value.

It is an equation that performs operations on worksheet data.

Formulas can perform mathematical operations such as addition, subtraction, division and multiplication.

A Formula is used to tell Ms-Excel how you want a particular value to be computed.

Functions.

It is a special command, which you can type into your formula to perform arithmetic operations.

It is an inbuilt equation that is used for calculations.

A Function is a short predefined (inbuilt) formula used to perform a given specific task.

Functions can be used to perform both simple and complex calculations.

EDITING CELL CONTENTS.

Double-click on the cell that contains the data you want to edit.

–Or–

Click in the cell, then press F2.

Edit (make changes to) the cell contents.

E.g., if you had left out a character, use the Left or Right Arrow key to move the insertion point to the position of the correction, then type the character. If you had typed wrong characters, use the Backspace or Delete to erase them.

To enter your changes to the active cell, press ENTER, then use the Arrow keys to move to another cell.

SAVING WORKBOOKS.

Purpose.

√ In order to use the worksheet at a later time.

√ If the saving is done periodically, say every 1 minute, it helps prevent data loss in case of power failure.

When you save a workbook for the first time, you assign a file name and indicate where you want to store the file on your computer’s hard disk or in another location. Each time you subsequently save the workbook, Ms-Excel updates the workbook file with your latest changes.

To save a new, unnamed workbook.

Click the Save button on the Standard

–OR–

On the File menu, choose Save (or press CTRL+S) to display the Save As dialog box.

In the File name box, enter a name for the worksheet.
In the Save in list, select the drive and/or folder where you want the worksheet to be saved.
Click the Save button.

To save a copy of a workbook (or save a workbook with a new name).

Open the workbook you want to make a copy of.
On the File menu, click Save As….
In the File name box, enter a new name for the file.

To save the copy in a different folder or drive, click a different location in the Save in list.

Click the Save button.

To save workbooks automatically as you work.

On the Tools menu, click Options, click the Save tab, then select the Save AutoRecover info every
In the minutes box, enter the interval for how often you want to save files.

OPENING A SAVED WORKSHEET.

Purpose.

You can open a saved worksheet (i.e., a worksheet stored on the hard disk of the computer or on a floppy disk) in order to:

√ Continue working on it, if it was saved before completion.

√ View the data it contains.

√ Update it, if the data it contains represents information that changes periodically. For example, A Weekly report.

Choose Open on the File menu,

–OR–

Click the Open button on the Standard toolbar (or press CTRL+O) to display the Open dialog box.

In the Look in drop down list, click the drive or folder that contains the file you want to open.
In the folder list, locate and open the folder that contains the file.
Double-click the file you want to open (or click the file, and then click the Open button).

Note. To open a recently opened file, select it from the bottom of the File menu.

Exiting / Quitting Ms-Excel.

Purpose.

√ You exit from Ms-Excel when you have finished working with it.

On the File menu, click

–OR–

Press ALT+F4),

–OR–

Click the Close button on the top right hand corner of the Title bar of the Ms-Excel window.

If the workbook was not saved before or the changes made to the open workbook are not saved, Ms-Excel will give you an option to save those changes by displaying the Save As dialog box. Choose Yes to save the changes, or No to discard the changes.

SELECTING DATA IN CELLS, ROWS OR COLUMNS.

To select Do this:

A single cell Click the cell, or press the Arrow keys to move to the cell.

Text in a cell Double-click in the cell (or click in the cell, press F2 to display the Insertion point), then select the text in the cell.

A range of cells 1. Click the first cell of the range, hold down the left mouse

button, then drag to the last cell in the range.

-OR-

Click the first cell in the range, hold down SHIFT key, then click the last cell in the range.

-OR-

Click the first cell in the range, hold down SHIFT key, then use the Arrow keys to extend the selection.

All cells on a worksheet Press CTRL+A (or on the Edit menu, click Select All).

Nonadjacent cells or cell ranges Select the first cell or range of cells, hold down CTRL & select the other cells or ranges.

An entire row or column Click the row or column heading.

Adjacent rows or columns Drag across the row or column headings.

–OR–

Select the first row or column, hold down SHIFT key, then select the last row or column.

Nonadjacent rows or columns Select the first row or column, hold down CTRL & select the other rows or columns.

Note. To cancel a selection of cells, click any cell on the worksheet.

A Range is any group of cells in a worksheet. The cells in a range can be adjacent or nonadjacent.

Clearing cell contents.

Clearing cells removes the cell contents (formulas and data), or formats (such as number formats, and borders), but leaves the blank cells on the worksheet.

Select the cells, rows, or columns you want to clear.
On the Edit menu, point to Clear, then click Formats or Contents.

Clicking All, will clear formats and contents, and also remove any cell comments and data validation.

Note. If you click a cell and then press the DELETE key, Ms-Excel will remove the cell contents but does not remove comments or cell formats.

Inserting blank cells, rows, or columns.

Purpose.

You can insert a row or column, to make room for additional information in the worksheet. This may be necessary when some extra information, which was not expected earlier, needs to be included.

To Insert new blank cells.

Select a range of existing cells where you want to insert the new blank cells. Select the same number of cells as you want to insert.
On the Insert menu, click
In the Insert dialog box, click Shift cells right, Shift cells down, Entire row, or Entire column.

To Insert Rows.

To insert a single row, select a row (or click a cell in the row) immediately below where you want the new row to appear.

For example, to insert a new row above row 5, click a cell in row 5. To insert multiple rows, select the same no. of rows as you want to insert.

On the Insert menu, click

To Insert Columns.

To insert a single column, select a column (or click a cell in the column) immediately to the right of where you want the new column to appear.

For example, to insert a new column to the left of column B, click a cell in column B. To insert multiple columns, select the same no. of columns as you want to insert.

On the Insert menu, click

Deleting cells, rows, or columns

Deleting removes the cells from the worksheet and shifts the surrounding cells to fill the space.

Select the cells, rows, or columns you want to delete.
On the Edit menu, click Delete.
If you are deleting cells, the Delete Cells dialog box appears. Click Shift cells left, Shift cells up, Entire row, or Entire column.

Exercise (a).

How many columns are there in an Excel worksheet?
Identify and explain the FOUR types of data in Spreadsheets.
Explain how you would do the following operations on a Worksheet in Microsoft Excel.
- Rename a worksheet.
- Delete a worksheet.
- Insert a single new worksheet.
- Move from one worksheet to another.
- Select a cell.
- Select a range of cells.
- Select nonadjacent cells or cell ranges.
- Select everything in a worksheet.
Define the following terms as used in Spreadsheets: (6 marks)
What is the difference between Clearing cells and Deleting cells?

Exercise (b).

What is the meaning of each of the following concepts?
Distinguish between Labels and Formulae with respect to Spreadsheets.

Exercise (c).

List FOUR types of information that can be entered into a cell. (4 marks).
Explain THREE cell data types in spreadsheet. (6 marks).

POSITIONING (ALIGNING) DATA IN A CELL.

Purpose.

Adjusting the alignment of the cell contents, helps to distinguish different types of information in cells.

Usually when you enter text data into a worksheet, it is normally aligned to the left in a cell, while numbers, dates & times are aligned to the right.

To center the data, or align data to the left or right in a cell.

Select the cells with the data you want to reposition.
On the Formatting toolbar, click the appropriate alignment button.

Click the Align Left button – to align text to the left of the cell.
Click the Center button – to center text in the cell.
Click the Align Right button – to align text to the right.

Merging cells across columns.

You can easily merge headings across the top of a range of cells. When you merge cells, the selected cells are combined into one cell. This spreads the content of one cell over many cells.

Copy the data you want into the upper-leftmost cell within the range.
Select the cells you want to merge.

Warning. Excel places only the data in the upper-leftmost cell of the selected range into the resulting merged cell. If there is data in other cells, the data is deleted when you merge the cells.

To merge cells in a row or column and center the cell contents, click the Merge and Center button on the Formatting toolbar,

–Or–

On the Format menu, click Cells, click the Alignment tab, then select the Merge cells checkbox.

This will combine the cells and center the heading in the new, wider cell.

HIDING ROWS OR COLUMNS.

Purpose.

√ Hiding rows or columns prevents the display and printing of data held in particular rows or columns. For instance, when your rows or columns contain confidential formulas not necessary in the printed report.

Select the rows or columns you want to hide.
On the Format menu, point to Row or Column, then click Hide.

The selected rows or columns including their headings will not be visible.

To display a hidden row or column.

To display hidden rows, select the row below and the row above the hidden rows.

To display hidden columns, select the column to the left and the column to the right of the hidden columns. For example, to redisplay hidden column C, select column B & column D.

If you want to redisplay noncontiguous columns, say, column C, D & F, select all the columns from B through G, i.e. columns B, E & G.

On the Format menu, point to Row or Column, then click Unhide.

Tip. If the first row or column of a worksheet is hidden, to display it;

Click Go To on the Edit
In the Reference box, type A1, and click OK.
On the Format menu, point to Row or Column, then click Unhide.

APPLYING BORDERS, SHADINGS & PATTERNS TO A WORKSHEET.

You can apply borders to cells, shade cells with a background color, or shade cells with a color pattern in order:

Purpose.

√ To distinguish between different types of information in a worksheet.

√ To make the worksheet more appealing to the eye.

√ To draw attention to important data in the worksheet.

To Apply a Border to cells.

Select the range of cells that you want to put a border around.
On the Format menu, select In the resulting dialog box, click on the Border tab.
Under the Presets section, select the Border style you want, e.g. Outline or Inside borders or both.
To change the line style for the border, click a style in the Style list, and then click a button to indicate the border placement.

You can specify the colour of the lines from the Color drop-down list.

Click the OK button when you are done.

To Apply or Remove cell Shadings.

Select the cells you want to apply shading to or remove shading from.
On the Format menu, click Cells, then click the Patterns
In the Cell shading box, click the color you want to shade the cells with.
To include a background color with the pattern, click the arrow next to the Pattern box, then click the pattern style and color you want.
Click the OK

The borders, shades and patterns that you have specified all apply to the range you had selected.

FORMATTING NUMBERS IN A WORKSHEET.

Purpose.

Formatting of numbers in a worksheet can make your worksheet much more presentable.

For example,

√ Long numbers without commas are difficult to read.

√ Too many uneven decimal places in a worksheet make it difficult to compare figures.

√ A worksheet that has some figures with six decimal places, others with commas and others with no decimal places has an untidy appearance.

To Add or Remove the Thousands separator in a number.

Method 1.

Select the range of cells containing the numbers whose format you want to change.
Click the Comma Style (,) button on the Formatting

Method 2.

On the Format menu, click Cells, then click the Number
In the Category list, click Number.
Select or clear the Use 1000 separator (,)

All numbers in the selected range will be displayed with commas separating the thousands and with two decimal points, e.g., 7,375.00

To Change the no. of Decimal places displayed in a number.

Method 1.

Select the range of cells whose decimal places you want to change.
To display more digits after the decimal point (to increase the no. of decimal places), click the Increase Decimal button on the Formatting

To display fewer digits after the decimal point (to decrease the no. of decimal places), click the Decrease Decimal button.

Method 2:

On the Format menu, click Cells, then click the Number
In the Category list, click Currency, Accounting, Percentage, or Scientific.
In the Decimal places box, enter the number of decimal places you want to display.

If you want to change the currency symbol, click the symbol you want to use in the Symbol list.

To Display numbers as Percentages or Fractions.

Method 1.

To quickly display nos. as percentages of 100, click the Percent Style (%) button on the Formatting toolbar.

Method 2.

Select the range cells you want to format as percentages.
On the Format menu, click Cells, then click the Number

To display nos. as percentages, click Percentage in the Category In the Decimal places box, enter the number of decimal places you want to display.

To display nos. as fractions, click Fraction in the Category list, then click the type of fraction you want to use.

To Add or Remove a Currency symbol.

Method 1.

Select the range of cells you want to format as currency.
Click the Currency Style ($) button on the Formatting

Method 2.

On the Format menu, click Cells, then click the Number
In the Category list, click Currency.
In the Symbol list, select the currency symbol that you want.

To remove a currency symbol, click None in the Symbol list.

To Display minus signs on negative numbers.

Select the cells you want to change.
On the Format menu, click Cells, then click the Number

For simple numbers, click Number in the Category list.

For currency, click Currency in the Category list.

In the Negative numbers box, select the display style for negative numbers.

To Reset a number format.

Select the cells you want to reset to the default number format.
On the Format menu, click Cells, then click the Number
In the Category list, click General.

Exercise.

Explain step-by-step how you would perform the following operations on a worksheet in Microsoft Excel.
- Enter data into a worksheet cell.
- Edit cell contents.
- Make text in a cell Bold, Italic and double-underlined.
- Adjust a column width to accommodate the longest cell entry in a range of cells.
Explain what are Label prefixes in spreadsheets. (10 Mk)
A worksheet table has columns A through N. The Chief Accountant doesn’t require the information contained in columns E, F and G. Give a step-by-step procedure on how to make sure that only the columns with the required information are printed.
You have the number 435273.7865 in a cell. How will it look if you format the cell as commas and 2 decimal places?

FINDING RECORDS.

Purpose.

Suppose you wanted to view records that meet given conditions, you would have to sort the table according to the conditions so as to find out where those records appear in the list. Such conditions are referred to as ‘Criteria’.

However, this method will require you to sort the table whenever you want to find something different.

Ms-Excel offers an easier solution to this through the Filter command on the Data menu.

Click on any cell in the table that contains the records you want to search for.
On the Data menu, choose Filter, then select AutoFilter from the submenu.

A downward arrow appears on the right of each field name.

Click the down arrow on a column to display the conditions that can be set. Select a condition (Criteria) from that list.

Note. If the criteria you want is not in the list or if you want to enter two conditions, then perform the following steps:

Select the column / field to search by clicking on the down arrow to the right of the field name.

The Custom AutoFilter dialog box appears.

In the Show rows where: box, select the conditions to use by clicking on the down arrow. The list includes ‘is greater than’; ‘is less than’, etc.
Enter the Value to compare the contents of the field width. You could type or select it from a drop down list of values available in the database.

Click the OK button to complete the task.

Note. To redisplay the records, click on the down arrow to the right of the field name that you had selected, and select the option All.

Example:

	A	B	C	D
1	Date	Person	Item	Amount
2	26-Jan-97	Morris	Bar	95
3	28-Mar-97	Albert	Take Away	136
4	28-Jan-97	Anne	Lunch	53
5	09-Mar-97	Susan	Breakfast	112
6	12-Jun-97	Jane	Snacks	56
7	12-Apr-97	Richard	Snacks	118
8	15-Mar-97	Peter	Bar	114
9	25-Mar-97	Mike	Take Away	80
10	01-Mar-97	James	Bar	167
11	09-Jun-97	Morris	Take Away	71
12	16-Jun-97	Susan	Lunch	80

Suppose you want to view all the sales that exceed 100 Shillings but are below 150 shillings from a week’s list of sales records.

The field to use for the search would be Amount. So, click on the down arrow on the right of the Amount field.
The Operator would be is greater than, and the value would be 100.
Enter the second criteria, as Amount is less than 150, then click the OK
All the records whose amount is between 100 and 150 will be displayed (Only the records matching the criteria are displayed).

	A	B	C	D
1	Date	Person	Item	Amount
3	28-Mar-97	Albert	Take Away	136
5	09-Mar-97	Susan	Breakfast	112
7	12-Apr-97	Richard	Snacks	118
8	15-Mar-97	Peter	Bar	114
10	01-Mar-97	James	Bar	167

PIVOT TABLES.

Purpose.

A Pivot table helps us to summarize and analyze large amounts of existing data, from a list or table, using the format and calculation methods of your choice.

Suppose we wanted the daily totals for each of the sales persons along with the total sale for each day: A PivotTable can help us get that kind of information much more easily.

Select any cell in the list or table you want to summarize.
On the Data menu, select PivotTable and PivotChart Report…
This will activate Step 1 of the PivotTable Wizard. In this step, select the source of data Ms-Excel will use to create the Pivot Table. From the choices given, select Microsoft Excel list or Database.

Click on the Next button.

Step 2 of the Wizard shows you the range containing the list of data detected around the position of your cell pointer of Step 1. If necessary, change the range.

Click on the Next button.

Click the Layout… button to specify how you want the PivotTable to appear.
On the right hand side of the PivotTable and PivotChart Wizard – Layout dialog box, the Pivot Wizard shows the column titles (field names) found in your list.
- Drag the field name whose contents you want to summarize downward to the area marked ROW.
- Drag the field name whose contents you want to summarize across the PivotTable to the area marked COLUMN.
- Drag the field name that contains the data to be summarized into the area marked DATA.
Step 3 of 3 will be displayed again allowing you to specify a convenient location for the PivotTable. The PivotTable may be positioned either as a new worksheet or on the existing worksheet.

If you select Existing worksheet in this dialog box, then you must specify the cell where the top left corner of the PivotTable will be positioned.

To specify a name for the PivotTable, click on the Options
Click on the Finish Ms-Excel places the Pivot Table in the location you specified.

Refreshing Records in the PivotTable.

Select a cell in the PivotTable.
On the PivotTable toolbar, click on the Refresh Data

Note. To refresh the PivotTable whenever you open the workbook, click Options on the PivotTable menu of the PivotTable toolbar. Under Data source options, select the Refresh on open checkbox.

CELL REFERENCES (Cell Addresses).

A Cell reference is the identity of a cell in a worksheet.

A Reference identifies a cell or a range of cells on a worksheet and tells Ms-Excel where to look for the values or data you want to use in a formula.

Examples of Cell references.

Single cell reference.
Mixed cell reference.
Label cell reference.
Relative cell reference.
Absolute cell reference.

REFERENCING OF CELLS.

A cell is identified by use of the Column letter heading & the Row number heading.

To refer to a cell, enter the column letter followed by the row number. For example, B2 refers to the cell at the intersection of column B & row 2.

Examples of cell references.

To refer to Type

The cell in column A & row 10 A10

The range of cells in column A & rows 10 to 20 A10:A20

The range of cells in row 15 & columns B to E B15:E15

All cells in row 5 5:5

All cells in rows 5 to 10 5:10

All cells in column H H:H

All cells in columns H to J H:J

The range of cells in columns A to E & rows 10 to 20 A10:E20

PERFORMING CALCULATIONS IN MS-EXCEL.

USING WORKSHEET FUNCTIONS.

A Function is a special command, which you can type into a formula to perform arithmetic operations.

A Worksheet function is a special inbuilt formula that performs an operation on the values that you provide.

It is an inbuilt equation that is used for calculation.

A function performs operations or calculations using specific values, called arguments. The arguments can be either cell references or values or both.

Categories of Functions in Ms-Excel.

Functions are grouped into broad categories by some common features particular to the function.

Financial functions.

Analyze investments and securities; determine depreciation, calculate cash flows and loans, e.g. the PMT function.

Date & Time functions.

Calculate values that represent dates and times.

E.g., the TODAY function is used to return the current date according to the computer’s internal clock.

Math & Trigonometry functions.

Can be used to perform simple mathematical operations, such as calculating Square roots (SQRT), rounding a number (ROUND), calculating the total value for a range of cells (SUM), etc.

They are also used to replace complex trigonometric calculations like Sine (SIN), Cosine (COS), etc.

E.g., ABS – gives the Absolute value of a number. The Absolute value of a number is the number without its sign.

Syntax: ABS(number)

Statistical functions.

Perform calculations (statistical analysis) on ranges of data.

E.g., AVERAGE – calculates the average (arithmetic mean) of a set of values in a range.

STDEV – Estimates Standard Deviation based on a sample. Standard Deviation is a measure of how widely values are dispersed from the Average value (Mean).

Syntax: STDEV(number1,number2,….)

Logical functions.

Calculate the results of logical formulas. E.g., the IF Function.

Look up & Reference functions.

Finds or refers to the contents of a cell. For example, the VLOOKUP function.

Database functions.

Perform statistical calculations and queries on database tables. For instance, DSUM will find the total of values in a particular field (column).

Information functions.

Return information about cells, ranges, the operating system, and some Ms-Excel tools, or to mark places where information is missing or incorrect.

E.g., CELL – returns information about the formatting, location or contents of a cell.

CREATING MS-EXCEL FORMULAS.

Purpose.

When you need to perform a calculation in Ms-Excel, you use a formula.

You can create simple formulas that can be used; lets say, to add the values in two cells, or you can create complex formulas that can calculate the Standard deviation of certain values.

For example, the formula ‘=SUM(D1:D7)’ uses a function to add the values in the range D1:D7. It gives the same result as the formula ‘=D1+D2+D3+D4+D5+D6+D7’.

Before you write your formula in Ms-Excel, it is advisable to do the following;

Decide what you want to be calculated, e.g., the Total Cost of items.
Note down the values in the worksheet required for the calculation and use them to write down the formula, e.g. Quantity * Price.
Substitute the values with their cell references, e.g. B3*D3.

Calculation operators in formulas.

Operator – A sign or a symbol that specifies the type of calculation to perform on the elements of a formula.

Excel includes 4 different types of calculation operators:

Arithmetic (Mathematical) operators.
Logical (Comparison) Logical operators.
Reference operators.
Text concatenation operators.

Arithmetic (Mathematical) operators.

Performs basic mathematical operations such as Addition, Subtraction, Division or Multiplication.

Arithmetic operator Meaning Example.

+ (Plus sign) Addition 3 + 3

– (Minus sign) Subtraction 3 – 1

* (Asterisk) Multiplication 3 * 3

/ (Forward slash) Division 3/3

% (Percent sign) Percent 20%

Logical (Comparison) operators.

Compares two values and produces a logical value, either TRUE or FALSE.

Comparison Meaning Example.

= (equal sign) Equal to A1=B1

> (greater than sign) Greater than A1>B1

< (less than sign) Less than A1<B1

>= (greater than or equal to sign) Greater than or equal to A1>=B1

<= (less than or equal to sign) Less than or equal to A1<=B1

<> (not equal to sign) Not equal to A1<>B1

Reference operators.

Combine ranges of cells for calculations.

Reference operator Meaning Example.

: (colon) Range operator; produces one B5:B9

reference to all the cells between

two references, including the two

references.

, (comma) Union operator; combines multiple SUM(B5:B9,D5:D9)

references into one reference.

Text concatenation operators.

Use the ampersand (&) to join one or more strings to produce a single piece of text.

Text operator Meaning Example.

& (ampersand) Connects two values to produce “North” & “wind” produces

one continuous text value “Northwind”

Creating a simple formula.

A Formula in Ms-Excel always begins with an equal (=) sign. Ms-Excel uses this sign to differentiate between a Label (text) and a Formula. The equal sign tells Ms-Excel that the characters that follow constitute a formula.

Following the equal sign are the elements to be calculated called Operands or Arguments. The Arguments are separated by calculation operators, and enclosed by an opening & closing parentheses (brackets).

Click on the cell in which you want to enter the formula.
Type the = (equal sign) to activate the Formula bar. The equal sign (=) tells Ms-Excel that you are entering a formula in the cell.
Type the formula directly into the Formula box.

To tell Ms-Excel where to find the data that will be used in the calculation, type a cell reference.

Press the ENTER Ms-Excel immediately calculates & shows the result in the cell, while the formula is displayed in the Formula bar.

Notes.

A Formula can refer to other cells on the same worksheet.

Ms-Excel calculates a formula from left to right, according to a specific order for each operator in the formula.

You can change the order of operations by using parenthesis. E.g., to calculate B4+25, then divide the result by the sum of the values in cells D5, E5 and F5, the formula would be: =(B4+25)/SUM(D5:F5)

In this example, the parentheses around the first part of the formula forces Ms-Excel to calculate B4+25 first, then divide the result by the sum of the values in cells D5, E5, and F5.

Creating a formula that contains a function.

Click the cell where the result of the formula will be displayed.
On the Insert menu, click Function, (or click the Paste Function button on the toolbar).
Click a function from the Function Category When you select a function, a description of the function appears in the dialog box.

Click the OK button.

Type in the arguments to compute in the parentheses in the formula. To enter a range, use a Colon to separate the first & the last cells in the range, or use a Comma to separate reference to individual cells.
After you complete the formula, click the OK button or press the ENTER

Note. The structure of a function begins with an Equal sign (=), followed by the Function name, & the Arguments for the function. The Arguments are separated by commas or a colon, and enclosed in an opening & closing parenthesis.

Performing Common Calculations.

ADDING NUMBERS.

Method 1.

Type the numbers directly into a cell and press the ENTER key to display the results.

Example: cells D5, E5 & F5 contain the values 5, 15 & 20. To add all the values in the range, type: =D5+E5+F5

-OR-

=5+15+20

To Add all numbers in a contiguous row or column.

You can insert a sum for a range of cells automatically using the AutoSum (Σ) button on the Standard toolbar.

Click a cell below the column of numbers or to the right of the row of numbers.
Click AutoSum on the Standard Ms-Excel suggests a formula.
To accept the formula, press the ENTER. To change the suggested formula, select the range before pressing the ENTER key.

To Add numbers that are not in a contiguous row or column.

Use the SUM function. SUM adds all the numbers in a range of cells.

Syntax: SUM(number1,number2,…..)

Number1,number2,… are the arguments for which you want the total value or sum.

Example 1: Cells A2, A3 & A4 contain values -5, 15, and 30.

To add Formula

The numbers in the cells A2 to A4. =SUM(A2:A4)

The numbers in cells A2:A4, and 15. =SUM(A2:A4, 15)

The values in cell A2, A4 and 2. =SUM(A2,A4, 2)

3 and 2 =SUM(3,2)

Example 2:

	A	B
1	Salesperson	Invoice
2	Buchanan	15,000
3	Buchanan	9,000
4	Suyama	8,000
5	Suyama	20,000
6	Buchanan	5,000
7	Dodsworth	22,500

Formula Adds

=SUM(B2:B4) the values in cells B2, B3 and B4.

=SUM(B2:B3, B5) two invoices from Buchanan, & 1 from Suyama

=SUM(B2,B5,B7) individual invoices from Buchanan, Suyama,& Dodsworth.

SUBTRACTING NUMBERS.

Type the formula ‘=10-5’ in a cell to display the result 5.

Example: cells A2, A3 & A4 contain the values 15,000, 9,000 & -8,000.

Formula Description Result

=A2-A3 Subtracts 9,000 from 15,000 6,000

=SUM(A2:A4) Adds all nos. in the list, including negative nos. 16,000

To calculate a running balance.

You can build a formula in a banking transaction to calculate your running balance.

Example 1.

Assume that cell F6 contains the previous balance of 4,000/=, cell D7 contains the first transaction’s deposit subtotal of 190,500, and cell E7 contains any cash-received amount of 50,000.

To calculate the current balance for the first transaction, enter the following formula in cell F7:

=SUM(F6,D7,-E7)

Example 2.

	A	B	C
1	Deposits	Withdrawals	Balance
2	$1,000	$625	=SUM(A2,-B2)
3	1000	740	=SUM(C2,A3,-B3)

TO INCREASE OR DECREASE A NUMBER BY A PERCENTAGE.

Example 1.

Assume that cell F5 contains a numeric value of 30,000. To increase the value stored in cell F5 by 5 percent;

=F5*(1+5%)

If the percentage amount is stored in a cell, let say, cell F2:

=F5*(1+$F$2) = (31,500)

Note. The reference to F2 is an Absolute cell reference so that the formula can be copied to other cells without changing the reference to F2.

Example 2.

	A	B
1	Number	Percent Increase
2	23	3%

Formula Description Result

=A2*(1+5%) Increases the no. in A2 by 5% 24.15

=A2*(1+B2) Increase the no. in A2 by the percent value in B2: 3% 23.69

=A2*(1-B2) Decrease the no. in A2 by the percent value in B2: 3% 22.31

MULTIPLYING NUMBERS.

Use the asterisk (*) operator or the PRODUCT function.

PRODUCT multiplies all the nos. given as arguments and returns the product.

Syntax: PRODUCT(number1,number2,…..)

Number1,number2,… are the numbers you want to multiply.

Formula Description Result

=5*10 50

=A2*B2 multiplies the contents in cells A2 and B2.

=(5+2)*3 adds 5 and 2 together then multiplies the result by 3 21

Example: Using the values shown in the worksheet below, calculate the cost of the milk.

	A	B	C	D
1	Item	Quantity	Price	Total cost
2	Milk	26 Litres	15.00
3	Sugar	19 Kgs	48.90

The Total cost of the milk will be given by, Quantity* Price. Therefore, in cell D2, type the formula; =B2*C2.

Note. If you omit ‘=’ symbol before B2, Ms-Excel will not recognize it as a formula and what you have typed will literally appear as ‘B2*C2’, which will not yield the expected result.

To Multiply numbers in different cells using a formula.

Cells A2, A3 & A4 contain the values 5, 15, 30.

To multiply Formula

The numbers in cells A2 & A3 =A2*A3

All the numbers in the range =PRODUCT(A2:A4)

All the numbers in the range, and 2. =PRODUCT(A2:A4,2)

DIVIDING NUMBERS.

Type a formula such as =10/5 in a cell to display the result 2.

Example.

Cells A2 & A3 contain values 15,000 and 12.

Formula Description Result

=A2/A3 Divides 15,000 by 12 1,250

GETTING THE SQUARE ROOT OF A NUMBER.

Use the SQRT function. SQRT gives a positive square root of a specific number.

Syntax: SQRT(number)

Number – is the number for which you want the square root. If number is negative, SQRT returns the #NUM! error value.

Example 1: Cell B2 contains the number 215; to get the square root, type:

=SQRT(215) -OR- =SQRT(B2)

Examples 2:

Formula Description Result

= SQRT(16) 4

=SQRT(-16) #NUM!

RAISING A NUMBER TO A POWER.

Use the POWER function. POWER gives the result of a no. raised to a power.

Syntax: POWER(number,power)

Number – is the base no. It can be any real number.

Power – is the exponent to which the base no. is raised.

Note. The up carat (^) operator can be used instead of POWER to indicate to what power the base no. is to be raised.

Description Formula Result

5 squared =5^2 -OR- =POWER(5,2) 25

5 cubed =5^3 -OR- =POWER(5,3) 125

4 raised to the power of 5/4 =4^05/4 -OR- =POWER(4,5/4) 5.656854

98.6 raised to the power of 3.2 =98.6^3.2 -OR- =POWER(98.6,3.2) 2401077

The PMT Function

PMT calculates the payment on a loan (principal) at a given interest rate for a specified no. of payment periods (term).

Syntax: =PMT(Principal – Amount,Interest-Rate,Term)

Principal and Terms are values. Interest is a decimal or percentage value greater than -1.

Example;

A businessman took out a Ksh. 800,000 loan for 4 years at an annual Interest Rate of 26%, compounded monthly. If the monthly installments are paid on the last day of each month, determine the installment to be paid.

=PMT(800000,0.26/12,48)

The Monthly installment is 26,973.85

Note. The Interest is divided by 12 in order to get the monthly rate, and term (in years) is multiplied by 12 to convert it into months.

The FV Function

FV calculates the future value of a fixed investment earning a fixed interest over a specified period.

E.g., let’s say, you want to plan for your retirement in 20 years and decide to invest Ksh. 20,000 each year. If the investment pays 20% interest compounded annually, the formula would be:

=FV(20%,20,-20000)

You would collect Ksh. 3,733,760 after 20 years.

ROUNDING OF NUMBERS.

The ROUND function rounds a given number to a specified no. of digits.

Syntax: ROUND(number,num_digits)

Number –is the no. you want to round.

num_digits – specifies the no. of digits to which you want to round the no.

Notes.

If num_digits is greater than 0 (zero), then number is rounded to the specified no. of decimal places.

If num_digits is 0 (zero), the number is rounded to the nearest Integer (whole no.).
If num_digits is less than 0 (zero), then number is rounded to the left of the decimal point.

Example 1:

Formula Description Result

=ROUND(2.15,1) 2.2

=ROUND(2.149,1) 2.1

=ROUND(21.5,-1) num_digits is less than 0 (zero), 20

Example 2: Cells A2:A4 contain values 20.3, 5.9 and -5.9.

Formula Description Result

=ROUND(A2,0) Rounds 20.3 down, because the fractional part is less than .5 20

=ROUND(A3,0) Rounds 5.9 up, because the fractional part is greater than .5 6

=ROUND(A4,0) Rounds -5.9 down, because the fractional part is less than -.5 -6

=ROUND(-1.475,2) -1.48

To Round a number to a near fraction.

For Example, cells A2 & A3 contain values 1.25 and 30.452.

Formula Description Result

=ROUND(A2,1) Rounds the no. to the nearest 1 decimal place.

Because the portion to be rounded is 0.05 or greater,

the no. is rounded up 1.3

=ROUND(A3,2) Rounds the no. to the nearest 2 decimal places.

Because the portion to be rounded, 0.002, is less than 0.005,

the no. is rounded down 30.45

GETTING THE LOGARITHM OF A NUMBER.

LOG – Gives the logarithm of a number to the base you specify.

Syntax: LOG(number,base)

Number -is the positive real no. for which you want the logarithm.

Base -is the base of the logarithm. If base is omitted, it is assumed to be 10.

Formula Result

=LOG(10) 1

=LOG(8, 2) 3

=LOG(86, 2.7182818) 4.454347

GETTING THE BASE-10 LOGARITHM OF A NUMBER.

LOG10 – Gives the base-10 logarithm of a number.

Syntax: LOG10(number)

Number –is the positive real number for which you want the base-10 logarithm.

Formula Description Result

=LOG10(86) Base-10 logarithm of 86 1.934498451

=LOG10(10) Base-10 logarithm of 10 1

=LOG10(10^5) Base-10 logarithm of 10 power 5 5

MOD – Gives the remainder after a number is divided by a divisor.

Usually, the result has the same sign as the divisor.

Syntax: MOD(number,divisor)

Number -is the number for which you want to find the remainder.

If divisor is 0, MOD returns the #DIV/0! error value.

Description Formula Result

Remainder of 3/2 =MOD(3, 2) 1

Remainder of -3/2 =MOD(-3, 2) 1

Remainder of 3/-2 =MOD(3, -2) -1

Remainder of -3/-2 =MOD(-3, -2) -1

COS – Gives the cosine of the given angle.

Syntax: COS(number)

Number – is the angle in radians for which you want the cosine. If the angle is in degrees, multiply it by PI()/180 to convert it to radians.

Description Formula Result in radians.

Cosine of 1.047 radians =COS(1.047) 0.500171

Cosine of 60 degrees =COS(60*PI()/180) 0.5

SIN – Gives the sine of the given angle.

Syntax: SIN(number)

Number -is the angle in radians for which you want the sine. If your argument is in degrees, multiply it by PI()/180 to convert it to radians.

Description Formula Result in radians.

Sine of pi/2 radians =SIN(PI()/2) 1

Sine of 30 degrees =SIN(30*PI()/180) 0.5

TAN – Gives the tangent of the given angle.

Syntax: TAN(number)

Number– is the angle in radians for which you want the tangent.

Description Formula Result in radians.

Tangent of 0.785 radians =TAN(0.785) 0.99920

Tangent of 45 degrees =TAN(45*PI()/180) 1

TRUNC – Truncates (shortens) a number to an Integer by removing the fractional part of the number.

Syntax: TRUNC(number,num_digits)

Number -is the number you want to truncate.

Num_digits -is a number specifying the precision of the truncation.

Description Formula Result

Integer part of 8.9 =TRUNC(8.9) 8

Integer part of -8.9 =TRUNC(-8.9) -8

CALCULATING THE AVERAGE (ARITHMETIC MEAN) OF NUMBERS.

Use the AVERAGE function. AVERAGE gives the average (arithmetic mean) of the arguments provided.

Syntax: AVERAGE(number1,number2,…)

Number1, number2, … are numeric arguments for which you want the average.

Note. The arguments must numbers or references that contain numbers. If a reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.

Example: Cells A2:A6 contain values 10, 7, 9, 27, & 4.

Description Formula Result

Average all of nos. in the list =AVERAGE(A2:A6) 11.4

Average cells A2 to A4 and A6 =AVERAGE(A2:A4,A6) 7.5

Average the nos. in cell A2 to A5, and 5 =AVERAGE(A2:A5, 5) 11.6

CALCULATE THE SMALLEST OR LARGEST NUMBER IN A RANGE.

Use the MIN or MAX functions.

MAX- Gives the largest value in a set of values.

MIN – Gives the smallest number in a set of values.

Syntax: MAX or MIN(number1,number2,…)

Number1, number2, .. are nos. for which you want to find the maximum or minimum value.

Notes. If the arguments in the reference contain no numbers, MAX or MIN returns 0 (zero). Empty cells, logical values, or text in the reference are ignored.

Example: Cells A2:A6 contain values 10, 7, 9, 27 & 2.

Description Formula Result

Largest number in the range =MAX(A2:A6) 27

Smallest number in the range =MIN(A2:A6) 2

Largest of the numbers in cells A2:A6, and 30 =MAX(A2:A6, 30)

Smallest of the numbers given, and 0 =MIN(A2:A6,0)

CALCULATE THE MEDIAN OF A GROUP OF NUMBERS.

Median is the value at the center of an ordered range of nos.

Use the MEDIAN function. MEDIAN gives the number in the middle of a set of numbers.

Syntax: MEDIAN(number1,number2,…)

Number1, number2, … are numbers for which you want the median.

Notes.

Cells with the value zero are included.
If there is an even number of nos. in the set, then MEDIAN calculates the average of the two numbers in the middle.

Example: Cells A2:A7 contain values 1, 2, 3, 4, 5 and 6.

Description Formula

Median of the first 5 nos. in the list =MEDIAN(A2:A6)

Median of all the nos. given, or the average of 3 and 4 =MEDIAN(A2:A7)

MODE – Gives the most frequently occurring, or repetitive, value in a range of data.

Syntax: MODE(number1,number2,…)

Number1, number2, … are the arguments for which you want to calculate the mode.

Note.

Cells with the value zero are included.
If the data set contains no duplicate data points, MODE returns the #N/A error value.

Example: Cells A2:A7 contain the values 5.6, 4, 4, 3, 2, and 4.

Description Formula

Mode, or most frequently occurring no. in the list =MODE(A2:A7)

Tip. In a set of values, the Mode is the most frequently occurring value; the Median is the middle value; and the Mean is the average value.

COUNTING CELLS THAT CONTAIN NUMBERS.

COUNT – Counts the no. of cells that contain numbers within the list of arguments.

Syntax: COUNT(value1,value2,…)

Value1, value2, … are the arguments that can contain or refer to a variety of different types of data, but only numbers are counted.

Note. Empty cells, logical values, text, or error values in the reference are ignored.

Example 1.

	A
1	Data
2	Sales
3	12/8/2007
4
5	19
6	22.44

Formula Description Result

=COUNT(A2:A6) Counts no. of cells that contain nos. in the list 3 (date is a number).

=COUNT(A2:A3,A6) Counts no. of cells that contain nos. in cells 2

A2:A3, & A6

Example 2.

	A
1	Sales
2	12/8/90
3
4	19
5	22.24
6	TRUE
7	#DIV/0!

Formula Description Result

=COUNT(A1:A7) Counts the no. of cells that contain nos. in the list 3

=COUNT(A5:A7) Counts the no. of cells that contain nos. in the last 3 rows

of the list 1

=COUNT(A1:A7,2) Counts the no. of cells that contain numbers in the list,

and the value 2 4

LOGICAL FUNCTIONS

Logical functions can be used either to test whether a condition is TRUE or FALSE or to check for multiple conditions.

For example, use the IF function to determine whether a condition is true or false. One value is returned if the condition is TRUE, and a different value is returned if the condition is FALSE.

NOT –Reverses the value of its argument. Use NOT when you want to make sure a value is not equal to one particular value.

If logical is FALSE, NOT returns TRUE; if logical is TRUE, NOT returns FALSE.

Syntax: NOT(logical)

Logical – is a value or expression that can be evaluated to TRUE or FALSE.

Formula Description Result

=NOT(FALSE) Reverses FALSE TRUE

=NOT(1+1=2) Reverses an equation that evaluates to TRUE FALSE

AND – Returns TRUE if all its arguments are TRUE; returns FALSE if one or more argument is FALSE.

Syntax: AND(logical1,logical2, …)

Logical1, logical2, .. are the conditions you want to test that can be either TRUE or FALSE.

Note. The arguments must evaluate to logical values such as TRUE or FALSE, or the arguments must be references that contain logical values. If the specified range contains no logical values, AND returns the #VALUE! error value.

Example 1.

Formula Description Result

=AND(TRUE, TRUE) All arguments are TRUE TRUE

=AND(TRUE, FALSE) One argument is FALSE FALSE

=AND(2+2=4, 2+3=5) All arguments evaluate to TRUE TRUE

Example 2. Cells A2:A3 contain values 50 and 104.

If A2 contains a number between 1 and 100, then:

Formula Result

=AND(1<A2,A2<100) TRUE

Suppose you want to display A3 if it contains a number strictly between 1 and 100, and you want to display a message if it is not. If A3 contains 104, then:

Formula Result

=IF(AND(1<A3,A3<100), A3,”The value is out of range.”) “The value is out of range”.

If A3 contains 50, then:

Formula Description Result

=IF(AND(1<A2, A2<100), A2, “The value is out of range.”) 50, because A3 it between 1 & 100.

OR – Returns TRUE if any argument is TRUE; returns FALSE if all arguments are FALSE.

Syntax: OR(logical1,logical2,…)

Logical1,logical2,… are conditions you want to test that can be either TRUE or FALSE.

Notes.

The arguments must evaluate to logical values such as TRUE or FALSE, or references that contain logical values. If the specified range contains no logical values, OR returns the #VALUE! error value.
If a reference argument contains text or empty cells, those values are ignored.

Formula Description Result

=OR(TRUE) One argument is TRUE TRUE

=OR(1+1=1,2+2=5) All arguments evaluate to FALSE FALSE

=OR(TRUE,FALSE,TRUE) At least one argument is TRUE TRUE

Example:

Cells A2, A3 & A4 contain the values 15, 9, and 8.

Formula Description Result

=AND(A2>A3, A2<A4) Is 15 greater than 9 and less than 8? FALSE

=OR(A2>A3, A2<A4) Is 15 greater than 9 or less than 8? TRUE

=NOT(A2+A3=24) Is 15 plus 9 not equal to 24? FALSE

THE “IF” function.

IF is used to conduct conditional tests on values and formulas.

It evaluates a condition and returns one of two values, depending on the result of the evaluation.

If the condition is TRUE, IF returns one value. If the condition is FALSE, IF returns the other value.

Format: IF(Condition, Action-to-be-taken when condition is true, Action-to-be-taken when condition is false)

Note. The condition is usually a logical formula.

E.g., A5=100 is a logical expression; if the value in cell A5 is equal to 100, the expression evaluates to TRUE. Otherwise, the expression evaluates to FALSE.

Example 1.

Cell A2 contains the value 50.

On a budget sheet, cell A5 contains a formula to calculate the current budget.

=IF(A2<=100,”Within budget”,”Over budget”)

If the result of the formula in A5 is less than or equal to 100, then the function displays “Within budget”. Otherwise, the function displays “Over budget”.

Example 2.

=IF(A2=100,SUM(B5:B15),””)

In this example, if the value in cell A2 is 100, then the condition is TRUE, and the total value for the range B5:B15 is calculated. Otherwise, condition is FALSE, an empty text (“”) is returned that leaves the cell that contains the IF function blank.

Example 3.

Suppose an expense worksheet contains in A2:A4 the data for “Actual Expenses” for January, February, and March: 1,500, 500 and 500. Cells B2:B4 contains the data for “Predicted Expenses” for the same periods: 900, 900, and 925.

	A	B	C
1	Actual Expenses	Predicted Expenses
2	1500	900
3	500	900
4	500	925

You can write a formula in cell C2:C4 to check whether you are over budget for a particular month, generating text for a message:

Formula Description Result

=IF(A2>B2,”Over Budget”,”OK”) Checks whether the 1^st row is over budget Over Budget

=IF(A3>B3,”Over Budget”,”OK”) Checks whether the 2^nd row is over budget OK

To check if a number is greater than or less than another number.

Cell A2, A3 & A4 contain the values 15,000; 9,000 and 8,000.

Formula Description Result

=A2>A3 Is A2 greater than no. in A3? TRUE

=IF(A3<=A4, “OK”,”Not OK”) Is A3 less than or equal to the no. in A4? Not OK

NESTING FUNCTIONS WITHIN FUNCTIONS.

You can use a function as one of the arguments of another function.

Note. When a function is used as an argument, it must return the same type of value that the argument uses.

For example, if the argument returns a TRUE or FALSE value, then the nested function must return a TRUE or FALSE. If it doesn’t, Ms-Excel displays a #VALUE error value.

Example 1.

=IF(SUM(K10:K19)>=5000,10%,5%)

In this example, the SUM function is being nested. Assume that the result of the SUM function is 935. Since the sum of the range K10:K19 is not greater than or equal to 5000, the result is 5%.

Example 2. Cells A2, A3 and A4 contain the values 45, 90, 78.

Suppose you want to assign letter grades to numbers referenced by the name AverageScore. See the table below.

If AverageScore is Then return

Greater than 89 A

From 80 to 89 B

From 70 to 79 C

From 60 to 69 D

Less than 60 F

Formula Description Result

=IF(A2>89,”A”,IF(A2>79,”B”, Assigns a letter grade to the first score F

IF(A2>69,”C”,IF(A2>59,”D”,”F”))))

=IF(A3>89,”A”,IF(A3>79,”B”, Assigns a letter grade to the second score A

IF(A3>69,”C”,IF(A3>59,”D”,”F”))))

=IF(A4>89,”A”,IF(A4>79,”B”, Assigns a letter grade to the third score C

IF(A4>69,”C”,IF(A4>59,”D”,”F”))))

In the above formula, the second IF statement is also the value_if_false argument to the first IF statement. Similarly, the third IF statement is the value_if_false argument to the second IF statement.

For example, if the first logical_test / condition (AverageScore>89) is TRUE, “A” is returned. If the first logical_test is FALSE, the second IF statement is evaluated, and so on.

EDIT/ CHANGE A FORMULA.

Select the cell containing the formula you want to edit.
Click in the Formula bar, make the changes to the formula, then press the ENTER

Note. If formulas are not used, there will be no automatic recalculation when any of the numbers change.

Automatic recalculation:

This means that, Spreadsheets are able to calculate values such as SUM, AVERAGES, PERCENTAGES, etc automatically without requiring the intervention of the user (or without putting the user into the hard task of thinking).

RELATIVE REFERENCES

When you create a formula, cells or ranges of cells will be referred to based on their position relative to the cell that contains the formula. If cell B6 contains the formula =A5; Ms-Excel finds the value one cell above and one cell to the left of B6.

If the position of the cell that contains the formula changes, the reference is changed.

A Relative reference is a cell reference, which changes automatically when the formula is copied to another cell or range. It describes the location of a cell in terms of its distance (in rows and columns) from another cell.

Note. When you copy a formula containing relative references down or across from one cell to another, Ms-Excel adjusts the references in the pasted formula automatically to refer to a different cell that is the same no. of rows & columns away from the formula.

Example 1:

If the formula in cell B6 (i.e., =A5) (which is one cell above & one cell to the left of B6) is copied to cell B7. Ms-Excel will adjust the formula in cell B7 to =A6, which refers to the cell that is one cell above and one cell to the left of cell B7.

Example 2:

If cell A3 contains the formula =A1+A2, and you copy cell A3 to cell B3, the formula in cell B3 becomes =B1+B2.

ABSOLUTE REFERENCES.

In a formula, an Absolute cell reference is the exact address of a cell, regardless of the position of the cell that contains the formula.

An absolute cell reference takes the form $A$1, $B$1, etc.

The table below shows the different types of references.

Reference:	Effect on a cell reference
A1	Relative reference.
$A$1	Both rows and column references are absolute
A$1, B$1	Absolute row reference, i.e., only the row reference is absolute.
$A1, $B1	Absolute column reference, i.e., only the column reference is absolute.

Unlike relative references, Absolute references don’t automatically adjust when you copy formulas across rows and down columns. For example, if you copy an absolute reference in cell B2 to cell B3, it stays the same in both cells.

Therefore, if you don’t want Ms-Excel to adjust references when you copy a formula to a different cell, i.e., if a formula refers to a particular cell and you would like to copy it such that the subsequent copies of cell references still refer to that same cell reference, you must use Absolute referencing.

For example,

If your formula multiplies cell A5 with cell C1 (=A5*C1), you can create an absolute reference to cell C1 by placing a dollar sign ($) before the parts of the reference that you don’t want them to change.

To create an absolute reference to cell C1, for instance, add dollar signs to the formula as follows: =A5*$C$1.

Note. To enter the dollar sign in a cell reference; move the cell pointer in the cell reference to be made absolute, then press the function key F4 or the keyboard combination SHIFT+4.

Worked Example:

	A	B	C	D	E	F	G	H
1	ABC Company Sales Performance Report
2
3	Salesman	Target	Qtr1	Qtr2	Qtr3	Qtr4	Total	Commission
4	Albert	750	148	156	171	140	615	*=G4$A$13**
5	Carl	650	122	131	153	118	524	=G5*$A$13
6	Cornell	800	211	243	246	250	950	=G6*$A$13
7	Edwin	700	129	150	92	218	589	=G7*$A$13
8	Francis	1,000	311	270	247	322	1,150	=G8*$A$13
9
10	Totals	3,900	921	950	909	1,048	7,728	=G10*$A$13
11
12	Commission Rate
13	15% (or 0.15)

To get the commission for each salesperson, the formula =G4*$A$13 is entered in cell H4. The dollar sign ($) indicates an absolute reference to the cell A13. This means that, whenever the commission rate formula is copied, it always refers to cell A13.

When the formula =G4*$A$13 is copied down to H10, the results will be as shown.

Determine which cell reference is to be absolute, e.g., in the example above cell A13.
Type the dollar sign ($) just before the part of the cell reference that you want to remain exactly the same when you copy the formula to another cell.
Copy the formula to the rest of the cells.

FORMULAS AND ERROR VALUES.

If a formula cannot properly evaluate a result, Ms-Excel will display an error value.

For example, error values can be as a result of using text where a formula expects a numeric value, deleting a cell that is referenced by a formula, or using a cell that is not wide enough to display the result.

#####

Causes.

This error value occurs when the cell contains a number, date or time that is wider than the cell.

-OR-

It occurs when the cell contains a date or a time formula that produces a negative result.

Suggested action.

Increase the width of the column by dragging the boundary between the column headings.

Apply a different number format in the cell to make the number fit within the existing cell width. g., decrease the no. of decimal places after the decimal point.

Ensure that the data and time formulas are correct. When you subtract dates and times, make sure you build the formula correctly.

If a formula has a result of a negative value, you can display the value by formatting the cell with a format that is not a date or time format.

Click Cells on the Format menu, click the Number tab, then select a format that is not a date or time format.

#N/A

The #NA error value occurs when a value is not available to a function or formula.

Possible cause Suggested action

Omitting 1 or more arguments in a function Enter all arguments in the function.

Using a custom worksheet function that is Make sure the function is working

not available properly

#DIV/0!

This error value occurs when you enter a formula that contains a division by zero (0).

E.g., =5/0. It may also occur when you divide a cell by another cell that is blank.

Suggested action.

Change the divisor to a number other than zero.

#NULL!

The #NULL! error value occurs when you specify an intersection of two areas that do not intersect. i.e., using an incorrect range operator or using an incorrect cell reference.

Suggested action.

Use the correct range operator. For instance, to refer to two areas that don’t intersect, use the Comma.

E.g. if the formula sums two ranges, separate the two ranges with a comma.

=SUM(A1:A9,C1:C6).

Check for typing errors in the reference to the ranges.

#NAME?

The #NAME? error value occurs when Ms-Excel doesn’t recognize text in a formula.

Possible cause Suggested action

Deleting a name used in the formula, or Make sure the name exists.

using a name that does not exist

Misspelling the name of a function Correct the spelling.

Omitting a colon (:) in a range reference Make sure all range references in the

formula use a colon.

E.g. =SUM(A1:A5)

Entering text in a formula without Enclose text in the formula in double

enclosing the text in double quotation marks (“). quotation marks.

Ms-Excel tries to interpret your entry as a name E.g. the following formula joins a

even though you intended it to be used as text. piece of text “The total amount is”

with the value in cell B5:

=”The total amount is” & B5

#NUM!

This occurs when a problem occurs with a number in a formula or function. E.g., Entering a formula that produces a number to a number that is too large or too small to be represented in Ms-Excel.

Suggested action

Change the formula so that its result is between – 1*10³⁰⁷ and 1*10³⁰⁷.

#VALUE!

The #VALUE error value occurs when the wrong type of argument or operand is used.

#REF!

The #REF error value occurs when a cell reference is not valid. For instance, deleting cells referred to by other formulas, or pasting moved cells over cells referred to by other formulas.

Suggested action

Change the formulas, or restore the cells on the worksheet by clicking Undo immediately after you delete or paste the cells.

Exercise.

You have entered a formula to add the contents of B5 and C4 in cell F5. What will it become when you copy it to cell H8?

______________________________________________

Explain the reason for your answer.

What causes the following error messages in Microsoft Excel. Show how we can solve them.

#####
#VALUE!
#DIV/0!
#NAME?

The first column in the table below contains formulas as entered into the cell D46. In the second column, enter the formulas as they would appear when copied to B56.

Formula in D46	Formula when copied to B56
=D1
=F5*C10
=H$46+J40
=$E12-D$14*$F$2

DATA SORTING.

Sorting is the process of arranging data within a range in a particular order.

Purpose.

√ Sorting helps in arranging data in some order of priority, i.e., from lowest to highest or from highest to lowest.

√ It also helps to quickly locate the highest or lowest value in a list.

When you sort, Ms-Excel rearranges rows, columns, or individual cells by using the sort order that you specify. You can sort a list in Ascending (1-9, A-Z) or Descending order (9-1, Z-A). You can perform a sort based on the contents of one or more columns.

Note. The data is sorted in reference to columns.

To sort rows in ascending or descending order based on the contents of one column.

Click a cell in the column by which you want to sort. The column on which the list is arranged is known as the Key.
To arrange the data from lowest to highest, click on the Sort Ascending button on the toolbar. To arrange the data from highest to lowest, click on the Sort Descending button on the toolbar.

-Or-

On the Data menu, click Sort. In the Sort by box, click the column you want to sort and then choose the sort order.

To sort rows based on the contents of two or more columns.

Click a cell in the list you want to sort.
On the Data menu, click Sort to display the Sort dialog box.
Under Sort By, specify the first column by which you want to sort, then choose the sort order by clicking on the Ascending or Descending
You can add up to two keys in the Then By boxes according to your need.

Assume that you need to sort by more than 3 columns, i.e., your list contains employee information and you need to organize it by Department, Title, Last Name, and First Name, sort the list twice. Click First Name in the first Sort by box and then sort the list. Click Department in the second Sort by box, click Title in the first Then by box, and click Last Name in the second Then by box, and then sort the list.

Select any other sort options you want, then click OK to perform the sort.

Sort columns based on the contents of rows.

Click a cell in the list you want to sort.
On the Data menu, click Sort.
Click the Options
Under Orientation, click Sort left to right, then click OK.
In the Sort by and Then by, click the rows you want to sort.

Examples:

A teacher may arrange pupil’s records according to the marks scored in a test, starting with the highest to the lowest in order to assign class positions.
An Accountant may arrange a list of financial records according to the date of the transaction and customer name in order for him to be able to quickly locate any record using the transaction date and name of customer.
Arranging a telephone list according to alphabetical order of last name in order to easily locate a name and phone number. If there are several people with similar last names, you can specify two keys such that the records are arranged in order of first name as well.

LINKING WORKSHEETS.

Purpose.

Sheets are normally independent. If a change in a value in one sheet is intended to affect other values in different sheets, it is advisable to link the sheets so that Ms-Excel will automatically update the affected values if you make any changes.

Alternatively, you can calculate the new values and manually make the changes to all the other sheets. This would be unreliable & cumbersome especially if this is to be done for many values in many large worksheets.

When typing in a formula that refers to a cell in another sheet, include the name of the sheet before that particular cell reference separated by a colon.

Example 1:

The formula =G6*Sheet1!B6 (instead of =G6*B6) will refer to B6 in Sheet 1 rather than in the current sheet.

Example 2:

Typing the formula =Salesinfo!A10 in cell A10 of Sheet2 will cause the contents of cell A10 in the Sheet named Salesinfo to be also the contents of A10 in Sheet2.

Exercise.

How would you display the contents of the cell B45 of worksheet named Price in the cell B5 of worksheet named Sales such that the two cells always display the same value?

CREATING CHARTS.

Purpose.

√ Charts are used to present data effectively. They make relationships among numbers easy for users to see because they turn numbers into shapes that can be compared to one another.

For instance, rather than having to analyze several columns on worksheet numbers, you can see at a glance whether sales are falling or rising over quarterly periods, or how the actual sales compare to the projected sales.

Different Types of Charts and their uses.

Line Chart: A Line graph is used to show trends.

Bar Chart: – It can be used to show comparison of Sales and Target.

A Stacked Bar Chart: – It can be used to show the distribution of sales by month and compare the performance of salesmen.

A Pie Chart: shows the distribution of sales.

Scatter

Column Charts.

Steps required when creating a simple chart.

Enter the data you want to be represented in the chart on the worksheet.
Select the cells or range that contains the data you want to be represented in chart.

If the cells you want to select for your chart are not in a continuous range,

Select the first group of cells that contain the data you want to include.
Hold down the CTRL, then select any additional cell groups you want to include. The nonadjacent selections must form a rectangle.

On the Insert menu, click Chart (or click the Chart Wizard button on the Standard toolbar). Then use the Chart Wizard to help you through the process of choosing the chart type and the various chart options.

Select Chart type.

In the Chart type dialog box, click the Standard Types tab or the Custom Types
Under Chart Type, click the chart category you want to use, then select the type of chart under Chart subtypes on the right.

A brief description of the chart selected appears below the sub-types. This helps you decide whether the type suits the data you have selected. You may also view a sample of the chart that will be produced.

Click on the Next

Specify the range of cells to include in the chart.

This gives you a chance to select your range again if necessary.

In the Chart Source data dialog box,

Click the Data range tab, then confirm the selected range or enter a new range.
Under Series in, click an option to change the way in which the data should be plotted; across Rows or down Columns. To help you decide the right option, the sample chart changes according to the selection you have made.
If you are sure about the range you have selected and the sample chart is what is desired, click on the Next

Select the Chart options.

In this step, there are several chart options as indicated by the various categories at the top of the Chart Options dialog box.

Click the Titles Click in the Chart Title area and type in the title for your chart. Type in the titles for axes in their respective places.
Click the Legend tab, and then select the Show Legend Under Placement, click an option to show where the legend will be placed.
Click on the Next

Legend – A box that identifies the patterns or colors that are assigned to the data series or categories in a chart. A legend indicates which color (pattern) represents what data item.

Axis – A line that borders one side of the plot area, providing a frame of reference for measurement or comparison in a chart.

For most charts, data values are plotted along the value axis, which is usually vertical (Y-axis), and categories are plotted along the category axis, which is usually horizontal (X-axis).

Note. Ms-Excel creates the axis values from the worksheet data.

Select the Location of Chart placement.

This step involves placing the chart you have created.

You can create a chart as an embedded object on the sheet you are working on or on its own sheet.

Under Place chart, click an option either to insert the chart as a new sheet or as an object in the current data sheet.

Click on the Finish

To change the Chart type.

Click the chart to activate the Chart
On the Chart menu, click Chart Type.
Click the Standard Types tab, click the inbuilt chart type you want to use, then click the OK button

Changing Chart Options.

Click the chart. On the Chart menu, click Chart Options to display the Chart Options dialog box.

To add or change the Chart Title.

Click the Titles tab.
Click in the Chart title box, and then type the text for the title.

To add a Legend to a chart.

Click the Legend
Select the Show legend check box.
Under Placement, click the option you want.

Note. When you click one of the Placement options, the legend moves, and the Plot Area (area bounded by the axes) automatically adjusts to accommodate it.

To change Data series names or the Legend text.

Click the chart. On the Chart menu, click Source Data.
On the Series tab, click the data series name you want to change.
In the Name box, specify the worksheet cell you want to use as the legend text or data series name. You can also type the name you want to use.

To edit the Chart title and the Axes titles.

On the chart, click the title you want to change.
Type the new text you want.
Press the ENTER key.

How worksheet data is represented in a chart.

A chart is linked to the worksheet data it’s created from and is updated automatically when you change the worksheet data.

To change the Cell range used to create a chart.

Click the chart.
On the Chart menu, click Source Data, then click the Data Range
Make sure the entire reference in the Data range box is selected.
On the worksheet, select the cells that contain the data you want to appear in the chart.

If you want the column and row labels to appear in the chart, include the cells that contain them in the selection.

To include a new range into an existing chart.

This helps to add information not already in the chart.

Select the range you want to add in the chart.
Position the mouse pointer along the edge of the selected range until it changes into an arrow.
Drag the range into the chart.

Ms-Excel will automatically update the chart so that it includes the new range.

To change the Placement of a chart.

Click the chart. On the Chart menu, click Location.
To place the chart on a new chart sheet, click As new sheet, then type a name for the new chart sheet in the As new sheet

To place the chart as an embedded object on a worksheet, click As object in, click a sheet name in the As object in box, and then click the OK button.

Drag the embedded chart where you want it on the worksheet.

To Move and resize chart items by using the Mouse.

Click the chart item you want to move or resize.

To move an item, point to the item, then drag it to another location of the sheet.

To resize a chart item, point to a Sizing handle. When the pointer changes to a double-headed arrow, drag the sizing handle until the item is the size you want.

Delete data from a chart

To delete data from both the worksheet and the chart.

Delete the data from the worksheet. The chart will be updated automatically.

To delete data from the chart only.

Click the data series you want to delete.
Press the DELETE key.

To delete data labels, titles, or legends in a chart.

Click the chart item you want to delete.
Press the DELETE key.

To change the Font, font Size, font Colour of text in a chart or make the text Bold, Italic or Underlined.

Click the chart text, or select the individual characters you want to format.
On the Formatting toolbar, click a button for the format you want.

Setting up a chart for printing.

You can adjust where the chart will print on the page by sizing and moving the chart with the mouse in Page break view.

Click the worksheet outside of the chart area.
On the View menu, click Page Break Preview.
To set printing options for a chart sheet, click Page Setup on the File
Click the Chart tab, and then select the options you want.

Tip. To print an embedded chart without its associated worksheet data, click the embedded chart to select it, and then follow the above instructions for chart sheets.

Chart area – the entire chart and all its elements.

To zoom or size the display of a chart sheet.

Click the tab for the chart sheet.
Click Zoom on the View menu, then click the option you want.

To size the chart sheet so that it fills the entire workbook window, click Sized with Window on the View menu. When a chart sheet is sized with the window, you cannot zoom in or out of it.

To view an embedded chart in a separate window.

Click the embedded chart you want to see in its own window.
On the View menu, click Chart Window.

Printing the chart.

Purpose.

To create a paper copy of the chart to present to other people.
To maintain a paper filing system alongside the computer filing system.

To print both the worksheet and the chart, click on the Print button on the toolbar.

To print the chart only, select the chart by clicking on it, then select Print on the File menu.

Under Print what in the resulting dialog box, click on Selected Chart, and then choose OK.

Exercise.

(a). What is a Chart?

(b). What are the steps required when creating a simple chart?

The chart has ‘Thousands’ displayed along the Y-axis, yet the figures are in Millions of Kenya Shillings. How do you change the chart such that it displays ‘Millions of Kenya Shillings’ instead?
You want the legends to become the X-axis titles and the X-axis titles to be used as the legends. How do you implement this?

PRINTING A WORKSHEET.

Purpose.

√ Whenever you need a paper copy of the worksheet to present to other people.

√ If you maintain a paper filing system alongside the computer filing system.

PAGE SETUP.

You can control the appearance or layout of printed worksheets by changing options in the Page Setup dialog box.

Purpose.

To define where one page ends and another page starts.
To print a large worksheet to fit on a single page.
To add descriptive information to be printed with your worksheet.
To define rows and columns you want to print on each page of the output.
To change the order in which various worksheets should print.

Setting the Page Margins.

Select the worksheet you want to print.
On the File menu, click Page Setup, then click the Margins
In the Top, Bottom, Left, and Right boxes, enter the margin size you want.

You can also tell Ms-Excel to automatically position your worksheet at the center of the page, both horizontally (across) and vertically (downwards) by clicking the options under Center on Page.

To set Header or Footer margins.

To change the distance from the top edge to the header, enter a new margin size in the Header

To change the distance from the bottom edge to the footer, enter a new margin size in the Footer

These settings should be smaller than your top and bottom margin settings.

Tip. To see how the margins will affect the printed document, click Print Preview before the document is printed.

Setting the paper Orientation.

Orientation specifies how the worksheet will be printed on a page.

On the Page Setup dialog box, click the Page
Under Orientation, click Portrait or Landscape.

To set the Paper size for printing.

Click the Page
In the Paper size box, select the size of paper you want to use from the resulting drop down list.
If you want Ms-Excel to fit your worksheet on one page; under Scaling, click on Fit to and make sure that the specification is “Fit to: 1 page(s) wide by 1 tall”.

Setting the print Quality.

You can speed up the time it takes to print a worksheet by temporarily changing the printing quality.

Click in the worksheet.
On the File menu, click Page Setup, then click the Page
In the Print quality box, click the resolution you want to use.

To print in Draft quality,

Click Draft in the Print quality box.

Note. Draft quality increases printing speed by ignoring formatting and most graphics.

To add header and/or footer comments to be printed with your worksheet.

On the Page Setup dialog box, click the Header/Footer
Under Header, type in the information you want to appear at the top of each page.

Under Footer, type in the information you want to appear at the bottom of each page.

Alternatively, you can click on the arrow on the right of the Header or Footer to reveal a list of preset headers and footers and then select one of them.

To print with or without Cell gridlines.

On the Page Setup dialog box, click the Sheet
Select or clear the Gridlines

Note. Worksheets print faster if you print without gridlines.

To print the Row and Column headings.

Row headings are the row numbers to the left of the worksheet. Column headings are the letters that appear at the top of the columns on a worksheet.

On the Page Setup dialog box, click the Sheet
Select the Row and column headings

To specify which areas of the sheet you want to print, click in the Print Area box, then drag through the worksheet the areas that you want to print.

Choosing the printer.

There are many types of printers and Ms-Excel communicates with each one differently. Therefore, you have to tell Ms-Excel which printer is connected in order to get the right results.

On the File menu, select Print to display the Print dialog box.
Select the printer you want to use from the list of printers shown in the Name

Note. If the wrong printer has been selected in the Printer Setup, the printer will produce funny characters (garbage) when you order Ms-Excel to print the worksheet.

To define what part of the worksheet to print.

Purpose.

To select a certain portion of the worksheet for printing.

To print a selected area of a worksheet.

On the View menu, click Page Break Preview.
Select the area you want to be printed.
Right-click a cell within the selection (or on the File menu, point to Print Area), then click Set Print Area.

When you save the document, your print area selection is also saved.

Note. Page break preview – shows you what data will go on each page so you can adjust the print area and page breaks.

To print a selection, or the active worksheet(s).

To print a specific selection, select the range of cells to print.
On the File menu, click Print.
Under Print what, select an option to print, i.e., Selection or Active sheet(s).

When you choose Selection, Ms-Excel prints the selection and ignores any print area defined on for printing on the worksheet.

To print more than one copy at a time.

In the Number of copies box, enter the number of copies you want to print.

Preview a page before printing

Click Print Preview on the File menu (or on the Standard toolbar) to see a picture of how your worksheet will look when it is printed on a paper.
Use the buttons on the toolbar to look over the page or make adjustments before printing.
If what you see in the Print Preview screen satisfies you, click the Print button on the toolbar to start printing.
To return to the normal Ms-Excel screen, click the Close button in the Print Preview

Print preview displays the printed page so you can adjust columns and margins. The way pages appear in the preview window depends on the available fonts, the resolution of the printer, and the available colors.

Teachers' Resources

English Grade 6 CBC Free Schemes of Work

October 5, 2025 Maverick John Leave a comment

NEW PRIMARY ENGLISH ACTIVITIES. GRADE 6 SCHEMES OF WORK

School: Teacher’s Name: Term Year


Wk	Ls n	Strand/Them e	Sub strand	Specific learning outcomes	Key inquiry Questions	Learning experiences	Learning Resources	Assessment methods	Ref l
1	1	PROPER USE OF LEISURE TIME	Listening and speaking: pronunciation and vocabulary- interactive listening	By the end of the lesson, the learner should be able to: a) Identify words with the sound /h/ in an oral text. b) listen to a text and tell words or phrases with sound /h/. c) Advocate importance of polite interruption and turn taking in oral communication.	Why should we take turns in a conversation? How can we interrupts a speaker politely? What are some of the moods or feelings we can show during a conversation?	Learner is guided to: • Pick out the sound /h/ as in holiday from an audio text. • Listen to a text and say words and phrases with the sound /h/.	Audio texts NPE Grd 6 TG pg. 108-110 NPE Grd 6 Learners Bk. pg. 93-95	Oral discussions Peers assessment
	2			By the end of the lesson, the learner should be able to: a) Identify words with the sound /h/ in an oral text. b) Take turns during a conversation. c) Advocate importance of polite interruption and turn taking in oral communication.	Why should we take turns in a conversation? How can we interrupts a speaker politely?	Learner is guided to: • Take turns during (short interviews, debates and discussions on grade appropriate topics)	Audio texts NPE Grd 6 TG pg. 108-110 NPE Grd 6 Learners Bk. pg. 93-95	Oral discussions Peers assessment
					What are some of the moods or feelings we can show

					during a conversation?
	3			By the end of the lesson, the learner should be able to: a) Interrupt a speaker appropriately during a conversation. b) Express appropriate moods during a conversation. c) Advocate importance of polite interruption and turn taking in oral communication.	Why should we take turns in a conversation? How can we interrupts a speaker politely? What are some of the moods or feelings we can show during a conversation?	Learner is guided to: • Interrupt appropriately during a class discussion, interview or debate. • Perform a choral verse (about six stanzas) or conversational poem in a reader’s theatre, and display various moods. • Practice using expressions such as fixed phrase: kill time; simile: sleep like a log; metaphor: my mother is hawk eyed. she sees everything; proverbs: there is no time like the present, idioms: day dream, phrasal verbs: good at,	Audio texts NPE Grd 6 TG pg. 108-110 NPE Grd 6 Learners Bk. pg. 93-95	Oral discussions Peers assessment
	4	Reading	Intensive reading	By the end of the lesson, the learner should be able to: a) Make connections between events in a text and real life experiences. b) Answer direct and inferential questions correctly for comprehension. c) Acknowledge the role of reading comprehension in lifelong learning.	How do you tell the meaning of new words from a text? Why do you think events in a story have a relationship with real life experiences?	Learners is guided to: • Preview a text (of about 500 words) for general understanding. • Make predictions about events. • Infer the meaning of new words using prior knowledge and clues. • Answer questions in pairs. • Retell events in a text in small groups. • Create a crossword puzzle using the learnt vocabulary.	Sample of a crossword puzzle NPE Grd 6 TG pg. 111-113 NPE Grd 6 Learners Bk. pg. 95-99	Written exercises, portfolio
2	1			By the end of the lesson, the learner should be able to: a) Predict events in a text accurately. b) Use contextual clues to infer the meaning of	How do you tell the meaning of new words from a text?	Learners is guided to: • Preview a text (of about 500 words) for general understanding. • Make predictions about events.	Sample of a crossword puzzle NPE Grd 6 TG pg. 111-113	Written exercises, portfolio

unfamiliar words and expressions such as proverbs, similes among others.

c) Summarize information in a text by restating it in own words.

d) Acknowledge the role of reading comprehension in lifelong learning.

Why do you think events in a story have a relationship with real life experiences?

• Infer the meaning of new words using prior knowledge and clues.

• Answer questions in pairs.

• Retell events in a text in small groups.

• Create a crossword puzzle using the learnt vocabulary.

NPE Grd 6

Learners Bk. pg. 95-99

Grammar

in use

Conjunctions

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

a) Identify conjunctions in a text.

b) Use conjunctions in varied contexts correctly.

c) Judge the appropriateness of conjunctions used in sentences.

Why should we write sentences correctly?

How do we join two or more sentences?

Learner is guided to:

• Identify the conjunctions since, so, nor, far, yet, for, unless, although, though, in a text in pairs.

• Construct sentences using conjunctions in small groups.

• Fill in blanks in sentences using conjunctions individually or in pairs.

• Collaborate with peers to construct sentences using conjunctions.

• Create a crossword puzzle using conjunctions and share it with others through

posters, charts or social media

Readers, newspapers, magazines

NPE Grd 6 TG pg. 114-116

NPE Grd 6

Learners Bk. pg. 99-100

Gap filling,

class competitio n, sentence constructio n, learner portfolio

By the end of the lesson, the

learner should be able to:

a) Identify conjunctions in a text.

b) Use conjunctions in varied contexts correctly.

c) Judge the appropriateness of conjunctions used in sentences.

Why should

we write sentences correctly?

How do we join two or more sentences?

Learner is guided to:

• Identify the conjunctions since, so, nor, far, yet, for, unless, although, though, in a text in pairs.

• Construct sentences using conjunctions in small groups.

• Fill in blanks in sentences using conjunctions individually or in pairs.

Readers,

newspapers, magazines

NPE Grd 6 TG pg. 114-116

NPE Grd 6

Learners Bk. pg. 99-100

Gap filling,

class competitio n, sentence constructio n, learner portfolio

• Collaborate with peers to construct sentences using conjunctions.

• Create a crossword puzzle using conjunctions and share it with others through posters, charts or social

media

By the end of the lesson, the

learner should be able to:

a) Identify conjunctions in a text.

b) Use conjunctions in varied contexts correctly.

c) Judge the appropriateness of conjunctions used in sentences.

Why should

we write sentences correctly?

How do we join two or more sentences?

Learner is guided to:

• Identify the conjunctions since, so, nor, far, yet, for, unless, although, though, in a text in pairs.

• Construct sentences using conjunctions in small groups.

• Fill in blanks in sentences using conjunctions individually or in pairs.

• Collaborate with peers to construct sentences using conjunctions.

• Create a crossword puzzle using conjunctions and share it with others through posters, charts or social

media

Readers,

newspapers, magazines

NPE Grd 6 TG pg. 114-116

NPE Grd 6

Learners Bk. pg. 99-100

Gap filling,

class competitio n, sentence constructio n, learner portfolio

Writing

Creative

writing

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

a) Use appropriate adjectives to describe a person, object or a place.

c) Plan a descriptive composition in preparation for writing.

c) Judge a descriptive composition for correctness of language, relevance to the topic, creativity and organization of ideas.

Why should we plan our compositions?

How do we describe objects, people or events?

Which words do we use to describe

people, objects or events?

Learner is guided to:

• Identify key points about an event such as a wedding ceremony, football match and dance, among others.

• Suggest people, events, places or objects that can be described in pairs.

Sample of descriptive composition

NPE Grd 6 TG pg. 116-119

NPE Grd 6

Learners Bk. pg. 101-102

Compositi

on writing, peer assessment

, learner portfolio

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

b) Discuss and Plan a descriptive composition in preparation for writing.

c) Create a descriptive composition on a variety of topics.

d) Judge a descriptive composition for correctness of language, relevance to the topic, creativity and organization of ideas.

Why should we plan our compositions?

How do we describe objects, people or events?

Which words do we use to describe people, objects or events?

Learner is guided to:

• Plan a descriptive composition of about (120- 160 words) in small groups.

• Select and use appropriate expressions such as proverbs and idioms in a composition.

• Write the introductory paragraph of the descriptive essay in small groups.

• Complete the descriptive composition individually.

• Proofread the composition with peers.

• Display the corrected composition in the classroom or share it over the internet,

email or social media.

Sample of descriptive composition

NPE Grd 6 TG pg. 116-119

NPE Grd 6

Learners Bk. pg. 101-102

Compositi

on writing, peer assessment

, learner portfolio

SPORTS:

INDORR GAMES

Listening and

speaking: pronunciation and vocabulary (audio files)

By the end of the lesson, the

learner should be able to:

a) Select sounds, words and phrases from a text for listening fluency.

b) Listen to audio stories and pick specific sounds

c) Appreciate the importance of effective listening in communication.

Why should

we look at people’s faces as they speak?

How are audio stories different from a storybook?

Learner is guided to:

• Listen to audio stories and pick put specific sounds, words, phrases or sentences in pairs.

• Say words with the sounds

/ʊ/ and /uː/ correctly.

Digital devices,

posters, charts

NPE Grd 6 TG pg. 120-123

NPE Grd 6

Learners Bk. pg. 103-104

Sentence

constructio n, peer assessment

, recitation

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

a) Use words and expressions such as proverbs, phrasal verbs, proverbs among others related to the theme in sentences.

b) Interpret non-verbal cues correctly during conversations.

Why should we look at people’s faces as they speak?

How are audio stories different from a storybook?

Learner is guided to:

• Listen to choral poems with the sounds /ʊ/ and

/uː/ in small groups and pick out words with the selected sounds.

• Say tongue twisters with the target sounds.

Digital devices, posters, charts

NPE Grd 6 TG pg. 120-123

NPE Grd 6

Learners Bk. pg. 103-104

Sentence

construction, peer assessment

, recitation

				c) Appreciate the importance of effective listening in communication.
4	1			By the end of the lesson, the learner should be able to: a) Interpret non-verbal cues correctly during conversations. b) Listen for specific details and main idea from audio recordings, internet, and radio or television programmers. c) Appreciate the importance of effective listening in communication.	Why should we look at people’s faces as they speak? How are audio stories different from a storybook?	Learner is guided to: • Practice using expressions such as fixed phrases: out of breath; similes: as bright as day; metaphor: Lodunga is a deer. He runs very fast. ; Idioms: get a head start; proverbs: look before you leap and phrasal verbs such as pass round.	Digital devices, posters, charts NPE Grd 6 TG pg. 120-123 NPE Grd 6 Learners Bk. pg. 103-104	Sentence constructio n, peer assessment , recitation
	2	Reading	Intensive reading – digital stories	By the end of the lesson, the learner should be able to: a) Identify words, phrases and proverbs from a digital text. b) Create mental images from viewed, heard or read text. c) Acknowledge the role of reading comprehension in lifelong learning.	How do you make predictions about a story you are about to read? How are digital stories different from storybooks?	Learner is guided to: • Participate in a reader’s theatre and read solo or choral poems in small groups. • Make predictions about a text by observing the cover or title. • Make connections between the pictures in a text and real life situations.	Digital devices, pictures, photographs NPE Grd 6 TG pg. 124-127 NPE Grd 6 Learners Bk. pg. 105-106	Learner summary of content, answering oral and written questions
	3			By the end of the lesson, the learner should be able to: a) Use contextual clues to infer the meaning of words and expressions. b) Answer direct and inferential questions correctly for comprehension. c) Acknowledge the role of reading comprehension in lifelong learning.	How do you make predictions about a story you are about to read? How are digital stories different from storybooks?	Learner is guided to: • Summarize important ideas and restate them in own words. • Retell events in a poem chronologically. • Use contextual clues to infer the meaning of expressions such as fixed phrases, similes, metaphors, idioms: proverbs and phrasal verbs.	Digital devices, pictures, photographs NPE Grd 6 TG pg. 124-127 NPE Grd 6 Learners Bk. pg. 105-106	Learner summary of content, answering oral and written questions

						• Summarize events in a text through retelling.
	4	Grammar in use	Interrogatives	By the end of the lesson, the learner should be able to: a) Identify interrogatives in print or digital texts. b) Use interrogatives correctly to express different meanings. c) Assess the appropriateness of conjunctions used in print and digital texts.	How do we form questions? Why do we ask questions?	Learners are guided to: • Discuss in pairs or groups which among the following words are not interrogatives: whip, how, what, when, whom, why which, whisper, where and whole	Photographs, charts, video clips NPE Grd 6 TG pg. 128-130 NPE Grd 6 Learners Bk. pg. 106-107	Writing sentence from substitutio n table and language game
5	1			By the end of the lesson, the learner should be able to: a) Identify interrogatives in print or digital texts. b) Use interrogatives correctly to express different meanings. c) Assess the appropriateness of conjunctions used in print and digital texts.	How do we form questions? Why do we ask questions?	Learners are guided to: • Practice using when clauses with present tense to show the future: ‘When are you going to school’ in pairs. • Collaborate with peers to use interrogatives in sentences correctly.	Photographs, charts, video clips NPE Grd 6 TG pg. 128-130 NPE Grd 6 Learners Bk. pg. 106-107	Writing sentence from substitutio n table and language game
	2			By the end of the lesson, the learner should be able to: a) Identify interrogatives in print or digital texts. b) Use interrogatives correctly to express different meanings. c) Assess the appropriateness of conjunctions used in print and digital texts.	How do we form questions? Why do we ask questions?	Learners are guided to: • Create lists of interrogative sentences using words related to the theme. • Type the list using a computer, laptop or tablet in groups and display his or her work to peers.	Photographs, charts, video clips NPE Grd 6 TG pg. 128-130 NPE Grd 6 Learners Bk. pg. 106-107	Writing sentence from substitutio n table and language game
	3	Writing	Spelling (synonyms and antonyms)	By the end of the lesson, the learner should be able to: a) Identify synonyms and antonyms correctly for writing fluency.	How do we tell the meaning of unfamiliar words?	Learner is guided to: • Listen/watch a video recording and identify words with synonyms and antonyms.	Newspapers, magazines, web resources, video clips, digital devices	Peer assessment , sentence constructio n, portfolio

b) Use synonyms, and antonyms correctly in sentences.

c) Advocate the use of a rich vocabulary in writing.

Which are some of the words with the same or opposite meaning?

• Form sentences in pairs or small groups using synonyms and antonyms.

• Identify synonyms and antonyms from newspapers, magazines or the internet in pairs and create a crossword puzzle.

• Display their work on posters.

NPE Grd 6 TG pg. 131-133

NPE Grd 6

Learners Bk. pg. 108-110

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

a) Identify synonyms and antonyms correctly for writing fluency.

b) Use synonyms, and antonyms correctly in sentences.

c) Advocate the use of a rich vocabulary in writing.

How do we tell the meaning of unfamiliar words?

Which are some of the words with the same or opposite meaning?

Learner is guided to:

• Listen/watch a video recording and identify words with synonyms and antonyms.

• Form sentences in pairs or small groups using synonyms and antonyms.

• Identify synonyms and antonyms from newspapers, magazines or the internet in pairs and create a crossword puzzle.

• Display their work on posters.

Newspapers, magazines, web resources, video clips, digital devices

NPE Grd 6 TG pg. 131-133

NPE Grd 6

Learners Bk. pg. 108-110

Peer

assessment

, sentence constructio n, portfolio

ENVIRON

MENTAL CONSERVA TION

Listening and

speaking: Pronunciation and vocabulary

By the end of the lesson, the

learner should be able to:

a) Listen for specific details such as sounds words, expressions such as proverbs, similes, metaphors, fixed phrases and idioms for effective oral communication.

b) explain how our hands, faces and eyes communicate

c) Judge the appropriateness of non-verbal cues in a conversation or video recordings.

Why should

we speak at the right speed, accurately and with expression?

How do our faces, hands and eyes help us communicate better?

Learner is guided to:

• Say words and phrases with the sounds / ʒ/ / ʤ/ correctly.

• Recite poems with words that have the sounds /ʒ/ / ʤ/.

• Listen for specific details such as fixed phrases – as long as, similes – as wide as the sky; metaphor – He is a tortoise. He walks slowly!; idioms – a drop in the ocean, proverbs – Prevention is better than cure; phrasal verbs

– clean up, cut down

Digital devices,

video clips, photographs, charts, posters

NPE Grd 6 TG pg. 134-136

NPE Grd 6

Learners Bk. pg. 111-113

Peer

assessment

, giving speeches, mock interview


2			By the end of the lesson, the learner should be able to: a) Make oral presentations such as speeches accurately, with minimal hesitations and with expressions. b) identify various non- verbal cues in an oral presentation c) Judge the appropriateness of non-verbal cues in a conversation or video recordings.	Why should we speak at the right speed, accurately and with expression? How do our faces, hands and eyes help us communicate better?	Learner is guided to: • Say words and phrases with the sounds / ʒ/ / ʤ/ correctly. • Recite poems with words that have the sounds /ʒ/ / ʤ/. • Listen for specific details such as fixed phrases – as long as, similes – as wide as the sky; metaphor – He is a tortoise. He walks slowly!; idioms – a drop in the ocean, proverbs – Prevention is better than cure; phrasal verbs – clean up, cut down	Digital devices, video clips, photographs, charts, posters NPE Grd 6 TG pg. 134-136 NPE Grd 6 Learners Bk. pg. 111-113	Peer assessment , giving speeches, mock interview
3			By the end of the lesson, the learner should be able to: a) Use non-verbal cues appropriately to enhance fluency. b) identify various non- verbal cues in an oral presentation c) Judge the appropriateness of non-verbal cues in a conversation or video recordings.	Why should we speak at the right speed, accurately and with expression? How do our faces, hands and eyes help us communicate better?	Learner is guided to: • Speak on topics based on content from other areas. • Participate in mock interviews in small groups. • View videos on recitations of poems or narration of narratives. • Recite choral and solo verses related to the theme. • Participate in a reader’s theatre in which he or she reads poems and narratives in groups.	Digital devices, video clips, photographs, charts, posters NPE Grd 6 TG pg. 134-136 NPE Grd 6 Learners Bk. pg. 111-113	Peer assessment , giving speeches, mock interview
4	Reading	Intensive reading	By the end of the lesson, the learner should be able to: a) Identify words, phrases, and proverbs used in a song or poem. b) Uses stress and rhythm correctly while reading lines	Why do some people enjoy songs more than reading a book? How are digital stories	Learner is guided to: • Participate in a reader’s theatre and read solo or choral poems in small groups. • Sing along as a video of poetry recitation or song	Digital resources, video clips, posters, charts, photographs NPE Grd 6 TG pg. 137-139	Recitation s Answering questions

				and words in a poem or song. c) Advocate the importance of correct stress and rhythm in communication.	different from printed storybooks?	plays with the lyrics provided.	NPE Grd 6 Learners Bk. pg. 114-116
7	1			By the end of the lesson, the learner should be able to: a) Identify and Create mental images from viewed, heard, or read poem events, characters, or places in a text. b) Use contextual clues to infer the meaning of words and expressions in a song or poem. c) Advocate the importance of correct stress and rhythm in communication.	Why do some people enjoy songs more than reading a book? How are digital stories different from printed storybooks?	Learner is guided to: • Make predictions about events in a poem by observing the cover or title. • Answer questions from a comprehension passage. • View pictures or events in a poem or song and compare them to real-life situations in pairs. • Infer the meaning of new words and expressions such as fixed phrases, proverbs, idioms, phrasal verbs and similes from the way they have been used in a text.	Digital resources, video clips, posters, charts, photographs NPE Grd 6 TG pg. 137-139 NPE Grd 6 Learners Bk. pg. 114-116	Recitation s Answering questions
	2			By the end of the lesson, the learner should be able to: a) Use contextual clues to infer the meaning of words and expressions in a song or poem. b) Answer direct and inferential questions correctly from a song or poem. c) Advocate the importance of correct stress and rhythm in communication.	Why do some people enjoy songs more than reading a book? How are digital stories different from printed storybooks?	Learner is guided to: • Make predictions about events in a poem by observing the cover or title. • Answer questions from a comprehension passage. • View pictures or events in a poem or song and compare them to real-life situations in pairs. • Infer the meaning of new words and expressions such as fixed phrases, proverbs, idioms, phrasal verbs and similes from the way they have been used in a text.	Digital resources, video clips, posters, charts, photographs NPE Grd 6 TG pg. 137-139 NPE Grd 6 Learners Bk. pg. 114-116	Recitation s Answering questions
	3	Grammar in use	Question tags	By the end of the lesson, the learner should be able to:	What is a question tag?	Learner is guided to:	Posters Web resources	Peer assessment , filling

a) Identify tag questions from a print or digital text for information.

b) Form tag questions from verbs to be, verbs to have, verbs to do, and modals.

c) Use tag questions correctly in oral and written texts.

d) Appreciate the importance of well-formed

sentences in communication.

How do we form a question tag?

• Identify the verbs to be, verbs to have verbs to do and modals.

• Form tag questions using verbs to be, verbs to have verbs to do and modals.

• Apply rules when forming tag questions. For example, a positive statement results in a negative tag question and vice versa.

NPE Grd 6 TG pg. 141-143

NPE Grd 6

Learners Bk. pg. 117-118

gaps,

dialogue completion

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

a) Identify tag questions from a print or digital text for information.

b) Form tag questions from verbs to be, verbs to have, verbs to do, and modals.

c) Use tag questions correctly in oral and written texts.

d) Appreciate the importance of well-formed

sentences in communication.

What is a question tag?

How do we form a question tag?

Learner is guided to:

• Search for examples of question tags on the Web.

• Practice using tag questions in dialogues and conversations.

• Make posters featuring tag questions in small groups and display them in class.

Posters

Web resources

NPE Grd 6 TG pg. 141-143

NPE Grd 6

Learners Bk. pg. 117-118

Peer

assessment

, filling gaps, dialogue completion

Writing

Functional

writing (personal journal)

By the end of the lesson, the

learner should be able to:

a) Identify all the components of a personal journal.

b) read a sample of a personal journal.

c) Judge the correctness sentences, relevance to the topic and the format of a personal journal.

How do we

record important occasions or dates in our lives?

Why do we keep journals and diaries?

Learner is guided to:

• Identify all the components of a personal journal in small groups.

• Read a sample personal journal in small groups.

• Create a personal journal for seven days in pairs.

• Peer-edit the personal journals – different pairs exchange their journals for

editing.

Sample personal

journals

NPE Grd 6 TG pg. 143-145

NPE Grd 6

Learners Bk. pg. 119-120

Peer

assessment

, portfolio, standard writing assessment

					• Revise personal journals. • Display the personal journals in class, on the school notice board, internet among others.
2			By the end of the lesson, the learner should be able to: a) Identify all the components of a personal journal. b) Use the correct format to create a personal journal. c) Judge the correctness sentences, relevance to the topic and the format of a personal journal.	How do we record important occasions or dates in our lives? Why do we keep journals and diaries?	Learner is guided to: • Identify all the components of a personal journal in small groups. • Read a sample personal journal in small groups. • Create a personal journal for seven days in pairs. • Peer-edit the personal journals – different pairs exchange their journals for editing. • Revise personal journals. • Display the personal journals in class, on the school notice board, internet among others.	Sample personal journals NPE Grd 6 TG pg. 143-145 NPE Grd 6 Learners Bk. pg. 119-120	Peer assessment , portfolio, standard writing assessment
3	MONEY- TRADE	Listening and speaking: pronunciation and Vocabulary – (intensive Listening)	By the end of the lesson, the learner should be able to: a) Identify specific sounds, words, phrases, and sentences from a text. b) Listen to a short text and rewrite it accurately. c) Advocate the need for attentive listening during oral comprehension.	Why should we listen carefully? What messages do we obtain from similes and proverbs? Which proverbs and similes are you familiar with?	Learner is guided to: • Dictate a story featuring proverbs and similes, pick them out and list them in pairs. • Rewrite a short text in his or her own words accurately.	Digital devices NPE Grd 6 TG pg. 147-149 NPE Grd 6 Learners Bk. pg. 121-122	Retelling a story Sentence constructio n
4			By the end of the lesson, the learner should be able to:	Why should we listen carefully?	Learner is guided to: • Read a written version of what they have listened to.	Digital devices NPE Grd 6 TG pg. 147-149	Retelling a story

a) Identify specific sounds, words, phrases, and sentences from a text.

b) Listen to a short text and rewrite it accurately.

c) Use similes, proverbs, fixed phrases idioms and metaphors in oral contexts correctly.

d) Advocate the need for attentive listening during oral comprehension.

What messages do we obtain from similes and proverbs?

Which proverbs and similes are you familiar with?

• Predict the likely outcome of events in a listening text.

• Pick out information such as amounts, dates, time, facts, characters, and the sequence of events from an oral text.

NPE Grd 6

Learners Bk. pg. 121-122

Sentence

constructio n

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

a) Identify similes, proverbs, fixed phrases idioms and metaphors in oral contexts

b) Use similes, proverbs, fixed phrases idioms and metaphors in oral contexts correctly.

c) Advocate the need for attentive listening during oral comprehension.

Why should we listen carefully?

What messages do we obtain from similes and proverbs?

Which proverbs and similes are you familiar with?

Learner is guided to:

• Use fixed phrases such as at once, no entry, similes

such as sell like hot cakes, as happy as a hippo; metaphors such as – Chebet is a hare.

She is so clever. Proverbs such as A stitch in time saves nine, grow on trees, idioms such as back to square one, to cut corners and phrasal verbs such as

count on, give in and give back.

Digital devices

NPE Grd 6 TG pg. 147-149

NPE Grd 6

Learners Bk. pg. 121-122

Retelling a

story Sentence constructio n

Reading

Extensive

reading

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

a) Select appropriate reading texts from print or digital collections.

b) Read a variety of print or digital texts for enjoyment and general understanding.

c) Appreciate the importance of extensive reading in lifelong learning.

How do we obtain information from a newspaper, book, or magazine quickly?

Which materials do

you enjoy reading?

Learner is guided to:

• Skim various texts to find out the general idea.

• Scan a text to find specific details such as key words.

• Read a variety of texts of about (1251 to 1500 words) newspaper, magazines, grade appropriate digital/print texts, articles.

Collection of books, newspapers, magazines, digital resources

NPE Grd 6 TG pg. 150-152

NPE Grd 6

Learners Bk. pg. 122

Summary

of read materials and peer assessment

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

a) Select appropriate reading texts from print or digital collections.

b) Read a variety of print or digital texts for enjoyment and general understanding.

c) Appreciate the importance of extensive reading in lifelong learning.

Why do we enjoy reading some materials and not others?

Why should we read widely?

Learner is guided to:

• Collaborate with peers to establish a class library.

• Read print and non-print materials (websites and blogs) independently.

• Read newspapers, magazines poems, and class readers.

• Read digital versions of newspapers and magazines for information.

Collection of books, newspapers, magazines, digital resources

NPE Grd 6 TG pg. 150-152

NPE Grd 6

Learners Bk. pg. 122

Summary

of read materials and peer assessment

Grammar

in use

Word classes:

prepositions

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

a) Identify prepositions correctly in oral and written texts.

b) Use prepositions correctly in varied texts.

c) Judge the appropriateness of prepositions used in various texts.

How do we describe where people or objects

Learner is guided to:

• Identify prepositions of time such as since, before, until, about, during, past directions: such as above, across, below, after agent such as by, and with instrument such as with and by

• Collaborate with peers to create visuals demonstrating the use of various

prepositions.

Visuals such as posters, charts, pictures, photographs

NPE Grd 6 TG pg. 152-154

NPE Grd 6

Learners Bk. pg. 123-124

Discrimina

tion, gap filling and drawing

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

a) Identify prepositions correctly in oral and written texts.

b) Use prepositions correctly in varied texts.

c) Judge the appropriateness of prepositions used in various texts.

How do we describe where people or objects

Learner is guided to:

• Create crossword puzzles using prepositions in pairs or small groups.

• Create visuals to demonstrate the use of various prepositions in sentences.

• Create charts or posters showing where objects are in pairs or small groups. ‘For example, ‘The pupils are inside the classroom.’

Visuals such as posters, charts, pictures, photographs

NPE Grd 6 TG pg. 152-154

NPE Grd 6

Learners Bk. pg. 123-124

Discrimina

tion, gap filling and drawing

Writing

Spelling

(Affixes)

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

a) Recognize affixes used to change the form and meaning of words.

b) Form new words using prefixes and suffixes.

c) Spell words correctly for writing fluency.

d) Determine the correctness and appropriateness of affixes used in various texts.

Why is it important to spell words correctly?

Why is it difficult to spell some words?

How can we become better at spelling?

Learner is guided to:

• Identify words with prefixes and suffixes and use them to create puzzles and lists in pairs or groups.

• Form words using prefixes and affixes in small groups.

• Match words with their appropriate affixes (-un,- cian, – sion, – tion).

• Use mind maps to generate a list of words related and change their form by adding affixes.

• Create a crossword puzzle

using the words they have generated.

Charts, posters, dictionaries and word builders.

NPE Grd 6 TG pg. 155-158

NPE Grd 6

Learners Bk. pg. 125-127

Peer

assessment

, learner journal and portfolio

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

a) Recognize affixes used to change the form and meaning of words.

b) Form new words using prefixes and suffixes.

c) Spell words correctly for writing fluency.

d) Determine the correctness and appropriateness of affixes used in various texts.

Why is it important to spell words correctly?

Why is it difficult to spell some words?

How can we become better at spelling?

Learner is guided to:

• Identify words with prefixes and suffixes and use them to create puzzles and lists in pairs or groups.

• Form words using prefixes and affixes in small groups.

• Match words with their appropriate affixes (-un,- cian, – sion, – tion).

• Use mind maps to generate a list of words related and change their form by adding affixes.

• Create a crossword puzzle using the words they have generated.

Charts, posters, dictionaries and word builders.

NPE Grd 6 TG pg. 155-158

NPE Grd 6

Learners Bk. pg. 125-127

Peer

assessment

, learner journal and portfolio

Teachers' Resources

Grade 8 Free Resources: Assessment Exams, Notes & Schemes of WorkDownload

October 5, 2025 Maverick John Leave a comment

In need of free CBC Teaching and learning resources for Grade Eight? Worry no more. Download grade 8 CBC exams, notes, and schemes of work for free. Enhance your learning with comprehensive resources.

All the grade 8 resources are completely free of charge:

G7 AGRIC & NUT TERM 2 NOTES SAMPLE

CIRCULAR_ON_UNAUTHORIZED_PERSONS_IN_THE_EXAMINATION_CENTRES_DURING

G8 AGRIC & NUT TERM 2 NOTES SAMPLE

G8 CRE TERM 2 NOTES SAMPLE

G8 CREATIVE ARTS & SPORTS (2)

G8 CREATIVE ARTS & SPORTS

G8 CREATIVE ARTS & SPORTS-2 (2)

G8 CREATIVE ARTS & SPORTS-2

G8 CREATIVE ARTS TERM 2 NOTES SAMPLE

G8 INT SCI TERM 2 NOTES SAMPLE

G8 PRE TECH COMPLETE NOTES SAMPLE

G8 pretechnical NOTES-1 (2)

G8 pretechnical NOTES-1

G8- PRETECHNICAL STUDIES NOTES

G8 SOCIAL STUDIES (2)

G8 SOCIAL STUDIES

G8 SST COMPLETE NOTES SAMPLE

G8 T1 AGRIC & NUTRITION MIDTERM

G8 T1 CRE MIDTERM

G8 T1 CREATIVE ARTS MIDTERM

G8 T1 ENGLISH MIDTERM

G8 T1 INTEGRATED SCIENCE MIDTERM

MATHEMATICS GRADE 8 NOTES

Grade-8-mtp-Agriculture-and-Nutrition-Schemes-of-work-Term-2

Grade-8-mtp-Agriculture-and-Nutrition-Schemes-of-work-Term-2 (3)

Grade-8-mtp-Agriculture-and-Nutrition-Schemes-of-work-Term-2 (2)

grade-8-integrated-science-notes-term-1

GRADE_8_TERM_2_2024_RATIONALIZED_PRE_TECHNICAL_STUDIES_SCHEMES_OF

GRADE_8_TERM_2_2024_RATIONALIZED_PRE_TECHNICAL_STUDIES_SCHEMES_OF (3)

GRADE_8_TERM_2_2024_RATIONALIZED_PRE_TECHNICAL_STUDIES_SCHEMES_OF (2)

GRADE_8_TERM_2_2024_MENTOR_INTEGRATED_SCIENCE_SCHEMES_OF_WORK

GRADE_8_TERM_2_2024_MENTOR_INTEGRATED_SCIENCE_SCHEMES_OF_WORK (3)

GRADE_8_TERM_2_2024_MENTOR_INTEGRATED_SCIENCE_SCHEMES_OF_WORK (2)

GRADE.8.SOCIAL.STUDIES

GRADE.8.PRE-TECHNICAL.STUDIES

GRADE.8.MATHEMATICS

GRADE.8.IRE_

GRADE.8.INTEGRATED.SCIENCE

GRADE.8.ENGLISH

GRADE.8.CREATIVE.ARTS_.SPORTS

GRADE.8.CRE_

GRADE.8.AGRICULTURE.NUTRITION

GRADE 8 TERM 2 CREATIVE ARTS SCHEMES-1

GRADE 8 TERM 2 CREATIVE ARTS SCHEMES-1 (2)

GRADE 8 TERM 2 2024AGRI NUTRITION SCHEMES OF WORK

GRADE 8 TERM 2 2024AGRI NUTRITION SCHEMES OF WORK (3)

GRADE 8 TERM 2 2024AGRI NUTRITION SCHEMES OF WORK (2)

GRADE 8 TERM 2 2024 RATIONALIZED ENGLISH SCHEMES OF WORK

GRADE 8 TERM 2 2024 RATIONALIZED ENGLISH SCHEMES OF WORK (3)

GRADE 8 TERM 2 2024 RATIONALIZED ENGLISH SCHEMES OF WORK (2)

GRADE 8 TERM 2 2024 MTP SOCIAL STUDIES SCHEMES OF WORK

GRADE 8 TERM 2 2024 MTP SOCIAL STUDIES SCHEMES OF WORK (4)

GRADE 8 TERM 2 2024 MTP SOCIAL STUDIES SCHEMES OF WORK (3)

GRADE 8 TERM 2 2024 MTP SOCIAL STUDIES SCHEMES OF WORK (2)

GRADE 8 TERM 2 2024 MENTOR CRE SCHEMES OF WORK

GRADE 8 TERM 2 2024 MENTOR CRE SCHEMES OF WORK (3)

GRADE 8 TERM 2 2024 MENTOR CRE SCHEMES OF WORK (2)

GRADE 8 PHE

GRADE 8 MID TERM 1 2024 EXAMINATION SET 3

GRADE 8 MID TERM 1 2024 EXAMINATION SET 3 (2)

GRADE 8 MID TERM 1 2024 EXAMINATION SET 2

GRADE 8 MID TERM 1 2024 EXAMINATION SET 2 (2)

GRADE 8 JSS ET1 HOLIDAY ASSIGNMENT 2024

GRADE 8 END TERM 1 2024 EXAMINATION SET 1

GRADE 8 END TERM 1 2024 EXAMINATION SET 1 (2)

GRADE 8 CURRICULUM DESIGNS- VISUAL ARTS

GRADE 8 CURRICULUM DESIGNS- PHYSICAL EDUCATION

GRADE 8 CURRICULUM DESIGNS- PERFORMING ARTS

GRADE 8 CURRICULUM DESIGNS- MATHEMATICS

GRADE 8 CURRICULUM DESIGNS- LIFE SKILLS

GRADE 8 CURRICULUM DESIGNS- LIFE SKILLS (2)

GRADE 8 CURRICULUM DESIGNS- KISWAHILI-2

GRADE 8 CURRICULUM DESIGNS- KISWAHILI

GRADE 8 CURRICULUM DESIGNS- KISWAHILI (2)

GRADE 8 CURRICULUM DESIGNS- INTEGRATED SCIENCE-1

GRADE 8 CURRICULUM DESIGNS- INTEGRATED SCIENCE

GRADE 8 CURRICULUM DESIGNS- INDIGENOUS LANGUAGES

GRADE 8 CURRICULUM DESIGNS- HOME SCIENCE

GRADE 8 CURRICULUM DESIGNS- HOME SCIENCE (2)

GRADE 8 CURRICULUM DESIGNS- HEALTH EDUCATION

GRADE 8 CURRICULUM DESIGNS- FRENCH

GRADE 8 CURRICULUM DESIGNS- ENGLISH

GRADE 8 CURRICULUM DESIGNS- ENGLISH (2)

GRADE 8 CURRICULUM DESIGNS- BUSINESS STUDIES

GRADE 8 CURRICULUM DESIGNS- BUSINESS STUDIES (2)

GRADE 8 CURRICULUM DESIGNS- ARABIC

GRADE 8 CURRICULUM DESIGNS- AGRICULTURE

GRADE 8 APRIL 2024 HOLIDAY ASSIGNMENT

GRADE 8 MID TERM 1 2024 EXAMINATION SET 1

GRADE 8 MID TERM 1 2024 EXAMINATION SET 1 (2)

G8 T2 PRE TECH UPDATED SOW

G8 T2 KIS UPDATED SOW

G8 T2 INT SCI UPDATED SOW

G8 T2 ENG UPDATED SOW

G8 T2 CREATIVE ARTS UPDATED SOW

G8 T2 CRE UPDATED SOW

G8 T2 AGRIC & NUT UPDATED SOW

G8 T1 SOCIAL STUDIES MIDTERM

G8 T1 PRETECHNICAL STUDIES MIDTERM

Teachers' Resources

Latest Guides For Secondary School Set Books 2022-2026

October 5, 2025 Maverick John Leave a comment

Latest Guides For Secondary School Set Books 2022-2026

A DOLL’S EXCERPTS S1 Q.pdf
A DOLL’S HOUSE GUIDE SP.pdf
A SILENT SONGS KCSE QNS (2).pdf
AN ARTIST OF FLOATING WORLD GUIDE SP-1.pdf
BasicEducationActNo_14of2013 (2).pdf
BEMBEA YA MAISHA REVISION S3.pdf
BEMBEA YA MAISHA S2 Q.pdf
BLOSSOMS ESSAYS S1 Q.pdf
CHOZI LA HERI GUIDE SP.pdf
CHOZI LA HERI KCSE QNS.pdf
FATHERS OF NATIONS ESSAYS S1.pdf
FATHERS OF NATIONS ESSAYS S2.pdf
FATHERS OF NATIONS EXCERPTS S1.pdf
FINAL_CIRCULAR_ON_DEPLOYMENT_OF_PRI_SCH_TCHRS_TO_JUNIOR_SEC_SCHOOLS.pdf
FORM 2 OPENER EXAM.pdf
ISIMU JAMII REVISION S1.pdf
KCSE CLOZE-TEST REVISION S1.pdf
KCSE ENGLISH PASSAGES S1.pdf
KCSE ENGLISH PP1 REVISION S1.pdf
KCSE ENGLISH PP1 REVISION S2.pdf
KCSE ENGLISH PP2 REVISION S1.pdf
KCSE ENGLISH PP2 REVISION S2.pdf
KCSE ENGLISH PP3 REVISION S1.pdf
KCSE GRAMMAR REV S1.pdf
KCSE INHERITANCE ESSAYS.pdf
KCSE POETRY REVISION S1.pdf
KCSE USHAIRI REVISION S1.pdf
MAPAMBAZUKO YA MACHWEO QNS-1.pdf
MOE-NEW-SETBOOKS(1).pdf
MWONGOZO WA BEMBEA YA MAISHA SAMPLE-1.pdf
MWONGOZO WA MAPAMBAZUKO SAMPLE-1.pdf
NGUU ZA JADI GUIDE SAMPLE-1.pdf
ORAL LITERATURE S1.pdf
PARLIAMENT OF OWLS GUIDE SP-1.pdf

Teachers' Resources

Free class 8 revision papers pdf

October 5, 2025 Maverick John Leave a comment

Are you searching for free Class 8 KCPE past papers, predictions, topicals, revisions, Jesma series and many other materials? Yes. You have found the right site for free revision materials. You can now download all these resources here at no cost.

Also remember to visit the TEACHERS’ RESOURCES PORTAL for more primary and secondary resources (including notes, schemes of work, termly exams, revision papers, predictor exams, lesson plans, topical resources and many more).

FREE CLASS 8 KCPE PAST PAPERS, PREDICTOR EXAMS AND OTHER REVISION MATERIALS.

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Teachers' Resources

Life Skills Grade 7 CBC Free Schemes of Work

October 5, 2025 Maverick John Leave a comment

GRADE 7 LIFE SKILLS EDUCATION SCHEMES OF WORK

NAME OF THE TEACHER SCHOOL YEAR TERM III

Week	LSN	strand	Sub-strand	Specific Learning Outcomes	Key Inquiry Question(s)	Learning Experiences	Learning Resources	Assessment Methods	Refl
1	1	DECISION MAKING SKILLS	Decision-Making Process	By the end of the lesson, the learner should be able to: a) describe decision-making process that leads to desirable actions or behaviour b) display values necessary in making appropriate decisions in their day-to-day life c) appreciate the importance of effective decision-making in different situations	1. Why do I make my decisions? 2. How has effective decision- making helped me in my life?	The learner is guided to: • search in pairs, using digital devices the meaning of decision-making processes and present in class • explore and analyze in groups situations that require decision-making • engage in puzzles and games like chess that demand multiple decisions to solve problems	• Vetted digital resources- TV/video/films/slides/ Internet sources • Approved textbooks and other printed resources • Library • Display boards • Drawing charts *Thriving Life Skills Grade 7 T.G Pg. 95-100* *Thriving Life skills Education Grade 7 P.b Pg.87-92*	a) checklist b) project c) written tests d) oral questions e) aural questions
2	1		Creative Thinking Skills	By the end of the lesson, the learner should be able to: a) describe different situations that require creative thinking b) Play games that promote creativity c) Exhibit values that foster creative thinking in different situations.	1. Why is creative thinking important for me? 2. How can I be a good creative thinker?	The learner is guided to: • use digital devices to search for the meaning of the term creative thinking • play games in small groups such as the jigsaw puzzle, snake and ladder and other relevant games that promote creativity	• Vetted digital resources- TV/video/films/slides/ Internet sources • Approved textbooks and other printed resources • Library • Display boards • Drawing charts *Thriving Life Skills Grade 7 T.G Pg. 101-106* *Thriving Life skills Education Grade 7 P.b Pg.93-99*	a) checklist b) project c) written tests d) oral questions e) aural questions
3	1		Creative Thinking Skills	By the end of the lesson, the learner should be able to: a) describe different situations that require creative thinking b) display creative thinking skills in different situations c) Exhibit values that foster creative thinking in different situations.	1. Why is creative thinking important for me? 2. How can I be a good creative thinker?	The learner is guided to: Read and discuss real-life stories from selected hard or soft copies, • watch video clips on fostering values in creativity, and discuss in class.	• Vetted digital resources- TV/video/films/slides/ Internet sources • Approved textbooks and other printed resources • Library • Display boards • Drawing charts *Thriving Life Skills Grade 7 T.G Pg. 101-106* *Thriving Life skills Education Grade 7 P.b Pg.93-99*	a) checklist b) project c) written tests d) oral questions e) aural questions
4	1		Critical Thinking	By the end of the lesson, the learner should be able to: a) describe different situations that require critical thinking in their day- to-day lives b) Play games that enhance critical thinking c) Appreciate the need for critical thinking in their everyday life.	1. What shows I am a consistent critical thinker? 2. What shows that I manage my time well?	The learner is guided to: • in groups solve number or word puzzles and discuss how critical thinking was applied • use digital devices to search for scenarios or case studies that show enhancement of critical thinking and present in class	• Vetted digital resources- TV/video/films/slides/ Internet sources • Approved textbooks and other printed resources • Library,Display boards • Drawing charts *Thriving Life Skills Grade 7 T.G Pg. 107-112* *Thriving Life skills Education Grade 7 P.b Pg.100-104*	a) checklist b) project c) written tests d) oral questions e) aural questions
5	1		Critical Thinking	By the end of the lesson, the learner should be able to: a) describe different situations that require critical thinking in their day- to-day lives b) apply critical thinking in their day-to-day lives c) Appreciate the need for critical thinking in their everyday life.	1. What shows I am a consistent critical thinker? 2. What shows that I manage my time well?	The learner is guided to: • role-play scenarios that require critical thinking skills and discuss the importance of being critical • discuss common instances that depict challenges in time management in the school community and note them down.	• Vetted digital resources- TV/video/films/slides/ Internet sources • Approved textbooks and other printed resources • Library, Display boards • Drawing charts *Thriving Life Skills Grade 7 T.G Pg. 107-112* *Thriving Life skills Education Grade 7 P.b Pg.100-104*	a) checklist b) project c) written tests d) oral questions e) aural questions
6	1		Problem- Solving Skills	By the end of the lesson, the learner should be able to: a) describe the term problem-solving as it relates to day-to-day life b) State the steps involved in problem solving c) exhibit values necessary for problem solving in their day-to-day lives	1. What guides me when solving my problems in life? 2. Why are skills of problem solving important in my life?	The learner is guided to: • buzz in pairs on the meaning of problem- solving • discuss in small groups some problems they face in their lives, and make presentations in class • search in groups using digital devices the steps used in problem-solving, and present in class	• Vetted digital resources- TV/video/films/slides/ Internet sources • Approved textbooks and other printed resources • Library,Display boards • Drawing charts *Thriving Life Skills Grade 7 T.G Pg. 113-117* *Thriving Life skills Education Grade 7 P.b Pg.105-107*	a) checklist b) project c) written tests d) oral questions e) aural questions
7	1		Problem- Solving Skills	By the end of the lesson, the learner should be able to: a) describe the term problem-solving as it relates to day-to-day life b) demonstrate ways of solving problems in their day-to-day lives c) exhibit values necessary for problem solving in their day-to-day lives	1. What guides me when solving my problems in life? 2. Why are skills of problem solving important in my life?	The learner is guided to: • search in groups using digital devices the steps used in problem-solving, and present in class • explore and analyze real-life stories depicting poor and excellent problem-solving skills and discuss in class • perform skits on problem solving and discuss the values displayed in class	• Vetted digital resources- TV/video/films/slides/ Internet sources • Approved textbooks and other printed resources • Library • Display boards • Drawing charts *Thriving Life Skills Grade 7 T.G Pg. 113-117* *Thriving Life skills Education Grade 7 P.b Pg.107-108*	a) checklist b) project c) written tests d) oral questions e) aural questions
8-9	END TERM ASSESSMENT/CLOSING

Teachers' Resources

KCSE Topical Questions and Answers

October 5, 2025 Maverick John Leave a comment

KCSE Topical Questions and Answers {The Latest & Best Collection}: Download all the KCSE Topical Questions and Answershere for all Subjects:

Key: A = Answers and Q = Questions

Also see: KCSE Topical Revision Resources For All Subjects

AGRICULTURE KCSE TOPICAL QUESTIONS & ANSWERS

AGRICULTURAL ECONOMICS IV

AGRICULTURE ECONOMICS

AGROFORESTRY

CROP PRODUCTION I (2)

CROP PRODUCTION I

CROP PRODUCTION II

CROP PRODUCTION III (2)

CROP PRODUCTION III

CROP PRODUCTION IV

CROP PRODUCTION V (2)

CROP PRODUCTION V

FACTORS WHICH INFLUENCE AGRICULTURE (2)

FACTORS WHICH INFLUENCE AGRICULTURE

FARM POWER AND MACHINERY (2)

FARM POWER AND MACHINERY

FARM TOOLS AND EQUIPMENT (2)

FARM TOOLS AND EQUIPMENT

FORAGE CROPS

INTRODUCTION TO AGRICULTURE

LIVESTOCK HEALTH II (2)

LIVESTOCK HEALTH II

LIVESTOCK HEALTH III

LIVESTOCK PRODUCTION I (2)

LIVESTOCK PRODUCTION I (3)

LIVESTOCK PRODUCTION I

LIVESTOCK PRODUCTION III (2)

LIVESTOCK PRODUCTION III

LIVESTOCK PRODUCTION IV

LIVESTOCK PRODUCTION V

SOIL FERTILITY II

WATER SUPPLY

WEEDS AND WEED CONTROL (2)

WEEDS AND WEED CONTROL

BIOLOGY KCSE TOPICAL QUESTIONS & ANSWERS

KCSE Topical Questions & Answers for All Subjects

KCSE Topical Questions & Answers for all Subjects

KCSE Topical Revision Resources per topic for all Subjects in F1-4

KCSE topical questions and answers (All subjects)

https://newsblaze.co.ke/kcse-topical-questions-and-answers-all-subjects/

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Teachers' Resources

Form 1, 2, 3 and 4 Exams For all subjects plus answers- 2023/2024

October 5, 2025 Maverick John Leave a comment

Form 1, 2, 3 and 4 Exams For all subjects plus answers- 2023/2024

Teachers' Resources

Updated Grade 4 CBC Schemes of Work- Term 1, 2 & 3

October 5, 2025 Maverick John Leave a comment

Updated Grade 4 CBC Schemes of Work – Term 1, 2 & 3

Discover the latest Grade 4 CBC Schemes of Work for Term 1, 2 & 3. Ensure effective curriculum planning for your students. Download the free grade four schemes of work here:

Teachers' Resources

Grade 4 revision papers 2021

October 5, 2025 Maverick John Leave a comment

Grade 4 CBC Assessment Exams Plus Marking Schemes are now available here for free and unlimited downloads. Get all the CBC resources for both teachers and learners on this site at no cost. More CBC materials can be found here; TEACHERS’ FREE RESOURCES PORTAL.

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Form 2 past papers with answers

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Looking for Two (2) comprehensive exams? look no further. Download all the updated Form 2 exams with marking schemes here. Check the TEACHERS’ RESOURCES PORTAL for more free resources.

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CBC Grade 7 Pre Technical Schemes of Work Free Editable Word, PDF Downloads

October 5, 2025 Maverick John Leave a comment

CBC Grade 7 Pre Technical Schemes of Work Free Editable Word, PDF Downloads

GRADE 7 KLB TOP SCHOLAR PRE- TECHNICAL SCHEMES OF WORK TERM 3

SCHOOL…………………………… TEACHER’S NAME………………………………………. TERM 3 YEAR

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

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Social Studies Grade 6 CBC Free Schemes of Work

October 5, 2025 Maverick John Leave a comment

GRADE 6 SPORTLIGHT SOCIAL STUDIES

SCHEME OF WORK TERM 3

SCHOOL	GRADE	LEARNING AREA	TERM	YEAR
	GRADE 6	SOCIAL STUDIES	3	2022

Week	Lesson	Strand	Sub-strand	Specific-Learning outcomes	Learning Experience	Key Inquiry Question(S)	Learning Resources	Assessment Methods	Reflection
1	1	Political Systems and Governance	Traditional forms of Government among the Buganda and Nyamwezi	By the end of the lesson, the learner should be able to: a) Identify the administrative units that make up the Buganda Kingdom. b) Explain the roles of Kabaka. c) Describe how the Buganda Kingdom was ruled in the past. d) Sing a song about the Buganda governance structure. e) Have fun and enjoy singing a song about the Buganda kingdom.	Learners are guided to: -Identify the administrative units that make up the Buganda Kingdom. -Explain the roles of Kabaka. -Describe how the Buganda Kingdom was ruled in the past. -Sing a song about the Buganda governance structure	How was the community ruled in the past? How was Buganda Kingdom ruled in the past?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 139-141 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Political Systems and Governance	Comparison between the Buganda and Nyamwezi traditional forms of government	By the end of the lesson, the learner should be able to: a) Identify the similarities between the Buganda and Nyamwezi Kingdom. b) Identify the values of good governance among the Nyamwezi. c) Recite the poem on learner’s book. d) Enjoy reciting the poem.	Learners are guided to: -Identify the similarities between the Buganda and Nyamwezi Kingdom. -Identify the values of good governance among the Nyamwezi. -Recite the poem on learner’s book.	What are the similarities between the Buganda and Nyamwezi Kingdom?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 142-144 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	3	Political Systems and Governance	Differences between the Buganda and Nyamwezi traditional forms of government.	By the end of the lesson, the learner should be able to: a) Identify the differences between the Buganda and Nyamwezi traditional forms of government. b) Illustrate the governance structure among the Buganda and Nyamwezi on a chart. c) Display the chart at the Social Studies corner.	Learners are guided to: -Identify the differences between the Buganda and Nyamwezi traditional forms of government. -Illustrate the governance structure among the Buganda and Nyamwezi on a chart.	What are the differences between the Buganda and Nyamwezi traditional forms of government?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 144-145 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
2	1	Political Systems and Governance	Aspects of good governance in traditional societies	By the end of the lesson, the learner should be able to: a) Discuss the aspects of good governance in traditional societies. b) Role ply the conversation on learner’s book. c) Have fun and enjoy role playing the conversation.	Learners are guided to: -Discuss the aspects of good governance in traditional societies. -Role ply the conversation on learner’s book.	What aspects of good governance have you learnt?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 145-147 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Political Systems and Governance	Regional Co-operations in Eastern Africa; Objectives of the East African Community.	By the end of the lesson, the learner should be able to: a) Read the newspaper article on learner’s book. b) List the objectives of the East African Community. c) Model member states of the Eastern African Community as shown on learner’s book. d) Have fun and enjoy modelling member states of the East African Community.	Learners are guided to: -Read the newspaper article on learner’s book. List the objectives of the East African Community. -Model member states of the Eastern African Community as shown on learner’s book	What are the objectives of the East African Community?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 147-149 Atlas Photographs Pictures Video clips Charts Realia Computing devices	Oral questions Oral Report Observation
	3	Political Systems and Governance	Benefits of the East African Community to Member States	By the end of the lesson, the learner should be able to: a) Identify the benefits of the East African Community to Member States. b) Read the story on learner’s book and answer the questions that follow. c) Create a poster on benefits of the East African Community. d) Appreciate the benefits of the East African Community to Member States.	Learners are guided to: -Identify the benefits of the East African Community to Member States. -Read the story on learner’s book and answer the questions that follow. -Create a poster on benefits of the East African Community.	What are the benefits of the East African Community to Member States?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 150-151 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
3	1	Political Systems and Governance	Challenges facing East African Community	By the end of the lesson, the learner should be able to: a) Discuss the challenges facing East African Community. b) Find out from appropriate sources the challenges facing the East African Community. c) Sing a song about the challenges facing East African Community. d) Have fun and enjoy singing a song.	Learners are guided to: -Discuss the challenges facing East African Community. -Find out from appropriate sources the challenges facing the East African Community. -Sing a song about the challenges facing East	What are the challenges facing East African Community?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 152-152 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Political Systems and Governance	Solutions to challenges facing the East African Community	By the end of the lesson, the learner should be able to: a) Discuss possible solutions to the challenges facing the East African Community. b) Complete the table on learner’s book by matching the solutions to the challenges. c) Sing the East African Anthem. d) Appreciate the solutions to challenges facing the East African Community	Learners are guided to: -Discuss possible solutions to the challenges facing the East African Community. -Complete the table on learner’s book by matching the solutions to the challenges. -Sing the East African Anthem.	What are the solutions to challenges facing the East African Community?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 153-155 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	3	Political Systems and Governance	Citizenship; Rights and responsibilities of a Kenyan citizen	By the end of the lesson, the learner should be able to: a) Study the pictures on learner’s book. b) Discuss the rights and responsibilities of a Kenyan Citizen. c) Make flashcards about the rights and responsibilities of a Kenyan citizen. d) Appreciate the importance of the rights and responsibilities of a Kenyan citizen.	Learners are guided to: -Study the pictures on learner’s book. -Discuss the rights and responsibilities of a Kenyan Citizen. -Make flashcards about the rights and responsibilities of a Kenyan citizen.	What are the rights and responsibilities of a Kenyan citizen?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 155-157 Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
4	1	Political Systems and Governance	Values of a good citizen	By the end of the lesson, the learner should be able to: a) Identify the values of a good citizen. b) Explain how to promote values of a good citizen. c) Create posters about the values of a good citizen. d) Appreciate the values of a good citizen.	Learners are guided to: -Identify the values of a good citizen. -Explain how to promote values of a good citizen. -Create posters about the values of a good citizen	How can we demonstrate good citizenship?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 158-160 Atlas Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Political Systems and Governance	Human Rights; Classification of human rights	By the end of the lesson, the learner should be able to: a) Define human rights. b) Identify human rights enjoyed by the people. c) Classify the rights they have identified as social, economic or political rights. d) Have fun and enjoy making a human rights wheel	Learners are guided to: -Define human rights. -Identify human rights enjoyed by the people. -Classify the rights they have identified as social, economic or political rights.	What is the meaning of human rights?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 161-163 Pictures Video clips Computing devices	Oral questions Oral Report Observation
	3	Political Systems and Governance	Ways in which human rights are violated in society.	By the end of the lesson, the learner should be able to: a) Identify ways in which human rights are violated in society. b) Make a chart on ways in which human rights are violated in the society. c) Have fun and enjoy making a chart.	Learners are guided to: -Identify ways in which human rights are violated in society. -Make a chart on ways in which human rights are violated in the society	How are human rights are violated in society?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 163-165 Video clips Charts Realia Computing devices	Oral questions Oral Report Observation
5	1	Political Systems and Governance	Peace and Conflict Resolution; Causes of conflict in society	By the end of the lesson, the learner should be able to: a) Define conflict. b) Identify the causes of conflicts in society. c) Read the following case study on learner’s book on causes of conflicts in society. d) Appreciate the importance of peace.	Learners are guided to: -Define conflict. -Identify the causes of conflicts in society. -Read the following case study on learner’s book on causes of conflicts in society.	What are the causes of conflict in society?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 165-167 Pictures Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Political Systems and Governance	Peace and Conflict Resolution; Causes of conflict in society	By the end of the lesson, the learner should be able to: a) Search the internet or any other appropriate sources for a story on a conflict that happened in the society. b) Match the causes of conflict in column A to its description in column B c) Appreciate the importance of maintaining peace in the society.	Learners are guided to: -Search the internet or any other appropriate sources for a story on a conflict that happened in the society. -Match the causes of conflict in column A to its description in column B	How do we resolve conflicts peacefully?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 167-168 Pictures Video clips Charts Realia Computing devices	Oral questions Oral Report Observation
	3	Political Systems and Governance	Peaceful methods of resolving conflicts in society	By the end of the lesson, the learner should be able to: a) Identify peaceful methods of resolving conflicts in society. b) Role play how to resolve the situations. c) Have fun and enjoy role playing how to resolve different situations	Learners are guided to: -Identify peaceful methods of resolving conflicts in society -In pairs, to discuss peaceful ways of resolving conflicts stated on the cards. -Role play how to resolve the situations	How do we live peacefully with each other in school and society?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 168-170 Pictures Video clips Charts Realia Computing devices	Oral questions Oral Report Observation
6	1	Political Systems and Governance	Peaceful methods of resolving conflicts in society	By the end of the lesson, the learner should be able to: a) Discuss the causes of conflicts in the society. b) Match statements with their meaning on the peaceful methods of resolving conflicts in society. c) Appreciate peaceful methods of resolving conflicts in society.	Learners are guided to: -Discuss the causes of conflicts in the society. -Match statements with their meaning on the peaceful methods of resolving conflicts in society.	What are the peaceful methods of resolving conflicts in society?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 170-171 Pictures Video clips Maps Charts Computing devices	Oral questions Oral Report Observation
	2	Political Systems and Governance	Benefits of resolving conflicts peacefully in society	By the end of the lesson, the learner should be able to: a) Identify the benefits of resolving conflicts peacefully in society. b) Design posters on ways of promoting peace in Eastern Africa. c) Recite the poem on learner’s book. d) Appreciate the benefits of resolving conflicts peacefully in the society.	Learners are guided to: -Identify the benefits of resolving conflicts peacefully in society. -Design posters on ways of promoting peace in Eastern Africa. -Recite the poem on learner’s book.	What are the benefits of resolving conflicts peacefully in society?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 172-174 Photographs Pictures Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	3	Political Systems and Governance	Governance in Kenya; Sources of Government Revenue and Expenditure	By the end of the lesson, the learner should be able to: a) Explain the meaning of revenue. b) Give reasons why we should pay taxes to the government. c) Match the sources in column A with the examples in column B d) Appreciate the importance of paying revenue.	Learners are guided to: -Explain the meaning of revenue. -Give reasons why we should pay taxes to the government. -Match the sources in column A with the examples in column B	What is the meaning of revenue? Why should we pay taxes to the government?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 174-175 Pictures Video clips Maps Charts Computing devices	Oral questions Oral Report Observation
7	1	Political Systems and Governance	Ways in which the National and County Governments in Kenya spend their revenue	By the end of the lesson, the learner should be able to: a) Study the pictures on learner’s book. b) Discuss ways in which the National and County Governments in Kenya spend their revenue. c) Draw the pictures on learner’s book. d) Appreciate the ways in which the National and County Governments in Kenya spend their revenue	Learners are guided to: -Study the pictures on learner’s book. -Discuss ways in which the National and County Governments in Kenya spend their revenue. -Draw the pictures on learner’s book.	What are the ways in which the National and County Governments in Kenya spend their revenue?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 176-177 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	2	Political Systems and Governance	Ways in which the National and County Governments in Kenya spend their revenue	By the end of the lesson, the learner should be able to: a) Find out from the internet, textbooks or any appropriate materials other ways in which the National and County Governments in Kenya spend their revenue. b) Make a poster of paying taxes to the Government of Kenya. c) Appreciate the importance of paying taxes to the Government of Kenya	Learners are guided to: -Find out from the internet, textbooks or any appropriate materials other ways in which the National and County Governments in Kenya spend their revenue. -Make a poster of paying taxes to the Government of Kenya.	What is the importance of paying taxes to the Government of Kenya?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 177-179 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	3	Political Systems and Governance	The Preamble of the Constitution of Kenya	By the end of the lesson, the learner should be able to: a) Define constitution. b) Listen to an audio or watch a video played by the teacher. c) Identify key words in the preamble of the constitution of Keya in the audio or video. d) Appreciate the Constitution of Kenya.	Learners are guided to: -Define constitution. -Listen to an audio or watch a video played by the teacher. -Identify key words in the preamble of the constitution of Keya in the audio or video.	What is the meaning of constitution?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 179 Pictures Video clips Maps Charts Computing devices	Oral questions Oral Report Observation
8	1	Political Systems and Governance	Interpretation of key words in the preamble of the constitution of Kenya	By the end of the lesson, the learner should be able to: a) Read the conversation on learner’s book. b) Write the key words in the Preamble of the Constitution from the conversation. c) Act out the conversation on learner’s book. d) Have fun and enjoy role playing the conversation.	Learners are guided to: -Read the conversation on learner’s book. -Write the key words in the Preamble of the Constitution from the conversation. -Act out the conversation on learner’s book.	What have you learnt about the Constitution of Kenya?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 180-181 Pictures Video clips Maps Charts Computing devices	Oral questions Oral Report Observation
	2	Political Systems and Governance	Interpretation of key words in the preamble of the constitution of Kenya	By the end of the lesson, the learner should be able to: a) Pick a card with a key word in the preamble of the Constitution of Kenya. b) Circle the key words in the preamble of the Constitution of Kenya in the puzzle on learner’s book. c) Have fun and enjoy playing the puzzle.	Learners are guided to: -Pick a card with a key word in the preamble of the Constitution of Kenya. -Circle the key words in the preamble of the Constitution of Kenya in the puzzle on learner’s book.	What have you learnt about the Constitution of Kenya?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 182 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
	3	Political Systems and Governance	Interpretation of key words in the preamble of the constitution of Kenya	By the end of the lesson, the learner should be able to: a) Discuss the activities people engage in to appreciate the preamble of the Constitution of Kenya. b) Design a card on a manila paper with various declaration messages. c) Sing the song on learner’s book. d) Have fun and enjoy designing cards.	Learners are guided to: -Discuss the activities people engage in to appreciate the preamble of the Constitution of Kenya. -Design a card on a manila paper with various declaration messages. -Sing the song on learner’s book	Which activities do people engage in to appreciate the preamble of the Constitution of Kenya?	Spotlight; Social Studies Learner’s Book Grade 6 pg. 183-184 Atlas Photographs Pictures Video clips Maps Charts Realia Computing devices	Oral questions Oral Report Observation
9	ASSESSMENT

Teachers' Resources

Biology Form One Termly Exams and Marking Schemes Free

October 5, 2025 Maverick John Leave a comment

Name: …………………………………………………………… Adm No: ………………………………

School: …………………………………………………………. Candidate’s Sign: …………………….

Date: ………………………………………………………….

BIOLOGY

TIME: 2 HOURS

END OF TERM 1 EXAM

Biology

FORM 1

BIOLOGY

INSTRUCTIONS TO THE CANDIDATES:-

Write your name and Admission number in the spaces provided.
Answer allthe questions in the spaces provided.
Mathematical tables and electronic calculators may be used
All working MUST be clearly shown where necessary.

For Examiner’s Use Only:

Question	Maximum score	Candidate’s score
1-16	100 MARKS

Biology is derived from two Greek words bios and logos. What is the meaning of

Bios (1mk)

…………………………………………………………………………………………………………………..

Logos (1mk)

…………………………………………………………………………………………………………………..

List three main branches of biology and for each give its definition (6mks)

…………………………………………………………………………………………………………………..

Describe six characteristics observed among living organisms (12mks)

…………………………………………………………………………………………………………………..

Identify the following apparatus and for each state the function (6mks

(a)

Name

…………………………………………………………………………………………………………………..

Function

…………………………………………………………………………………………………………………..

(b)

Name

…………………………………………………………………………………………………………………..

Function

…………………………………………………………………………………………………………………..

(c)

Name

…………………………………………………………………………………………………………………..

Function

…………………………………………………………………………………………………………………..

Outline the four precautions to be observed during collection and observations of organisms during practical study. (4mks)

…………………………………………………………………………………………………………………..

The diagram below shows an instrument used in the laboratory

(a) Name the instrument (1mk)

…………………………………………………………………………………………………………………..

Label the parts (3mks)

…………………………………………………………………………………………………………………..

What is the function of the instrument?

…………………………………………………………………………………………………………………..

The student observed the housefly whose actual length was 8cm. she used the apparatus named above 6(a) above and the total magnification was X4. Calculate the length of the drawing. Show your working. (3mks)

…………………………………………………………………………………………………………………..

…………………………………………………………………………………………………………………..…………………………………………………………………………………………………………………..

(a) What is classification? (1mk)

…………………………………………………………………………………………………………………..

(b) What is the need for classification? (4mks)

…………………………………………………………………………………………………………………..

Fill the table below by identifying the correct kingdom and appropriate representative in each case (5mks)

kingdom	representative
a)	Hydra
b)	Protozoa
c)	Yeast
d) Monera
e)	Garden pea

Distinguish between magnification and resolution (2mks)

…………………………………………………………………………………………………………………..

Fill the table below (3mks)

Eye-piece lens	Objective lens	Total magnification
X30	(i) ……………………………….	X600
X14	X5	(ii)………………………………
(iii) ………………………	X40	X2000

Study the diagram below and answer the questions that follow

The diagram represents the field of view observed under the light microscope during the form one practical lesson.

If the students counted 10 cells across the field of view, calculate the size of one cell in micrometers. Show your working. (3mks)

…………………………………………………………………………………………………………………..

What is the importance of the following practices in biological preparation of the specimen?
Cutting very thin sections (1mk)

…………………………………………………………………………………………………………………..

Staining the cells using common dyes (1mk)

…………………………………………………………………………………………………………………..

Adding a drop of water on the cell (1mk)

…………………………………………………………………………………………………………………..

Distinguish between unicellular and multicellular organisms. (2mks)

…………………………………………………………………………………………………………………..

Identify three types of cells found in plants. (3mks)

…………………………………………………………………………………………………………………..

The figure shows a microscope
Name the parts of the microscope shown below. (4mks)

…………………………………………………………………………………………………………………..

State the functions of the parts (5mks)

…………………………………………………………………………………………………………………..

State three importance of studying biology (3mks)

…………………………………………………………………………………………………………………..

For the table below, identify the cell organelle and state the appropriate function (10mks)

CELL ORGANELLE	FUNCTION
a) Cell wall	……………………………………………………………
b) ……………………………………	Add carbohydrates to protein and transport them in the cell
c) Nucleus	…………………………………………………………
d) Nucleolus	…………………………………………………………
e) ……………………………………	Protein synthesis
f) Chloroplast	…………………………………………………………
g) ………………………………………	Contain lytic enzymes
h) Rough endoplasmic reticulum	…………………………………………………………….
i) ………………………………………	Transport lipids
j) ………………………………………	Site for respiration

Name the taxonomic units of classification in order of hierarchy (7mks)

…………………………………………………………………………………………………………………..

(a) What is the name given to the double naming of living organisms? (1mk)

…………………………………………………………………………………………………………………..

(b) The scientific name of a cat is Feliscatas.Which taxonomic group does the name Felis and catas

refer to? (2mks)

Felis

…………………………………………………………………………………………………………………..

Catas

…………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………..

…………………………………………………………………………………………………………………..

*******

233

BIOLOGY

TERM 1

Form 1

TERM 1 2020

MARKING SCHEME

FORM ONE

BIOLOGY

END OF TERM 1 EXAMS

MARKING SCHEME

Bios-life

Logos-knowledge

Botany-study of plants

Zoology- study of animals

Microbiology- study of microscopic organisms (micro-organisms)

Nutrition-process by which organisms acquire and utilize nutrients;

Respiration-process by which food substances are broken down in cells to release energy;

Gaseous exchange-process by which respiratory gases (oxygen and carbon (IV) oxide) are passed across the respiratory surface;

Excretion-process by which waste or harmful materials resulting from metabolic reactions within cells of organisms are eliminated;

Growth and development-Growth is the irreversible increase in size and mass while development is the irreversible change in complexity of structure of living organisms;

Reproduction-is the process by which living things give rise to new individuals of the same kind;

Irritability-is the ability of living things to perceive changes in their surroundings and respond to them appropriately;

Movement-is the change in position by part of an organism while locomotion is where the whole organism moves or change in position

Name-sweep net;

Function-used for catching flying insects’ e.g. bees;

Name-pooter;

Function-used for sucking small animals from rock surfaces or barks of trees e.g. ants and termites;

Name-pitfall trap;

Function-used for catching small crawling animals e.g. millipedes, spiders and cockroach;

Rej-function if the name is wrong.

Rej-if name are function are interchanged.

Collect only the number of specimen needed to avoid wastage;
Not to destroy the natural habitat of the specimens.
Dangerous / injurious specimens to be handled with care as stinging insects or plants can sting or injure a person; a pair of forceps or hand gloves should be used for protection;
Do not harm/injure the specimen during the collection exercise; to avoid distorting the features of the specimen.
live specimens should be returned to their habitats whenever possible ; to maintain ecological balance
Highly mobile animals to be immobilized using suitable chemical substance tetrachloromethane or chloroform, ethoxyethane; (mark the first 4)

Hand lens;
X-convex lens ;

Y-Frame;

Z-Handle;

Used to enlarge objects (external features of collected specimens)
Magnification=;

Length of the drawing= drawing magnification X length of the object

X4 x X8cm;

=32cm;

It is the grouping of living organisms based on their structures;
-Grouping brings together living things with similar characteristics but separates those with different features;

-helps in placing living organisms in their correct group for reference;

-helps us to arrange information about living organisms in an orderly manner to avoid chaos and confusion that could arise if these were done arbitrarily;

-helps us to understand the evolutionary relationships between different organisms;

KINGDOM	REPRESENTATIVE
a) Animalia
b) Protoctista
c) Fungi
d) …………………………………..	Bacteria
e) Plantae

Rej: wrong spellings

Magnification is the ratio of an object’s image to its real size( enlargement of specimen compared to its real size); while resolution is the ability to distinguish two structures that are very close together as district entities;

Eye-piece lens	Objective lens	Total magnification
	i X20;
		ii X70
iii X50

Rej- if X (magnification) is missing.

c)1mm=1000 micrometers ()

4mm=?

4mm x 1000= 4000

1mm

Length of 1 cell =

Cell length =

Length of 1 cell=400

To allow light to pass through;
For clear visibility/ to make observations clear;
To make the cells turgid/ to avoid dehydration;

Unicellular organisms- are organisms with one cell

Multicellular organisms- are organisms with many cells;

Root hair cell

Guard cell

Palisade cell.

A -Eye piece;

C -Fine adjustment knob;

J -Stage;

D -Mirror; ( reg: wrong spellings)

B –(Coarse adjustment knob)- brings image into rough focus by raising and lowering the body tube;

E – (Diaphragm)-an aperture that regulates the amount of light passing through the condenser to illuminate the specimen;

F – (Objective lens)-contains a second set of lenses used in combination with eye-piece lenses to bring the desired magnification;

G – (Body tube) – holds the eye piece and the resolving nose piece (in position);

H – (Base)-provides firm and stable support;

Enables one to understand the development stages in human body;
Enables one to pursue careers i.e. medicine(any other relevant);
Imparts/enables one to acquire scientific skills i.e. drawing, observing, measuring, classifying, analyzing and evaluating data;
Used to solve environmental problems e.g. food shortage, pollution, drought, poor health and conservation of resources like forests, wildlife and soil;
Used to enhance/promote international co-operation in medicine, environmental conservation; (mark the 1^st three)

	CELL ORGANELLE	FUNCTION
a		-give cell a definite shape; provide mechanical support;provides protection against mechanical injury;
b	Golgi bodies(golgi apparatus);
c		Control all activities of the cell;
d		Manufacture ribosomes;
e	Ribosomes ;
f		Contain chlorophyll that traps light energy that is used during photosynrhesis;
g	Lysosomes ;
h		Transport proteins;
i	Smooth endoplasmic reticulum;
j	Mitochondria; acc motochondrion

Kingdom ;

Phylum/division;

Class ;

Order;

Family;

Genus;

Species;

Rej- if order is not followed.

Binomial nomenclature
Felis –genus;

Catus-species

-The first part of the scientific name i.e. genus and should begin with a capital letter and the specific name should be written in small letters;

-Scientific names should be printed in italics in books and printed works, but in hand written manuscripts should be underlined as separate words;

-Specific name a times is written with the name of a scientist who first adequately described and named the organism (who invented);

-Biologist must give a latinised name for a newly described animal or plant species;

Teachers' Resources

Physics Form 1-4 Notes, Revision Questions And Answers PDF Free

October 5, 2025 Maverick John Leave a comment

INTRODUCTION TO PHYSICS

The primary school science syllabus covers topics such as matter and its properties, energy in its various forms for example heat, light, sound and their corresponding sources, machines and the way they make work easier, balancing and weighing of various shapes of objects, electricity and magnetism.

These topics and more are covered in physics.

MEANING OF PHYSICS

Physics is the study of matter and its relation to energy. Matter is anything that occupies space and has weight.

The study of physics allows one to understand and enjoy other subjects

As a subject, the study of physics involves measurement of quantities and collection of data. Through experimentation and observation, hypotheses are drawn, test and laws and principles established.

Physics explain the how and why behind the following phenomena;

Formation of rainbow.
Occurrence eclipse.
The falling of the objects towards the earth’s surface.
The seasonal occurrence of ocean and sea tides
The crackling sound heard when nylon cloth is removed from the body.
Formation of shadow and many more.

Physics gives scientific, systematic and consistent explanation based on the concepts of physics.

BRANCHES OF PHYSICS

Physics may be split into the following key areas;

Mechanics- is a branch of physics that deals with the study of the motion of the bodies under the influence of forces. It is divided into two key areas namely; kinematics and dynamics. Kinematics is the study of the motion of the bodies disregarding the forces acting on it while dynamics is the study of the motion of bodies with regard to forces acting on the body. Under this branch, we look into details the aspects of linear, circular and oscillatory motions as well as motion of fluids.
Electricity and magnetism- this branch looks at the interaction between electric fields and magnetic fields and the applications of such interactions g. electric motors, microphones, electric speakers etc.
Thermodynamics- This branch looks at how heat as a form of energy is transformed to/from other forms of energy.
Geometrical optics- This branch takes a keen look at the behavior of light in various media g. optic fibre, microscopes, and lenses e.t.c.
Waves- It deals with the study of the propagation of energy through space. It involves properties of waves such as refraction, reflection, diffraction and polarization
Atomic physics– This area of study is targeted at the behavior of particles of the nucleus and the accompanying energy changes. It involves radioactivity, nuclear fission and fusion. It is the basis of the production of nuclear energy.

RELATIONSHIP BETWEEN PHYSICS AND OTHER SUBJECTS

Physics does not only relate the remaining two science subjects but also enjoys a relationship with other subjects as well. For instance, it is the foundation of technological development in any country.

Physics and history- Carbon dating is an application of radioactivity which serves as a crucial tool to history in establishing fossil age and hence past pattern of life.
Physics and Geography- Establishment of weather patterns rely on accurate use of instruments like thermometer, wind vane and hygrometer .Heat transfer by convection explains the formation of conventional rainfall and pressure variation that determine wind patterns. All these are physics concepts.
Physics and Home Science
Physics and religion- Systems in the universe reveal great orderliness which can be traced back to the creator. Study of physics has come up with findings which are in total agreement with orderliness. Matter can be reduced to nothing scientifically the reverse is true which confirms that matter was created from nothing by God.
Physics and Biology- Knowledge of lenses in physics are used in making microscope used in study of cells in biology. Physics formulae are used in calculation of magnification by microscopes.
Physics and Chemistry- Physics has helped in explaining forces within atoms and therefore atomic structure. It is this structure of the atom that then determines the reactivity of the atom as explained in chemistry
Physics and Mathematics- Many physics concepts are expressed mathematically. Many physics formulae are expressed mathematically.
Physics and Technology- some areas of technology that requires knowledge of physics are:

a) Medicine; in medicine, x-rays, lasers, scanners which are applications of physics are used in diagnosis and treatment of diseases.
b) Communication; satellite communication, internet, fibre optics are applications of internet which requires strong foundation in physics.
c) Industrial application; in the area of defense, physics has many applications e.g. war planes, LGB (laser-guided bombs) which has high level accuracy.

In entrainment industry, knowledge of physics has use in mixing various colours to bring out the desirable stage effects. Is application of science to solve problems in everyday situation most forms of technology are due to Physics e.g. Information and Technology, Computer Science, Mobile Phones, building technology, automotive technology.

CAREER OPPORTUNITIES IN PHYSICS

The study of Physics can open up many avenues of professions including engineering, degree, diploma or certificate courses.

A physics student will have the following opportunities in the following areas;

Bachelor of Architecture.
Bachelor of pharmacy.
Bachelor of medicine.
Bachelor of dental surgery.
Bachelor of science(nursing)
Bachelor of education science(physics)
Bachelor of science(Electrical and electronic Engineering)
Bachelor of Veterinary Medicine.

At college level, some of the courses are offered.

Diploma in building and construction.
Diploma in mechanical Engineering.
Diploma in physiotherapy.
Diploma in electrical Engineering.
Diploma in computer science.

BASIC LABORATORY RULES

LABORATORY– This is a room containing facilities, apparatus and equipment that aid the investigative study of physics

BASIC LABORATORY RULES

Proper dressing
Note the location of electricity switches, fire-fighting equipments, First aid kit, gas supply and water supply taps.
When in the laboratory open doors and windows to let in fresh air.
Follow instructions given carefully.
No eating or drinking in the laboratory.
Turn off electrical switches, gas and water taps when not in use.
When handling electrical apparatus hands must be dry.
Do not plug foreign objects into electrical sockets.
Keep floors and working surfaces dry.
Clean and return all apparatus used in their correct location.
All equipments should not be taken out of the laboratory.
Wash your hands before leaving the laboratory.
All instructions given must be followed strictly. Never attempt anything while in doubt.
Windows and doors should be kept open while working in the laboratory
Any wastes after experiments must be disposed appropriately after use

FIRST AID MEASURES

CUTS -These may result from poor handling of glass apparatus or cutting tools like razors and scalpels. In case of cuts, assistance should be sought to stop bleeding and for immediate depressing up of the wound.
BURNS – Burns may result from naked flames or even splashes of concentrated acids and bases. In case of burns caused by acids or bases, quickly run cold water over the affected part as you seek help for further treatment.
POISONING – This may result from inhaling poisonous fumes or actual swallowing of poisonous chemicals. Assistance should be sought immediately.
EYE DAMAGE -Eyes must be safeguarded from dangerous chemicals and bits of solids. In case an irritating chemical lands in the eye, it should be washed off immediately with a lot of cold water
ELECTRIC SHOCK -This may result from touching exposed wires or using faulty electrical appliances. When such an accident occurs, first put off the main switch before treating for the shock.

TOPIC 2: MEASUREMENT

Scientists from various parts of the world were giving measurements in different units and languages. Some used pounds, inches and seconds while others were using grams, centimetres and seconds. This was undesirable, especially when a comparison of results was necessary.

This made it impossible for them to compare discoveries. Consequently, scientists agreed on one international system of units to be used, the Systeme International d’Unites (International System of Units), shortened to SI units, in all languages. This system has seven basic physical quantities and units on one Universal System of units called system international d’ unites (International system of units) SI units which assigned seven basic quantities as shown below.

UNIT	Symbol of quantity	S.I UNIT	SYMBOL OF UNIT
1. Length	L	metres	m
2. Mass	m	kilogram	kg
3. Time	t	seconds	s
4. Electric Current	I	ampere	A
5. Thermodynamic temperature	T	kelvin	K
6. Luminous Intensity		Candela	Cd
7. Amount of Substance		mole	mol

These quantities above cannot be obtained from any other physical quantities. Measurements are made by comparing the magnitude of a quantity with that of a given unit of that quantity. A physical quantity is a measurable aspect of matter.

Basic Physical Quantity -These are quantities that cannot be obtained by any other quantity e.g. mass, time, length.

Derived Quantity-These are quantities obtained by multiplication or division of basic physical quantities e.g. Area, Volume, Density.

LENGTH

This is the distance between two fixed points. It is the measure of distance between two points in space. The SI unit for length is the metre (m).

Other units of length include;

unit	symbol	Equivalence in metres
Kilometre	Km	1000
Hectometre	Hm	100
Decametre	Dm	10
Decimetre	dm	0.1
Centimetre	Cm	0.01
Millimetre	mm	0.001
Micrometre	μm	0.000001

MEASUREMENT OF LENGTH

Length can be estimated or measured accurately using appropriate measuring instrument. The type of instrument to be used at any time depends on two factors:

The size of the object to be measured
The desired accuracy

The methods used include;

Approximation/ Estimation
Accurate measuring using standard instruments
Estimation

This method involves comparing the object to be measured with another of standard measure. For example, the height of a tall flag post can be compared with that of a wooden rod whose length is known. Thus at any given time;

Height of flag post = Length of shadow of post

Height of rod Length of shadow of rod

From this expression, the height of the flag post can be estimated.

Example;

Suppose the height of the rod= 1m, length of shadow of rod= 120cm and length of shadow of post= 480cm, then the height of the flag post is given by;

Height of post, H_p = 480cm

100cm 120cm

Height of post, H_p= 100 x 4

= 400cm

Also, the thickness of a sheet of paper may be estimated by taking several sheets of the paper and measuring their thickness then dividing by the number of sheets of paper;

Thickness of a sheet of paper = Thickness of n papers

Number of papers, n

Using a standard measure(instruments)

This involves the use of standard measure or instruments. To measure length accurately, the instruments used are metre rules, half metre rules, tape measure, vernier calipers and micrometer screw gauges

Metre rule

A metre rule is marked in centimetres. It is marked 0 and 100cm at its extreme ends.

0 100cm

a metre rule

The smallest scale division of a metre rule is 0.1cm (1mm). The smallest scale division of any instrument is known as its accuracy. Thus the accuracy of a metre rule is 0.1cm.

When using a metre, one must ensure the following:

That the object to be measured is in contact with the metre rule.
That one end of the object is at 0cm mark i.e. zero (0) mark to coincide with the start of the object to be measured.
That the eye is perpendicular to the scale so as to avoid parallax error. This ensures that accurate reading is obtained.

Metre rules and half metre rules used are graduated in centimetres and millimetre.

They are made of wood, plastic or steel.

When using a ruler the following precautions should be taken;

Never drop a metre rule
Never use it as a walking stick
Never use it as a cane
Keep it in a dry place away from corrosive substances

EXAMPLE 1

The reading should be taken in terms of the least count of the metre rule. For a metre rule the least count is 0.001m=0.1cm=1mm.

The reading shown above is 0.0165m=1.65cm=16.5mm.The metre rule cannot read 4th, 2nd or 1st decimal places of metre, centimeters or millimeters respectively. This is only approximated.

EXAMPLE 2

Figure below shows a fencing post whose length is being measured using a strip of a measuring tape.

(a) State the accuracy of the tape:

(b)What is the length of the post?

SOLN

(a)Accuracy of measuring tape is 10mm or o.1 cm + 5cm or o.o5m.

(b)Length of post is 1.5 m

Tape measure

It is graduated in millimetre (mm) or centimetre (cm)

They are three types;

Tailor’s tape measure
Carpenter’s tape measure

Surveyor’s tape measure

NOTE: The choice of a tape measure depends on accuracy required and the size of object to measure. A tape measure can be made up of cloth, steel or flexible plastic. Always ensure that the tape measure is taut when measuring.

MEASUREMENT OF CURVED LENGTH

Curved length can be measured using a thread. The thread is placed along the required length and the length is found by placing the thread on a scale.

EXPERIMENT: Measuring the circumference of a cylinder using a thread.

APPARATUS: A cylinder, a thread and a metre rule

PROCEDURE

Wrap a thin thread say 10 times around the cylinder
Mark with ink the beginning and end of turns as shown

The circumference of the cylinder will be given by;

Circumference = [length of thread]

But; Circumference =π d or 2πr (where r is the radius of the cylinder)

ESTIMATION OF LENGTH

EXPERIMENT: To estimate the height of a tree

APPARATUS: A metre rule, tape measure

PROCEDURE

Measure the length of the metre rule when upright using a tape measure followed by measuring its shadow.
Measure the shadow of the tree in the school compound.

RESULTS

Height of metre rule = …………Cm

Height of shadow of metre rule=…………Cm

Height of shadow of the tree =……………Cm

Estimation of the height of the tree is given by the formula provided above.

AREA

Area is defined as the measure of surface enclosed by the boundaries of the body. Its SI Unit is the square metre (m²). Since it is measured in metre-square (m²), this means it’s a derived quantity.

Other multiples and sub-multiples of area are; cm², mm², km², hectares etc.

Area can also be estimated or calculated accurately.

CONVERTING

mm²to m2

1m²= 1000 X 1000

= 1000000 mm²

1mm² = {1÷1000000} m2 (Divide by 1million)

= 0.000001 m²

m²to mm²

1m²= 1000000 mm² {multiply by 1 million}

cm²to m²

1cm = 0.01m

1cm² = 0.01m X 0.01m

= 0.0001m²{multiply by 0.0001}

m2 to cm²

1m = 100cm

1m2 = 100cm X 100cm

= 10000cm² {multiply by 10000}

EXERCISE

Convert 7.5m² to cm²
Convert 940mm² to cm²
Convert 12000mm² to m²

Measurement of area (Accurate Measurement)

The area of regularly shaped objects can be found by applying an appropriate formula shown below;

APPROXIMATION OF AREA OF IRREGULAR BODIES

We trace their outline on the square paper of 1cm² e.g.

Full squares = …………cm²

½ full squares = ………..cm²

AREA = full square+½full squares

Consider the figure below of an irregularly- shaped object.

The number of complete squares covered by the shape= 14

The number of incomplete squares covered by the shape=19

Therefore, the number of complete squares covered by the shape is approximately (14+ 19/2) = 23.5 squares.

Suppose the area of one square is 1cm², and then the area of the shape is approximately;

Area = 23.5 x 1

= 23.5 cm²

EXAMPLE 3

Estimate the area of the irregular surface shown below by counting the small squares.

SOLN

The number of complete squares = 39

Number of incomplete squares = 34

These are equal to 34 = 17 complete squares

Therefore, the number of complete squares = 39 + 17 = 56

Hence, the estimated of the area of the surface = 56 x 1 cm²= 56cm²

VOLUME

Volume is the amount of space occupied by space. The SI unit of volume is cubic metres [m³].

It is a derived quantity of length

Multiples and submultiples are; mm³, cm³ and km³

CONVERTING

a) From m³ to mm³

1m = 1000mm

1m³ = 1000mm X 1000mm X 1000mm

= 1000000000mm³

To change m3 to mm3 you multiply by 1 billion

b) From mm³ to m³

To change m³ to mm³ you divide by 1 billion i.e. 1/10000000000

EXAMPLE 4

Express 9cm³ in m³
Express 9000000000mm³ in m³
Express 0.0546m³ to cm³

MEASUREMENT OF VOLUME

The volume of regularly shaped solids can be obtained by applying the appropriate formula i.e

EXAMPLE 5

A block of glass is 5.0 cm long, 4.0 cm thick and 2.5 cm high. Calculate its volume.

SOLN

Volume of the glass block = area of cross section x height

= 5.0 x 4.0 x 2.5

= 50.0 cm³

EXAMPLE 6

Find the volume of cylindrical tin of radius 7.0 cm and height 3.0 cm.

SOLN

Volume of the tin = area of cross section x height

= 22 x 7 x 7 x 3

= 462.0 cm³

EXAMPLE 7

Find the volume of the triangular prism shown below given that base length is 12.0 cm, h= 5.0 cm and the width 6.0 cm:

SOLN

Volume of the prism = area of cross section x height

= ½ x 6.0 x 5.0 x 12.0

= 180.0 cm³

EXAMPLE 8

Find the volume of a sphere whose radius is 3.0 cm

SOLN

Volume of a sphere = 4/3 πr³

= 4 x 22 x 3.0 x 3.0 x 3.0

3 7

= 113.14 cm³

EXAMPLE 9

A sphere of diameter 6.0 cm is moulded into a thin uniform wire of diameter 0.2 mm. Calculate the length of the wire in metres. (Take π = 22/7)

SOLN

Volume of the sphere and the wire are equal

Volume of the sphere = volume of the wire

4 x 22 x 3.0 x 3.0 x 3.0 = 22 x 0.01 x0.01 x L

3 7 7

4 x 3.0 x 3.0 x 3.0 = L

3 x 0.01 x 0.01

Therefore, length L = 360000cm

= 3600 m

MEASUREMENT OF VOLUME OF LIQUIDS

Liquids have no definite shape but they assume the shapes of the container in which they are put.

One of the methods which can be used to measure the volume of liquids is to pour the liquids into a container with a uniform cross-section as shown,

Volume = Area of cross-section x height

= A h; where A=LX b

= l b h

Instruments can also be used to measure the volume of liquids. They include; Burette, Pipette, Measuring cylinder, graduated beaker and Volumetric flask.

NOTE: The scale of the Burette begins from zero at the top and increases downwards to the maximum value e.g. a reading of 31.0ml on the burette means that volume of the liquid is [50-31] ml = 19ml.

MEASUREMENT OF VOLUME OF IRREGULAR OBJECTS

Using a measuring cylinder

PROCEDURE

Fill the measuring cylinder with water.
Record the volume of water as V₁
Submerge gently a stone [irregular object] tied around a thread.
Record the volume of water and the stone as V₂.
Volume of the stone = V₂– V₁

Using a Eureka can

A Eureka or displacement can is a container with a spout from the side.

Apparatus; Eureka can, measuring cylinder, irregular object e.g. a stone, water

Procedure

Fill the Eureka can with water until it flows out of the spout.
Place a measuring cylinder under the spout of the can.
Tie the solid [irregular object] with a thread and submerge it gently inside the can.
The result [water] collected to the measuring cylinder is the volume of the irregular object.

EXERCISE 2.5 KLB

MASS

Mass is a quantity of matter in a body. Its S.I unit is kilogrammes (Kg)

It is measured using a beam balance or top pan balance.

The multiples and submultiples include;

Unit symbol Equivalence in Kg

Tonne t 1000

Gram g 0.001

Milligram mg 0.000001

The mass of an object is the same everywhere because the number of particles in an object remains constant.

MEASUREMENT OF MASS

There are two common types of balances for measuring mass; Electrical and mechanical types.

Electrical types are very accurate and the mass of the object is read on display

(Top Pan Balance).

A Mechanical type (Beam Balance), the object whose mass to be measured is balanced against a known standard mass on an equal level.

The three balances used in measuring are;

1) Top Pan Balance

2) Beam balance

3) Level balance

In a level balance combination of levers moves the pointer along a scale when the mass is placed on it.

EXERCISE 2.6 KLB

DENSITY

The density of a substance is defined as its mass per unit volume. Its symbol is rho (ρ).

The SI unit is kilogram per cubic metre (Kg/m³)

Conversion from kg/m³ to g/cm³

1g/cm³ = 1000kg/m³

EXAMPLE 10

A Block of glass of mass 187.5g is 5cm long, 2.0cm and 7.5cm high. Calculate the density of the glass block.

Solution

Density = mass

Volume

= 187.5g

2.0cm X 5cm X 7.5cm

= 2.5g/cm3 or 2500kg/m³

EXAMPLE 11

A block of glass of mass 187.5 g is 5.0 cm long, 2.0 cm thick and 7.5 cm high. Calculate the density of the glass in kgm-3.

SOLN

Density = mass / volume

= (187.5 /1000) / (2.0 × 7.5 × 5.0 /1,000,000)

= 2500 kgm^-3.

EXAMPLE 12

The density of concentrated sulphuric acid is 1.8 g/cm3. Calculate the volume of 3.1 kg of the acid.

SOLN

Volume = mass / density

= 3,100 / 1.8

= 1722 cm³or 0.001722 m³.

MEASUREMENT OF DENSITY

The density of an object is calculated from the formula;

Density = mass

Volume

Density of common substances

DENSITY BOTTLE

A Density bottle is a small glass bottle fitted with a glass stopper which has a hole through which excess liquid flows out.

Normally, the density bottle has its capacity indicated on the side.

To find the density of the liquid using a density, measure the mass m₁ of a dry clean density bottle with its stopper.

Fill the bottle with liquid and replace the stopper. Dry the bottle on outside (excess liquid overflows through the hole in the stopper).

Measure the mass m₂ of the bottle plus the liquid.

If the volume of the liquid is V then;

Density = (m₂-m₁)

PRECAUTIONS

The bottle is held by the neck when wiping it dry. This is because when held in hands, it may expand due to warmth from the hand.
The outside of the bottle must be wiped carefully.
Ensure that there is no air bubbles when the bottle is filled with liquid

TO MEASURE THE DENSITY OF A SOLID USING A DENSITY BOTTLE

This method is used for solids in form of grains, beads or turnings

Apparatus: density bottle, lead shots and beam balance.

PROCEDURE

Measure the mass m₁ of a clean dry empty density bottle
Fill the bottle partly with the solid (lead shots) and measure mass m₂
Fill up the bottle with water up to the neck and measure its mass as m₃.
Empty the bottle and rinse it
Fill it with water and replace it with the stopper, wipe outside dry and measure the mass m₄ of the bottle filled with water.

RESULTS

Mass of water = (m₄– m₁) g

Volume of water = (m₄– m₁) cm3 (since density of water is 1g/cm3)

Mass of lead shots (solid) = (m₂– m₁) g

Mass of water present when the bottle is filled with lead and water = (m₃– m₂) g

Volume of water = (m₃– m₂) cm³

Volume of lead shots = (m₄-m₁)-(m₃-m₂) cm³ (since density of water is 1g/cm³)

Therefore density of lead shot = (m₂-m₁)-{(m₄-m₁)-(m₃-m₂)}

NOTE: This method is unsuitable for solids which are either soluble or react with it.

EXAMPLE 13

The mass of a density bottle is 20g when empty and 45g when full of water. When full of mercury, its mass is 360g. Calculate the density of mercury.

SOLUTION

Mass of water = 45-20 =25g

Volume of water = 25g/1g/cm³

= 25cm³

Volume of bottle = 25cm³

Mass of mercury = 360-20 =340g

Volume of mercury= 25cm³

Density of mercury= 340 ÷25

=13.6g/cm³ or 13600kg/m³

EXAMPLE 14

In an experiment to determine the density of sand using a density bottle, the following measurements were recorded:

Mass of empty density bottle =43.2g

Mass of density bottle full of water =66.4g

Mass of density bottle with some sand =67.5g

Mass of density bottle with some sand filled up with water=82.3g

Use above data to determine the;

(a) Mass of water that completely filled the bottle.

(b) Volume of water that completely filled the bottle.

(d) Mass of sand.

(e) Mass of water that filled the space above the sand.

(f) Volume of the sand.

(g) Density of the sand.

SOLN

a) 66.4 – 43.2 = 23.2g
b) 23.2cm³
c) 23.2cm³
d) (67.5 – 43.2) g = 24.3g
e) 82.3 – 67.5 = 14.8g
f) Volume of the sand = volume of bottle – volume of added water

= 23.2 – 14.8= 8.4cm³

g) P = M/V = 24.3g / 2.893cm³

= 8.4cm³

EXAMPLE 15

The mass of an empty density bottle is 20 g. Its mass when filled with water is 40.0 g and 50.0 g when filled with liquid X. Calculate the density of liquid X if the density of water is 1000 kgm^-3.

SOLN

Mass of water = 40 – 20 = 20 g = 0.02 kg.

Volume of water = 0.02 / 1,000

= 0.00002 m³.

Volume of liquid = volume of bottle

Mass of liquid = 50 – 20

= 30 g = 0.03 kg

Therefore density of liquid = 0.03 / 0.00002

= 1500 kgm^-3

DENSITY OF MIXTURES

A Mixture is obtained by putting together two or more substances such that they do not react with one another. The density of the mixture lies between the densities of its constituent substances and depends on their proportions.

Density of the mixture = mass of the mixture

Volume of the mixture

EXAMPLE 16

100cm3 of fresh water of density 1000kg/m3 is mixed with 100cm3 of sea water of density 1030kg/m3. Calculate the density of the mixture.

Solution

Mass of fresh water = density x volume

= 1g/cm³ x100cm³

= 100g

Mass of sea water = 1.03 x 100

= 103g

Mass of the mixture = 100+103

= 203g

Volume of the mixture= 100+100

= 200cm³

Density of the mixture = 203÷200

= 1.015g/cm³

Exercise 2.7 no. 2 &3 KLB

TIME

It is a measure of duration of an event. Some ancient measuring instruments were the sundial and the hour glass

The SI unit of time is seconds (s)

MULTIPLES AND SUBMULTIPLES OF TIME

Time	symbol	Equivalent in seconds
Microsecond	µ s	0.000001
millisecond	ms	0.001
Minute	min	60
Hour	hr	3600
Day	day	86400
Week	wk	604800

Measurement of time

Time is measured using either a stopwatch (digital) or stop clock

They are used depending on the accuracy required.

QUESTIONS ON THE TOPIC

State two factors that should be controlled in manufacturing a cylindrical container of uniform thickness, which should normally be in a standing position.
The figure shows a measuring cylinder which contains water initially at level A. A solid mass 11g is immersed in the water, the level rises to B.

Determine the density of the solid. (Give your answer to 1 decimal point)

A butcher has a beam balance and masses 0.5 kg and 2 kg. How would he measure 1.5 kg of meat on the balance at once?

Determine the density in kg/m³ of a solid whose mass is 40g and whose dimensions in cm are 30 x 4 x 3
Record as accurately as possible the masses indicated by the pointer in figures A.

Figure 1 shows the reading on a burette after 55 drops of a liquid have been used.

If the initial reading was at 0cm mark, determine the volume of one drop

1 shows the change in volume of water in a measuring cylinder when an irregular solid is immersed in it.

Given that the mass of the solid is 567g, determine the density of the solid in gcm^-3. (Give your answer correct to 2 decimal places.

A thin wire was wound 30 times closely over a boiling tube. The total length of the windings was found to be 9.3 mm. Calculate the radius of the wire.
(a) Given that a kilogram of copper contains about 10²⁵ atoms and that density of copper is about 9000kg/m³_,estimate the diameter of the copper atom?

(b) State the assumption made in (9a) above.

The density of concentrated Sulphuric acid is 1.8gcm^-3. Calculate the volume of 3.6kg of the acid.
1600 cm³ of fresh water of density l g/cm³ are mixed with 1400cm³ of seawater of density 1.25g/cm³. Determine the density of the mixture.
With the aid of a diagram, illustrate the meaning of the parallax error
Describe how you can measure the density of a rock which has no definite shape.
A shopkeeper has a scale balance and masses of 250g and 2kg. How would he measure 1.75kg of flour on this scale at once
A pebble of mass 50g is placed in a measuring cylinder containing some water. The reading of the water level increased from 75cm³ to 95cm³. Calculate the density of the pebble
The container shown below is filled to a depth of 5cm with a liquid.

3.5cm

9cm

Liquid 5cm

Using pie as 22/7, determine the volume of the liquid.
If the mass of the liquid in the container is 2.554kg, estimate the density of mercury in g/cm³.
Calculate the mass of water that would be needed to completely fill the remaining space in the container above the liquid. (Density of water is 1g/cm³)
A pebble of density 9g/cm³ is gently dropped into the container full of water and the liquid. Describe and explain what is observed.

SOLUTIONS

height, base area
Volume of one molecule = 18/ (6×10²³) = 3x 10^-23cm

X³ = 3x 10^-23 cm³

X = 3.11 x 10 ^-8 cm³

d= m/v=40g/ 30 x 4 x 3cm^{3 =}1111 g/cm³
5 kg
D= m/r =⁵⁶⁷/_(150-80) = ^576-80 /_70g/cm3
2000 cm³
12g/cm³

TOPIC 3: FORCE

Force is a pull or a push or that which changes a body way of motion and distort it

Its SI unit is newtons (N)

EFFECTS OF FORCE

It can increase the speed of a moving object or make a stationary object start moving.
Slow down or stop a moving object.
Change the direction of a moving object.
Distort (change) the shape of an object.

Force is that which changes a body’s state of motion or shape. Some forces are small and others are large.

Force is represented by a line with an arrow showing the direction it acts. i.e.

Force can be categorized in two ways. These are:

As either a push or a pull
As either contact or non-contact force

Contact forces are those forces between bodies which are in contact e.g. action and reaction, viscous drag, friction etc. Non-contact forces act between bodies at a distance e.g. gravitational force, magnetic force, electrostatic force etc.

TYPES OF FORCES

Gravitational force
Tensional force

Upthrust

Frictional force
Magnetic force
Centripetal force

Cohesive and adhesive force
Molecular force

Electric force
Nuclear force
Electrostatic force

GRAVITATIONAL FORCE

This is a force of attraction between two bodies of given mass. Objects thrown from the earth’s surface always falls back to the surface of the earth. This force which pulls the body towards the centre of the earth is called Gravitational force.

Moon and other planets also have their gravitational force to objects.

The pull of gravity on the body towards the centre is called weight. The weight of an object varies on different planets because of different gravitational pull.

TENSION FORCE

Tension force is as a result of two opposing forces applied. The pull or compression of a string or spring at both of its ends is called Tension.

Compressed or stretched object will tend to regain its original shape, when the stretching or compressing force is removed .Materials that can be extended without breaking are called elastic materials. Such materials can be used to make a spring balance an instrument used to measure force. Other examples include; bows and catapults.

UPTHRUST FORCE

The upward force acting on an object immersed in a fluid (liquid or gas) is called upthrust force.

An object in a vacuum will not experience upthrust.

EXAMPLE 1

An object weighs 80N in air and 60N when immersed in water. Calculate force acting on the object.

Solution

Upthrust force = weight of object in air –weight of object in the liquid

= 80 – 60

= 20N

Exercise

An object weighs 100N in air and 26N when immersed in water. Calculate the apparent loss weight of the object. Calculate also the mass of object in water. (1Kg=10N).
2kg blue band weighs 20N when placed in air .The apparent loss in water is 2N .Calculate the mass of blue band in water.

FRICTIONAL FORCE

Frictional force is a force that opposes relative motion between two surfaces in contact.

The opposing force involving a fluid is called viscous drag (viscosity).This viscous drag limits the speed with which a body can move in a liquid.

Friction can be applied during walking.

EXPERIMENT: To investigate frictional force.

Apparatus: wooden block, rollers.

Procedure:

Put a block of wood on a horizontal surface such as a bench as shown.
Pull the block gradually, increasing the force.
Repeat the experiment, this time resting on rollers as shown above

Conclusion

The wooden block starts to move when the applied force is just greater than frictional force between the block and the surface of the bench.

Frictional force can be reduced by using rollers, oiling and smoothening.

MAGNETIC FORCE

Magnetic force is the force of attraction or repulsion between a magnetic material and a magnet.

A magnet has two types of poles, a north pole and a south pole. Like poles repel while unlike poles attract. Some materials are attracted by a magnet while others are not .Those that are attracted are called magnetic materials e.g. iron ,steel ,nickel and cobalt while those that are not attracted are called non-magnetic materials e.g. wood and aluminium.

COHESIVE AND ADHESIVE FORCES

The force of attraction between molecules of the same kind is known as cohesive force e.g. A water molecule and another water molecule. The attraction between molecules of different kinds is known as adhesive force e.g. between water molecules and molecules of the container in which the liquid is put.

EXPERIMENT: To see the behaviour of water on different surfaces.

Water wets glass

Observation

Water on the glass slide spreads

Water forms spherical water drops on waxed surface

OBSERVATION

Small spherical balls was observed on a waxed glass

EXPLANATION

Water wets the glass surface because the adhesive forces between the water molecules and the glass molecules are greater than the cohesive forces between water molecules.

Water does not wet the waxed glass surface because the cohesive force is greater than the adhesive.

If mercury was used in the experiment it could be observed that small drops on a clean glass dish collect into spherical ball as shown below

This is due stronger cohesive forces between mercury molecules which forms small spherical drops. The adhesive force between mercury and glass makes mercury not wet glass.

N/B: Mercury is poisonous and should not be handled in ordinary laboratory.

EXPERIMENT: To demonstrate cohesive and adhesive forces of liquids on narrow tubes

APPARATUS: narrow tubes of different size of bore, beaker and water

a) Glass tubes dipped in water b) Glass tubes dipped in mercury

OBSERVATION

The level of the water inside the tubes is higher than outside the tubes. A meniscus is formed at the top of the water level and it curves upwards (concave).

The rise in the tube with a smaller bore is higher than in the tube with a larger bore.

Different liquids rise by different heights depending on the diameter of the glass tube.

When mercury is used, the level of mercury inside the tubes goes lower than that outside the tubes. The surface of the mercury will curve downwards (convex).

EXPLANATION

Adhesive forces between the water and glass is greater than cohesive forces between the water molecules, the water rises up the tube so that more water molecules can be in contact with the glass. This wets the glass. Liquids such as glycerol, kerosene and methylated spirit rise in tubes.

On the other hand, the force of cohesion with the mercury is greater than the force of adhesion between glass and mercury. The mercury sinks to enable mercury molecules to keep together.

SURFACE TENSION

This is a force that causes the surface of a liquid to behave like a stretched plastic skin.

The force is due to the force of attraction between individual molecules in a liquid. Its due to this force that liquids form drops, water wets the surface but runs off others, some insects like pond skaters manage to rest on the surface of water without sinking, water rises up in narrow glass tubes but mercury is pushed down to a lower level in the same tube and steel needle or razor blade floats on water even though steel is denser than water

EXPERIMENT: To investigate the behaviour of a liquid surface

APPARATUS: Beaker, water, soup solution, razor blade or steel needle.

PROCEDURE:

Fill the beaker with clean water to the brim as shown

Place a dry steel needle or razor blade at the edge of the beaker and carefully introduce it on the surface of water. Take care not to break the surface of water. Observe what happens.
Put a few drops of soap solution and observe what happens.
Depress the tip of the needle into the water and observe what happens.

OBSERVATIONS

The razor blade/needle floats on the surface of water and remains resting so long as the water surface is not broken.
When drops of soap solution are put on the surface of the water around the razor blade/steel needle, the razor blade/steel needle sinks after a few minutes.
Depressing the razor blade highly allows it to sink very quickly

EXPLANATION

The razor blade/needle floats because the surface of water behaves like a fully stretched, thin, elastic skin. The force which causes the surface of a liquid to behave like a stretched skin is called surface tension. This force is due to the force of attraction individual molecules of the liquid (cohesive force)

The needle or blade sinks when drops of soap solution are put near the razor/needle because the soap solution reduces surface tension of the water.

When the tip of the needle or razor is depressed into the liquid, it pierces the surface skin and sinks.

MOLECULAR EXPLANATION OF SURFACE TENSION

A Molecule say C deep in the liquid is surrounded by molecules on all sides so that the net force in it is zero. However, molecules of the surface, say A and B will have fewer molecules on the vapour side and hence it will experience a resultant inward force causing the surface of the liquid to be in tension.

FACTORS AFFECTING SURFACE TENSION

Impurities – impurities reduces surface tension of a liquid. Detergents weaken the cohesive forces between the liquid molecules.
Temperature – Increasing the temperature of a liquid increases kinetic theory of molecules. The inter-molecular distance increases and the force of cohesion is decreased hence surface tension is lowered.

CONSEQUENCES/EFFECTS OF SURFACE TENSION

Water insects can rest on the surface of water without breaking the surface. The insects skate across the surface at high speed.
Mosquito larvae float on water surface. Oiling the surface using kerosene lower surface tension making larvae to sink

NOTE:

Behaviour of soap bubbles- the soap bubbles flatten into thin films and try to rise up the funnel. This is because the surface tension makes it to behave as if it is a stretched elastic skin. As it tries to make its surface as small as possible, the bubble rises up the funnel.
Behaviour of soap film-the soap films in the wire loop with thread loosely tied across are used in this case. It is observed that when the film is broken on one side, the thread assume a perfect curve. This is because the surface tension will act on one side of the thread. Water tries to make its surface as small as possible, thus pulling the thread in such a way that it forms a perfect curve.
The appearance of water drops coming out of a tube- it is observed that the water drop grows to a large spherical drop before falling down. The water behaves as if there is an elastic membrane which stretches as more water gets into it. When it can not hold any more water, it falls.
Surface tension of soap is less than that of water- A matchstick or a small toy boat is rubbed with soap at one end and placed on the water surface, it start moving immediately. It moves in one direction only and in such a way that the end that is not rubbed with soap is always in front. The soap lowers/weaken/reduce the surface tension at the end of the stick. The surface tension at the other end which is now greater pulls the stick and makes it move in that direction. The movement gradually weakens and ultimately ceases when the whole surface of water is covered with soap solution. Camphor has the same effect as that of soap.
A glass tumbler can be filled with water above the brim. This is because the surface of the water behaves as if it is a thin elastic membrane as it stretches to hold more water.
When a brush is in water, the bristles spread but when it is taken out of water, they cling together. When in water, there in no surface tension since the tension is only on the exposed surface. When the brush is taken out of the water, the surface tension acting on the surface of water tends to be as small as possible thus pulling the bristles together.
When it is raining, it is advisable not to touch a canvas tent from inside. Touching the canvas tent or umbrella with lower/reduce/weaken the surface tension thus making water to leak into the tent.

ELECTROSTATIC FORCE

This is a type of force which causes attraction or repulsion between charges.

Charges can be positive or negative.

Like charges repel and unlike charges attract

EXAMPLES

A plastic pen or ruler rubbed on a dry hair or fur picks up small pieces of paper lying on a table when it’s brought near them. (Charges are created on the pen and attract the pieces of paper). The same pen or ruler attracts a stream of water from a tap. The rubbing creates static charges
When a glass window is wiped with a dry cloth on a dry day, dust particles are attracted on it.
When shoes are brushed, they tend to attract dust particles
When you remove cloth at night you observe sparks. The sparks are due to neutralization of the static charges formed when a nylon cloth is being pulled off.

ELECTRIC FORCE

It’s a force which acts on two conductors carrying electricity.

ACTION AND REACTION

They are two equal forces but acting in opposite to each other. When a block of wood is placed on a table, its weight acts on a table (action). It is pressed on the surface downwards. The reaction (opposite force) of the table acts on the block.

When one force acts on a body, an equal and opposite force acts on one another.

MASS AND WEIGHT

Mass is the quantity of matter in an object while weight is a measure of the pull of gravity on an object. The S.I unit of mass is kg (kilogram) and of weight is Newton (N).

Mass of an object is a scalar quantity while weight is a vector quantity (since weight is a pull of gravity directed to the centre of the earth).

Due to the shape and rotation of the earth, the weight of an object varies from place to place while mass is constant (does not change).

A body weighs more at the poles than at the equator.

DIFFERENCES BETWEEN MASS AND WEIGHT

Mass	Weight
1. Its a quantity of matter on a body.	1. It is a pull of gravity on a body.
2. It’s measured in kg.	2. It is measured in (N)
3. Same everywhere.	3. Varies from one place to another.
4. Measured using a beam balance.	4.Measured using a spring balance
5.Has magnitude only (scalar quantity)	5.Has both magnitude and direction.(vector quantity)

RELATIONSHIP BETWEEN MASS AND WEIGHT

Weight = Mass x gravitational

W = mg

EXAMPLE 2

Find the weight of an object whose mass is 50 kg.

W = mg

= 50 x10

= 500 N

Find the mass of an object whose weight is 900N

W = mg

900/10 = 10/10m

Mass, m = 90kg

An astronaut weighs 900N on earth .On the moon; he weighs 150 N.

Calculate the moon’s gravitational strength. (g=10N/Kg)

Mass, m = w/g

= 900/10

= 90kg

On moon, w = mg

g = w/m

= 150/90

= 1.67N/Kg

3.2(NOs. 1, 2, 4) KLB

MEASURING FORCE

Force is measured using an instrument called a spring balance.

The extension of a spring can be used to measure an applied force. The larger the force, the more the spring extends.

A spring balance measures forces and should therefore calibrated in newtons.

Some spring balances are calibrated in kilograms. In such cases, one is advised to convert from kilograms to newtons. (1Kg=10N)

EXAMPLE 3

The length of a spring is 16.0cm. Its length becomes 20.0cm when supporting a weight of 5.0N. Calculate the length the length of the spring when supporting a weight of; a)2.5N b)6.0N c)200N

Solution

a) 5N – 4cm b) 5N – 4cm c) 5N = 4cm

2.5 N- ? 6 N- ? 200N =?

(2.5 x 4)/5=2cm (6 x 4)/5 =4.8cm (200 x 4)/5= 160

2+16=18cm 4.8+16 = 20.8cm 160+16 =176cm

Note; In c) extension is too large and spring may straighten out.

EXAMPLE 4

A spring stretches by 8.0mm when supporting a load of 2.0N. (i) By how much will it stretch when supporting a load of 6.0N? (ii) What load would make the spring extend by 2.5cm?

Solution

i) 0mm -2.0N ii) 8.0mm -2.0N

?-5.0N 25mm=?

x 8)/2 =20mm (25 x2)/8 = 6.25N

EXAMPLE 5

8kg

The figure below shows two identical spring balances supported as shown:

A B

State the reading on each spring balance.

Each spring will read =80/2=40N

EXAMPLE 6

Three identical arranged as shown below were used to support a load of weight 20N. If the beam has a weight of 1N and each spring would extend by 1cm if a load of weight 4N is suspended from it, determine the extension of each spring.

20N

A B

Extension in spring A = Extension in spring B

= {(21/2) x1cm}/4N

= 2.265cm

Extension in spring C = (20Nx1cm)/4N

= 5cm

Exercise 3.3 no.2 KLB

SCALAR AND VECTOR QUANTITIES

A SCALAR QUANTITY – is a quantity which has magnitude (size) only. It can be specified by a number and unit. Examples include; mass, area, density, volume, energy, time, pressure, temperature, and length.

Scalar quantities are added by the normal rules of arithmetic e.g.3cm2+4cm2=7cm2

A VECTOR QUANTITY – is a quantity which has direction and magnitude (size). It can be specified by a number, unit and direction. Examples include; weight, force, velocity, displacement, acceleration, momentum and magnetic field strength.

A vector quantity is represented on a diagram by a straight line with an arrow i.e.

10N or 2N

The sum of two or more vectors is the resultant vector. Parallel forces which act on an object can be added arithmetically.

Examples of addition of parallel forces on a body

NOTE; Forces acting in opposite directions, the resultant is their difference.

To specify resultant force, both magnitude and direction are given

QUESTIONS ON THE TOPIC

A student was heard saying “the mass of a ball on the moon is one sixth its mass on earth”. Give a reason why this statement is wrong.
In the study of a free fall, it is assumed that the force f acting on a given body of mass m is gravitational, given by F= mg. State two other forces that act on the same body.
State how a lubricant reduces friction in the bearings of moving part of a machine.
Distinguish between mass and weight of a body stating the units for each.
State with reason the purpose of the oil that circulates in a motorcar engine.
Name two types of forces which can act between objects without contact.
A house in which a cylinder containing cooking gas is kept unfortunately catches fire. The cylinder explodes. Give a reason for the explosion.
Give a reason why the weight of a body varies from place to place
State why a pin floating on water sinks when a detergent is added.

Fig 8 shows water drops on two surfaces. In 8 (a), the glass surface is smeared with wax while in 8 (b) the glass surface is clean.

Explain the difference in the shapes of the drops.

An astronaut is on the moon. He drops a hammer from a height of 3.2m and it takes 2.0s to hit the lunar landscape. What is the acceleration due to gravity of the moon?
An unloaded spring has a length of 15cm and when under a load of 24N it has a length of 12cm. What will be the load on the spring when length is 10cm?
Give a reason why the weight of the body varies from place to place
A metal pin was observed to float on the surface of pure water. However the pin sank when a few drops of soap solution were carefully added to the water. Explain his observation.
A bag of sugar is found to have the same weight on planet earth as an identical bag of dry sawdust on planet Jupiter. Explain why the masses of the two bags must be different.
Fig 4 shows water drops on two surfaces. In (a) the glass surface is smeared with wax while in (b) the glass surface is clean.

Explain the difference in the shapes of the drops.

The diagram in figure 5 shows two glass tubes of different diameters dipped in water. Explain why h2 is greater than h1
Name two forces that determine the shape of liquid drop on the solid surface.

SOLUTIONS

The mass of the body is constant as the number of particles in a body remains constant. Mass is constant everywhere
Up thrust and frictional force
By going between two moving parts so that the parts slid on oil instead of each other.
– Weight is a vector quantity while mass is a scalar quantity.

– Weight varies from place to place while mass is constant.

– Weight is measured using a spring balance while mass is measured using beam balance.

To lubricate the engine/ reduce frictional force
Magnetic, electrostatic and gravitational.
Kinetic energies of molecules increase hence the pressure increases.
Because gravitational force varies with distance from the centre of the earth. Since weight depends on the gravitational pull, then it also varies.
The soap reduces the surface tension and hence the weight of pin becomes greater the surface tension.
In (a) adhesive forces between glass and wax are weaker than cohesive forces between water & water. The opposite is true (b)
6m /s²
40N
Either altitude or latitude/ radius of earth changes/ acceleration due to gravity from place to place away from the earth
Addition of soap solution to pure water reduces the strength of the skin total was holding pin from sinking and so it sinks. Surface tension supports the pin. Addition of soap reduces tension/weakens/broken.
Acceleration of gravity on Jupiter is higher than that of earth, so a bag of saw dust must be less massive if the greater acceleration on earth is to produce the same pull as sugar bag on earth.
In (a) cohesive forces between water molecules are greater than adhesive forces between water and wax while in (b) adhesive forces between water and glass molecules are greater than cohesive forces between water molecules.
Surface tension / adhesive forces supports water column or more capillarity in tube 2 than tube 1Surface tension is the same in both tubes and equal to the weight of water column supported Narrow tube has longer column to equate weight to wider tube. Volume of water in the tubes is same hence narrower tube higher column

MORE QUESTIONS

Figure 2 shows a funnel dipped into a liquid soap solution.

Explain what happens to the soap bubble when the funnel is removed.

An alloy contains 40% by mass of lead and 60% by mass of tin. Determine the density of the alloy in kgm³. (Density of lead = 1 l.4g/cm³ and density of tin = 7.3g/cm³

The water level in a burette is 35cm³. If 20 drops of water are added, what is the new level if each drop has a volume of 0.15cm³? A cylinder of height 25cm is completely melted and a sphere of the same radius made. Determine the radius of the sphere in metres and express your answer in standard form.
The figure below shows the change in volume of a liquid in a measuring cylinder when an irregular solid is immersed in it.

Given that the mass of the solid is 540g, determine the density of the solid in g/cm³.

Figure 2 below shows a measuring cylinder containing some water.

New reading …………………
New reading

Another 10 cm³ of water was added to the cylinder from a burette delivering volume from 0cm³ to 50cm³. Record in the spaces provided the new reading indicated on each vessel.

Figure 1 shows a millimeter scale placed in a position to measure the length of a block. An observer takes readings from position A and then from position B

3cm

2cm

1cm

•

Fig 1

State the difference in readings.

Two burettes A and B were arranged as shown below.

Burette A leaked into burette B at a rate of 10 drops per minute. If the initial reading on both burettes was 25ml, what would be their readings at the end of one hour if B does not leak and the average volume of one drop of water is 2.0 x 10^-8m³?

State any two factors that determine the choice of instrument for measuring length
The figure 1 below shows the level of mercury and water in a beaker.

Water

Mercury

Explain the difference in the shape of the meniscus.

The figure below shows part of a measuring cylinder containing a certain liquid

Use this information to answer questions below

State the accuracy of the measuring cylinder
What is the volume of the liquid in the measuring cylinder?

TOPIC 4: PRESSURE

Pressure is the force acting normally (perpendicularly) per unit area. The SI unit of pressure is N/m² or Nm^-2, which is also called Pascal (Pa).

Pressure in solids depends on two main factors i.e. force and area

EXAMPLE 1

A force of 100N is applied to an area 100mm2. What is the pressure exerted on the area in Nm^-2.

Solution

Area; 100mm² = .0000001m² and Force = 100N

Pressure = F/A

= 100 ÷ 0.0000001

= 1.0 x 10⁹Nm^-2

A man whose mass is 90kg stands on a floor.

If the area of contact between his feet and the floor is 0.0368m², determine how much pressure he able to exert on the floor.

Pressure, P = F/A

= 900N/0.0368m²

= 24,456.5217N/m².

What pressure will he exert on the floor if now he stands on one foot?

Pressure, P = 900N/ (0.0368/2)

= 48,913.0435N/m²

MAXIMUM AND MINIMUM PRESSURE

Maximum pressure = Force

Minimum area

Maximum Pressure P_max = F

A_min

Minimum pressure = Force

Maximum area

Minimum pressure P_min = F/A_max.

EXAMPLE 2

A block of wood measures 2cm by 3cm by 4cm and has a mass of 6 kg.

Calculate its pressure when; a) Area is minimum (maximum pressure) b) Area is maximum (minimum pressure).

Area -2 x 3 =6cm2

-2 x 4 =8cm2

-3 x 4 =12cm2

A min =6cm2 =0.006m2 and F =60N

P max =60/0.006 =100,000Nm^-2

A max =12cm2=0.0012m2 and f = 60 N

P_min = 60/0.0012 =50,000Nm^-2

EXERCISE

A block of wood measures 3m by 6m by 2m and mass 3kg. Calculate;
Maximum pressure
Minimum pressure
A brick 20cm by 10cm by 5cm has a mass of 500g. Find maximum and minimum pressure. (take g = 10N/kg)
How much force must be applied on a blade of length 4cm and thickness 0.1mm to exert pressure of 5,000,000 Pa.?

Exercise 4.1 (no 1, 2, 3, 4, 5) KLB

PRESSURE IN LIQUIDS

Pressure in liquids depends on the following;

Ø Depth of the liquid

Ø Density of the liquid

Pressure in liquids increases with depth and density.

EXPERIMENT: To show variation of pressure in liquids

APPARATUS: A tall tin, nail and water

PROCEDURE

Using the nail, make 3 holes A, B, C of the same diameter on a vertical line of one side of the tin
Fill the tin with water as shown below.
Observe water jets from the holes A, B, C.

OBSERVATION

The lower hole, A, throws water farthest, followed by B and lastly by c

EXPLANATION

The pressure of water at A is greatest than pressure at B and pressure at B is greater than pressure at C. Hence, pressure increases with depth.

QUESTION

Explain why a diver at the bottom of the dam experiences greatest pressure

At the bottom of the dam depth is greatest and therefore the diver experiences greatest pressure due to the weight above him.

LIQUID LEVELS

When a liquid is poured into a set of connected tubes with different shapes, it flows until the level are the same in all tubes as shown

This shows that the liquid flows to find its own level.

LIQUID LEVELS IN A U-TUBE

When water is poured into a u-tube, it will flow into other arm. Water will settle in the tube with the levels on both arms being the same.

When one arm is blown into with the mouth, the level moves downwards, while on the other arm it rises. This is caused by pressure difference between the two arms as shown,

Pressure in liquids increases with depth below its surface

Pressure in a liquid at a particular depth is same in all directions.

Pressure in a liquid increases with density of the liquid.

FLUID PRESSURE FORMULA

Consider a container containing a liquid as shown below;

If A is the cross-section area of the column, h the height of the column and ρ the density of the liquid then;

Volume of the liquid = cross-section area x density

= Ah

Mass of the liquid = volume of the liquid x density

= A h ρ

Therefore, Weight of the liquid = mass x gravitational force

= A h ρ g

From definition of pressure P = force/area

Pressure = A h ρ g

= h ρ g

From the formula (p = h ρ g) pressure is directly proportional to;

Height of the column
The density of the liquid

NOTE: Pressure in liquids does not depend on the cross-section area of the container.

The formula is also used to determine pressure due to a gas column.

EXAMPLE 3

A diver is 10m below the surface of water in a dam. If the density of water is 1000kg/m3, determine the pressure due to the water on the diver. (Take g=10N/Kg)

Solution

Pressure = h ρ g

= (10 x 1000 x 10)

= 100,000 N/m2

EXAMPLE 4

The density of mercury is 13600Kg/m3. Determine the liquid pressure at a point 76cm below mercury level.

Solution

Pressure = hρg

= 0.76 x 13600 x 10

= 103,360 N/m²

EXAMPLE 5

Calculate the pressure due to water experienced by a diver working 15m below the surface. (Take g = 10N/kg and density of sea water = 1.03g/cm³)

TRANSMISSION OF PRESSURE IN LIQUIDS

Pressure applied at one part in a liquid is transmitted equally to all other parts of the enclosed liquid. (Plunger)

This is the principle of transmission of pressure in liquids called Pascal’s principle which states that pressure applied at a given point of the liquid is transmitted uniformly or equally to all other parts of the enclosed liquid or gas.

Gases may transmit pressure in a similar way when they are confined and incompressible.

HYDRAULIC MACHINES

The principle of transmission of pressure in liquids is made use in hydraulic machines where a small force applied at one point of a liquid produces a much larger force at some other point of the liquid.

HYDRAULIC LIFT

The hydraulic lift consists of a small piston S of cross-section A1 and a large piston L of cross-section area A₂. When a force is applied on piston S, the pressure exerted by the force is transmitted throughout the liquid to piston L.

At the smaller piston S the force applied F₁ cause a pressure P₁ at the cross section area A₁.

Therefore, Pressure P₁= F₁

A₁

The pressure is equally transmitted throughout the liquid to the larger piston.

Thus at small piston pressure is equal to the pressure at the large piston

F₂= P₁ x A₂

But, P₁ = F₁

A₁

F₂= F₁ x A₂

A₁

F₂ = A₂

F₁ A₁

NOTE; Equation applies if pistons are at the same level

EXAMPLE 6

Find F₂ if A₁ = 0.52m², A₂ = 10m²and F₁= 100N

F₂ = 10

100 0.25

F₂= (100 x 10)

0.25

= 4000N

EXAMPLE 7

Determine f2 in the figure below. Density of the liquid =800kg/m3 and

g=10N/kg

Pressure at A, P_A= Pressure at B, P_B

(60 x 10) = (F₂) + (0.15 x 800 x 10)

0.008 0.00025

0.00025(7500 -1200) = F₂

F₂= 18.45N

Exercise 4.2 no.7

HYDRAULIC BRAKE SYSTEM

The force applied on the foot pedal exerts pressure on the master cylinder. The pressure is transmitted by the brake fluid to the slave cylinder. This causes the pistons of the slave cylinder to open the brake shoe and hence the brake lining presses the drum. The rotation of the wheel is thus resisted. When the force on the foot pedal is withdrawn the return spring pulls back the brake shoe which then pushes the slave cylinder piston back.

Advantage of this system is that the pressure exerted in master cylinder is transmitted equally to all four wheel cylinders.

The liquid to be used as a brake fluid should have the following properties;

Be compressible, to ensure that pressure exerted at one point is transmitted equally to all other parts in the liquid
Have low freezing point and high boiling point.
Should not corrode the parts of the brake system.

ASSIGNMENT (exercise 4.2 no 1, 2, 3,4,5,6 & 8) KLB

ATMOSPHERIC PRESSURE

Atmosphere means the air surrounding the earth. The air is bound round the earth by the earth’s gravity. The atmosphere thins outwards indicating the density of air decreases with the distance from the surface of the earth

The pressure exerted on the surface of the earth by the weight of the air column is called air pressure

Atmospheric pressure can be demonstrated by crushing can experiment.

EXPERIMENT: To demonstrate the existence of the atmospheric pressure

APPARATUS: Tin container with a tight-fitting cork, water, tripod stand, Bunsen burner.

PROCEDURE

Remove the cork from the container and pour in some little water.
Boil the water for several minutes.
Replace the cork and allow the container to cool or pour cold water to cool it faster.

OBSERVATION

During cooling, the container crushes in.

EXPLANATION

Steam from boiling water drives out most of the air inside the container. When heating, the steam pressure inside the container balances with atmospheric pressure outside.

On cooling the steam condenses. A partial vacuum is therefore created inside the container. Since pressure inside the container is less than the atmospheric pressure outside, the container crushes in.

NOTE: Steam inside the container condenses lowering the pressure. The outside atmospheric pressure exceeds the pressure inside the container thereby crushing it.

MAXIMUM COLUMN OF LIQUID THAT CAN BE SUPPORTED BY

ATMOSPHERIC PRESSURE

When water is sucked up a straw, the air inside the straw reduces. The atmospheric pressure acting on the surface is now greater than the pressure inside the straw. Water is thus pushed up the straw by atmospheric pressure.

If the straw was long enough and sealed at the top, it would be possible to estimate the height of water that would be supported by atmospheric pressure

In case of water the column is too large.

At sea level the atmospheric pressure supports approximately 76cm of mercury column or approximately 10m of water column.

EXAMPLE 8

A girl in a school situated in the coast (sea level) plans to make a barometer using sea-water of density 1030 kg/m³. If atmospheric pressure is 103,000 N/m², what is the minimum length of the tube that she will require?

Solution

P = h e g but p is atmospheric pressure

103,000 = h x 1030 x 10

H = 10m

EXAMPLE 9

A sea diver is 35m below the surface of sea water. If the density of the sea water is 1.03g/cm³ and g=10N/kg. Determine the total pressure on him.

Solution

Total pressure, P_T = Pa + h e g

= 103,000 + (35 x 1030 x 10)

= 463,500N/m²

EXAMPLE 10

The air pressure at the base of a mountain is 75cm of mercury while at the top is 60cm of mercury. Given that the average density is 1.25kg/m³ and density of mercury is 13,600kg/m³. Calculate the height of the mountain.

Solution

Pressure difference due to column of air = pressure difference due to mercury column

h_aρ_ag = h_m ρ_m g

h_a= h_mρ_m g

ρ_a g

h_a = (0.15 x 13600 x 10)

(1.25 x 10)

= 1632m

EXERCISE

The barometric height at sea level is 76cm of mercury while that at a point on a highland is 74cm of mercury. What is the altitude (height) of the point? Take g =10N/kg, density of mercury =13600kg/m³ and density of air =1.25kg/m³.
A student in a place where the mercury barometer reads 75cm wanted to make an alcohol barometer, if alcohol has a density of 800kg/m³, what is the minimum length of the tube that could be used?

MEASUREMENT OF PRESSURE

THE U-TUBE MANOMETER

Is an instrument used to measure fluid pressure.

It consists of a u-tube filled with water or any other suitable liquid or gas as shown

Pressure at Z = Atmospheric pressure due to column of water.

Pressure at X = pressure at Z

Pressure at X = P_g

Pressure at Z = atmospheric pressure + pressure due to column of water

P_g = P_a + h ρ g.

Since the density of water and gravitational force is known we can determine pressure of a gas if the atmospheric pressure is known.

EXAMPLE 11

Suppose h=20cm, Pa = 103,000N/m² and density=1000kg/m³, determine the total pressure (P_g)

Solution

P_g = 103,000 + (0.2 x 1000 x 10)

= 105,000N/m²

SIMPLE MERCURY BAROMETER

At sea level atmospheric pressure supports approximately 76cm of mercury column or 10m of water column. This difference in height column between mercury and water is that mercury is much denser than water.

Mercury column forms a simple barometer, its height changing inside on the glass tube as air pressure outside changes.

The space above mercury in the barometer tube must contain air or water vapour since the barometer reading will be as shown above.

The space above in mercury in the tube when upright is called toricellian vacuum

The height h of the column is a measure of the atmospheric pressure.

At sea level, h=76cm since density of mercury = 13600kg/m³.

Atmospheric pressure, Pa = h ρ g

= 0.76 x 13600 x 10

= 103,360N/m² (it is also referred as one atmosphere 1 atm)

FORTIN BAROMETER.

This is an improved version of a simple mercury barometer. Was designed by

FORTIN

The ivory pointer acts as the zero mark of the main scale. The leather bag acts as reservoir of mercury height.

Before taking the reading, the level of mercury surface in the reservoir is adjusted by turning the adjusting screw until the surface of mercury just touches the tip of the ivory index.

The height is the read from the main scale and vernier scale. The readings obtained from the barometer are in terms of the height of mercury column and written as mmHg or cmHg.

For example at sea level h=760mmHg and density of mercury=13600kg/m3

Pa = h ρ g

= 0.76 x 13600 x 10

= 103,360Nm^-2

ANEROID BAROMETER

Is a portable type of barometer consisting of a sealed, corrugated metal box as shown below

The pointer would indicate a particular value of atmospheric pressure of the surrounding so that any changes in pressure would be noticeable by movement of the pointer to either side of this atmospheric value on the scale.

The aneroid barometer movement makes it adaptable to measure heights.

Aneroid barometers (Altimeters) are used in aircrafts to measure heights. Its normally calibrated in millibars. 1 bar=100,000Nm^-2

1millibar (mbar) = 100Nm^-2

PRESSURE GAUGES

They are portable and are used mostly for measuring gas pressure, tyre pressure, pressure of compressed air compressors and steam pressure

It is made of coiled flexible metal tubes which uncoil when the pressure inside increases. The movement of the tube is made to drive a pointer across a scale, through a combined system of levers and gears.

EXAMPLE 12

The pressure of a car tyre, measured with a pressure gauge is 40Ncm-2. What is the total pressure of the tyre in Nm^-2?

P_Total= P_a +gauge pressure

= 103,360 + (40 x 10,000)

= 503,360Nm-2

APPLICATION OF PRESSURE IN LIQUIDS AND GASES

THE BICYCLE PUMP

A bicycle pump is a simple form of compression pump.

The pump is connected to a tyre which has a rubber valve in it. When the pump handle is drawn out air below the washer expands and its pressure is reduced below the atmospheric pressure.

Air from outside the pump the flows past the leather washer into the barrel. The higher air pressure in the tyre closes the tyre valve.

When the pump handle is pushed in, the air in the pump barrel is compressed.

The high pressure in the barrel presses the leather washer against the sides of the barrel. When the pressure of the compressed air becomes greater than that of air in the tyre, air is forced into the tyre through the tyre valve which now opens.

NOTE: There is an increase in temperature of the pump barrel during pumping because work is done during compressing the air.

THE LIFT PUMP

It is used to raise water from wells. It consists of a cylindrical metal barrel with a side tube. It has two valves P & Q.

UPSTROKE

When the plunger moves during upstroke, valve P closes due to weight and pressure of water above it. At the same time, air above valve Q expands and the pressure reduces below atmospheric pressure.

The atmospheric pressure on the water surface in the well below this pushes water up past valve Q into the barrel. The plunger is moved up and down until the space between P and Q is filled with water.

DOWNSTROKE

During down stroke valve Q closes due to its weight and pressure of water above its piston.

Limitations of Lift Pump

The atmospheric pressure support only 10m column of water, which is actually a theoretical value but practically this pump raises the water less than 10m because of;

Low atmospheric pressure in places high above sea level.
Leakages at the valves and pistons

FORCE PUMP

This pump can be used to raise water to heights more than 10m.

UPSTROKE

During upstroke, air above the valve S expands and its pressure reduces below atmospheric pressure. The atmospheric pressure on the water in the well below pushes water up past valve S into the barrel.

NOTE: Pressure above valve T is atmospheric hence the valve does not open.

DOWNSTROKE

During down stroke, the valve S closes. Increase in pressure in the water in the barrel opens valve T and forces water into chamber C so that as water fill the chamber air is trapped and compressed at the upper part.

During the next stroke, valve T closes and the compressed air expands ensuring continuous flow.

Advantages of a Force Pump over a Lift pump

Force pump enables continuous flow of water.
Height to which water can be raised does not depend on the atmospheric pressure. It depends on;
Amount of forces applied during down stroke.
Ability of the pump and its working parts to withstand pressure.

THE SIPHON

A tube can be used to empty tanks or draw petrol from petrol tanks in cars.

When used in this way it is referred as a siphon

Pressure on the surface of the liquid is atmospheric pressure. Since end C of the tube is below the surface A by height h, pressure at C is greater than that at the surface.

The tube is first filled with the liquid after which it will continue to run so long as end C is below the liquid surface.

Pressure at C = pa + h e g. The excess pressure (h e g) cause the liquid to flow out of end C

The siphon will work only if;

End of the tube C is below the surface of A of the liquid to be emptied.
The tube is first filled with the liquid, without any bubbles in it.
The tube does not rise above the barometric height of the liquid from the surface A of the liquid to be emptied.
One end of the tube is inside the liquid to be emptied.

NOTE: A siphon can operate in a vacuum.

REVISION QUESTIONS

The atmospheric pressure on a particular day was measured as 750mmHg. Express this in Nm-2. (Density of mercury = 13600kg/m³ and g=10N/kg)

Solution

P = h e g

= 0.75 x 13600 x 10

A roof has a surface area of 20,000cm². If atmospheric pressure exerted on the roof is 100,000Nm^-2, determine the force on it. (Take g = 10N/kg)

The diagram below shows a simple barometer

(i)Name the part labeled A

(ii)Explain what would happen to the level of mercury in the tube if the barometer was taken high up the mountain

Force applied to brake pads

Figure 2 below represents a car hydraulic braking system.

Fluid

Slave piston

Master piston

Foot pedal

Use the information given in the diagram above to answer questions

a) State one property the fluid should have.
b) Explain briefly how the system operates.
The diagram below shows a water tank of height h?

What is the relationship between the velocity V of the water jet and the height h

State the possible reason why, if water is used as a barometer liquid, the glass tube required to hold the column of the liquid is longer
State the definition of atmospheric pressure
What is the density of alcohol?
A person’s lung pressure as recorded by a mercury manometer is 90 mm Hg. Express this pressure in SI units.
The barometric height at sea level is 76cm of mercury while at a point on a highland it is 74cm of mercury. What is the altitude of the point? (Take g = 10m/s^2, density of mercury = 13600kg/m³and density of air as 1.25kg/m³)
Figure 4 below shows a measuring cylinder of height 30cm filled to a height of 20cm with water and the rest occupied by kerosene

Fig. 4

Given that density of water = 1000Kgm^-3, density of kerosene = 800Kgm^-3 and atmospheric pressure = 1.03×10⁵ Pa, determine the pressure acting on the base of the container

State Pascal’s principle of transmission of pressure
A helical spring extends by 1 cm when a force of 1.5N is applied to it. Find the elastic potential energy stored in it.
Two immiscible liquids are poured in a container to the levels shown in the diagram below.

If the densities of the liquids A and B are 1g/cm³ and 0.8g/cm³ respectively, find the pressure acting upon solid C at the bottom of the container due to the liquids

Mark the position of the water levels in the manometer when the gas supply is fully turned on
Calculate the pressure of the gas supply (Atmospheric pressure = 1.0×10⁵Pa)

A small nail may pierce an inflated car tyre and remain there without pressure reduction in the tyre. Explain the observation
(a) State two ways of increasing pressure in solids

(b) The figure 1 shows a liquid in a pail

Suggest a reason why pail manufacturers prefer the shape shown to other shapes

A block measuring 20cm x 10cm by 5cm rests on a flat surface. The block has a weight of 3N. Determine the maximum pressure it exerts on the surface.

(Effort)

10KN

LOAD

Liquid X

60cm

The figure below shows a hydraulic press P which is used to raise a load of 10KN. A force F of 25N is applied at the end of a lever pivoted at O to raise the load

(a) State one property of liquid X

(b) Determine the distance x indicated on the press if force on piston B is 100N

Mercury –in-glass barometer shows a height of 70cm. What height would be shown in the barometer at the same place if water density 1.0 x 10³kg/m³ is used. (Density of mercury = 13600kgm^-3)
The total weight of a car with passengers is 25,000N. The area of contact of each of the four tyres with the ground is 0.025m². Determine the minimum car tyre pressure
(a) The diagram below represents a u-shaped glass tube sealed at one end and containing mercury

(i) What is the pressure of the gas as shown in the diagram above?

(ii) Explain why the gas should be dry if it is to be used to verify a gas law

(iii) Describe how the arrangement can be used to verify Boyle’s law.

(b) Use the kinetic theory of gases to explain why;

(i) The pressure of a gas increases with temperature increase

(ii) The pressure of a gas decreases as volume increases

The reading on a mercury barometer at Mombasa is 760mm. Calculate the pressure at Mombasa (density mercury is 1.36xl0⁴Kgm^-3 )
The figure below is a manometer containing water. Air is blown across the month of one tube and the levels of the water changes as the figure below.

Blow air

Explain why the level of water in the right limb of manometer is higher.

In the diagram below, the U-tube contains two liquids; X and Y which do not mix. If the density of liquid Y is 900Kgm^-3 and that of X is 1200Kgm^-3, calculate the height of liquid Y

SOLUTIONS

Because of its low density
Atmospheric pressure is the pressure exerted on the surface of the surface of the earth by the weight of the air column
h_wƍ_wg = h_wƍ_wg

∴ h_wƍ_w =h_aƍ_a

Density of alcohol = 16 cm x 1g/cm³ x 1000

20 cm

= 800 kgm^-3

P = h ƍ g

= 90 m x 13600kgm^-3 x 10Nkg^-1

1000

= 12 240 Nm^-2

(76 – 74) X 13600 X 10 = h X 1.25 X 10

100

H = 2 X 13600

100 1.25

= 217. 6 m

Pressure due to kerosene = h kg

= 800 x 0.1 x 10 = 800p.aÖ1

Pressure due to water = w h w g

= 1000 x 0.2 x 10 = 2000p.aÖ1

Atmospheric pressure = 103,000p.a

Total pressure = 800 + 2000 + 103000

= 105800 Pa

Pressure applied at one pat in a liquid is transmitted equally to all other parts of the enclosed
Pressure on = L f g

Solid at c = (0.02 x 1000 x 10) + (0.04 x 800 x 10);

= 200 + 320

= 520 N/m²

Difference in the level of water should be 20cm
Pressure of the gas = Atmospheric pressure + ehg;

= 1.0 x 10⁵ + 20 x 1000 x 10

100

= 1.0 x 105 + 2.0 x 103Nm^-2

= 1.02 x 105Pa;

– Rubber is elastic; and when a nail is pushed through it stretches and grips firmly the nail without allowing air leakage; or – Valve effect pressure from inside causes tyre rubber to press firmly on the nail;
(a) – Increasing the force (weight)

(b) Slanting sides increase the area supporting the weight of the liquid, hence its effect

on the bottom of the container

Max pressure = ^Force/_{Min Area} Ö 1

= ^3N/ 0.1 X _0.05Ö1

= 600N/m² Ö 1

(a) – Incompressible

– Not corrosive

– Has low freezing point and high boiling point (any one)

h₁p₁g = h₂p₂g

h₂ = h₁p₁

p₂

= 0.7 x 13600Kg/m³

1000kgm^-3

= 9.52m

Pressure = Force

Area

= 2500

4 x 0.025

= 250,000Pa

a) i) Atmospheric pressure 1.05 x 10⁵N/M²
ii) Any water vapour available is near its condensing point. Intermolecular forces

are therefore appreciable Ö, so it does not behave like an ideal gas

iii) – Fix a millimeter scale to read the length ( L) of air column B Ö and the difference in height (h) between the levels A and CÖ

– Adjust the level of C by adding more mercury a little at a time and record the

corresponding values of L and h each time Ö

A graph of L against h represents Boyle’s law Ö
i) Increase in temperature causes gas molecules to move faster(increases in kinetic energy), Ö hence they generate greater/ higher impulsive force on impact Ö
With increase in volume gas molecules are sparsely spaced Ö so the rate of collision is reduced/ lowered

MORE QUESTIONS

The total weight of a car with passengers is 25000N. The area of contact of each of the FOUR tyres with the ground is 0.025m².

Determine the minimum car tyre pressure.

I Write an expression for pressure on a liquid in hydraulic jack
II While using a jack, a mechanic applied a force of 100N on the effort piston while raising the rear part of a car.

Determine the maximum load that can be raised
Give a reason why gas is not suitable for use in place of the liquid in a jack.

The lift pump is effective for pumping water as long as the well is less than 10m deep. Explain.
The reading on a mercury barometer at Mombasa is 760mm. Calculate the pressure at Mombasa (density of mercury = 1.36 x 10⁴ Kgm^-3)
State one property of a barometer liquid and explain its effects.

Figure 1 below shows a liquid being siphoned from one beaker to another. Refer to this diagram where answering questions 5, 6 and 7

Indicate on the diagram the direction of flow of the liquid
Show that the force driving the liquid through the U – tube is proportional to the height, h
State what would happen to the flow if the system in figure 2 were put in vacuum.
Figure above shows a U tube containing two liquids L1 and L2 of densities 0.8 g cm^-3 and 1.8 cm^-3 respectively in equilibrium. Given that h2 = 8 cm determine the value of h1
A small nail may pierce an inflated car tyre and remain there without pressure reduction in the tyre. Explain this observation
The height of the mercury column in a barometer at a place is 64cm. What would be the height of a column of paraffin in barometer at the same place? (Density of paraffin = 8.0 x 102 kgm^-3)
A vacuum pump was used to pump out air from the glass tube immersed in liquids as shown in figure 3.

After sometime the level of paraffin rose to position X. Mark the corresponding position for the water level. Give a reason for your answer.

A hole of area 2.0 cm²at the bottom of a tank 2.0m deep is closed with a cork. Determine the force on the cork when the tank is filled with water. (Density of water is 1000kg/m³ and acceleration due to gravity is 10m/s²).
The reading on a mercury barometer at a place in 700mm. What is the pressure at the place Nm^-2 (Density of mercury is 1.36 x 104 kgm^-3)
In an experiment to demonstrate atmospheric pressure, a plastic bottle is partially filled with hot water and the bottle is then tightly corked. After some time the bottle starts to get deformed

(a) State the purpose of the hot water.

(b) State the reason why the bottle gets deformed. Explain your answer.

Figure 4 shows a lift pump.

(a)Explain why, when the piston is;

i) Pulled upwards, valve A opens while valve B closes.
ii) Pushed downwards, valve A closes while valve B opens.
After several strokes, water rises above the piston as shown in Figure 5.
State how water is removed from the cylinder through the spout.
c) A lift pump can lift water to a maximum height of 10m.

Determine the maximum height to which the pump can raise paraffin. (Take density of paraffin as 800kgm^-3 and density of water as 1000kgm^-3).

State one factor that determines the height to which a force pump can lift water.
Explain why a dam is thicker at its base than at the top.
The pressure exerted by the atmosphere on a table is 100,000Pa. What does this mean?
On a dining table of area 1m², air pushes down with force of 101,000N (atmospheric pressure = 101,000Pa). Explain why the table does not collapse or break.
Explain why the level of mercury in a mercury barometer varies from day to day.
If atmospheric pressure is 101,000 N/m², what force is exerted on a wall of area 12m²?
Explain why you can fill a bucket from a downstairs tap quicker than from an upstairs tap
Explain why a giraffe must have a stronger large heart compared to a human being.
State why a barometer will show a greater reading when taken down a 200m pit.
A hydraulic press has the small piston of area 5cm² and a force of 40N is applied to it.
(i) Calculate the pressure transmitted throughout the liquid.

(ii) If the larger piston has an area of 20cm², what is the force exerted on it?

Explain why a sharp knife cuts well than a blunt one.
State Pascal’s principle of pressure.
Explain why the atmospheric pressure decreases with increasing the height or altitude.
Explain why we do not feel the great air pressure around us.
Why do deep sea divers wear diving suits?
Why are planes pressurized?
Explain how a drinking straw operates when in use.
Explain how a syringe operates when being used.
Describe the working of a hydraulic press
Study the diagram below:

ρ₁ρ₂20cm

h₁

If ρ₁= 2000kg/m³ and ρ₂ = 1500kg/m³, calculate h₁.

Explain why walking on a murrum road in bare feet is more painful than walking on sand.
A pressure of 2000Pa acts on an area of 0.05m². What force is produced?
At sea level, what is the approximate value of atmospheric pressure in

(a) Pa

(b) MmHg

Why is mercury used in a barometer rather than water?
Study the diagram below:

65 Mercury

Gas supply

40cm meter rule

(a) Record the excess pressure shown by the meter in mmHg

(b) If the atmospheric pressure is 760mmHg, what is the pressure of the gas supply?

State one advantage of fitting wide tyres on a vehicle that moves on earth roads.
A small nail may piece an inflated car tyre and remain there without pressure reduction in the tyre. Explain this observation.
The height of the mercury column in a barometer at a place is 74cm. What would be the height of a column of a water barometer at the same place? (Density of mercury is 13.2g/cm³ and water 1g/cm³.)
Explain why it may not be possible to suck a liquid into your mouth using a drinking straw on the moon surface
Derive the formula P=h ρ g where P = pressure, h = height or depth, ρ = density of liquid and g = gravity.
The figure below shows a manometer connected to a small funnel whose mouth is covered by a rubber membrane. The funnel is dipped into water in a container.

h₁

Water

Mercury

3.0m

Rubber and funnel

(a) Given that the density of mercury is 13.6g/cm³ and that of water is 1g/cm³, determine the pressure indicated by the manometer.

(b) Determine the height h₁.

The diagram below shows a liquid being siphoned from one beaker to another. Use this information to answer the questions that follow:

(a) Indicate on the diagram the direction of flow of the liquid

(b) Show that the force driving the liquid through the pipe is proportional to the height h.

State and explain what would happen to the flow in question 2 above if the system in the diagram were put in a vacuum.
Give a reason why water is not a suitable liquid for a barometer.
A rectangular block measures 10cn x 5cm x 4cm and has a mass of 2.2kg.
a) (i) If the gravitational field intensity is 10N/kg, what is the weight of the block?

(ii) What is the area of the smallest face of the block?

(iii) What pressure will the block exert when it is resting on a table on its smallest face?

(iv) What is the least pressure the block exerts on the table?

(b) Calculate the volume of the block.

A diving bell is pressurized inside to a pressure of 1,000,000Pa above atmospheric pressure. This diving bell is made for use at 100m below the sea surface for oil exploration. The pressure outside the diving bell must be equal to the pressure inside for its door to open. (Opens from inside.)
1. Calculate the pressure at 100m depth in water.
2. Explain what would happen to the diving bell when the door opens at :
  1. 10m below the surface.
  2. 200m below the surface.

When the diving bell is under the sea, how is the pressure on top of it different from that underneath it?

Explain why the pressure difference in (c) produces buoyancy (upthrust).

Study the figure below:

The piston can be pushed in and out but no water can escape. If the larger piston is pushed into the pipe by a force of 200N,

Calculate the pressure applied to the water.
Determine the force exerted on the smaller piston.

pipe

Piston area 500cm²waterpiston area120cm²

(a) The figure below shows two cylinders connected by a pipe. in each cylinder there is a piston and the space below each piston is full of water.

10kg mass

P Q

Water

The area of piston P is 40cm² and the area of piston Q is 2500cm². A 10kg mass is placed on piston P.

Calculate the weight of the 10kg mass.
What is the downward force on piston P.

Determine the pressure on the water

State the pressure on the water at Q.
Calculate the upward force on Q.

(b) Kamau suggested that the above device could be used as a car jack.

Which piston (A, or B) would you use to support the car? Explain your answer.
Name the above device.
(a) If a lorry weighs 100,000N and has 4 tyres.
- Calculate the force exerted on the road by each tyre
- What assumption have you made in the calculation above
- If each tyre has an area of 0.2m² in contact with the road, calculate the pressure exerted.

(b) Using a diagram, explain how a bicycle pump operates when filling a tyre with air.

clip

30cm 50cm

Density density (ρ)

1000kg/m³

Calculate the density ρ of the other liquid.

(a) A car containing six adults and their luggage weighs 20500N. The area of contact of each tyre with the ground is 0.025m².
- Calculate the pressure exerted by each tyre on the ground.
- State any two assumptions made.
- The car has to be driven off the road and cross a patch of soft damp sand. The driver thinks that the tyres will sink into the sand and stop the car moving. One of the passengers suggests that the sinking can be prevented by letting some air out of the tyres.
  - I What effect would this have on the shape of the tyres?
  - II How would letting air out of the tyres stop the wheels from sinking.
  - III What other change could be made to stop the tyres sinking into the sand.
- The air pressure near the ground is about 101KPa. Some aircrafts fly at height of about 20km where the air pressure is only 27KPa.
  1. State two reasons why the outside air pressure is less at 20km than at the ground.
  2. If the air inside the aircraft is 101KPa, what is the difference in air pressure between the inside of the aircraft when fling at a height of 20km?

How does this difference in air pressure influence the choice of material used in the construction of the aircraft.

The door of the aircraft is designed to fit into the door frame from inside the aircraft. Explain why the door is designed to fit in this way.
If the fuselage of the aircraft has an area of 4000m², determine the force acting on the fuselage due to the difference in air pressure between the inside and outside of the aircraft at a height of 20km.

(a) The diagram below shows a manometer connected to a gas supply.

Gas in

U – Tube

The pressure of the gas supply above atmospheric pressure is equivalent to 20cm column of water.

Complete the diagram by marking the position of the levels of the water in the manometer when the gas supply is connected.
If the gas supply had only been partly turned on, what effect, if any, would this have had on the levels of the water in the manometer? Explain your answer.

Calculate the pressure of the gas supply above atmospheric pressure in Pascal’s. (ρ_w=1000kg/m³ )

(b) The diagram shows water standing to a depth of 20cm in a measuring cylinder. There are 500cm³ of water in the measuring cylinder.

Water 20cm

I If the density of water is 1g/cm³, calculate the mass and weight of the water in the measuring cylinder
II Using the weight in part (i), calculate the pressure exerted by the water on the bottom of the measuring cylinder.
III Mark with a letter P on the diagram above a position where the pressure exerted by the water is a quarter of the pressure calculated in part (ii)

a) A newspaper article claimed that a woman wearing shoes with heels which had a small area exerted more pressure on the ground than a n elephant.
- Explain in terms of the area how this is possible.
- The article claims that the pressure exerted on the ground by a woman weighing 600N wearing shoes with heels each having an area of 0.9cm² was 666.7N/m². What assumption was made about the way the woman was standing? Explain your answer.
- A typical elephant weighs 30,000N. If each of the elephant feet has an area of 600cm², calculate the pressure exerted by the elephant on the ground.

(b) A water storage tank is 20m above a tap. Given the density of water as 1g/cm³,

Calculate the pressure of the water at the tap in N/m².
The area at the end of the tap is 2.0x m²; calculate the force needed to stop the water leaving the tap.

When a shower is directly connected to another water storage tank, it is found that water will only flow when the shower head is lowered and not when it is raised. Why is this so? In which way can this problem be overcome?

(a) Describe a laboratory experiment to show that the pressure in a liquid increases with depth.

(b) The experiment in (a) is repeated with a liquid of lower density. What effect, if any, does this have on the pressure at different depths? Explain your answer.

Taken into account when constructing the wall of a dam.
Used in the measurement with a manometer of the excess pressure of the gas supply.

(b) The diagram below shows the inner details of a device called bourdon gauge which can be used to measure air pressure.

B C Pivots

Scale Flexible tube

Air pressure

As the air pressure increases the flexible tube straightens out. Explain why the pointer moves towards B when the air pressure increases.

The graph below shows how the pressure in water changes with depth below the water surface of a creek.

Pressure (kPa)

(880, 960)

(0, 100) Depth (m)

Use the graph to find the pressure at a depth of 800m.
Calculate the force exerted by the water on 2.0m² of the outside surface of a submarine at a depth of 800m.

State why the pressure is not zero at the surface of the water.

The part of the submarine containing the crew contains air at normal atmospheric pressure. Explain why the outside walls of this part of the submarine are usually made from very thick steel.
Explain why at a depth of 100m the pressure in sea water is different from lake water.
The diagram below shows a water storage tank supplying water to a tap at A.

Water storage tank

B A

If the water level in the tank is 4m above tap at A, calculate the pressure at A due to this water. (density of water = 1000kg/m³)
The tap is moved from A to B. Explain why the water pressure at the tap is unchanged.

The diagram is drawn to scale. An object becomes stuck in the pipe at C and the water is unable to flow to the tap. Calculate the pressure at C due to the water and explain your calculation.

If the cross section area of the pipe is 1.2x m², what force is acting on the object at C due to the water above it?
A pressure sensor attached to an airbag can be used to determine the weight of passengers in a train carriage. See diagram below.

Movable floor

Pressure sensor

Trail

In a trial using different number of passengers in a carriage the following results were obtained.

Numbers of passengers in a carriage	20	40	60	80	100	120
Pressure in MPa	8.8	11.2	12.2	14.0	15.0	16.8

Plot a graph of pressure (y-axis) against the number of passengers in the carriage.
What is the pressure when we have 55 passengers in the carriage?

Explain why
1. The graph does not pass through the point (0,0)
2. The points do not lie on a straight line
3. Similar readings would have been obtained if the pressure sensor had been placed at the other end of the airbag.

Rubber sucker– this is a shallow rubber cap. Before use it is moistened to get a good seal then pressed firmly on a smooth surface so that the air inside is pushed out. The atmospheric pressure will then hold it firmly against the surface as shown below. They are used by printing machines to lift papers, lifting glass panes, heavy metal sheets

-Drinking straw– when a liquid is drawn using a straw air is sucked through the straw to the lungs. This leaves the space in the straw partially evacuated. The atmospheric pressure pushing down the liquid in the container becomes greater than the pressure inside the straw and this forces the liquid into your mouth.

-The syringe– they work in the principle as the straw. They are used by the doctors in hospitals for giving injections.

State two reasons why mercury is preferred as a barometric liquid and not water
The diagram in figure 5 below shows hydraulic brake system.

Oil

Master cylinder

Slave piston

5000N

Foot pedal

Fig 5

A force of 20N is applied on the foot pedal to a piston of area 50cm² and this causes a stopping force of 5000N.

Determine;

Pressure in the master cylinder.
Area of the slave piston.

The height of mercury column in a barometer density 13600kg/ m^-3, at a place is 64cm. What would be the height of a column of paraffin in barometer at the same place?

(Density of paraffin = 8.0 x 10² kg /m³).

The figure 3 shows hydraulic press system using a lever of negligible mass, on the ride of the small piston pivoted at a point P. A force of 50N is applied at R.

Oil

Weight

Area 100cm²

Area 5cm²

50N

Calculate

Force exerted by small piston on the liquid.
Pressure of liquid below the small piston.
The weight of object supported on the larger piston

Water tanks in houses are erected as high as possible. Explain.

– Water will flow at high pressure√¹

Or- for water to have high potential energy √

The figure below is a gas jar completely filled with water and covered with a wire gauze.

Water

State the observation when the set-up is suddenly inverted.
Explain the observation made in (a) above.

TOPIC 5: PARTICULATE NATURE OF MATTER

Matter is anything that occupies space and has mass. Matter commonly exists in three states i.e. solid, liquid and Gas

The process of sub-dividing matter into smaller units and smaller units continues indefinitely, suggesting that matter is not continuous, but is made up of even smaller parts e.g. A piece of paper can be cut endlessly until a stage when the small pieces cannot be cut into pieces. This suggests that the sheet of paper is made up of tiny particles

DEMONSTRATION OF DILUTION

APPARATUS: Beaker and potassium permanganate crystals

PROCEDURE

Pour water into the beaker to half full.
Dissolve the potassium permanganate crystals until the solution is purple.
Transfer half of the solution to another beaker and add water
Continue the process with other beakers, comparing the colour to each other.

OBSERVATION

The process of dilution can continue until the solution appears colourless. This suggests that the particles of potassium permanganate are spread evenly on water.

As water particles increase, the particles of potassium permanganate are spread further, making the purple colourless and less until it appears colourless.

CONCLUSION

Potassium permanganate is made up of tiny particles.

DISSOLVING A SOLID IN A SOLVENT

100g of salt is put into the flask and water added carefully using a pipette without shaking the salt until it is full.
The stopper is then inserted to the mouth of the flask and shaken to dissolve the salt.

OBSERVATION

The volume of the solution of salt is less.

CONCLUSION

Particles of salt are able to occupy some spaces between the water particles.

This suggests that the particles of salt differ in size.

The particles of the solution pack more closely in the available space, thus reducing the volume. This further suggests that particles of salt are broken down to fit into spaces between water particles.

BROWNIAN MOTION

This is the random movement of particles of a substance in fluids. A fluid is anything that is capable of flowing, e.g. a gas or a liquid.

The particles in a fluid are in a constant random motion.

BROWNIAN MOTION IN LIQUIDS

DEMONSTRATION OF THE BROWNIAN MOTION

Apparatus: Beaker, hand lens, chalk dust, transparent lid.

PROCEDURE

Pour water into the beaker about full as shown

Sprinkle pollen grains or chalk dust on the surface of water (particles should be small in size, light and sprinkled evenly).
Cover the beaker with a transparent lid and with the help of a hand lens observes what happens to pollen grains or chalk dust.

OBSERVATION

The pollen grains or chalk dust is in constant random motion.

CONCLUSION

The particles are hit continually by the movement of small invisible particles of water. The movement is random, suggesting that the particles of water are in constant random movement. This kind of movement is called Brownian motion a tribute to a scientist Robert Brown who first observed the effect.

BROWNIAN MOTION IN GASES

THE SMOKE CELL EXPERIMENT

DEMONSTRATION OF THE BROWNIAN MOTION IN AIR

Apparatus: Drinking straw, smoke cell, microscope and a bright light source

In this case, one end of the straw is burnt and let the smoke from the other end of the straw into the smoke cell as shown above. The smoke is then covered using a transparent glass lid. The smoke cell is covered to seal the content of the smoke cell. This ensures that the smoke molecules do not escape from the smoke cell. The lid is transparent to allow for easy visible of the smoke cell. The cell is illuminate with bright light. Therefore, the work of lamp in this case is to provide light which illuminates the content of the smoke cell. A hand lens is used to focus the light on the smoke particles in the smoke cell. The microscope is adjusted until bright specks are seen against the grey background. The work of the microscope is therefore to enlarge/magnify the smoke particles in the smoke cell for easy visibility.

OBSERVATION

In this experiment, the smoke particles (which are seen as bright specks) are seen moving in continuous random motion.

EXPLANATION

The smoke particles appear as bright specks since they scatter the light shining on them and appear as bright points. They move about in a continuous random movement because of uneven bombardment by the invisible particles or molecules in air. This suggests that air is made up of small particles which are in constant motion.

When this experiment is repeated at a higher temperature, the smoke particles move faster in a continuous random manner. This is due to increased kinetic energies of the molecules. The opposite is true when the temperature of the content is reduced.

CONCLUSION

From the experiments above, matter is made up of very small particles which are in constant random motion. This is called kinetic theory of matter.

ARRANGEMENT OF PARTICLES IN THE STATES OF MATTER

SOLID

The particles of solids are closely packed together in an organised way.
The closely knit structure is due strong attractive forces (cohesive forces) between the particles.
In their fixed positions, they vibrate to and from so that increasing the temperature of the solid increases this vibratory motion.
At a certain temperature the solid breaks away from this knit structure and the solid is said to have melted.

LIQUIDS

The particles are further apart. They are not fixed as in solids but move about in Brownian motion.
Liquids can break a solute put in it. It’s easier to dissolve a solute in hot water because the particles have increased energy.
The cohesive forces between the particles in liquids are weaker compared to those in solids. Due to this liquids can flow and take up the shape of the container in which they are put.
When a liquid is heated molecules gain kinetic energy, they vibrate about and expand. The space between them widens further apart and the liquid changes into gaseous state by a process called

GASES

The particles are further apart and have increased random motion compared to those in the liquid state.
The cohesive force between the particles is extremely small and as the particles move they collide with each other and with the walls of the container in which they are trapped. This produces gas pressure.
Gases are easier to compress indicates that there exists a large intermolecular distance in gas than in liquids. Gas molecules or particles can lose some of their energy and fall back into the liquid state by a process known as

NOTE: Solids which when heated change directly into gas undergo the process called sublimation.

DIFFUSION

This is the process by which particles spread from regions of high concentration to those of low concentration. Diffusion takes place in solids, liquids and gases.
In solids, diffusion is exceedingly slow but occurs when two metals are placed in contact with each other e.g. lead and gold, metal block vibrating atoms breaks away from the substances to which they belong and enter the other substance to be trapped by its attractive forces. This process is speeded up by high temperature.
Diffusion in liquids occurs at a faster rate than in solids.
Diffusion in gases is faster due to their low density, high kinetic energy and weak cohesive forces.

DIFFUSION IN LIQUIDS

To investigate diffusion in liquids

Apparatus: Funnel, beaker, copper (II) sulphate solution.

PROCEDURE

Pour water into the beaker until it is half full.
Pour saturated copper (II) sulphate solution down the funnel slowly and notice how the two liquids settle.
Remove the funnel carefully so that the liquids are not disturbed.
Repeat the same steps for another set of apparatus but using warm liquids. Make observation.

OBSERVATION AND EXPLANATION

Initially, the water layer floats on top of the saturated copper (II) sulphate because it is less dense. After sometime, the boundary disappears and the liquids form a homogeneous pale blue mixture.
Formation of the mixture is faster with hot liquids than because the movement of particles is faster due to increased energy. There is greater movement of water particles (molecules) from the water layer into copper (II) sulphate layer because it has greater concentration of water molecules than copper (II) sulphate particles.
Similarly, there is a greater movement of particles from copper (II) sulphate layer into the water layer because of greater concentration of copper (II) sulphate particles than water molecules.

DIFFUSION IN GASES

OBSERVATION AND EXPLANATION

The bromine gas spreads into the gas jar B at a greater speed than it returns to gas jar A because of high concentration of bromine particles.
Likewise, air spreads in gas jar A at a greater rate than it returns to gas jar B because of high concentration of air particles in B.
A homogenous pale brown mixture forms in the two jars and because this happens in a very short time, it suggests that the random movement of particles is rapid (faster) than diffusion in liquids.

NOTE: Performing the same experiment with the jars held vertically instead of horizontally slows down the rate of diffusion because of the densities of the gases. The less dense gas diffuses much faster into the more dense gas.

RATES OF DIFFUSION

To investigate the rates of diffusion of ammonium gas and hydrochloric gas

OBSERVATION AND EXPLANATION

A white deposit of ammonium chloride forms on the walls of the glass tube in the region nearer end B. This suggests that ammonia gas diffused at a higher rate than hydraulic acid gas.
Different gases have different rates of diffusion. A gas of high density has heavier particles hence moves more slowly than lighter one.

DIFFUSION THROUGH POROUS MATERIALS

The porous pot has very fine holes through which the hydrogen gas diffuses into the pot and air diffuses out.
Hydrogen gas bubbles out of the glass tube as shown in the set up above.
When the gas supply is stopped hydrogen gas diffuses out of the pot through the fine holes at a faster rate than air gets back to the pot. This decreases the gas pressure acting on the water surface in the beaker to push water up the tube.

NOTE: The beaker is used to confine the hydrogen gas around the porous pot.

QUESTIONS

Explain why rotten eggs broken at one end soon spreads the room.
Explain the cause of random motion of smoke particles as observed in Brownian motion experiment using a smoke cell.
Two identical tubes A and B held horizontally contain air and water respectively. A small quantity of coloured gas is introduced at one end of A while a small quantity of coloured water is introduced at one end of B. State with reason the tube in which the colour will reach the other end faster.
Distinguish between solid and liquid states of matter in terms of intermolecular forces
A bottle containing a smelling gas is opened at the front bench of a classroom. State the reason why the gas is detected throughout the room.
Motion of smoke particles can be studied by using the apparatus shown in figure 9 to observe the motion; some smoke is enclosed in the smoke cell and then observed through the microscope.

Explain the role of the smoke particle, lens and microscope in the experiment
State and explain the nature of the observed motion of the smoke particles
State what will be observed about the motion of the smoke particles if the temperature surrounding the smoke cell is raised slightly.

SOLUTIONS

The spreading is due to diffusion. The odour moves from a region of higher concentration to a region of lower concentration through diffusion.
Air molecules are in constant random motion; smoke particles collide with these air molecules hence their random motion.
A or tube with air; Gas molecules move faster/quicker than water molecules OR Diffusion of gases is Faster/more than in water/Grahams law the density of air is less than that of water
In solids the molecules are held in position by intermolecular forces that are very large. In liquids the molecules are able to roll over one another since the forces are smaller
The gas diffuse/ from the region of higher concentration to a region of low concentration.
(a) Smoke particles show the behavior or movement of air molecule

Smoke particles are larger than air molecules/ visible and light enough to move when bombarded by air molecules; Lens Focuses the light from the lamp on the smoke particle; causing them to be observable; Microscope enlarge the smoke particles that they are visible/ magnifies smoke particles.

(b) Smoke particle move randomly / zigzag / haphazardly Air molecules bombard the smoke particles/ knock/ hit Air molecules are in random motion

(c)The speed of motion of smoke particles will be observed to be higher smocking particles move faster, speed increases, increased random motion

MORE QUESTIONS

Describe the motion solid molecules experience.
What type of motion do molecules in the liquid and gaseous state experience
Describe Brownian motion.
When food is being cooked in the kitchen, why is it possible to smell this food in other rooms in the house?
State the forms of energy possessed by particles in (a) solids (b) liquids (c) gases.
State the type of motions described by a molecule in (a) solid (b) liquid (c) gas.
What do you see when you use a microscope to study illuminated smoke floating in air?
Describe the main difference between molecules in the gaseous state and those in the liquid or solid state.
Describe and explain Brownian motion.
Explain why perfume can be smelt some distance away from the person wearing it.
A house in which a cylinder containing cooking gas is kept unfortunately catches fire. The cylinder explodes. Explain why.
Two identical containers A and B are placed on a bench. Container A is filled with oxygen gas and container B with hydrogen gas. The two gases have equal masses. The containers are maintained at the same temperature. State with reason the container in which the pressure is higher.
(a) A substance has molecules which are moving completely free and random manner.
1. Is the substance a solid, liquid or gas?
2. Draw below a diagram to show the path followed by one of these molecules when it is moving randomly.

How can the speed of such a molecule be reduced?

What name is given to the temperature at which all molecular motion ceases?

(b) The behavior of substances as they change from solid state to the liquid state can be described using kinetic theory of matter. This assumes that matter is made of small moving particles or molecules.

What is the typical diameter of one of these molecules?
In the spaces in the table below describe the difference in solids and liquids.

	Solids	Liquids
Type of motion of molecules
Position of molecules
Spacing of molecules

(a) A substance has molecules which are in a close packed regular arrangement undergoing vibrations about fixed positions.
1. Is the substance a solid, liquid or a gas?
2. What is meant by `undergoing vibrations about fixed positions’?

How can the size of these vibrations be increased?

State the name given to the temperature at which the arrangement ceases to be close packed and regular.

(b) Describe a laboratory experiment using a syringe which shows that molecules of water are closely packed. How can this closely packed arrangement are completely destroyed.

(c) Matter exists in three states, solid, liquid, and gas. Complete the following table by writing in the state best described by each molecular property.

Molecular Property	State
1. Close packed
2.Spacing very large
3. Moving independently
4. Very strong forces of attraction
5. Vibrating about a fixed point

A small amount of air is trapped in an open glass capillary tube by a pellet of mercury as shown below.

Glass capillary tube

Mercury pellet

Trapped air

Describe the spacing and motion of the molecules in the liquid mercury and then the trapped air.
How does the pressure of the trapped air compare with that of the air outside the tube?

What difference, if any, are there in the speed and spacing of the trapped air molecules compared with those of the outside air (Temperature of both samples of air is the same.)

(a) The diagram below shows an apparatus which may be used for observing Brownian motion
When the apparatus was being used, points of light were observed moving about in a random manner.
1. What are these points of light?
2. Why are they moving randomly?
3. Name two ways by which this random motion could be made less vigorous.

(b) A sealed packet of crisps bought in a shop at sea level was found to appear like a balloon when taken to the top of a mountain.

Why did the packet appear to be inflated in this way?
Assuming there was no difference in temperature between sea level and the top of the mountain, what were the similarities and differences in motion of the air molecules inside the packet at sea level and on the top of the mountain.

(a) Some smoke is trapped in a small glass cell containing air and is brightly lit. When the mixture is viewed through a microscope, small bright specks which dance about in a random fashion can be seen.
1. What are small bright specks?
2. Explain what makes them dance in a random fashion.

Complete the diagram below by adding lines to show the movement of the small speck shown.

Bright speck

State three assumptions of the kinetic theory of gases.
Figure below shows apparatus used to observe the behaviour of smoke particles in a smoke cell.

Explain what was observed
Explain what happens if the temperature was raised.
State why diffusion is faster in gases than in liquids.

TOPIC 6: THERMAL EXPANSION

TEMPERATURE

This is the degree of hotness or coldness of a body. Temperature of a body is measured by an instrument called a thermometer.

Temperature is a basic physical quantity and is measured in degrees celcious (⁰C) or Kelvin (K).

The S.I unit of temperature is Kelvin (K) which is a scalar quantity.

MEASURING TEMPERATURE

A thermometer is an instrument used for measuring temperature. There are various types of thermometers in use. A thermometer is designed according to the purpose for which it is required. The following are some of the commonly used thermometers:

Liquid-in-glass thermometer.
Clinical thermometer
Six’s maximum and minimum thermometer

LIQUID-IN-GLASS THERMOMETER

A liquid-in-glass thermometer commonly in use is mercury or coloured alcohol as the thermometric substance.

The volume of the liquid changes uniformly with the change in temperature

The characteristics of the liquid in the bulb include;

Be easily seen (visible).
Expand or contract uniformly and by a large amount over a small range of temperature.

Not stick to the inside of the tube. (Should not wet the inside of the tube)

Have a wide range of temperature.

THERMOMETRIC LIQUIDS

The most common in use is mercury and alcohol.

Mercury freezes at -39^oC and boils at 357^oC while alcohol freezes at -115^oC and boils at 78^oC. Alcohol is therefore suitable for measuring temperatures below – 39^oC.

PROPERTIES OF THE TWO THERMOMETRIC LIQUIDS

ALCOHOL MERCURY

Low boiling point, 78oC – High boiling point, 357oC
Low melting point, -115oC – Relatively higher melting point, -39oC
Poor thermal conductor – Good thermal conductor
Expansion slightly irregular – Expands regularly
Wets glass – Does not wet glass
Coloured to make it visible – Opaque and silvery

Water is not used as a thermometric liquid because it undergoes anomalous expansion.

TEMPERATURE SCALE

The scale of a thermometer is obtained by selecting two temperatures called fixed points; the lower fixed point and the upper fixed point. The lower fixed point is the temperature of pure melting ice. It is taken to be 0⁰C. The upper fixed point is the temperature of steam above pure boiling water at normal atmospheric pressure. It is taken to be 100⁰C. The temperature of steam is used since impurities do not affect its temperature but will raise the boiling point of water. The temperature of boiling water itself is not used because any impurities in water would raise its boiling point. The temperature of steam is not affected by impurities in water.

The range between these two points is then divided into equal divisions. Each division is called degree.

FEATURES OF A COMMON THERMOMETER

The basic features of a common laboratory are as shown below.

Bulb- Carries the liquid in the thermometer. It has a thin glass wall for effective heat transmission between the liquid and body whose temperature is taken.
Capillary bore – Liquid expands and contracts along the capillary tube. It is narrow for high degree of accuracy.
Glass stem – this is a thick wall surrounding the capillary bore. It also serves as a magnifying glass for easy reading of scale.

CELCIOUS AND KELVIN SCALE

They are the commonly used temperature scale. The celcious scale has the fixed points at 0^oC and 100^oC. In Kelvin scale, the temperature of pure melting ice is 273K while that of pure boiling water at normal atmospheric pressure is 373K.

The lowest temperature in the Kelvin scale (0K) is referred as absolute zero.

This is the temperature at which the energy of the particles in material is zero.

To change ^oC to Kelvin

T = (ѳ – 273) K where ѳ is the temperature in ^oC

EXAMPLE 1

Convert 25^oC in Kelvin

SOLN

T = (25 + 273)

= 298 K

To change Kelvin to ^oC

Ѳ = (T- 273) ⁰C where T is the temperature in Kelvin

EXAMPLE 2

Convert 1 K

SOLN

Ѳ = 1-273

= -272^oC

ASSIGNMENT

Convert the following into Kelvin:

35⁰C b) -111⁰C c) -273 ⁰C

Convert the following into ⁰C:

123 K b) 323 K

NOTE: Temperature in Kelvin scale cannot have a negative value because the absolute zero, (0K), is the lowest temperature attainable.

CLINICAL THERMOMETER

A clinical thermometer is an instrument used to measure the temperature of a human body.

It uses mercury as its thermometric substance and has a narrow constriction in the tube just above the bulb.

The diagram below shows the main features of a clinical thermometer.

The constriction prevents the mercury level from falling down when it contacts with the human body.

The clinical thermometer has a short scale of temperature from 35^oC to 43^oC spread over its entire level. This is because the human body temperature falls slightly above or below 37^oC which is the temperature of a normal and healthy person. Methylated spirit is used to sterilize the clinical thermometer. Boiling water is not used because its temperature is quite far away from the maximum temperature of the clinical thermometer. This can destroy the thermometer. The thermometer can be reset by a simple flick.

SIX’S MAXIMUM AND MINIMUM THERMOMETER

This thermometer is used to record the maximum and minimum temperature of a place during a day. The thermometer consists of a U-tube connected to two bulbs. The U-tube contains mercury. The two bulbs contain alcohol.

The figure below shows the main features of a six’s maximum and minimum thermometer.

Working of the Thermometer

When temperature raises alcohol occupying volume of bulb A expand and forces mercury in the U-tube to rise on the right hand side.

The mercury in turn pushes the steel index A upwards. The maximum temperature can be noted from the lower end of the steel index A.

On the other hand when the temperature falls, alcohol in the bulb A contracts and the mercury is pulled back rising u the left hand side of the U-tube. The index B is then pushed up. During contraction of the alcohol, index A is left behind (in the alcohol) by the falling mercury.

The minimum temperature is then read from the lower end of index B.

NOTE: To reset the thermometer, a magnet is used to return the steel indices to the mercury surfaces.

THE BIMETALLIC THERMOMETER

It is made up of a coiled bimetallic strip whose one end is fixed and the other end connected to a pointer. Commonly used metals are brass and invar. When the temperature rises brass expands more than invar. The strip thus curls forcing the pointer to move over a calibrated scale.

THERMAL EXPANSION AND CONTRACTION OF SOLIDS, LIQUIDS

AND GASES

All substances increase in size when heated. This increase in size of a substance is called expansion. On the other hand when a substance is cooled it decreases in size. This decrease in size is called contraction.

EXPANSION IN SOLIDS

Thermal expansion and contraction in solids can be demonstrated using a ball and ring experiment. Set the apparatus as shown below.

NOTE: The ball should pass through the ring when both are at room temperature

Heat the ball and try to pass it through the ring. Observe what happens.
Leave it for sometime

OBSERVATION

When both the ball and the ring are at the same room temperature, the ball just passes through the ring.
When the ball is heated; it does not go through the ring but when left there for sometime, it goes through.

EXPLANATION

When heated, the ball expands so that it cannot go through the ring.

When left on the ring for some time, the temperature of the ball decreases and it contracts.

At the same time, the temperature of the ring increases and it expands so that the ball goes through.

WHY SOLIDS EXPANDS ON HEATING

The molecules of a solid are closely packed together and are continuously vibrating in their fixed positions When a solid is heated the molecules gain more kinetic energy and therefore make larger vibrations about their fixed positions. This increase in vibration means that the molecules collide with each other with larger forces and the molecules increases and so the solid expand.

LINEAR EXPANSIVITY

The measure of the tendency of a particular material to expand is called its expansivity e.g. aluminium expands more than iron thus aluminium has higher expansivity than iron.

The knowledge of linear expansivity values is applied in the designing of materials to ensure that they are able to operate well under varying thermal conditions.

Ordinary glass expands at a higher rate than Pyrex glass. When hot water is poured into a tumbler made of glass it breaks but does break in Pyrex glass.

Concrete and steel are reinforced together because they are of the same linear expansivity. Hence cannot crack under varying thermal conditions.

THE BIMETALLIC STRIP

When two metals of different linear expansivity are riveted together they form a bimetallic strip.

Brass and iron are used to make the bimetallic strip.

On heating the bimetallic strip, brass expands more than iron. The brass thus becomes longer than the iron for the same temperature range. Hence, the bimetallic strip bends with brass on the outside of the curve as shown in (b) below

On cooling, the brass contracts more than iron. It therefore becomes shorter than the iron and thus ends up being on the inner side of the curve as shown in (c) above

APPLICATIONS OF EXPANSION AND CONTRACTION IN SOLIDS

RAILWAY LINES

Gaps are left between the rails. Expansion for the rail is provided by overlapping the plane ends using overlapping joints as shown in the figure below

If these gaps for the expansion are not provided then during hot weather, they rails may buckle out, bend and cause derailment of the train leading to destruction and accidents.

STEAM PIPES

Pipes carrying steam from boilers are fitted with loops or expansion joints to allow pipes to expand and contract easily when steam passes through and when it cools down.

TELEPHONE WIRES

They are loosely fixed to allow for contraction and expansion. During cold weather, they contract and when it is warm they expand.

Telephone or electricity wires appear to be shorter and taut in the morning.

However in hot afternoons, the wires appear longer and slackened.

STEEL BRIDGES

In bridges made of steel girders, one end is fixed and the other end placed on rollers to allow for expansion as shown

RIVETS

Thick metal plates, sheets and girders in ships are joined together by means of rivets.

The rivet is fitted when hot and then hammered flat. On cooling, it contracts, pulling the two firmly together as shown

ELECTRIC THERMOSTAT

A thermostat is used to maintain a steady temperature in some devices such as electric iron box, refrigerators, fire alarm and flashing unit for indicator lamp in motor cars.

EXPANSION AND CONTRACTION IN LIQUIDS

The experimental set up below can be used to demonstrate expansion of a liquid.

A glass flask is filled with coloured water and heated as shown above

OBSERVATION

Immediately the level of coloured water on the tube drops slightly at first and then starts rising.

EXPLANATION

The initial fall of the level of the water is due to the expansion of the glass flask which gets heated first. The water starts expanding when heat finally reaches it and it rises up the tube.

NOTE: The water expands faster than the glass.

QUESTION

Explain why there is a drop in the level of the water initially followed by a steady rise in the level of water.

Different liquids expand more than others for a given temperature as shown in the diagram

In this case, methylated spirit expands most, followed by alcohol and finally water.

EXPANSION IN GASES

The experiment below can be used to demonstrate expansion of air.

Invert the flask with glass tube dipped into the water as shown.

Warm the flask with your hands for some time and note what happens.

Remove your hand and let the flask cool while the tube is still inserted in water.

OBSERVATION AND EXPLANATION

When the flask is warmed the level of water column inside the glass tube drops indicating air expands. When the flask is warmed further, some bubbles are seen at the end of the glass tube.

On cooling the air inside the flask contracts and water rises up the glass tube.

THE ANOMALOUS (UNUSUAL) EXPANSION OF WATER

Solids, liquids and gases expands when heated and contracts when cooled.

Water however shows an anomalous (unusual) behaviour in that it contracts when it is temperature is raised from 0^oC to about 4^oc.

When ice is heated from say -20^oC, it expands until its temperature reaches 0^oC and it melts with no change in temperature. The melting is accompanied by contraction. The water formed will still contract as its temperature rises from

0^oC as shown

Above 4⁰C, the water expands with increase in temperature. Since volume of a given mass of water is minimum at 4^oC, water at this temperature has a maximum density, slightly higher than 1g/cm³.

A sketch of the variation of density with temperature

At the melting point of water (^o0C) there is a drastic increase in the volume, resulting in a large decrease in density as the ice forms.

EFFECTS OF ANAMALOUS EXPANSION OF WATER

Freezing of lakes and ponds

Water in lakes and ponds usually freezes in winter. Ice is less dense than water and floats on water. Since ice a bad conductor of heat it insulates the water below against heat losses to the cold air above.

Water remains at 40C being the most dense, remains at the bottom of a lake while ice being less dense floats on layers of water at different temperatures as shown.

Fish and other aquatic animals and plants can therefore survive by living in the liquid layers below the ice.

Icebergs

Since the density of ice (0.92g/cm³) is slightly less than that of water it floats with only a small portion above the water surface. The rest and bigger portion rests under water. A big mass of such submerged ice is known as an iceberg.

It poses a great danger to ships as navigators cannot see the submerged part.

Weathering of Rocks

When water in a crack in a rock freezes, it expands. This expansion breaks the rock into small pieces.

Water pipes

Water pipes bursts when the water flowing through the pipes freezes

QUESTIONS

One property of a liquid that is considered while construction a liquid – in – glass thermometer is that the liquid expands more than the glass for the same temperature change. State any other two properties of the liquids that are considered
Explain why a glass container with thick walls is more likely to crack than one with a thin wall when a very hot liquid is poured into them.
Figure 1 shows a circuit diagram for controlling the temperature of a room.

Describe how the circuit controls the temperature when the switch is closed

Fig 2 shows a fire alarm circuit. Explain how the alarm functions.
Figure 3 shows a bimetallic strip at room temperature. Brass expands more than invar when heated equally.

Sketch the bimetallic strip after being cooled several degrees below room temperature.

In the set up shown in Figure 5, it is observed that the level of the water initially drops before starting to rise.

Explain this observation.

Figure 6 shows a bimetallic strip with a wooden handle, suspended horizontally using a thin thread.

The strip is heated at the point shown. Explain why the system tips to the right

A clinical thermometer has a constriction in the bore just above the bulb. State the use of this constriction.
7 shows a flask fitted with a glass tube dipped into a beaker containing water at room temperature. The cork fixing the glass tube to the flask is airtight.

Explain what is observed when ice- cold water is poured on the flask.

The melting point of oxygen is given as -281.3⁰ Covert this temperature to Kelvin

SOLUTIONS

The liquid expand uniformly, expansion is measurable (large enough), thermal conductivity
Glass is a bad conductor of heart, the difference in temperature between the inside and the outside cause unequal expansion.
Bimetallic strip bends and straightens or the metals expand differently. Current flows, heating takes place, temperature rises, strip is heated and bends way from contact; disconnects heater; temperature; drops reconnected heater or completes circuit.
When mercury is heated (during a fire); it expands and makes contact, completing the circuit to ring the bell. Since the strip is bimetallic when temperature rises the outer metal expands more than the inner metal; causing the strip to try and fold more; this causes the pointer to move as shown
Glass flask initially expands / Heating increases the volume of the flask; hence the level drops. Eventually water expands more than glass, leading to the level rising.; Cold water causes air in the flask to contract // reduces pressure inside flask or when cold water is poured it causes a decrease in volume of air the flask or pressure increases in the flask // volume of the flask decreases.
On heating, the bimetallic strip bends; this causes the position of the centre of gravity of the section to the left to shift to the right causing imbalance and so tips to the right.
Prevents/ holds, traps breaks mercury thread/ stops return of mercury to bulb When thermometer is removed from a particular body of the surrounding
Water rises up the tube into the flask or water is sucked into the tube or bubbles are seen momentarily.
273+ -281.3 = 8.3K

MORE QUESTIONS

Figure 5 shows a clinical thermometer which is not graduated.

Name the parts indicated with letters: A and
Mark the appropriate scale range in degrees Celsius

A bimetallic strip is made from aluminium and copper. When heated, it bends as shown below.

Aluminium

Copper

Sketch a diagram showing the strip when cooled below room temperature.

Explain why fish can survive under water when the surface is already frozen.
Explain the purpose of the constriction in a clinical thermometer.
It is not advisable to fix electrical cables tightly during the day. Give a reason for this.

Cell

The diagram below shows circuit of a fire alarm. When fire breaks it rings the bell to alert people that there is fire. Name two properties of mercury that makes it suitable to be used.

Mercury

Bell

In an attempt to prepare a cup of tea, a student placed boiling water into a glass tumbler. The glass tumbler broke into pieces. Explain this observation.
Figure 5 shows a flask fitted with a tube dipped into a beaker containing water at room temperature. The cork fixing the glass tube is tight.

State with reason what would be observed if cold water is poured on to the flask

Explain why steel is selected for use to reinforce a concreter beam
State two properties of mercury that make it a suitable thermometric liquid.
The diagram below shows a six’s maximum and minimum thermometer.

Saturated vapour

Mercury

What is the thermometric liquid in the thermometer?
Why is it necessary for the vapour in bulb B to be saturated?

Explain how the thermometer indicates maximum and minimum temperature.

Indicate on the figure the two points where the reading of the temperature shown by the thermometer can be made.
Explain why a lemon juice bottle always has space between the top of the liquid and the cap.
Explain the difference between heat and temperature.
Convert 450⁰C to Kelvin.
The figure below shows a bimetallic strip.

Invar

Brass

This strip is at room temperature. Sketch the bimetallic strip after being cooled several degrees below room temperature. Explain your answer.

A metallic disc is thin and has a hole passing through its centre. Describe what happens to the size of the hole when the disc is heated uniformly.
Give a reason why a concrete beam reinforced with steel does not crack when subjected to changes in temperature.
Describe the thermal expansion of a solid using kinetic theory of matter.
Explain the application of expansion in telephone and electric overhead cables.
Describe how a bimetallic thermometer works.
Explain why aquatic animals are able to survive under water when the surface is already frozen.
When a mercury thermometer is used to measure the temperature of hot water, it is observed that the mercury level first drops before beginning to rise. Explain this observation.
The coefficient of linear expansion of lead is 2.7 x per ⁰ Explain this statement.
Compare the expansion of brass and iron.
Air in a bulb may be used as a thermometric substance. State:
- One property of air that would enable the temperature to be measured.
- One limitation of such a thermometer.
What is meant by absolute zero temperature?
Explain why a thick glass container is more likely to crack than a thin one when boiling water is suddenly poured in.
One property of a liquid that is considered while constructing a liquid in glass thermometer is that the liquid must expand more than the glass for the same temperature range. State any other two properties of the liquid that are considered.
Describe and explain the features of a thermometer which will make it: (a) sensitive (b) Quick acting.
Why would you crawl close to the flow in a smoke filled room when trying to move out?
State three properties of a liquid for it to be considered in constructing a glass thermometer.
Sketch a volume against temperature graph for water that cools from 10⁰C to – 4⁰C
The figure below shows a flask fitted with a glass tube dipped into a beaker containing water at room temperature. The cork fixing the glass tube to the flask is air tight. The flask is warmed with the hands.

Warm hands

Air

Flask

Water

State and explain the observations made.

(a) Explain why in warm coastal regions, a cool breeze often blows from the sea to the land during the day time.

(b) Describe and explain what happens at night in question (a).

State	Temperature ⁰C	Density (kg/m³)
Liquid	8.0	999.85
Liquid	6.0	999.94
Liquid	4.0	999.97
Liquid	2.0	999.94
Liquid	0.0	999.84
Solid	0.0	916.59

Use the density data above to describe how the volume of the liquid changes as it cools from 8⁰C to 0⁰C^.
Describe the change in volume of water as it changes from liquid to solid.
Describe what happens to a sealed glass bottle full of water if it were placed in the freezing compartment of a refrigerator.

(a) Two glass spheres contain equal volumes of air at the same temperature and pressure. The spheres are connected by a narrow glass tube containing a mercury pellet as shown below.

Glass sphere P air glass sphere Q

Narrow glass tube

Mercury pellet

Describe how the air molecules exert a pressure on the walls of the glass spheres.
Describe and explain using the ideas of molecules what happens to the mercury pellet when sphere Q is gently heated while sphere P is kept at its original temperature.

(b) The diagram below shows an experiment which can be used to demonstrate the thermal expansion of a solid metal bar. Pointer

Heavy weight solid metal bar

Heat roller

Table

Describe what happens when the bar is heated.
Explain what happens in (i) using kinetic theory of matter.

Give an example of an everyday situation where allowance must be made for the expansion of a solid. Explain how this allowance is made for the expansion.

(a) When liquids are stored in a sealed bottle, they are not completely filled out, but a space is left between the cap and the surface of the liquid as shown below.

Cap

Space

Bottle liquid

Describe what happens to the contents of the bottle when the temperature is increased slowly and uniformly.
Explain what happens in (i) in terms of the expansion of liquids and solids.
Give a use of the above effect.
Describe and explain what happens to the gas in the space above the liquid using kinetic theory.
A cylindrical copper rod is heated. State and explain what happens to the density of copper as the rod is being heated.

a) The diagram below shows a long silver rod, a light pointer and a pivot.

Fixed support

Long silver rod

Light pointer

Pivot

Describe how this apparatus can be used to measure the expansion of the silver rod as its temperature increases.
State a problem of repeating the above experiment using a polythene rod of the same shape and size as the silver rod.
State two extra pieces of apparatus that would be needed

(a) Place in ticks in the table below to show which liquid is better in each case.

Characteristic	Mercury	Alcohol
Expands more evenly
Expands more
A better conductor of heat
Useful at higher temperatures
Useful at lower temperatures

(b) In terms of the forces of attraction between the particles, the particle spacing and their motion describe and explain the change in volume that occurs on boiling.

TOPIC 7: HEAT TRANSFER

HEAT AND TEMPERATURE

Heat is a form of energy which passes from a body at high temperature to a body at a lower temperature. When a body receives heat energy its temperature increases whereas the temperature of a body that gives away energy decreases.

Thermal equilibrium- Condition when if two bodies at the same temperature are in contact, there is no net flow from one body to the other.

The SI unit of heat is joules.

Heat cannot be measured directly by an instrument as temperature is measured by a thermometer.

MODES OF HEAT TRANSFER

Heat can travel through a medium as well as in a vacuum. There are three (3) modes of heat transfer namely;

Conduction – takes place in solids.
Convection – takes place in fluids (liquids and gases).

Radiation – takes place in gases (vacuum)

CONDUCTION

In stirring a hot tea the handle of a spoon becomes warm. The mechanism to this is explained below,

Heat energy entering the spoon from the hot end increases vibrations of the atoms at this ends. These atoms in turn collide with neighbouring atoms, increasing their vibrations and hence passing the heat energy along.
Metals have free electrons which travel throughout the body of the metal. Heat energy injected at the hot end of the metal spoon increases the vibration of the particles at the end. The free electrons in that region gain more kinetic energy and because they are free to move, they spread heat energy to the other parts of the spoon.

THERMAL CONDUCTIVITIES OF VARIOUS CONDUCTORS

Different materials have different thermal conductivities. Metals are generally good conductors of heat. Non-metals are poor conductors of heat (insulator).

Solids that are good conductors of heat use both atom vibration and free electrons to conduct heat.

Solids that are poor conductors of heat like glass, wood, rubber make use of atom vibration as a mechanism to conduct heat because they have no free or mobile electrons.

The table below shows some of the good and poor conductors in decreasing order of thermal conductivity.

Good conductors	Poor conductors
Silver	Concrete
Copper	Glass
Aluminium	Brick
Brass	Asbestos paper
Zinc	Rubber

NOTE: During thermal condition, heat flows through the materials without the material shifting or flowing. Conduction is therefore transfer of heat as a result of vibration of particles.

CONDUCTIVITY OF WOOD AND IRON RODS

The following set up is used;

Observation and explanation

The paper gets charred (blackened) on the region covering the wooden rod. This is because the wood does not conduct heat from the paper. Wood is said to be a bad conductor of heat while iron is a good conductor.

FACTORS AFFECTING THERMAL CONDUCTIVITY

Thermal conductivity in materials depends on the following factors;

Temperature difference ( Ѳ) between the ends of the conductor.
The length of the conductor.
The cross-sectional area (A) of the conductor.
The nature of the material (K)

Temperature difference

To demonstrate how temperature difference ( Ѳ) affects thermal conductivity, the following set up is used.

Observation

It will be observed that the rod placed in the flame becomes too hot faster than the one placed in the boiling water.

Explanation

The rate of heat flow (thermal conduction) increases with increase in temperature.

Thermal conduction in metals is by two mechanisms i.e. vibration of atoms and by free electrons.

A high temperature difference between the ends of the conductors sets the atoms into vibrations more vigorously and the vibrations are passed more quickly to the cooler end. The electrons on the other hand gain a lot of kinetic energy causing them to spread the heat energy to cooler parts of the metal within a short time.

Length of the conductor

Consider the set up below

Observation

It will be observed that the end of metal B held in hand becomes too hot earlier than metal A. Thermal conductivity increases with decrease in length.

Explanation

Heat travels within a conductor along imaginary lines called lines of heat flow.

These lines diverge from the hot end as shown

The graph of temperature (Ѳ) against length (l) is as shown.

When the heat energy gets to the surface of the metal it is easily lost to the surroundings.

The lines of heat are more divergent near the hot end than they are far away (position A and B).

The slope of the graph in the above figure is steeper at A (near the hot end) than at B further away. This indicates that the shorter the length of the material, the higher the rate of heat flow.

The cross-sectional area of the conductor

Consider the set up below,

Observation

The end of metal A held in the hand becomes too hot earlier than metal B.

Thermal conductivity increases with increase in area of cross-section of the conducting material.

Explanation

The number of free electrons per unit length of the thicker length A is more than those in the thin metal rod B.

The nature of the material K

To demonstrate how the type of the material K affects thermal conductivity, consider the diagram below,

Observation

In this case, it is observed that end of copper rod held in the hand becomes too hot earlier than iron rod.

This shows that thermal conductivity depends on the nature of the material.

Explanation

Different materials have different strength of force bonding the atoms within the material. The number of free electrons also differs from one material to another material.

Materials with many free electrons are better conductors of heat e.g. copper has more free electrons than iron.

Rate of heat flow = thermal conductivity x cross-sectional area x temperature difference

Length L

LAGGING

This is the covering of good conductors of heat with insulators to reduce heat loss through surface effects. For example, iron pipes carrying hot water from boilers are covered with thick asbestos material.

The figure below shows lines of heat flow in a lagged metal bar.

A graph of temperature (ѳ) against the position along the lagged conductor is as shown below.

THERMAL CONDUCTIVITY IN LIQUIDS

To demonstrate that water is a poor conductor, the following set up considered,

Observation and explanation

It will be noted that water at the top of the boiling tube boils while ice remains unmelted. This shows that water is a poor conductor.

NOTE: The boiling tube is made of glass (poor conductor of heat) which limits possible conduction of heat down the tube.

The ice is wrapped in wire gauze to ensure it does not float. The fact that the wire gauze is a good conductor of heat and yet ice remained unmelted shows that there is very little heat conduction in water, unable to melt the ice.

Water is heated at the top to eliminate possibility of heat transfer to the ice by convection.

Although liquids are in generally poor conductors of heat, some liquids are better heat conductors than others e.g. mercury is a better conductor of heat than water.

Why Liquids Are Poor Conductors of Heat

Pure liquids have molecules further apart from each other. Although molecules move about within the liquid, they are slow to pass heat to other regions compared to the free electrons in metals. This is because there are large intermolecular distances between liquid molecules. There are also fewer and rare collisions between the molecules.

Electrolytes e.g. salt solution, are better conductors of heat than pure liquids because of increased compactness of the particles.

Mercury is a metal existing as a liquid at room temperature. Bromine, the only non-metal existing as a liquid at room temperature, is a poor conductor.

THERMAL CONDUCTIVITY IN GASES

Since thermal conductivity is by means of vibration of atoms and presence of free electrons, gases are worse conductors of heat because of large intermolecular distance.

A match stick held within the unburnt gas region of a flame cannot be ignited by the heat from the hot part of the flame. This is because gas is a poor conductor of heat.

APPLICATIONS OF GOOD AND POOR CONDUCTORS

Cooking utensils, soldering irons and boilers are made of metals which conduct heat rapidly. For cooking utensils, the handles are made of insulators such as wood or plastic. Metal pipes carrying hot water from boilers are lagged with cloth soaked in a plaster of Paris to prevent heat losses.
Overheating of integrated circuits (ICs) and transistors in electronic devices can drastically affect their performance such components are fixed to a heat sink (a metal plate with fins) to conduct away undesired heat. The fins increase the surface area of heat sink and conduct more heat away to the surrounding.
Fire fighters put on suits made of asbestos material to keep them safe while putting out fire.
Birds flap their wings after getting wet as a means of introducing air pockets in their feathers. Air being a poor conductor reduces heat loss from their bodies.
In modern buildings where desired inside temperatures is to be stabilised, double walls are constructed. Materials that are good insulators of heat and can trap air put between the walls. Examples of such materials that are glass, wool (fibre glass) and foam plastic Air on its own may not effectively give the desired insulation because it undergoes convection. Double glazed windows used for the same purpose have air trapped between two glass sheets.
In experiment involving heating water or liquid, the beaker is placed on the wire gauze. The gauze is heated and spreads the heat to a large area of the beaker. If the gauze is not used, heat from the Bunsen burner may concentrate on a small area and may make the beaker crack.

CONVECTION

Convection is the process by which heat is transferred through fluids (liquids and gases). The heat transfer is by actual movement of the fluid called convection currents, which arise out of the following;

Natural convection – It involves change in density of the fluid with temperature.

Forced convection – Mixing of hot and cold parts of the fluid through some external stirring like a fan or pump.

CONVECTION IN LIQUIDS

To demonstrate convection in liquids the set up below is used

Observation

A purple colourisation rises up from the potassium permanganate, forming a loop.

Observation

The colourisation arising from the potassium permanganate flow in clockwise direction

From the experiments, it is clear that when a liquid is heated, it rises while cold liquid replaces it.

Explanation

When a liquid is heated, it expands and this lowers its density. The less dense liquid rises and its place is taken by more dense colder liquid. This movement of liquid forms convection currents

CONVECTION IN GASES

To demonstrate convection currents in gases, consider the set up below

Observation

Smoke is sucked into the box through chimney A and exists through chimney B.

When the candle is put off, the smoke is not drawn into the box.

This shows convection currents are set up when air or gas is heated.

Explanation

The candle heats up the air above it, which expands and rises up because of lower density. Cold heavier air particles is drawn into chimney A, carrying along the smoke which replaces the air that is escaping through chimney B.

MOLECULAR EXPLANATION OF CONVECTION IN FLUIDS

Molecules in fluids are further apart and have negligible cohesive force. Heating a fluid increases the kinetic energy of the vibrating molecules and their random movement.

As the fluid rises, these molecules pass energy to the molecules in the colder regions which have less energy. Because the molecules are further away from the heating source, their temperature is reduced.

Pressure near the heating source decreases because of the depletion of molecules as they rise. Colder molecules move into the low pressure zone to fill up the void being created.

This movement of molecules constitutes convection currents. Convection currents are set up much faster in gases than in liquids because of relatively low cohesive force in gases.

APPLICATION OF CONVECTION IN FLUIDS

Domestic hot water system

Initially, the two beakers A and B have cold water. Water in beaker A is coloured to distinguish it from that in beaker B. When the water in beaker A is heated, it is observed to rise up through tube X and emerges on top of cold water in beaker B. The cold water flows down from beaker B to beaker A.

As long as heating continues, there will be movement of hot water into beaker B and cold water will flow down into beaker A. Thermometer will show increase in temperature for water in beaker B.

The commercial domestic hot water system utilizes the same principle of operation. The hot water rises up because of the effective lowering of density.

The force of gravity helps the cold water to flow down from the cold tank.

The hot water tap and expansion pipe are connected to the upper region of the cylinder. The expansion pipe is an outlet for excess water that could have resulted from overheating.

Once the cold water flows down the cylinder, the main pipe allows more cold water to flow into the tank. When filled to capacity, the ball cork floating on water closes a valve i the main pipe, stopping further in flow of cold water.

An overflow pipe lets out water from the cold tank when the valve is not sufficiently functional.

Lagging is done on the pipe that conveys hot water to minimise heat losses.

Ventilation

This is the supply of fresh air into the room. Air expelled by the room occupants is warm and less dense. It rises up and escapes through the ventilation holes.

Cold fresh air flows into the room to replace the rising warm air. The room gets continuous flow of fresh air.

NOTE: Some devices are fitted with air conditioning devices which cause forced convection of air, giving out cold dry air and absorbing warm moist air.

Car Engine Cooling System

Heat conduction and convection play a very crucial role of taking away heat from a car engine that would reduce its efficiency.

The engine is surrounded by a metal water jacket that is connected to the radiator. The metal surface conducts heat away from the engine. This heats up the water, setting up convection currents. The hot water is pumped into the radiator which has thin copper fins that conduct away heat from water.

Fast flowing air past the fins speeds up the cooling process.

Land And Sea Breezes

This is a natural convection of air, and occurs at sea shores because of temperature difference between the mass of water and the land.

The mass of water takes longer time than land nearby land by the same temperature from the sun. Water also takes a longer time to cool than the land after being raised at the same temperature.

During the day, the land heats up much faster than the sea. The air just above the land gets heated up and rises because of reduced density. Cold air above the sea blows towards the land to replace the void created by warm air rising. This is called sea breeze.

In the evening, temperature of the sea water is higher than that of the land. The air above the sea gets heated up and rises. Cold air from the land blows to the sea. This is called land breeze.

RADIATION

Heat from the sun to the earth reaches us by radiation. Thermal radiation is heat transfer through a vacuum.

All bodies absorb and emit radiation. The higher the temperature of the object, the greater the amount of radiation A body emitting thermal radiation can also emit visible light when it is hot enough.

An electric bulb in a room produces both light and radiant heat. The radiant heat is absorbed by the materials in the room, which in turn give out radiant heat of lower energy.

NATURE OF RADIANT HEAT

To demonstrate the radiant heat;

Consider light rays travelling from sun light to hand lens as shown,

OBSERVATION

When light rays are focused onto the paper, it burns out.

EXPLANATION

Radiant heat, like light can be concentrated to a point using a lens. Thermal radiation is a wave like light and can be reflected. Because of the nature of production, radiant heat is an electromagnet wave which causes heating effect in objects that absorb it.

Radiation can also be described as the flow of heat from one place to another by means of electromagnetic waves.

EMISSION AND ABSORPTION OF RADIATION

To compare radiation from different surfaces (shiny and black surfaces),

Consider the set up below,

The two surfaces are heated to a certain temperature say 80⁰C. The temperatures of the two tins taken after sometime

Observation

After sometime, it is noted that the temperature recorded by T_Bis lower than that recorded by T_S.

Explanation

The experiment shows that black surfaces are better emitters than shiny surfaces.

A graph of temperature against time for temperatures recorded by each thermometer

The graph shows water in a shiny tin lost heat less rapidly than the blackened tin (good emitter).

To Compare Absorption of Radiant Heat by Different Surfaces

Set up the apparatus as shown

Observation

The cork fixed on the dull/black surface falls off after the wax, melts, while the cork polished/shiny plate remains fixed for a longer time.

Consider also the set up below,

Observation

The thermometer T_B immersed in water in the blackened tin records higher reading than that of thermometer T_S, when the heater is placed mid-way between tin A and tin B.

A graph of temperature (^oC) against time (minutes) is as shown,

The graph shows that temperature of water in the polished tin does not increase as fast as temperature of water in blackened tin.

EXPLANATION

Black surfaces are good absorbers of radiant heat than polished surfaces.

NOTE: Good absorbers of radiant heat also good emitters while poor absorbers of heat are also poor emitters.

Poor emitters of heat are also good reflectors.

APPLICATIONS OF THERMAL RADIATION

Kettles, cooking pan and iron boxes have polished surfaces to reduce heat lose through radiation.
Petrol tanks are painted silvery bright to reflect away as much heat as possible.
Houses in hot areas have their walls and roofs painted with bright colours to reflect away heat, while those in cold areas have walls and roofs painted with dull colours.
In solar concentrators, the electromagnetic waves in form of radiant heat are reflected to a common point (focus) by a concave reflector. The temperature at this point can be sufficiently high to boil water.
The green house effect- A green house has a glass roof through which radiant heat energy from the sun passes. This heat is absorbed by objects in the house, which then emit radiation of lower energy that cannot penetrate through glass. The cumulative effect is that temperature of the houses increases substantially. Greenhouses are used in providing appropriate conditions for plants in cold regions.

NOTE: Carbon dioxide (CO2) and other air pollutants in the lower layers of the atmosphere show the same properties of glass, raising the temperature on earth to dangerous levels.

Solar heater

The solar heater uses solar energy to heat water. The figure below shows the solar heater,

The solar heater consists of a coiled blackened copper pipe on an insulating surface. Radiant heat from the sun passes through glass and is absorbed by black copper pipes that contain water, which is heated up. Copper pipes are used because they are good conductors and they are painted black to increase their absorbing power.

Lower energy emitted after absorption of radiant energy does not escape because it cannot penetrate the glass. The temperature of the air above the pipe thus increases boosting the heating of water. A good insulating material is used at the base.

THERMOS FLASK (VACUUM FLASK)

A thermos flask is designed such that heat transfer by conduction, convection and radiation between the contents of the flask and its surrounding is reduced to a minimum.

The vacuum is a double walled glass vessel with a vacuum in the space between the walls. This minimises the transfer of heat by conduction and convection.

The inside of glass walls, in the vacuum side, is silvered to reduce heat losses by radiation (Poor emitter and absorber). The felt pads on the sides and at the bottom support the vessel vertically.

The heat loss by evaporation from the liquid surface is prevented by a well fitting cork.

QUESTIONS

In the set up shown in figure 1, water near the top of the boiling tube boils while at the bottom it remains cold.

Give a reason for the observation

When a Bunsen burner is lit below wire gauze, it is noted that the flame initially burns below the gauze as shown in Figure 2 (i).After sometime, the flame burns below as well as above the gauze as shown in Figure 3(ii).

Explain this observation

Two identical aluminum rods as shown in figure 3. One rests on metal block the other on the wooden block. The protruding ends are heated on Bunsen burners shown.

State with reason on which bar the wax is likely to melt

4 shows a hot water bath with metal rods inserted through one of its sides. Some wax is fixed at the end of each rod. Use this information to answer questions below

What property of metals could be tested using this set-up?

Two identical empty metal containers P and Q are placed over identical Bunsen burners and the burners lit. P is dull black while Q is shiny bright. After each container attains a temperature of 100⁰C the burners are turned off. Identical test tubes containing water are suspended in each container without touching the sides as shown

Explain why the container Q may become hot faster than P.
Explain why the water in test- tube in P becomes hot faster than in Q

In a vacuum flask the walls enclosing the vacuum are silvered on the inside. State the reason for this.
Give a reason why heat transfer by radiation is faster than heat transfer by conduction.
A wooden bench and a metal bench are both left in the sun for along time. Explain why the metal bench feels hotter to touch.
An electric heater is placed at equal distances from two similar cans A and B filled with water at room temperature. The outer surface of can A is shiny while that of can B is dull black. State with reasons, which of the cans will be at higher temperature after the heater is switched on for some time.
In the set up shown in figure 4, it is observed that the level of the water initially drops before starting to rise.

Explain this observation.

In a vacuum flask the walls enclosing the vacuum are silvered on the inside. State the reason for this

Figure 4 shows two identical balloons A and B. The balloons were filled with equal amounts of the same type of gas. The balloons are suspended at distances X₁ and X₂ from a metal cube filled with boiling water and placed on an insulating material. Use this information to answers questions 12 and 13 below:

State the mode by which heat travels from the cube to the balloons
The face of the cube towards A is bright and shiny and the face towards B is dull black. State with reason the adjustments that should be made on the distances X₁ and X₂ so that the rate of change of temperature in both balloons is the same.
Temperature scale in clinical thermometer ranges from 35⁰c to 43⁰ Explain.
State one application of expansion in gases
Why is it that boiling is not used for sterilization of clinical thermometer?
Describe ONE advantage and ONE Disadvantage of anomalous behavior of water.
(a) Draw a well labeled diagram of a vacuum flask

(b) Stating the specific parts in the flask explain how heat loss is reduced through:

(i) Conduction

(ii) Convection

(iii) Radiation

SOLUTIONS

Water/ or glass are poor conductor of heat
Initially the wire gauze conducts heat away so that the gas above does not reach the ignition temp/point. Finally the wire gauze becomes hot raising the temp of the gas above ignition point.
Wooden Block; Wooden block is a poor conductor of heat all the heat goes in melting the wax.
Heat conductivity/ rates of conduction/ thermal conductivity
Dull surface radiate faster than bright surface P- Looses more of the heat supplied by burner than Q or Q shinny surface is a poorer radiator/ emitter of heat thus retains more heat absorbed Or P- Dull surface is a better radiator/ emitter i.e. retains less of the heat absorbed. Heat travels from container to test tube by radiation so the dull surface P, gives more heat to the test tube.
Reduce/ minimize the transfer of heat by radiation OR Reduce the loss of heat OR gain of heat by radiation.
Radiation is at the electromagnetic waves Φ infrared while conduction involves particles, which move at lower speed
This is because metal is a good conductor, so that heat is conducted from outer parts to the point touched; while wood is a poor conductor
Can B is a good absorber of radiation/better absorber of radiation or heat.
Glass flask expands first (creating more volume for water) Water then expands using the tube.
To reflect heat outwards or inwards hence reduce heat loss by radiation.
– x² is made larger than X₁
– Since B receives radiation at a higher rate, it must be moved further from source for rates to be equal.
Since the quantity of water in A is smaller, heat produces greater change of temperature in A; a decrease in density causing the cork to sink further.

MORE QUESTIONS

Figure below shows two corks X and Y fixed on a polished plate and a dark plate with candle wax

Explain the observation, when the heater is switched on for a short time.

What feature of a vacuum flask minimizes heat loss by radiation? Explain how this is achieved.
Explain why fuel carrying tankers are painted white or silvery.
When a thermometer is immersed in ice cold water, the mercury thread is observed to rise before dropping steadily in the capillary tube. Explain.
Figure below shows two glass bulbs C and D of the same size. Bulb C is painted dull black while D is polished. A hot metal ball is placed equidistant from the two bulbs.

State and explain what will happen to the levels of the liquid in the manometer.

When a Bunsen burner is lit below wire gauze, it is noted that the flame initially burns below the gauze as shown in figure 4 below. After sometime the flame burns below as well as above the gauze.

Explain this observation

State the reason why it is colder during the night when the sky is clear than when it is cloudy.

Wax

The figure below shows an experiment carried out by form one students.

Thin iron rod

Thick iron rod

Hot water

The students dipped two iron rods of the same length but different thickness into a beaker of hot water at the same time. What was the experiment about?
State and explain the observations made after about 10 minutes.
If the two rods were much longer, state and explain any difference from C (ii) above that would be made in the observation.

TOPIC 8: RECTILINEAR PROPAGATION AND REFLECTION AT PLANE SURFACES

Light is a form of energy. It enables us to see the surrounding objects. Light itself is not visible but its effect is felt by the eye.

Light is also very essential as a source of energy for the process by which plants their own food (photosynthesis).

SOURCES OF LIGHT

Luminous (incandescent) source – these are objects that produce their own light e.g. sun, stars, burning candles, wood or charcoal, electric bulbs, television screens, glow worms e.t.c.

Non-luminous source – these are objects which do not produce light of their own. They are seen when light falling on them from luminous sources is reflected (bounces off their surfaces) e.g. the moon, planets, plants, people, books, walls, clothes e.t.c.

RAYS AND BEAMS OF LIGHT

A source of light produces pulses of energy which spread out in all directions.

The path along which light energy travels is referred to as a ray of light. Rays are represented by lines with arrows on them to show the direction of travel.

A stream of light energy is called a beam. It is also considered to be a bundle of rays of light. Beams of light can be seen;

In the morning as the sunlight breaks through the clouds or leaves.
When a spotlight is shown in a smoky room or a car driven along a dusty road at night with its headlamps on.
When sunlight streams into a smoky dark room through a small opening

TYPES OF BEAMS OF LIGHT

Diverging beam
Converging beam
Parallel beam

Diverging beam – These are beams of light that appear to spread out (diverging) e.g. light from a spotlight.

Converging beams – these are beams which appear to collect (converge) to a point.

Parallel beam – are those beams which appear to be perfectly parallel to each other e.g. a beam of light from the sun reaching the earth’s surface.

OPAQUE, TRANSLUCENT AND TRANSPARENT OBJECTS

OPAQUE – these are objects that do not allow light to pass through them at all e.g. brick walls, metals, wood, stones e.t.c.

TRANSLUCENT – these are objects that allow light to pass through but we cannot see through e.g. glass panes used in toilets and bathroom window and greased paper.

TRANSPARENT – these are objects which allow light to pass through and we see clearly through them e.g. car wind screen and ordinary window panes.

RECTILINEAR PROPAGATION OF LIGHT

Light does not need a material medium to carry it. In a vacuum, the speed of light is 3.0 x 10⁸m/s. Light from the sun reaches the earth having travelled mostly through a vacuum.

When light falls on an opaque object, it casts a shadow of the object with sharp edges on a screen behind it. This suggests that light travels in a straight line.

TO INVESTIGATE HOW LIGHT TRAVELS

Apparatus: three cardboards, source of light.

Arrange the apparatus as shown

The cardboards are arranged such that holes are exactly in line.

OBSERVATION

When the holes in the three cardboards are in line, the eye can see the lamp.

However when the middle cardboard is displaced, the eye can no longer see the lamp.

EXPLANATION

When the holes in the cardboards are in a straight line, light travels through the holes and the lamp is seen from the other side. When one of the cardboards is displaced, the beam of light is cut off and since light cannot bend to follow the displaced hole, the lamp cannot be seen.

CONCLUSION

Light travels in a straight line. This property is known as rectilinear propagation of light.

SHADOWS

Shadows are formed when an opaque object is on the path of light. The type of shadow formed depends on;

The size of source of light.
The size of opaque object.

The distance between the object and the source of light.

To study the formation of shadows by a point source of light

Consider the set up below,

Observation and Explanation

A uniformly and totally dark shadow is seen on the screen. This shadow is called umbra (Latin for shade)

The shadow has a sharp edge, supporting that light travels in straight lines.

To study the formation of shadows by extended (larger) source of light

Consider the set up below (source of light made larger)

Observation

The centre of the shadow remains uniformly dark as before, but smaller in size.

The shadow is edged with a border of partial shadow called penumbra.

Explanation

The centre of the shadow still receives no light at all from the source. Light from some parts of the extended source of light reaches the centre parts of the shadow on the screen, but light from other parts is cut off by the opaque object, resulting in a partial shadow at the edges.

NOTE: Extended light source produce light that is much softer and without sharp edges.

Application

It is used in frosted light bulbs and lamp shades to provide a more a more pleasant lighting with less sharp edges.

To study the formation of shadows by extended (larger) source of light when object distance is changed

Consider the set ups below,

Object moved closer to source

Object moved away from the source

Observations

When the ball is moved closer to the source, a ring of penumbra is formed. No umbra is seen.

When the ball is far away from the source, there is umbra surrounded by penumbra.

Explanation

The centre of the shadow receives light from the extended source. Since the object (ball) is smaller than the source of light, its umbra does not reach the screen because of the distance.

When the object is moved away from the source, the tip of the umbra reaches the screen.

ECLIPSE

An eclipse is a phenomenon of shadow formation which occurs once in a while.

It’s the total or partial disappearance of the sun or moon as seen from the earth.

Eclipses are explained in terms of relative positions of the earth, the moon and the sun.

THE PHASES OF THE MOON

At any given moment, about half the surface of the moon is lit by the sun while another half is in darkness.

The lighted part is bright enough to be seen easily at night from the earth and can be seen at day time. The darkened part is usually invisible.

When we look at the moon, we normally notice only the shape of the lighted part.

SOLAR ECLIPSE (ECLIPSE OF THE SUN)

When the moon, revolving around the earth, comes in between the sun and the earth, the shadow of the moon is formed on the earth. This is called eclipse of the sun.

Depending on the position of the moon, some parts of the earth lie in the region of umbra and some in the region of penumbra. Total eclipse occurs in the regions of umbra and partial eclipse in the regions of penumbra.

ANNULAR ECLIPSE

Sometimes the umbra of the moon is not long enough to reach the earth because sometimes the distance between the moon and earth varies (the moon’s orbit is elliptical). When the moon is further away from the earth, its disc is slightly smaller than the sun’s disc. So when a solar eclipse occurs, the moon is not large enough to cover the sun totally. A bright ring of sunlight can be seen round the edge of the dark disc of the moon. This is called Annular or ring eclipse.

LUNAR ECLIPSE (ECLIPSE OF THE MOON)

The moon is a non luminous object. It can only be seen when light from the sun is incident on it. When we look at the moon, we see only the shape of the lighted portion. When the earth comes in between the sun and the moon, lunar eclipse occurs. Depending on the position of the moon, a total or partial eclipse of the moon will occur. Total lunar eclipse will occur if the moon is in the region of umbra and partial eclipse will occur if any part of the moon is in the region of penumbra as shown,

A lunar eclipse occurs when the moon passes through the earth’s umbra.

PINHOLE CAMERA

A pinhole camera consists of a box with pinhole on one side and a translucent screen on the opposite side. Light rays from an object pass through the pinhole and form an image on the screen as shown

The image formed is real and is inverted. A pinhole camera has a large depth of focus i.e. objects that are far and near form focused images on the screen.

CHARACTERISTICS OF IMAGES FORMED ON THE PINHOLE

Consider the sets below;

When the object is near the pinhole, the image is larger.

When the object distance is increased from the pinhole the image is smaller.

When more holes are added close to the first pinhole, images of each point are seen overlapping on the screen.

If the camera was made in such a way that it could be elongated by moving the screen farther away from pinhole but keeping the distance between the object and pinhole fixed, it could be seen that the image enlarges when length of the camera is increased and diminishes when the length of the camera is reduced.

Length of camera decreased, image smaller
Length of camera increased, image bigger (larger)

MAGNIFICATION

Magnification is the change in size of an image to that of the object or it’s the ratio of the height of the image and that of the object.

Magnification, m= Image distance, v

Object distance, u

Also,

Magnification, m= Height of the image, h_i

Height of the object, h_o

Hence, magnification, m = Image distance, v = Height of the image, h_i

Object distance, u Height of the object, h_o

= h_i = v

h_ou

EXAMPLE 1

The distance between the pinhole and screen of a pinhole camera is10cm. The height of the screen is 20cm.At what distance from the pinhole must a man 1.6m tall stand if a full length is required

SOLN

h_i = v

h_ou

But, hi=20cm, ho=1.6m and v=10cm

Magnification, m = 20 = 10

160u

Hence, u = (160 x 10) / 20

= 80 cm or 0.8 m

EXAMPLE 2

An object of height 5m is placed 10m away from a pinhole camera. Calculate

The size of the image if it’s magnification is 0.01
The length of the pinhole camera.

SOLN

a) Magnification, m = h_i = v

h_ou

0.01 = h_i

Thus, hi =0.05m (image is 0.05m high)

b) h_i = v

h_ou

0.05 = v

510

Hence, v =0.1m (length of pinhole camera is 0.1m)

EXERCISE

The length of pinhole camera is 25cm. An object 2m high is placed 10cm from the pinhole. Calculate the height of the image produced and its magnification.
a) A pinhole camera of length 20cm is used to view the image of a tree of height 12m which is 40m from the pinhole. Calculate the height of the image of the tree obtained on the screen.
b) If the pinhole is moved by 10m towards the tree, what will be the height of the tree on the screen?

TAKING PHOTOGRAPHS WITH A PINHOLE CAMERA

The pinhole camera can be used to take still photographs if it is modified as follows,

The box should be painted black to eliminate reflection of light.
The translucent screen should be replaced by a light-tight lid with a photographic film fitted on the inside. The film should be fitted in a dark room.

The pinhole should be covered with a thin black card which acts as a shutter as shown,

REFLECTION OF LIGHT (PLANE SURFACES)

All objects, except self luminous objects, become visible because they bounce light back to our eyes. This bouncing off light is called reflection.

There are two types of reflection namely regular and diffused reflections.

When light is reflected by a plane smooth surface, the reflection is regular (specular) and when reflection occurs at a rough surface it is called a diffused reflection. Plane mirrors forms images while shiny sheet of papers cannot. This is because with papers, there is irregular/diffused reflection while image formation requires regular/specular reflections only.

REFLECTION BY PLANE MIRRORS

A plane mirror is a flat smooth reflecting surface which forms images by regular reflection. It is often made by bounding a thin polished metal surface to the back of a flat sheet of glass or silvering the back side of the flat sheet of glass.

The silvered side is normally coated with some paint to protect the silver coating. If the clear and the silvered surfaces are in parallel plane, the mirror is called a plane mirror.

If the surfaces are curved, the mirror is called curved mirrors.

The silvered side of the mirror is shown by shading behind the reflecting surface.

DEFINITION OF TERMS USED IN REFLECTION

Consider the set up below,

Incident ray – is the ray that travels from the source to the reflecting surface.

Angle of incident (i) – is the angle between the incident ray and the normal.

Normal – is the line drawn perpendicularly at the point where the incident ray strikes the reflecting surface.

Reflected ray – is the ray that bounces from the reflecting surface.

Angle of reflection (r) – is the angle between the reflected ray and the normal.

LAWS OF REFLECTION

The incident ray, the reflected ray and the normal at the point of incidence all lie on the same plane.
The angle of incidence, i, equals the angle of reflection, r.

Experiments to show the laws of reflection (exp. 8.6) KLB

ROTATION OF A MIRROR THROUGH AN ANGLE

Consider the mirrors below,

In figure (a), the angle of incidence is 30⁰. The angle of reflection is also 30^o.

Therefore the angle between the incident ray and the reflected ray is 60^o i.e., (30^o + 30^o).

In figure (b), mirror m₁ is rotated by an angle 10^o to the new position m₂. The normal BN moves through an angle 10^o. Angle between the two normals is 10^o.

In figure (c), for the same incident ray AB, the new angle of incident = 30^o+

10^o =40^o. The new angle of reflection = 40^o. Hence the new angle between the angle of incidence and the angle of reflection = 40^o+ 40⁰=80⁰.

In figure (d), the angle between the two reflected rays BC and BD =20^o.

For the same incident ray, the angle of rotation of the reflected ray is twice the angle of rotation of the mirror.

EXAMPLE 3

A ray of light is incident along the normal in a plane mirror. The mirror is then rotated through an angle of 200. Calculate the angle between the first reflected ray and the second reflected ray.

SOLN

Angle of rotation of reflected rays = 2 x angle of rotation of the mirror

=2 x 20⁰

=40^o

EXAMPLE 4

The figure below shows a ray incident at an angle of 25o at position 1.

The mirror is turned through 6⁰ to position 2. Through what angle is the reflected ray rotated.

SOLN

Rotation change the angle of incidence from 25^o to (25+6) =31⁰.

Hence the angle of reflection is 31o from the new normal. The total change in the angle of reflected ray is 12^o

EXAMPLE 5

A suspended plane mirror makes an angle of 20^o with a wall. Light from a window strikes the mirror horizontally. Find;

Angle of incidence.
The angle between the horizontal and the reflected ray

FORMATION OF IMAGES BY PLANE MIRRORS

Images formed are far behind the mirror as the object is in front of the mirror i.e. image distance is equal to object distance from the mirror

Characteristics of images formed by plane mirrors

Image formed is the same size as the object.
The image is formed far behind the mirror as the object is in front of the mirror.
Images formed are laterally inverted g. when you raise your right hand, the image raises its left hand.

Virtual images – are formed by rays that appear to come from the image. Such images are not formed on the screen as they are only imaginary.

EXAMPLE 6

A girl stands 2m in front of a plane mirror.

Calculate the distance between the girl and her image
If the mirror is moved 0.6m to the girl, what will be the distance between her and image.

SOLN

2+2 = 4m
Object distance =2-0.6 =1.4m

Total distance = 1.4 + 1.4 = 2.8m

IMAGES FORMED BY MIRRORS AT AN ANGLE

When an angle Ѳ is 90^o, the number of images formed, n, is 3, i.e.

n = 360− 1 =3 images

When the angle Ѳ is 60^o, the number of images formed, n, is 5, i.e.

n = 360− 1 = 5 images

In general if the angle between two placed mirrors is Ѳ, then the number of images formed, n, is given by,

n = 360^o − 1

EXAMPLE 7

Two plane mirrors are kept inclined to each other at 120^o. Calculate the number of images formed by the mirrors.

SOLN

n = 360− 1 =2 images

120

EXAMPLE 8

At what angle would the two mirrors inclined to form 17 images.

SOLN

17 = 360 – 1

18Ѳ = 360⁰

Ѳ = 20^o

Mirror Parallel To Each Other

When the mirrors are parallel i.e. Ѳ= 0^o, the number of images is given by,

n = 360^o− 1 =∞ (infinite number of images)

0^o

In this case, each image acts as an object in the second and first mirror as illustrated below;

EXAMPLE 9

Two parallel plane mirrors are placed 30cm apart. An object placed between them 10cm from one mirror. Determine the image distance of two nearest images formed by each mirror.

SOLN

Image distance = object distance

Image distance on mirror 1= 10cm

Image distance on mirror 2 = 20cm

EXAMPLE 10

Two plane mirrors inclined at an angle 60^o to each other. A ray of light makes an angle of 40^owith mirror M₁ and goes on to strike mirror M₂.

Find the angle of reflection on the second mirror M₂.

The angle of reflection = 10^o

APPLICATIONS OF PLANE MIRRORS

The kaleidoscope

A kaleidoscope or mirror scope is a device used to produce a series of beautiful symmetrical images. Two plane mirrors are placed at an angle of 60^o inside a long tube.

The bottom of the tube is a ground glass plate for admitting light. On this plate is small scattered small pieces of brightly coloured glass, which act as objects.

When one looks down the tube, five images of the object are seen which together with the object form a symmetrical pattern in six sectors as shown below

The instrument is used by designers to obtain ideas on systematic patterns.

The periscope

This is an instrument used to view objects over obstacles. It is used in submarines and also to watch over crowds. The images seen with the aid of the instrument are erect and virtual.

A periscope uses two plane mirrors kept parallel to each other and the polished surfaces facing each other. Each plane mirror makes an angle of 45^owith the horizontal. Light from the object is turned through 90⁰at each mirror and reaches the eye as shown

The rays from the object are reflected by the top and then reflected again by the bottom into the observer. The image formed is virtual, upright and same size as the object.

Barber shops and saloon

QUESTIONS

What is meant by a virtual image?
The figure below shows an object O being viewed using two inclined mirrors M₁ and M₂.

Complete the diagram by sketching rays to show the position of the image as seen by the eye E

The figure below shows an object O placed in front of a plane mirror

On the same diagram, draw rays to locate the position of the image 1 as seen from the eye E.

The diagram shows a ray of light incident on a plane mirror at point O.

The mirror is rotated clockwise through an angle of 30⁰ about an axis perpendicular to the paper. Determine the angle through which the reflected ray rotated.

A luminous point object took 3 s to move from P to Q in front of a pinhole camera as shown below.

What is speed in cm/s of the image on the screen?

The diagram shows the image of a watch face in a plane mirror

What is the time shown on the watch face?

(a) Give two main reasons why concave mirrors are unsuitable as driving mirrors

(b) State one disadvantage of a convex mirror as a driving mirror

Explain why a concave mirror is suitable for use as a make up mirror.
In the space provided below, sketch a labeled diagram to show how a pinhole camera forms an image of a vertical object placed in front of the pinhole
A building standing 100m from a pinhole camera produces on the screen of the camera an image 5 cm high 10 cm behind the pinhole. Determine the actual height of the building.
What property of light is suggested by the formation of shadows?
State the reason why when a ray of light strikes a mirror at 90o, the reflected ray travels along the same path as the incident ray.
Figure 1 shows two point objects A, and B, placed in front of a mirror M

Sketch a ray diagram to show the positions of their images as seen by the eye.

What is meant by virtual image?
Figure 2 shows a ray of light incident on plane mirror at point O.

The mirror is rotated clockwise through an angle 300 about an axis perpendicular to the paper. Determine the angle through which the reflected ray rotated.

3 shows an object O being viewed using tow inclined mirrors M1 and M2.

Complete the diagram by sketching rays to show the position of the image as seen by the eye.

Sketch the same diagram, the path of the ray until it leaves the two mirrors. Indicate the angles at each reflection

In a certain pinhole camera, the screen is 10cm from the pinhole. When the camera is placed 6m away from a tree, a sharp image of the tree 16cm high is formed on the screen. Determine the height of the tree
Figure 4 shows three point sources of light with an opaque object placed between them and the screen.

Explain the nature of the shadow formed along B and C.

State the number of images formed when an object is between two plane mirrors placed in parallel.
Figure 5 shows a ray of light incident on a mirror at an angle of 450. Another mirror is placed at an angle of 450 to the first one as shown .Sketch the path of the ray until it emerges

SOLUTION

– Image that cannot be formed on screen.

– Always on the opposite side of the object

Angle of rotation of reflected ray = 2(angle of rotation of mirrors)

= 2x 30⁰

=60⁰

Measure P₁Q₁in cm (i.e. length of image on the screen as shown below)

Divide this value by 3 seconds i.e. velocity = distance / time

4:05 p.m
a) -Key form real inverted images

-Highly magnified images which give a wrong perception of object distance.

-Small field of view.

b) Very small images, giving the illusion that the objects are far away.

Can from magnified, erected images.

Where O = object; h = pin-hole; u- Object distance; v- Image distance

u =100m

h_i = 0.5cm

TOPIC 9: ELECTROSTATICS 1

This is the study of static charges. There are two types of charges i.e. negative charge and positive charge.

When a plastic ruler is brought near to small pieces of paper, it will be noted that it cannot be able to attract the small pieces of paper. This is because the ruler is electrically neutral.

When the ruler is rubbed against fur or hair the static charges becomes active. In this case, between the ruler and fur or hair they interchange charges whereby one becomes positively charged and the other negatively charged. Because of this the ruler is able to attract the small pieces of paper.

The SI unit of charge is coulomb (C). Millicoulombs and micro-coulombs are also used.

1000 millicoulombs = 1 coulomb

1000000 micro-coulomb = 1 coulomb

Origin of Charge

Matter is made up of atoms. An atom has particles known as protons, electrons and neutrons. Protons are positively charged, electrons are negatively charged and neutrons are neutral.

Protons and neutrons are found at the centre and nucleus of the atom while electrons are found moving around the energy levels.

The nucleus has positive charge due to the charges on the protons. Electrons in the outermost orbit are weakly held by the nucleus and can be transfer easily from one material to another by rubbing.

The material that gains electrons becomes negatively charged and that which loses electrons becomes positively charged. A negatively or positively charged atom is called an ion.

Materials like polythene and plastic they acquire electrons when they are rubbed hence they become negatively charged while materials like acetate, Perspex and glass have their electrons removed from their surface when rubbed and they become positively charged.

In general origin of charge is based on the atom of any given substance; each atom contains protons, electrons and neutrons.

Basic Law of Charges

This law is based on the relationship between charges when they are brought near to each other. It states that unlike charges attract while like charges repel.

CHARGING MATERIALS

Materials can be charged by the following methods;

Induction
Contact
Separation

INDUCTION

This is the ability in which a body which is charged finds to influence another adjacent to acquire an opposite.

A positively charged material, when it is brought near to another uncharged material, it will influence another body to acquire some charge.

The positive charges in B which has been repelled are removed by the process of earthing.

Earthing is the process through which electrons are made to the ground or from the ground through a conductor.

In the above case when a conductor is connected to B, electrons will flow from the ground to neutralise the positive charges.

After the positive charges have been neutralised, the conductor in B is removed fast while the two bodies are maintained adjacent to one another. This is to enable the electrons in B to remain within that body but if you remove body A while the conductor is connected with B, those electrons in B will escape to the ground.

When body A and B are separated as far as possible the negative charges will distribute uniformly.

CHARGING BY CONTACT

In this method two bodies are brought directly into contact, because of this some charges are able to cross over between their surfaces.

In this method, one of the bodies must be charged. That charge will influence the other body to acquire some charge.

NOTE: When a body is charged by contact method, it acquires charges that are similar to the ones on the charging rod.

In the diagram above body A was charged positively and because of this charge when it is in contact to body B it attracts negative charges and repel with positive charge.

When the two are made to be in contact the negative charge in body B crosses to body A to neutralise part of its positive charge.

If this process continues with time the number of positive charges in A will reduce and the number of the positive charges in B will increase.

Finally when the two bodies are separated the positive charges in B will distribute uniformly.

CHARGING BY SEPARATION

In this case two uncharged bodies are brought near to charged material. By the process of induction the two bodies will acquire an opposite charge because of attraction and repulsion.

The positive charge in A influence negative charges in X because of attraction while it influences positive charges in Y because of repulsion.

NOTE: In order to sustain the two opposite charge in X and Y in the two bodies, they are first separated while the position in body A is maintained. Finally when they are separated the two bodies will distribute uniformly as shown.

THE ELECTROSCOPE

This is an instrument which works on the principle of electrostatic charges. It is also used for investigating the effects of electric charges.

The gold-leaf electroscope consists of a thin gold or aluminium leaf of plate connected to a metal rod that has a brass cap at the top as shown,

The cap acquires the charges through induction or contact and spreads it through the rod to the plate and leaf.

The cap is circular to ensure uniform distribution of charges.

Both the leaf and the plate show the presence of charges by repelling each other, making the leaf to diverge. The absence of charges is also shown when leaf divergence decreases.

Metal casing is for protecting the leaf from the effects of draught. The casing has a glass window through which observations are made.

The rod is supported by passing it through a plug of good insulating material such as rubber. The insulator stops charge given to the cap from spreading onto the case and leaking away. The casing may be a terminal connected to the earth.

When the electroscope is touched by a finger or connected to the earth by a wire, electrons either flow to the earth, depending on the charge on the electroscope.

The process of losing to or gaining charges from the earth through a conductor is called earthing.

Charging an Electroscope by Contact Method

In this method, a charged body is brought into contact with the cap of the electroscope as shown in the figure below,

Because the positive charge on the rod are in contact with the negative charge at the cap, the two charges neutralise i.e. negative charges move to the rod and positive charge move to the cap.

It will be observed that at the leaf, the leaf diverges because of like charges at the point (positive charges).

The more positive charges at the leaf will make the leaf to diverge at a greater angle. If the process is continued, the electroscope will charge to a maximum point in which the leaf cannot diverge any further.

NOTE: The charged material coming into contact with the cap of the electroscope is an insulator. Only charges on the rod’s surface coming into contact with the cap are used in neutralizing the charges induced on the cap.

Charging Through Induction

In this method a charged body is brought near to the cap of the electroscope and because of attraction the cap is going to have opposite charge while at the leaf is going to have same charge because of repulsion as shown,

The positive charges at rod attract the negative charge at the cap and repel positive charge at the leaf. The positive charges at the leaf repel one another thus making the leaf to diverge through an angle.

In order to eliminate the charges at the leaf, one is required to earth the cap by the use of a finger or a wire while maintaining the position of the charging rod as shown;

Through earthing electrons are going to flow from the ground through the cap down the leaf to neutralise the positive charge hence making the leaf to fall.

These electrons when they are passing through the cap, they are not affected by the negative charge at the cap. This is because the negative charge at the cap and the positive charge on the rod are strongly attached because of attraction.

While maintaining the position of the rod removes the finger or the earth wire first in order to avoid the negative charge at the cap not to escape down to the ground.

Finally remove the positive charged rod away from the cap. Because of like charges at the cap they will repel one another in order to distribute uniformly on the cap and the leaf.

The negative charges which move to the leaf diverge once more indicating electroscope has been charged.

ASSIGNMENT

Use a negatively charged rod to explain how to charge an electroscope using induction method.

USES OF THE ELECTROSCOPE

To detect the presence of charge on a body

–The material to be tested is placed on or close to the cap of the electroscope. If it is not charged, the leaf does not diverge.

To test the sign of charge on a charged body

–Charge an electroscope negatively by contact method. Slowly bring a negative rod to be tested close to the cap of the electroscope. The leaf diverges more. It does so because the negative charges on the rod repel more charges from the cap to the plate and the leaf. Similar charges in the plate and the leaf are repelled more.

–When a strong positively charged rod is brought from high position towards a negatively charged electroscope, the leaf divergence first decreases then increases as the rod approaches the cap. The leaf divergence reduces slightly first because the positive on the rod attract negative charges on the leaf and plate, making the electroscope neutral. On moving the rod, much lower, the leaf divergence increases again to higher position. This is because the strong positively charged rod attracts more electrons from the plate and leaf, making them more positive. Hence, they repel further.

NOTE:

The same observations are made when a negatively charged rod is brought towards a positively charged electroscope. On moving a neutral conductor close to a charged electroscope, leaf divergence decreases. Charges on the electroscope induce opposite charges on the conductor.

Charge on the electroscope	Charge brought near the cap	Effect on the leaf divergence
+	+	Increase
–	–	Increase
+	–	Decrease
–	+	Decrease
+ or –	Uncharged	Decrease

An increase in divergence of the leaf is therefore the only sure way of confirming the kind of charge on a body.

To test the quantity of charge on a charged body

–Small bodies have few charges compared to big ones of the same kind.

To test for insulation properties of a material

–Materials like copper, iron, aluminium, zinc and graphite make the leaf divergence decrease. Materials like plastic, glass, charcoal and wood do not affect the divergence of the leaf. For metals and graphite, the leaf decreases in divergence because they allow electrons to flow between the electroscope and the earth. Such materials are called conductors. In conductors, electrons freely move from one atom to another. Such electrons are called free electrons.

For materials like plastic, glass, wood there is no change in leaf divergence because they do not allow electrons to flow between the electroscope and the earth. In these materials, electrons are not free to move and are strongly bound to their nuclei. These materials are called insulators. There are other materials like silicon and germanium which conduct under special conditions. This conductivity is between conductivity of insulators and conductors. Such materials are called semi-conductors.

CHARGES IN AIR

Air can also be charged. It is shown by heating air above a charged electroscope. It is observed that the leaf divergence decreases.

When fuel burns, chemical reactions yield ionised products. The ions move and collide with air molecules making air to be ionised. Ionisation produces both negative and positive charges.

The ions carrying opposite charge to the electroscope are attracted to the cap of the electroscope, resulting in the discharge of the electroscope.

APPLICATION OF ELECTROSTATIC CHARGES

Electrostatic precipitator

It is used in industries to reduce pollutants. The figure below shows a common precipitator used in chimneys.

It consists of a cylindrical metal plate fixed along the walls of the chimney and a wire mesh suspended through the middle. The plate is charged positively at a potential of about 5000V while the wire mesh is negatively charged.

A strong electric field is set up between the plates, which ionises the particles of the pollutants. These are attracted to the plate.

Spray painting

The can is filled with paint and nozzle charged. During spraying, the paint droplets acquire similar charges and therefore spread out finely due to repulsion.

As they approach the metallic body they induce opposite charges which in turn attract them to the surface. Therefore little paint is used.

Finger printing and photocopying

DANGERS OF ELECTROSTATICS

When a liquid flows through a pipe its molecules become charged due to rubbing on the inner surface of the pipe. If the liquid is inflammable it can cause sparks and explode.

Similarly, explosive fuel carried in plastic cans can get charged due to rubbing which may result in sparks and even explosion.

It is therefore advisable to store fuels in metal cans so that any charges generated continually leak.

QUESTIONS

Explain why fuel tankers have a loose chain hanging under them to touch the ground as they move?
Why do some motor tyres contain graphite?
Two isolated and insulated spheres A and B carry the same positive charge. Sketch the electric lines of force of their field when placed close to each other but not touching some.
State the observation on the leaves of a positively charged electroscope when a negative charge is brought near it.
The fig shows sketches of two types of houses built in a lighting prone area. State with reasons, which house is safer to stay in during lighting and thunderstorms?

The diagram below shows a circuit with a capacitor C and a lamp L. When the sketch is closed at Y, the lamp L lights. When the switch is closed at X, L does not light. Explain the observation.

In the clothing and textile industries the machines experiences electrostatics forces at certain points. Suggest one method of reducing these forces.
State two other factors to be considered in constructing a capacitor other than the surface area of the plates.
State the precaution that is taken when charging a metal object.
(a) (i) State coulombs law of electrostatic force

(ii) Define capacitance

(b) Describe how the type of charge on a charged metal rod can be determined

(c) The fig. Shows hollow negatively charged sphere with a metal disk attached to an insulator placed inside. State what would happen to the leaf of an uncharged electroscope if the metal disk were brought near the cap of the electroscope. Give a reason for your answer.

(d) State two ways of charging the magnitude of the deflection of the leaf of an electroscope.

Explain why the leaf of an uncharged object is brought near the cap.
A glass rod can be charged positively by rubbing it with silk. Explain what happens when the glass rod is being charged.
State the law of electrostatic charges.
A positively charged rod is brought near the cap of a leaf electroscope. The cap is the earthed momentarily by touching with the finger. Finally the rod is withdrawn. The electroscope is found to be negatively charged. Explain how this charge is acquired.

SOLUTIONS

To induce/effect earthing process thus allows unnecessary charges to leak to the ground, causing neutralization of the charges. This prevents the formation of sparks which can cause explosion

Graphite has free and mobile electrons. This causes neutralizations of the electrostatic charges.

The leaf in the electroscope falls
Metal roofed house. Because there is less resistance of the flow of charges to the ground so if struck by lighting it would conduct it to the ground. The other one would burn or have the people inside struck by the lightening.
At x the capacitor is charged only once and the keeps charging and discharging in opposite directions hence current keeps alternating at the a.c frequency. This lights the bulb continuously.
Earthing the machines/using spikes.
Material used between the two plates of the capacitor.
Well insulated / avoid touching
a)Ability to store charge given by the quantity of charge it can store per unit p.d
b) Bring it near a charged electroscope (say +vely). If not, charge the electroscope – vely and bring the rod near. If divergence is observed then they have the same charge. Note that if decrease in divergence is observed in both cases then the rod is simply a conductor and it’s not charged.
c) Nothing would happen to the leaf of the electroscope. This is because in a hollow charged conductor, the charged conductor and not inside
d) – Earthing or using another

– Charged body

Like charges repel unlike charges attract.
On earthing negative charges flow to the leaves from earth to neutralize positive charges when the rod is withdrawn the leaves are left with net negative

SCHEMES OF WORK FORM FOUR ENGLISH TERM 1-3

October 5, 2025 Maverick John Leave a comment

	SCHEME OF WORK FORM FOUR ENGLISH TERM ONE 20…………………
*WK NO*	L/ NO	*TOPIC*	*SUBTOPIC*	*LESSON / SPECIFIC* *OBJECTIVES*	*TEACHING/ LEARNING* *ACTIVITIES*	MATERIALS / RESOURCES	REFERENCES
1	1	Listening and speaking.	Etiquette. Paying attention.	By the end of the lesson, the learner should be able to: Highlight importance of paying attention. Identify some attention detractors. Suggest ways of improving skill in paying attention.	Listening. Speaking. Discussion.	Class readers.	Integrated English Bk IV Pg 1-3
	2	Reading.	Comprehension.	Answer questions and make sentences using vocabulary learnt.	Silent reading. Reading aloud. Discussion. Writing.	Dictionary.	Integrated English Bk IV Pg 3-4
	3	Grammar.	Nouns as subjects.	State whether a noun has been used as a subject or object in a sentence.	Reading. Writing. Listening. Detailed discussion.	Extracts from set books.	Integrated English Bk IV Pg 7-8
	4	Grammar.	Nouns as objects / complements.	Identify nouns used as direct or indirect objects. Identify nouns used as complements.	Reading. Writing. Listening. Detailed discussion. Written exercise.	Extracts from set books.	Integrated English Bk IV Pg 9-11
	5	Writing.	Paraphrasing.	Paraphrase a given passage. State differences between a paraphrase and a summary.	Review summary writing; Reading. Writing. Discussion.	Extracts from set books. Chart.	Integrated English Bk IV Pg 12-14
	6	Speaking.	Verbal and non- verbal cues that enhance listening & speaking.	Demonstrate ability to use verbal and non-verbal skills in narrating a story.	Role-play. Speaking. Guided discussion. Group competitions.	Readers.	Readers.
	7 & 8	Reading.	Intensive reading: Set book.	Read some chapters and analyse language and literally appreciation.	Detailed discussion. Reading. Written exercises.	Set book guide.	Set book.
2	1	Listening and speaking.	Stress to distinguish word class.	Use stress to distinguish word class.	Guided practice & supervision. Group work.	Flash cards.	Integrated English Bk IV Pg 15-16
	2	Reading. Poetry- mood.	Reading skills: Study reading.	Define mood as used in poetry. Identify adjectives used to describe mood.	Reading. Listening. Answering questions. Discussion.	Extracts from literature set books. Charts.	Integrated English Bk IV 16-17
	3	Reading.	Comprehension.	Answer comprehension questions on the set passage correctly.	Reading. Speaking. Writing. Guided discussion.	Readers. Charts. Dictionary.	Integrated English Bk IV Pg 18-21
	4	Writing.	Debate.	Write points for and against a motion on a given subject.	Speaking. Writing. Guided discussion.		Integrated English Bk IV Pg 21-22
	5	Grammar.	Relative pronouns.	The learner should be able: Identify and use relative pronouns. Form and use compound relative pronouns.	Listening & speaking Answer questions. Written exercises.	Extracts. From set books.	Integrated English Bk IV Pg 22-26
	6	Writing.	Public writing.	Write formal and informal requests. Decline a request politely.	Reading. Discussion. Written exercise.		Integrated English Bk IV Pg 26-32
	7 & 8	Reading.	Intensive reading of Set book.	Read analytically and identify themes style and character traits.	Reading. Answering probing questions. Detailed discussion.	Set book guide.	Set book.

3	1	Writing.	Dictation.	Take a dictation taking note of punctuation marks.	Reading aloud. Writing. Reviewing.		Integrated English Bk IV Pg 33
	2	Reading.	Interpretive reading.	Bring out meaning that is not explicitly stated in a given text.	Reading aloud. Discussion.	Readers. Newspapers. Journal.	Integrated English Bk IV Pg 33-34
	3, 4	Grammar.	Interrogative pronouns. Compound interrogative pronouns.	Identify interrogative pronouns. Use interrogative pronouns correctly. Form compound interrogative pronouns.	Listening & speaking Answer questions. Written exercises.	Readers.	Integrated English Bk IV Pg 35-39
	5,6	Writing.	Personal writing. Recipes.	Define a recipe. Identify words used in recipes. Write a recipe of a dish for preparing a meal for an occasion.	Listening. Reading. Answer questions. Writing. Review exercise.		Integrated English Bk IV Pg 40-43
	7 & 8	Reading.	Intensive reading: Set book.	Read the assigned chapters and discuss language aspects as well as literally devices.	Reading. Detailed discussion. Written exercises .	Set book guide.	Set book.

4	1,2	Listening and speaking.	Polite interruption and disagreeing.	Demonstrate the etiquette of interrupting and disagreeing politely.	Silent reading. Group work. Guided discussion.	Readers.	Integrated English Bk IV Pg 44-45
	3	Reading.	Comprehension.	Answer comprehension questions on a passage and use vocabulary correctly.	Reading aloud. Silent reading. Writing. Guided discussion.	Readers. Charts. Dictionary.	Integrated English Bk IV Pg 48-49
	4	Grammar.	Relative pronouns II.	Use relative pronouns as interrogative pronouns and interrogative adjectives.	Discussion. Oral exercise. Written exercise.		Integrated English Bk IV Pg 50-51
	5,6	Reading.	Reading skills: Critical reading. Telestiches.	The learner should be able: Apply critical reading skills to analyse a given text.	Review acrostic poetry. Reading. Guided discussion. Group writing.		Integrated English Bk IV Pg 51-52
	6	Reading.	Intensive reading: Poetry: Atmosphere	Read a poem & identify the prevailing atmosphere projected.	Oral exercise: reciting. Written exercises. Presentation.	Anthologies of poem.	Poem extracts.
	7 & 8	Reading.	Intensive reading: Set book.	Read the assigned sections and discuss grammar & literally devices.	Read paragraphs and Identify the devices Guided discussion. Assignment: common devices.	Set book guide.	Set book.

5	1	Listening & Speaking.	Use of tone to reveal attitude.	The learner should be able: Interpret and express attitude using tone.	Listening. Guided discussion. Group work.	Readers. Charts.	Integrated English Bk IV Pg 53-54
	2	Writing.	E-mail.	Use e-mail efficiently in communication.	Oral exercise: Written exercise. Discussion.	Newspapers. Magazines. Computers.	Integrated English Bk IV Pg 51-52
	3	Reading.	Responsive reading.	Relate what is in a text to own experiences.	Reading. Discussion.		Integrated English Bk IV Pg 54-58
	4	Grammar.	Parts of speech – revision.	Write correct form of verbs. Complete sentences according to instructions given.	Review parts of speech. Oral and written exercises.		Integrated English Bk IV Pg 58-59
	5	Writing.	Public writing. Letter of inquiry.	Write a letter of inquiry in the correct format.	Reading aloud. Discussion.	Newspapers.	Integrated English Bk IV Pg 59-60
	6	Reading.	Intensive reading: Poetry. Figurative language.	Read a poem and identify metaphors, similes, and hyperbole.	Listening & writing an exercise. Reciting poems. Guided discussions.	Anthologies of poems for further reading.	Poems from East Africa by Cook and Rubadiri.
	7 & 8	Reading.	Intensive set book reading:	Read the assigned sections and discuss grammar & literally devices.	Reading. Discussion.	Video& Audio tapes. Prescribed set books guides	Prescribed set books.

6	1	Listening & speaking.	Oral poetry – Recitations.	Analyse a poem that is in form of a recitation.	Reading aloud. Exposition. Guided discussion. Writing.	Readers. Charts. Dictionary.	Integrated English Bk IV Pg 63-64
	2	Reading.	Critical reading.	Identify literal, implied and inferred meanings in a text.	Reading texts. Writing. Listening. Discussion.	Extracts from Prescribed set books.	Integrated English Bk IV Pg 64-66
	3	Reading.	Comprehension.	Answer comprehension questions correctly.	Guided practical activity. Reading. Inferring meanings of given words.	Readers. Charts.	Integrated English Bk IV Pg 63-64
	4	Grammar.	Verbs – participle phrases.	Rewrite sentences using participle phrases.	Q/A to review participle tenses. Discussion. Reading. Listening.	Dictionary. Audio tapes.	Integrated English Bk IV Pg 67-69
	5	Writing.	Advertisement.	Highlight details that should be included in advertisements.	Discussion. Group work. Group resentations.	Sample adverts.	Integrated English Bk IV Pg 70-71
	6	Reading.	Intensive reading: Poetry:	Critically analyse issues raised, style, and themes in a given poem.	Listening. Speaking. Reading. Writing.	Poetry book.
	7 & 8	Reading.	Intensive reading: Set book.	Critically analyse plot, characters, themes, and style in the novel.	Guided discussion. Probing questions. Dramatization. Written exercise.	set book guide.	Selected set book.
7	1	Listening & speaking.	Tongue twisters.	State functions of tongue twisters. Translate tongue twisters to other languages.	Reading aloud. Discussion. Formulating tongue twisters.		Integrated English Bk IV Pg 70-71
	2	Reading.	Reading skill: Facts and opinions.	Distinguish facts from opinions.	Reading. Discussion.		Integrated English Bk IV Pg 73-75
	3	Grammar.	Verbs –the gerund.	Identify a gerund used as a subject or object.	Discussion. Oral and written exercises.		Integrated English Bk IV Pg 75-76
	4	Writing.	Institutional writing. Speeches.	Outline points to be highlighted in a speech. Write a sensible speech.	Exposition. Discussion. Written exercise.		Integrated English Bk IV Pg 77-80
	5 & 6	Reading.	Intensive reading: Set book.	Critically analyse plot, characters, themes and style in a novel.	Guided discussion. Probing questions. Dramatization. Written exercise.	Set book guide, Audiotapes.	One of the set books.
	7-8	TEST & MID-TERM BREAK

8	1	Listening & speaking.	Ogre narrative.	Identify features of style used in a given narrative. Cite moral lesson(s) from a given narrative.	Silent reading. Role playing. Practise oral renditions. Discuss characters, moral lessons.	Readers.	Integrated English Bk IV Pg 84-86.
	2	Reading.	Study reading. Textual information.	Interpret textual information.	Exposition. Oral and written exercises.		Integrated English Bk IV Pg 77-80
	3	Reading.	Reading comprehension.	Answer comprehension questions correctly. Infer meanings of given words and phrases.	Reading. Inferring meanings of given words. Look words from the dictionary.	Dictionary.	Integrated English Bk IV Pg 87-89
	4	Grammar.	Adverbs.	Identify types of adverbs. Form adverbs from adjectives.	Q/A to review parts of speech. Oral and written exercises.		Integrated English Bk IV Pg 89-93
	5-6	Writing.	Writing reviews.	Write a review of a narrative.	Guided discussion. Reading. Listening Group presentations.		Integrated English Bk IV Pg 93-96
	7 & 8	Reading.	Reading Intensive reading Set book.	Critically analyse plot, themes, characters and style in a set book.	Guided discussion. Reading. Listening & speaking.	Video & and audiotapes, Set book guide.	Selected set book.
9	1	Listening and speaking.	Proverbs.	Complete proverbs and interpret them.	Group competitions. Discussion. Essay writing to illustrate a given proverb.		Integrated English Bk IV Pg 97
	2	Reading and writing.	Reading Comprehension.	Answer questions based on a passage.	Reading aloud. Writing.	Readers. Dictionary.	Integrated English Bk IV Pg 98-100
	3	Writing and speaking.	Persuasive speech.	Write short speeches and present them to class.	Individual and group reflections.	Readers.	Integrated English Bk IV Pg 101
	4	Writing.	Study writing. Questionnaires.	Structure questionnaires. Fill in questionnaires.	Exposition. Individual and group reflections.	Sample questionnaires.	Integrated English Bk IV Pg 105-110
	5-6	Grammar.	Typical endings of adverbs.	Form adverbs using typical endings.	Discussion. Oral exercise. Written exercise. Exercise review.		Integrated English Bk IV Pg 101-104
	7 & 8	Reading.	Intensive reading Set book.	Evaluate the plot, characters, styles, and themes in the novel.	Oral & written exercises. Dramatization. Guided discussion.	Audio tapes. Set book guide.	Prescribed set book.

10	1-2	Intensive reading.	Background and setting of a story.	Describe the background and setting of a story. Identify the time-span of events in a story.		Brain storming. Probing questions. Discussion.		Integrated English Bk IV Pg 111-4
	3	Intensive reading.	Character and characterization.	Analyse characters in literary texts.		Probing questions. Oral questions. Guided discussion.	Extracts.	Integrated English Bk IV Pg 115-6
	4	Listening & speaking.	Themes.	List down themes revealed in a story. Arrange themes in order of prominence.		Brain storming. Probing questions. Discussion.		Integrated English Bk IV Pg 116-7
	5-6	Intensive reading.	Style.	Identify stylistic devices used in stories / narratives.				Integrated English Bk IV Pg 117-9
	7 & 8	Intensive reading:	Contextual questions.	Answer context questions on set books.		Guided tasks. Written exercise. Review of the exercise.	Set book guide.	Set book.
11	1	Listening & speaking.	Features of proverbs.		Describe features of proverbs. Translate proverbs to English.	Exposition of new concepts. Give examples of proverbs. Discussion.		Integrated English Bk IV Pg 120-2
	2	Study reading.	Non-textual information.		Derive non-textual information from diagrams.	Examine diagrams. Probing questions. Discuss derived information.		Integrated English Bk IV Pg 123-4
	3	Grammar.	Prepositions.		Identify prepositions in given sentences. Use simple and complex prepositions correctly. Identify words that serve as prepositions and adverbs.	Q/A to elicit preposition of time, place, direction. Oral and written exercises.		Integrated English Bk IV Pg 124-7
11	4	Reading.	Comprehension.		The learner should be able to answer questions based on a comprehension.	Reading. Writing. Marking. Infer meanings of new words.		Supplementary readers.
	5	Writing.	Writing reviews.		Review a short story using the 5W and H technique.	Probing questions. Discussion.	Supplementary readers.	Integrated English Bk IV Pg 127-9
	6	Reading.	Vocabulary.		The learner should be able to use new words in sentences correctly.	Reading. Listening. Q/A. Speaking. Take an exercise.	Dictionary. Flash cards. Group competitions.	Supplementary readers.
	7-8	Reading.	Intensive reading.		The learner should be able to analyse characters and themes in a given text.	Reading. Discussion. Writing.	Set book guide.	Set book.
12-13	END OF TERM ONE EXAMS

		SCHEME OF WORK FORM FOUR ENGLISH TERM TWO 20…………………
*WK NO*	L/ NO	*TOPIC*	*SUBTOPIC*	*LESSON / SPECIFIC* *OBJECTIVES*	*TEACHING/ LEARNING* *ACTIVITIES*	MATERIALS / RESOURCES	REFERENCES	REMARKS
1	1	Grammar.	Short and long vowels.	Pronounce short and long vowels.	Reading. Writing. Review exercise.		Integrated English Bk IV Pg 130
	2-3	Reading.	Comprehension:	Answer questions on a text and analyse theme, style, and issues raised.	Expressive reading. Detailed discussion. Writing an exercise.	Extracts from readers and supplementary readers.	Integrated English Bk IV Pg 131-2
	4	Writing and speaking.	Duality of words.	Spell words backwards. Give meanings of new words formed.	Group competitions. Group presentations.		Teacher’s choice.
	5-6	Writing.	Social writing. Emails and faxes.	Write informal and formal emails / faxes.	Guided practical activities.	Computers /mobile phones, telephone lines, modem.	Integrated English Bk IV Pg 134-6
	7 & 8	Reading.	Intensive Reading: Set book.	Analyse plot, themes, characters, and style.	Role-play. Listening. Writing.	Set book guide.	Set book.

2	1		Reading.	Intensive Reading Tone and attitude.	Identify tone and attitude in a given poem.	Silent reading. Reading aloud. Guided discussion.	Anthologies of poems.	Poems of East Africa / Teacher’s choice/ Integrated English Bk IV Pg 137-9
	2-3		Grammar.	Inverted sentences.	Write inverted sentences. Give reasons for sentence inversion.	Oral exercise. Discussion. Written exercise. Exercise review.		Integrated English Bk IV Pg 140-2
	4-5		Writing.	Report writing.	Identify sections of a report. Write a sensible report.		Sample reports.	Integrated English Bk IV Pg 143-5
	6	Reading.		Comprehension:	The learner should be able to: Answer questions from a given passage.	Q/A: discussion. Expressive reading. Writing.	Supplementary readers. Dictionary.	Teacher’s choice.
	7 & 8	Reading.		Intensive reading: Set book.	Analyse themes and style in a novel.	Examples. Oral exercise. Written exercise. Dramatization.	Set book guide.	Prescribed set book.

3		1	Listening and speaking.	Etiquette. Turn- taking.	Demonstrate proper turn-taking skills in discussions, presentations and speeches.	Reading. Listening. Simulations. Discussion.		Integrated English Bk IV Pg 148-9
		2	Grammar.	Sentence connectors.	Identify some sentence connectors. Join sentences using connectors.	Brain storming. Oral and written exercises.		Integrated English Bk IV Pg 152-4
		3	Writing.	Writing a confidential report.	Write a confidential report / reference letter.	Q/A to review a formal letter format. Read a sample report. Written exercise.		Integrated English Bk IV Pg 155-6
	4		Speaking.	Discussion.	The learner should be able to: Initiate and sustain a discussion on a given topic.	Read a passage. Deduce the implications of the words used by the speakers.		Teacher’s choice.
	5		Listening & speaking.	Giving and receiving instructions.	The learner should be able to: Give instructions in given situations.	Oral examples. Written exercise. Guided discussion.	Set of instructions. Magazines. Newspapers.	Teacher’s choice.
	6		Reading.	Intensive reading: Characterization.	The learner should be able to: Discuss characters in specific contexts.	Expressive reading. Discuss characters. Assignments & their review.		Literature set books. Readers.
	7 & 8		Reading.	Intensive reading: Set book.	The learner should be able to: Analyse plot, themes, and style in a novel.	Brain storming. Discussion. Written exercise.	Set book guide.	Set book.

4	1-2	Reading.	Comprehension.	The learner should be able to: Answer questions on a given passage correctly.	Reading a passage. Answer questions. Review the exercise.	Supplementary readers. Dictionary.	Integrated English Bk IV Pg 157-161
	3	Grammar.	Sentence and paragraph connectors (review)	Rewrite sentences adding sentence and paragraph connectors appropriately.	Oral and written exercises. Discussion.		Integrated English Bk IV Pg 164
	4	Writing.	Essay writing.	Write an application letter with reference to an advertisement.	Reading. Writing. Discussion.		Integrated English Bk IV Pg 161
	5	Reading.	Reading skills. Note-making.	Make notes based on a given passage.		Supplementary readers.	Integrated English Bk IV Pg 162-3
	6	Writing.	Creative writing. Autobiography.	Differentiate between a biography and an autobiography. Outline important aspects of an autobiography.	Exposition. Reading. Writing. Discussion.	Supplementary readers.	Integrated English Bk IV Pg 165-8
	7 & 8	Reading.	Intensive reading: Set book.	The learner should be able to: Analyse themes and style in a novel.	Brain storming. Discussion. Written exercise.	Set book guide.	Set book.

5	1	Listening & speaking.	The vowel sound.	Write down words that have the same vowel sound.	Reading. Writing. Discussion.		Integrated English Bk IV Pg 169
5	2	Reading.	Comprehension.	The learner should be able to: Answer questions on a given passage correctly.	Reading a passage. Answer questions. Review the exercise.	Dictionary.	Integrated English Bk IV Pg 170-4
5	3	Grammar.	Conjunctions.	Outline functions of conjunction.	Oral exercise. Written exercise. Exercise review.		Integrated English Bk IV Pg 175-7
	4-5	Writing.	Institutional writing. Curriculum vitae.	Write a C.V. in the correct format.	Reading. Writing. Discussion.discussion.round to the writing.wel sound.	Supplementary readers.	Integrated English Bk IV Pg 178-180
	6	Reading.	Institutional writing. Curriculum vitae.	The learner should be able to: Write a CV from a passage.	Expressive reading. Guided discussion. Written exercise.	Supplementary readers.	Integrated English Bk IV Pg 181-2
	7 & 8	Reading.	Intensive reading: Drama: Introduction to the play.	List characteristics of a particular play and give the background to the writer.	Written exercise. Expressive reading. Guided discussion.		Prescribed Set books.

6	1-2	Listening and speaking.	Role play. Negotiation skills.	Demonstrate proper negotiation skills.	Reading. Guided discussion.		Integrated English Bk IV Pg 183-7
	3	Reading.	Comprehension.	The learner should be able to: Answer questions on a given passage correctly.	Reading a passage. Answer questions. Review the exercise.	Dictionary.	Integrated English Bk IV Pg 188-190
	4	Grammar.	Revision exercise.	Answer questions correctly.	Written exercise. Exercise review.
	5-6	Writing.	Argumentative essay.	Write an argumentative essay based on a given topic.	Discussion in groups. Writing. Guided discussion.		Integrated English Bk IV Pg 191
	7 & 8	Reading.	Intensive reading: Set book.	Analyse plot, characters, themes and style in the play.	Oral questions & written exercise. Dramatizing.	Set book guide. Audio and video tapes.	Set book guide.	Set book.
7	1	Listening & speaking.	Study skill.	Answer questions from a read- out passage.	Listening. Writing. Answering questions.	Selected set book	Integrated English Bk IV Pg 192
	2	Reading.	Comprehension.	Answer questions on a given passage correctly.	Written exercise. Oral exercise. Mixed exercise.	Supplementary readers.	Integrated English Bk IV Pg 192-5
	3	Grammar.	Punctuation.	Use punctuation marks correctly.	Written exercise. Exercise review.		Integrated English Bk IV Pg 195
	4	Writing.	Devices for presenting titles, quotations and headings.	Present titles of publications, quotations and headings in the correct format.	Exposition. Supervised practice.		Integrated English Bk IV Pg 195-9
	5 & 6	Reading.	Intensive reading: Set book.	Analyse plot, characters, themes and style in a given play.	Oral questions. Written exercise. Dramatizing.	Set book guide. Audio and video tapes.	Set book.
	7-8	TEST & MID-TERM BREAK

8	1-2	Listening & speaking.	Oral reports. Discourse markers.	The learner should be able to: Explain functions of discourse markers.	Exposition. Brain storming. Oral exercise.		Integrated English Bk IV Pg 200-1
	3	Listening & speaking.	Oral reports. Signposting.	Give examples of signposting as used in oral presentations.	Exposition. Brain storming. Oral exercise.		Integrated English Bk IV Pg 202-3
	4-5	Reading.	Reading comprehension.	Answer questions on a given passage correctly.	Written exercise. Mixed exercise.	Supplementary readers.	Integrated English Bk IV Pg 208-9
	6	Writing.	Clauses.	Rewrite sentences according to instructions given.	Written exercise. Mixed exercise.		Integrated English Bk IV Pg 205-8
	7-8	Writing.	Creative writing. Biography.	Describe components of a biography.	Exposition. Reading. Group work.		Integrated English Bk IV Pg 209-214

9	1	Listening and speaking.	Debate.	Give points for / against a given subject in a motion.	Group debate. Inter-group debate.		Integrated English Bk IV Pg 221
	2-3	Reading.	Reading comprehension.	Answer questions on a given passage correctly.	Written exercise. Mixed exercise.	Supplementary readers.	Integrated English Bk IV Pg 221-3
	4	Grammar.	Typical endings of adjectives.	Form adjectives from nouns and verbs.	Discussion. Oral questions. Written exercise.		Integrated English Bk IV Pg 223-8
	5-6	Writing.	Expository writing.	Plan and present expository essays.	Exposition. Discussion. Written exercise.		Integrated English Bk IV Pg 229-231
	7 & 8	Reading.	Intensive reading: Set book.	Analyse plot, characters, themes, and style of the play.	Oral and written exercises. Discussion on the set books.	Set book guide.	Selected set book.

10	1	Listening & speaking.	Etiquette. Table manners.	Cite bad habits that may be exhibited at the table.	Reading aloud. Open discussion.		Integrated English Bk IV Pg 232-3
	2-3	Reading.	Reading comprehension.	Answer questions on a given passage correctly.	Written exercise. Mixed exercise.	Supplementary readers.	Integrated English Bk IV Pg 234-6
	4	Grammar.	Adjectives.	Outline functions of adjectives in sentences.	Discussion. Oral questions. Written exercise.		Integrated English Bk IV Pg 236-8
10	5	Writing.	Summary.	Write a cohesive summary on a section of a given subject.	Read a passage. Make a summary as guided.	Prescribed literature set books.	Teacher’s resources.
	6	Writing.	Public writing. Letter of application.	Write a letter of application for a job.	Reading an advert. Letter writing.		Integrated English Bk IV Pg 240
	7-8	Reading.	Intensive reading: Set book.	Analyse plot, characters, themes, and style of the play.	Oral and written exercises. Discussion on the set books.	Set book guide.	Selected set book.
11	1	Listening & speaking.	Stress in words.	Write down sentences that bring out two meanings of a given word.	Oral and written exercises. Guided discussion.		Integrated English Bk IV Pg 241
	2	Reading.	Comprehension.	The learner should be able to: Answer questions on the passage correctly.	Read a passage. Answer questions. Infer meanings of new words.	Supplementary readers. Dictionary.	Integrated English Bk IV Pg 241-3
	3	Grammar.	Cloze and indirect speech.	Fill gaps with suitable prepositions. Rewrite questions in indirect speech.	Oral and written exercise; Exercise review.	Extracts from set books.	Integrated English Bk IV Pg 245-6
	4	Writing.	Summary.	The learner should be able to: Write a summary of a passage.	Written exercise. Reading a passage. Marking exercises.	Newspapers. Magazines. Reports.	Integrated English Bk IV Pg 243-5
	5-6	Social Writing.	Giving instructions to family and friends.	The learner should be able to: Give instructions to family and friends in point form.	Oral and written exercises. Listening & speaking.	Prescribed set books.	Integrated English Bk IV Pg 246-7
	7 & 8	Reading.	Intensive reading: Set book.	Analyse plot, characters, themes and style of a given play.	Oral exercises. Discussion on the set books. Dramatization.	Prescribed literature set books.	Literature set book guides.
	END OF TERM TWO EXAMINATIONS
	SCHEME OF WORK FORM FOUR ENGLISH TERM ONE 20…………………
*WK NO*	L/ NO	*TOPIC*	*SUBTOPIC*	*LESSON / SPECIFIC* *OBJECTIVES*	*TEACHING/ LEARNING* *ACTIVITIES*	MATERIALS / RESOURCES	REFERENCES	REMARKS
1	1	Listening & speaking.	Poetry.	Answer questions based on a poem that has been read out.	Listening; Oral and written exercises. Detailed discussion.	Readers. Resource persons.	Integrated English Bk IV Pg 249-250
	2	Reading.	Comprehension.	Answer questions on the set passage correctly.	Written exercise. Reading a passage. Listening & speaking.	Section of a set book.	Integrated English Bk IV Pg 245-6
	3	Writing.	Composition based on a set book.	Write a composition based on a set book.	Written exercises; General review.	Section of a set book.	Integrated English Bk IV Pg 253
	4-5	Writing.	Essay writing.	Write an essay using new terms illustrated in a tree diagram.	Look up terms in the dictionary; Writing; General review.	Dictionary.	Integrated English Bk IV Pg 254
	6	Grammar.	Indirect speech and idioms.	The learner should be able to: Rewrite sentences in indirect speech. Explain the meanings of idioms / phrases.	Written exercise; Exercise review.		Integrated English Bk IV Pg 253
	7 & 8	Reading	Intensive reading: Set book.	Analyse plot, characters, themes, character, plot and style of the play.	Oral exercises. Discussion on the set books. Dramatization.	Prescribed literature set books.	Literature set books.

2	1 2	Listening & speaking	Features of oral poetry.	Read a passage and answer questions based on it. Translate an oral poem from a given community into English.	Silent reading; Writing. Reading an oral poem; Writing translations; Group reflections.		Integrated English Bk IV Pg 256
	3	Writing	Summary writing.	The learner should be able to: Write a summary based on a text.	Reading; Writing; General review.		Integrated English Bk IV Pg 259
	4	Grammar.	Clauses; Substitution.	Define substitution as used in clauses. Identify aspects of substitution in sentences.	Reading examples; Oral exercise; Written exercise.		Integrated English Bk IV Pg 259-260
	5	Reading.	Comprehension	Answer questions on a given passage.	Written exercise. Reading a passage. Listening & speaking.	Readers.	Integrated English Bk IV Pg 257
	6	Writing.	Writing reviews. Film writing.	Review a film using various techniques.	Guided practical activities; Group reflections; General review.		Integrated English Bk IV Pg 261-2
	7 & 8	Reading	Intensive reading: Set book.	Analyse plot, characters, themes, character, plot and style of the play.	Oral exercises. Discussion on the set books. Dramatization.	Set book guides.	Literature set books.

3	1	Reading	Comprehension.	Answer questions on the set passage correctly.	Reading aloud. Guided discussion.	Readers.	Integrated English Bk IV Pg 265-6
	2 3	Grammar.	Clauses; Illipsis.	Read a dialogue and identify where illipsis has been used. Provide the missing words. Identify instances of illipsis and supply words that have been omitted. Rewrite sentences using illipsis.	Guided discussion; Oral and written exercises.		Integrated English Bk IV Pg 267-270
	4-5	Writing.	Report writing.	The learner should be able to: Write a report base on graphs and diagrams.	Oral and written exercises. Listening & speaking.	Graphs, Diagrams, charts.	Integrated English Bk IV Pg 271-2
	6	Listening & speaking.	Poetry games I.	Compose poems using same-start-letter style.	Reading a poem aloud; Guided discussion; Group writing; General review.		Integrated English Bk IV Pg 264-5
	7 & 8	Reading.	Intensive reading: Set book.	Answer questions based on set books.	Guided revision; Answer review questions.	Set book guide.	Literature set book.

4	1	Listening & speaking.	Poetry games II.	Compose poem using same-end-letter style.	Reading a poem aloud; Guided discussion; Group writing; General review.		Integrated English Bk IV Pg 273-4
	2 3	Reading.	Poetry. Alliteration and assonance. Metaphors, irony and contrast.	Define the terms alliteration and assonance. Identify instances where Alliteration and assonance are used. Describe use of metaphors, irony and contrast and provide textual evidence from a text.	Reading a poem aloud; Guided discussion; Writing; General review.		Integrated English Bk IV Pg 276-7
	4-5	Institutional Writing.	Notification of a meeting, memo and CV writing.	The learner should be able to: Write a notification of a meeting, memo and CV correctly.	Writing.		Integrated English Bk IV Pg 279-280
	6	Grammar.	Rewriting sentences to convey same meaning.	The learner should be able to: Rewrite sentences to convey same meaning.	Oral and written exercises.		Integrated English Bk IV Pg 278-9
	7 & 8	Reading	Intensive reading: Set book.	Answer questions based on set books.	Guided revision; Answer review questions.	Set book guide.	Literature set book.
5-6		EXAMINATION-TYPE QUESTIONS
6-10		K.C.S.E. EXAMINATIONS