A variable is a quantity that changes in value.

A variable is usually represented by an alphabet, for example x, y.

EXAMPLES

The number of participants in a competition can be represented by n.

The output of eggs at a poultry can be represented by x.

A constant is a quantity of a fixed value.EXAMPLES

1 m = 100 cm

1 kg = 1000 g

The values of a variable can be expressed in the form of integers, fractions and decimals.EXAMPLES

31 km

50.75 g

7.2 FORMULAE A formula is an equation that relates a few variables.

The value of a variable in a formula can be determined if the values of other variables are given.

Subject of a formula is a variable to be expressed in term of other variables.

EXAMPLE

a is the subject of the formula in terms of t, u and v.

Expressing a certain variable as the subject of the formula is a process of rewriting a formula so that one of the variables becomes the subject of the formula.

This often involves

- the operations of addition, subtraction, multiplication and division.

- the operations of indices.

If a variable occurs at both sides of an equation, the variable is NOT a subject.EXAMPLE

Then, a is not the subject.

EXAMPLESExpress x as the subject of the formula for each formula below.

CHAPTER 8SOLID GEOMETRY III

8.1 RIGHT PRISM AND RIGHT CIRCULAR CYLINDER

A prism is a solid which has two or more parallel and congruent polygons as faces.

A right prism is a prism where the two end-faces are polygons that are at right angles to the other rectangular surface.

A cylinder is a solid with two circular ends and uniform cross section of circular shape.

A right circular cylinder with its axis perpendicular to both its ends.

Axis of a cylinder is the line connecting the centre of both of its ends.

Volume of a right prism.

Volume of a right circular cylinder.

A pyramid is a solid with its base in the form of a polygon and other surfaces in the form of triangles with a common vertex.

A right pyramid is a pyramid with its vertex situated vertically above the centre of the base.

8.2 RIGHT PYRAMID AND RIGHT CIRCULAR CONE

A right circular cone is a solid in the form of a right pyramid, but its base is in the form of a circle and has only one curved surface.

Volume of a right pyramid.

Volume of a right circular cone.

8.3 SPHERE

A sphere is a solid where all the points on its surface are the same distance from a fixed point.

The fixed point is known as the centre of the sphere.

Hemisphere

Volume of a sphere.

Volume of a hemisphere.

8.4 COMPOSITE SOLID

Volume of a composite solid can be calculated by identifying each solid and finding their volumes separately.

Then, total up the volumes of all parts.

EXAMPLE

CHAPTER 9SCALE DRAWINGS

9.1 SCALE DRAWINGS

A scale drawing is a drawing that represents a real object with its size reduced or enlarged according to a given ratio.

Scale of a drawing

A scale is a ratio that compares a length on a drawing in relation to its actual length.

(i) The scale is normally in the form of 1 : n where n = 1, 2, 3, 4 and so on.

(ii) For a scale of 1 : n,(a) If n = 1, the size of the drawing is the same as

the size of the actual object.

(b) If n > 1, the size of the drawing is smaller than the size of the actual object.

(c) If n < 1, the size of the drawing is bigger than the size of the actual object.

EXAMPLE 1

In the diagram below, CD is the scale drawing of AB.

Find the scale used. Solution:

Scale = 4cm : 12 cm = 4 : 12 = 1 : 4

EXAMPLE 2

In the diagram, draw trapezium P, using the scale of 1 : 2.

Solution:

EXAMPLE 3 Draw the above shape to the scale of 1 : 5.

Solution:

CHAPTER 10TRANSFORMATIONS II

10.1 SIMILARITY

The word similar implies a comparison between objects which have the same properties in common.

Similar figures have the same shape but the sizes may be different.

Two shapes are similar if the

- corresponding angles are the same.

- pair of corresponding sides are in a constant ratio.