EXAMPLE 1In the diagram above, which two figures are similar?

Solution: If all the corresponding angles of the two figures are the same and all their corresponding sides are similar in the same ratio, then the two figures are similar. Therefore, figure B is similar to figure C.

EXAMPLE 2 Find the value of x. Solution:

10.2 ENLARGEMENT

Enlargement is a transformation with a fixed point known as the centre of enlargement.

All the other points on the plane will move from the fixed point following a constant ratio.

The ratio is known as scale factor.

Properties of enlargement

- the object is similar to the image.

- C'B' is the image of CB under an enlargement at centre O and scale factor of k.

EXAMPLE

Draw the image of triangle PQR under an enlargement at centre O with scale factor 3.

Solution:

Area of image:

Where k is the scale factor.

CHAPTER 11LINEAR EQUATIONS II

11.1 LINEAR EQUATIONS IN TWO VARIABLES

Linear equation in two variables is an equation involving numbers and linear terms in two variables.

Example : x + 2y

Linear equation in two variables can be formed based on given information.

The value of a variable can be determined when the value of the other variable is given.

EXAMPLE

Given that x + 2y = 5, find the value of x if y = 1.

Solution:

Substitute y = 1 in the equation, x + 2 (1) = 5 x = 5 - 2 x = 3

EXAMPLES

Determine whether 2x + 3 = 9 is a linear equations in two variables.

Solution:

No, because it is a linear equation in one variable.

Form a linear equation in two variables based on the given information. Siti bought a few postcards, some postcards cost RM1.20 and some cost 80 sen each. The total amount Siti paid is RM4.00.

Solution:

Let the number of postcards costs RM1.20 be x and the number of postcards costs RM0.80 be y.

Therefore, 1.2x + 0.8y = 4 Multiply by 2.5, 3x + 2y = 10

Given that 7x - y = 3, find the value of y, if x = 1.

Solution:

7(1) - y = 3 y = 7 - 3 y = 4

11.2 SIMULTANEOUS LINEAR EQUATIONS IN TWO VARIABLES

Simultaneous linear equation in two variables are two linear equations in two variables having a common solution.

Both equations must have two common variables.

Simultaneous linear equations in two variables can be solved by substitution method and elimination method.

EXAMPLE 1Solve the following simultaneous equations.

2x + 5y = 3 x - y = 5

Method 1: Substitution

2x + 5y = 3 ...! x - y = 5 ..."

From ", x = 5 + y Substitute x into !,

2 (5 + y) + 5y = 3 10 + 2y + 5y =3 2y + 5y = 3 - 10 7y = -7 y = -1

From ", x = 5 + (-1) = 5 - 1 = 4

Therefore, x = 4, y = -1

Method 2: Elimination

2x + 5y = 3 ...! x - y = 5 ..."

! 2x + 5y = 3 " x 5 = 5x - 5y = 25 Form an equation which is # ... (2x + 5y) + (5x - 5y) = 3 + 25 2x + 5y + 5x - 5y = 28 7x = 28 x = 4

From ", 4 - y = 5 -y = 5 - 4 y = -1

Therefore, x = 4, y = -1

CHAPTER 12LINEAR INEQUALITIES

12.1 INEQUALITIES

An inequality is a relationship between two unequal quantities.

Symbol Definition

Greater than

Less than

Greater than or equal to

Less than or equal to

12.2 LINEAR INEQUALITIES

Linear inequalities can be represented on number lines.

Symbols on the number line:

Symbol Definition

Include

Not included

12.3 OPERATIONS INVOLVING LINEAR INEQUALITIES

The condition of inequality is unchanged when both sides are;

(a) added or subtracted from a number (b) multiplied or divided by a positive number.

EXAMPLES (a) 15 > 7 15 + 4 > 7 + 4 19 > 11

(b) x > 10 x - 4 > 10 - 4 x - 4 > 6

(c) 21 < 27 21 x 3 < 27 x 3 63 < 81

State the new inequalities when a number is added to or subtracted from both sides of the following inequalities.

(a) 15 > 7 (add 4) (b) x > 10 (subtract 4) (c) 21 < 27 (multiplied by 3)

When an inequality is multiplied or divided by a negative number on both sides, the inequality symbol is reversed.EXAMPLESState a new inequality when both sides of the following inequalities are multiplied or divided by a negative number.

(a) 4 > -3, multiplied by -2

(b) x < -18, divided by -6

12.4 SOLVING LINEAR INEQUALITIES IN ONE VARIABLE

The solution for a linear inequality in one variable is the equivalent inequality in its simplest form.

EXAMPLE

12.5 SIMULTANEOUS LINEAR INEQUALITIES IN ONE VARIABLE

Solutions for two simultaneous linear inequalities in one unknown are the common values that satisfy both inequalities.

EXAMPLESSolve the following linear inequalities.

CHAPTER 13GRAPHS OF FUNCTIONS

13.1 FUNCTIONS

A function expresses the relationship of a variable in term of another variable.

For a coordinate (x,y), x is called the independent variable and y is called the dependent variable.

EXAMPLES