Page 135 - Cambridge+Checkpoint+Mathematics+Coursebook+9

End-of-unit review

End-of-unit review

1 Solve these equations.
a 15 + 10x = 105 b 10x − 105 = 15 c 10(15 + x) = 105 d 15 − 10x = 105

2 Solve these equations.
a 6m − 5 = 2m + 29 b 6(m − 5) = 2(m + 29) c 6m − 5 = 29 − 2m
3 The lengths in the diagram are in centimetres. 2x x + 8
The square and the rectangle have perimeters of the same length. 10
a Write an equation to show this. 2x
b Solve the equation.
c Find the length of the rectangle.

4 Read Zalika’s number problem.

I am thinking of a number, N.
Twice (N + 10) is the same as four times (N − 10).

a Write down an equation to show this.
Write down an equation to show this.

b Solve the equation to find the value of N.
5 Solve these simultaneous equations.
a x + y = 24 b 2x + y = 100 c x + y = 26
y = 2x y = 2(x − 10) 3x + y = 56
6 The sum of two numbers is 100.
The difference between the two numbers is 95.
Work out the two numbers.
7 The equation 3x + x² = 60 has a solution between 5 and 10.
Use trial and improvement to find the solution, correct to one decimal place. Show your trials.

8 Solve these inequalities.
a 4x + 12 ≥ 40 b 3(x + 8) ≤ 12 c 5x − 14 > 3x + 15

9 Show the solution sets from question 8 on a number line.
x + 1
10 The lengths of the sides of this hexagon are in metres.
a The perimeter is less than 50 metres. Write an inequality for this. x x
b Solve the inequality.

c If x is an integer, find its largest possible value.
x + 1 x + 1
x

11 x + 5.5 = 0
State whether these statements are true or false.
a 2(x + 3) ≤ −5 b 3 − 2x > 12 c x² + x < 24.75

134 13 Equations and inequalities