Module 6 · Answers
Answers & working
Workings shown so you can see where each answer comes from.
Section A — Easy
01
(a) x = 5 (b) x = 7 (c) x = 6 (d) x = 24
02
(a) x = 4 (b) x = 5 (c) x = 4
03
20 cm²
A = ½ × 8 × 5 = 20.
04
84 cm²
A = base × height = 12 × 7.
05
(a) Square (b) Trapezium (c) Kite
Section B — Medium
06
(a) x = 6 (b) x = 4 (c) x = −3
(a) 5x − 2 = 3x + 10 → 2x = 12.
(b) 4x + 1 = x + 13 → 3x = 12.
(c) 7x + 3 = 2x − 12 → 5x = −15.
(b) 4x + 1 = x + 13 → 3x = 12.
(c) 7x + 3 = 2x − 12 → 5x = −15.
07
(a) x = 3 (b) x = 5 (c) x = 9
(a) 3x + 12 = 21 → 3x = 9.
(b) 4x − 2 = 18 → 4x = 20.
(c) 5x − 15 = 2x + 12 → 3x = 27.
(b) 4x − 2 = 18 → 4x = 20.
(c) 5x − 15 = 2x + 12 → 3x = 27.
08
32 cm²
A = ½ × (6 + 10) × 4 = ½ × 16 × 4 = 32.
09
8 cm
36 = ½ × 9 × h → h = 72 ÷ 9 = 8.
10
x = 6
Perimeter = 2(length + width).
2(3x + 2 + 5) = 50
3x + 7 = 25
3x = 18 → x = 6.
2(3x + 2 + 5) = 50
3x + 7 = 25
3x = 18 → x = 6.
Section C — Hard
11
x = 6
6x − 2 − 3x − 6 = x + 4
3x − 8 = x + 4
2x = 12 → x = 6.
3x − 8 = x + 4
2x = 12 → x = 6.
12
x = 65
x + (x + 20) + (2x − 30) + 110 = 360
4x + 100 = 360
4x = 260 → x = 65.
4x + 100 = 360
4x = 260 → x = 65.
13
6 cm
60 = ½ × (7 + 13) × h = 10h → h = 6.
14
5
Let n be the number. 4n − 9 = n + 6 → 3n = 15 → n = 5.
15
Base = 14 cm, height = 7 cm
Let h be the height; base = 2h.
A = ½ × 2h × h = h² = 49 → h = 7.
Base = 14.
A = ½ × 2h × h = h² = 49 → h = 7.
Base = 14.