year 8 maths

605
2 a xy − x2
b 33 m 2 c 2x + 2y d 26 m
4
e Area = xy − x2
, Perimeter = 2x + 2y
3
f i Area is reduced by x2
12
ii Perimeter remains the same
Chapter 2
Pre-test
1 a 11 m b a c 9n d 10a − 10
e −3x
f 12pq
2 a 3m + 12 b 2a + 2b c 3x + 21 d −2x + 6
3 a 5m + 15 b 17x + 21
4 a 3 b a c x d m
5 12
6 a 8 b 4 c −2
7 a −6 b 1 8
c 4 d 3
8 a 4 b 8 c 4 d 6
9 a 16, 8 b 15, 14 c 10, 20, 4 d 4, 2
Exercise 2A
1 a true b false c true d false
e true
f true
2 a 13 b 9 c 2 d 2
3 a 7 b 9 c 15 d 8
4 a 25 b 25
c yes
d e.g. x + 2 = 7 (other answers possible)
5 a true b true c false d false
e true
f false
6 a true b false c true d true
e false
f true
7 a C b I c C d C
8 a x = 7 b x = 13 c v = 3 d p = 19
e x = 2 f x = 8 g u = 7 h k = 11
i a = 3
9 a 2x + 7 = 10 b x + x 2 = 12
c 25 + a = 2a d h + 30 = 147
e 4c + 3t = 21 f 8c + 2000 = 3600
10 a 7 b 42 c 13 d −8 e 40 f −13
11 a 3.2x = 9.6 b x = 3
12 a E + 10 = 3E b E = 5
c 5 years old d 15
13 t = 3, t = 7
14 a 3 2 = 3 × 3 = 9 b (−3) 2 = −3 × −3 = 9
c x = 8, x = −8
d 0 and −0 are the same number, but 1 and −1 are different
numbers.
e A number multiplied by itself cannot be negative;
e.g. neg. × neg = pos.
15 a No number can equal 3 more than itself.
b Addition is commutative.
c If x = 7 it is true, if x = 6 it is false.
d i S ii S iii N
iv S v A vi S
vii N viii S ix A
e 7 + x = x + 7. Other answers are possible.
16 a p = 1, p = −3 b one
c Many answers possible,
e.g. (p − 2) × (p − 3) × (p − 5) = 0 has 3 solutions.
17 a a = 10, b = 6, c = 12, d = 20, e = 2
b f = 1 2
18 a c = 4, d = 6 (or c = 6, d = 4)
b c = 11, d = 3
c c = 24, d = 6
d c = 7, d = 0 (or c = 0, d = −7)
Exercise 2B
1 a 3x + 4 = 14
b 11 + k = 18
c 9 = 2x + 4
2 a 12 b 25 c 16 d 4z
3 a 8 b x = 8
4 B
5 a 2x = 20 b 2 + q = 10 c 18 = 17 − q
d 12x = 24 e 7p + 6 = 2p + 10 f 3q = 2q
6 a x = 3 b q = −3
c x = 5 d p = 7 (missing operation: ÷ 4)
e x = 3 f p = 6 (missing operation: ×3)
7 a a = 3 b t = 7 c q = 9 d k = 9
e x = 10 f h = −10 g l = −4 h g = −9
8 a h = 3 b u = 4 c s = 3 d w = 8
e x = −4 f w = −5 g a = 2 h y = −8
9 a d = 3 b j = −6 c a = 2 d y = 2
e k = −4 f n = −7 g b = −3 h b = 4
10 a x = 7 2
b q = 1 3
c b = 1 2
d x = 5 2
e x = − 5 f p = − 23 g y = 13
2
2
5
h y = − 3 2
11 a p + 8 = 15, p = 7 b q × −3 = 12, q = −4
c 2k − 4 = 18, k = 11 d 3r + 4 = 34, r = 10
e 10 − x = 6, x = 4 f 10 − 3y = 16, y = −2
12 a x = 2 b x = 2 c x = 6
14
13 a x = 7, y =
5
b x = 2, y = 26
c x = 10
3
d p = 15, q = 13
4
14 10x + 6x = 194.88, hourly rate = $12.18
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.