year 8 maths

607
5 a u = 6 b j = 3 c p = 6 d m = 4
e n = 5 f a = 3
6 a p = −2 b u = −3 c v = −5 d r = −4
e b = −7 f d = 3
7 a y = 3 b l = 2 c w = 2 d c = 2
e d = 2 f w = 6 g p = 4 h k = 2
i c = 10
8 a x = 7 b r = 5 c f = 3 d p = 2
e h = 4 f r = 5 g r = 5 h p = 6
i a = 5
9 a r = 7 b l = 2 c x = 7 d s = 8
e y = 7 f h = 3
10 a d + 4 b 2(d + 4)
c 2(d + 4) = 50 d 21
11 a 5w + 3(w + 4) b $11.50
12 a 2(k − 5) = 3(k − 10) b 20
13 a 3.5 b 80
14 The equation is 2(x + 3) = 4x − 11, which would mean
8.5 people next door.
15 Equation 3(x − 5) = 9(x + 1) has solution x = −4.
He cannot be −4 years old.
16 a 2n + 6 = 2n + 3 implies 6 = 3.
b 8x + 12 = 8x + 3 implies 12 = 3, but if x = 0 then
4(2x + 3) = 4x + 12 is true.
17 a x = 3 2
e x = 8 5
Exercise 2F
b p = 36
5
f m = 1 4
c n = − 81
10
1 a i 9 and 9 ii 36 and 36
iii 1 and 1 iv 100 and 100
b They are equal.
d q = 0
2 a i 9 ii 49 iii 169 iv 64
b no
3 a 9, 3, −3 b 25, 5, −5 c 121, 11, −11
4 a ±2 b ±7 c ±10 d ±8
e ±1 f ±12 g ±6 h ±11
i ±13 j ±16 k ±30 l ±100
5 a ±2.45 b ±3.46 c ±6.08 d ±6.40
e ±10.20 f ±17.80 g ±19.75 h ±26.34
6 a 2 b 2 c 2 d 0
e 0 f 1 g 1 h 2
7 20 m 8 4 m
9 a ±2 b ±1 c ±3 d ±2
e ±5 f 0 g ±6 h ±10
10 a x = 0 is the only number that squares to give 0.
b x 2 is positive for all values of x.
11 a 4 b −5 c −7 d 14
12 a ±√11 b ±√17 c ±√33 d ±√156
13 a i yes ii yes iii no
iv yes v no vi yes
b There are none.
14 a ±2 b ±1 c ±3
d ±1 e ±2 f ±5
g ±2 h ±3 i ±6
Exercise 2G
1 a 11 b 6 c 7 d −28
2 B 3 A
4 a A = 19 b A = 51 c A = −1 d A = 33
5 a a = 5 b a = 11 c a = −2
6 a y = 10 b x = 6 c x = −2
7 m = 5.5
8 a y = 4 b y = 8 c x = 4.5 d x = 6
9 a G = 43 b a = 9
10 a $23
b i 161 = 3 + 2d ii d = 79 iii 79 km
11 a 18 b 1 c S = 4t + 2c + d
12 a A = 60 b h = 4 c 11
13 a T = V + 5. Other answers are possible.
2
b 44 mL if using rule above. Other answers are possible.
(10 − 10) 2
(20 − 10)2
c
+ 10 = 10 and + 10 = 15
20
20
14 a 92 b 24
15 A and C
16 a −40°C = −40°F
b 160°C = 320°F
c 1.8x = 1.8x + 32 implies 0 = 32.
17 a A charges $14.80, B charges $16.20.
b 45 minutes
c 2 minutes per call
d t = 50 and c = 40. Other answers are possible.
e 40 minutes
Exercise 2H
1 a D b A c E d C e B
2 a B b C c A d D
3 a p = 6 b x = 9 c k = 4 d a = 3
4 a Let c = cost of one cup. b 4c = 13.2
c c = 3.3 d $3.30
5 a Let c = cost of one chair. b 6c + 1740 = 3000
c c = 210 d $210
6 a 2(4 + b) = 72 or 8 + 2b = 72
b b = 32
c 32 cm
7 a Let t = time spent (hours). b 70 + 52t = 252
c t = 3.5
d 210 minutes
8 2
9 a 4s = 26, s = 6.5 b 42.25 cm 2
10 Alison is 18.
11 x = 65, y = 115
12 a 118
b 119
c 12688
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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