year 8 maths

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609
Exercise 2J
1 a true b true c false d false
2 a true b false c false d true
3 a 4 b x < 4
4 a 6, 3 b x ⩾ 3 c true
5 a x > 3 b l ⩾ 3 c g > 5 d r ⩽ 7
e k > 2 f s < 5 g a > 4 h n ⩾ 5
i d ⩾ 7 j h < 5 k r ⩽ 2 l y < 4
6 a d > 29 b y ⩽ 10 c x > 11 d q ⩽ 18
e x > 7 f h < 1 g p ⩾ 2 h j < 5
7 a x > 1 b s ⩽ 2 c n < 5 d j > 10
e v ⩾ −2 f j ⩾ −5 g c ⩽ 2 h h ⩾ 0
i s < −3 j v < −2 k v ⩽ −2 l v > −5
8 a C b A c B d D
9 a 4c + 20 > 25 b c > 1.25 c $1.30
10 a 6g + 4 ⩽ 36
16
b g ⩽
3
c 5 goals
11 a C ⩾ 15 b C ⩽ 20
c 15 ⩽ C ⩽ 20 d 47.7 . ⩽ C ⩽ 57.7 .
12 a x > 4 b k > 3
c a < −2
d −3 < a < −2
13 a If 5x − 2 > 0 then x > 2 , so x is positive.
5
b If 2x + 6 > 0 then x > −3 , so x + 5 > 2 is positive.
c Yes, for example if x = 4 .
14 a clues B and D b x = 8
d no
15 a x > 2 b a ⩽ −2 c b < −3 d c < −4
16 a x ⩽ 3 b a > −3 c b ⩽ 8 d c > 2
e k > 20 f g < −5 g a > 8 h k ⩽ 9
i p > 4.5
Puzzles and challenges
1 a 13 b 7.5 c 9 years
d $44.44 e 15
2 a 2 nd step or 3 rd line (cannot divide by 0 )
b 0 = 1
×28 ×28
0 = 28
+22 +22
22 = 50
3 6 ⩽ x ⩽ 7
4 2x = 2(3 + x) − 1 or 3x + 1 = 2 + 3(x + 1)
5 a 65 kg , 62 kg , 55 kg b 70 kg , 60 kg , 48 kg
c 35 kg , 42 kg , 45 kg , 48 kg
Multiple-choice questions
1 A 2 D 3 C 4 C 5 B
6 B 7 D 8 E 9 A 10 A
Short-answer questions
1 a false b true c true
2 a m = 4 b m = −12 c a = −1 d m = 1 5
e m = 15 f a = 6
3 a 2m + 3 = 3m b 5(n + 4) = 20 c x + x + 2 = 74
4 a subtract 15 b add 5 c subtract 2a
5 a a = 4 b y = −9 c x = −4 d x = 4
e x = 2 f a = 1
6 a m = −6 b x = 8 c y = −18 d k = −58
e w = −2 f a = 43
7 a x = 14 b x = 6 c x = 40
8 a a = 8 b m = 1 2
c x = 4 d a = 2
e x = −8 f x = 9
9 a x = 3 b x = −4 c x = −4 d a = 4
e a = −7 f m = 4 g a = −3 h x = 17
i x = 1
10 a 12 b 4x − 5 = 2x + 3 c 8.5
11 a ±2 b ±10 c ±7
d ±2.83 e ±6.24 f ±30.23
12 a 1 b 2 c 1 d 1 e 1 f 0
Extended-response questions
1 a S = 20 + 0.12n b 30 times
c Y = 15 + 0.2n d 25
e 20 + 0.12n = 15 + 0.2n, n = 62.5 , so 63 is the
minimum number.
2 a 18x − 180
b i $35.50 ii $41 iii $459
c $25 d $30 e 30 ⩽ x ⩽ 35
Chapter 3
Pre-test
1 a 300 cm b 200 mm c 1800 m d 25 cm
e 3.5 cm f 4.2 km g 5 m h 0.1 m
i 120 s j 3000 mL k 4 L l 3 kg
2 a circle b square c rectangle
d parallelogram e rhombus f kite
g triangle h trapezium
3 a 30 cm 2 b 25 m 2 c 16 cm 2 d 20 cm 2
4 a 30 m b 14.5 cm c 38 cm
5 a 10 b 27 c 25 d 121
e 58.5 f 6 g 9 h 12
6 a 12 cm 3 b 250 m 2 c 4200 cm 3
Exercise 3A
1 a 10 b 100 c 1000 d 100000
e 1000 f 1000000
2 a 1000 b 100000 c 1000000
3 a 10 b 10 c 2
4 a 12 m b 22 cm c 10 mm d 44 km
e 1.4 cm
f 3.6 m
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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