year 8 maths

604
11 a Verify
b 3 2 × 3 4 = 3 × 3 × 3 × 3 × 3 × 3,
9 6 = 9 × 9 × 9 × 9 × 9 × 9, which is obviously
different
c The base should stay the same.
12 a i 4 ii −8 iii 16 iv −32
b i positive ii negative c 1024
13 a 5 0 b 1 c 1 d 1
14 a that a − b = 2 b 125
15 a m 5 b x 10 c x 10 d x 6
e a 19 f m 4 g m 7 h a 3
i w 12 j x 6
16 a 125xy 2 b a 5 c abcde d 120q 15
17 a 20
x 6
Exercise 1K
1 B
2 C
b 4abc15
7
c −100x 7 y 8
3 a 27, 9, 3, 1 b divide by 3 each time
4 a i 4096 ii 1024 iii 4096
b 4 6
iv A very large number (7.04 × 10 13 )
d 4x3
3
5 a 2 12 b 3 16 c 7 36 d 6 9
e 7 24 f 2 50
6 a 2 21 b 5 18 c 7 23 d 3 22
e 2 18 f 11 18 g 5 10 h 11 8
i 11 13 j 2 14 k 3 5 l 11 2
7 a 1 b 1 c 2
d 4 e 1 f 1
g 1 h 3 i 1
8 a 5 b 3 c 5 d 2
9 a 5 24 b 5 60 c ((2 3 ) 4 ) 5 ,(2 7 ) 10 , 2 100 , ((2 5 ) 6 ) 7
10 a i 2 ii 5 iii 6 b 54
11 a x 7 b x 12 c x = 0, x = 1
12 a 1 b 5 2−2 = 5 0 c 3 0 − 3 2−2 = 32
3 2 = 9 9 = 1
d 100 0 = 100 2−2 = 1002 10000
=
2
100 10000 = 1
e 02
cannot be calculated (dividing by zero).
2
0
13 a Both equal 2 12 . b B
c 3, 5. Other answers are possible.
14 a 9 b 3 c 3 d 6
15 a 1 b Many answers are possible.
16 a 1 b 6 c a 14 d 4w 12
e 1 f 7 g a 14 h 9a 14
i 1 j 3
17 a x 14 b m 24 c x 10 d a 14
e m 16 f m 12 n 4 g 8a 21 h 25m 8
i 36x 8 j 216a 6 b 15
18 a 5 4 b x 8 c x 4 y 9 d a 7 b 12 c 10
e x 80 y 10
Puzzles and challenges
1 10m + 10 = 10(m + 1)
2 Any list with 6 − 2a central; 2 − a, 6a − 5 together; a − 7,
4(a + 1) together. e.g. 2 − a, 6a − 5, 6 − 2a, a − 7,
4(a + 1)
3 4 1999 , 16 1000 , 2 4001 , 8 1334
4 a 65
4
5 a 5 − 4a
30
b 225
4
b 9x + 4
42
c 0
6 a 8 b 45 c 4
7 a All perimeters = 4a
Areas: a 2 , 3 4 a2 , 6 9 a2 , 10
16 a2 , 15
25 a2
b P = 24, A = 9009 or approximately 18.
500
Multiple-choice questions
1 C 2 D 3 B 4 D 5 E
6 C 7 E 8 E 9 E 10 B
Short-answer questions
1 a false b true c true
d false
e true
2 a 2 b 3 c 4 d 6
3 a 11 b 14 c 29 d 8
4 a −3 b 3 c −9 d 14
5 3
e −3 f 12
6 a 16m b 2a + 5b c 2x 2 − x + 1
d 7x + 7y e 9x + x 2 f −m − 12n
7 a 36ab b 15xy c 16xy
8 a 5x b −4c c 15x d 3ab
9 a x b 6a + b c 9 d 3b
4
15 x
2
10 a 3x − 12 b −10 − 2x c 3kl − 4km d 7x − 6y
e 13 − 3x f 10 − 20x g 18x + 2
11 a 2(x + 3) b 8(3 − 2g) c 3x(4 + y) d 7a(a + 2b)
12 a a + 2 b 12
1
c
4 + 3q
13 a 7 b 3 c 6 d 1
14 a 5 7 b 6 8 c 7 2 d 5
e 2 12 f 6 6
15 a 6 b 1 c 5
Extended-response questions
1 a 120 + 80n b 80 + 100n
c A costs $360, B costs $380.
d any more than two hours
e 520 + 440n f $2720
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.