CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: TEACHER’S RESOURCE
Learner’s Book
answers
Unit 1 Getting started
1
a
144
b
9
c
125
d
4
2
a
512
b
128
3
a
157
b
153
4
a
4 and 3000 and 225
b
5
10
8
b
The square root of any integer between
144 and 169 is a possible answer.
a
14
b
6
10 a
i
9
All of them.
6
Exercise 1.1
1
2
3
4
5
7
1
ii
1
iii
2
b
( 5 + 1) × ( 5 − 1) = 4, and so on
c
( N + 1) × ( N − 1) = N − 1
d
Learner’s own answer.
a
integer 3
b
irrational
c
irrational
d
integer 7
e
irrational
a
1, 7 , −38 and − 2.25 are rational.
Reflection:
a
i
b
200 is the only irrational number.
b
a
integer
b
surd
c
surd
No. It might be a repeating pattern or it
might not.
d
integer
e
integer
f
surd
a
irrational because 2 is irrational
b
rational because it is equal to 4 = 2
c
irrational because 3 4 is irrational
d
rational because it is equal to 3 8 = 2
a
5
12
Learner’s own answer. For example:
2 and 2 − 2
i
4
ii
6
iii
10
iv
6
b
They are all positive integers.
c
Learner’s own answer.
d
Learner’s own answer.
a
7² = 49 and 8² = 64
b
4³ = 64 and 5³ = 125
11 a
b
aLearner’s own answer. For example:
2 and − 2 .
b
6
aThe square root of any integer between
16 and 25 is a possible answer.
3
No. It is not a repeating pattern.
Learner’s own answer.
true ii
true iii
false
Exercise 1.2
1
2
3
a
3 × 105
b
3.2 × 105
c
3.28 × 105
d
3.2871 × 105
a
6.3 × 107
b
4.88 × 108
c
3.04 × 106
d
5.2 × 1011
a
5400
b
1 410 000
c
23 370 000 000
d
87 250 000
4
Mercury 5.79 × 107 km; Mars 2.279 × 108;
Uranus 2.87 × 109
5
a
Russia
c
The largest country is approximately 9
times larger than the smallest country.
a
7 × 10−6
b
8.12 × 10−4
c
6.691 × 10−5
d
2.05 × 10−7
6
b
Indonesia
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021
CAMBRIDGE LOWER SECONDARY MATHEMATICS 9: TEACHER’S RESOURCE
7
a
0.0015
b
0.000 012 34
c
0.000 000 079
d
0.000 900 3
8
a
30
b
9.11 × 10−25 kg
9
a
z
b y
10 a
a
36
8
a
1 b
81
9
a
i
2
b
i
x=5
10 a
65 is not between 1 and 10.
1
36
c
1
d
1
216
1
c
225
1
ii 4
4
1
d
1
400
ii
1
iii 9
9
x = 10
i
3
5
ii
39
iii
310
iv
36
i
3
ii
3−1
iv
3−2
v
3−3
b
6.5 × 105
c
4.83 × 107
11 a
1.5 × 10−2
b
2.73 × 10−3
c
5 × 10−8
12 a
6.1 × 106
b
6.17 × 105
11 a
56 b 52
c
5−2
c
1.75 × 105
12 a
6−1
b
73
13 a
7.6 × 10−6
c
11−10
d
4−4
b
8.02 × 10−5
13 a
x=4
b
x=6
c
1.6 × 10
c
x = −2
d
x=5
i
22
ii
43
iii
51 or 5
iv
23
14 a
b
−7
i
7 × 106
ii
3.4 × 107
iii
4.1 × 10−4
iv
1.37 × 10−3
b
To multiply a number in standard form by
10, you add 1 to the index.
c
To multiply a number in standard form
by 1000, you add 3 to the index. To divide
a number in standard form by 1000, you
subtract 3 from the index.
Reflection: You can compare them easily. You
can write the number without using a lot of zeros.
You can enter them in a calculator.
Exercise 1.3
1
a
d
1
4
1
216
b
1
8
e
1
f
10 000
c
1
81
1
32
2
3 , 2 and 4 are equal, 5 , 6
3
a
2−1
b
2−2
c
d
2
e
2
0
f 2
a
102
b
103
c
100
d
10−1
e
10−3
f
10−6
a
64−1
b
c
4−3
d
a
3 or 9 or 81
b
The three ways in part a.
4
5
6
2
b
7
−3
−4
−2
−6
−4
−2
−1
−1
Learner’s own answers.
d
Learner’s own answers.
14 a
b
Learner’s own answers.
c
Learner’s own answers.
32
d 5−6
15 a
6−3
b
9−1
c
15−4
d
10−5
16 a
25
b
87
c
5−6
d
122
17 a
26
b
2−6
c
36
d
3−6
e
93
f
9−3
Check your progress
1
0
26
c
iii
2
−3
a
rational
b
irrational
c
rational
d
irrational
e
rational
a
rational because it is equal to 25 = 5
b
irrational because it is 3 + 7 and 7 is
a surd
3
n=3
8−2
4
a
2−6
5
C, D, A, B
6
a
b
8.6 × 1010
1
49
b
1
81
6.45 × 10−6
c
1
128
Cambridge Lower Secondary Mathematics 9 – Byrd, Byrd & Pearce © Cambridge University Press 2021