Cambridge Checkpoint Mathematics Practice Book 8 matches the
requirements of stage 8 of the revised Cambridge Secondary 1
curriculum framework. It is endorsed by Cambridge International
Examinations for use with their programme. The series is written
by an author team with extensive experience of both teaching and
writing for secondary mathematics.
This supportive Practice Book is intended to be used alongside
the Cambridge Checkpoint Mathematics Coursebook 8. It contains
exercises that will help students develop the skills they need to
succeed with the Secondary 1 programme.
The Practice Book:
rcontains exercises for each Coursebook topic, arranged in the
same order as the topics in the Coursebook
rallows students to practise using the concepts they have learned
and develop their problem-solving skills.
Answers to the exercises are included on the Teacher’s Resource 8
CD-ROM.
Other components of Cambridge Checkpoint Mathematics 8:
Coursebook 8
Teacher’s Resource 8
Greg Byrd, Lynn Byrd and Chris Pearce
Cambridge Checkpoint
Mathematics
Practice book
Practice Book 8
ISBN 978-1-107-69787-4
ISBN 978-1-107-62245-6
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Byrd, Byrd and Pearce
9781107665996 Byrd, Byrd & Pearce: Cambridge Checkpoint Mathematics Practice Book 8 Cover. C M Y K
Greg Byrd, Lynn Byrd and Chris Pearce
Cambridge Checkpoint Mathematics
Cambridge Checkpoint
Mathematics
Practice Book 8
8
Greg Byrd, Lynn Byrd and Chris Pearce
Cambridge Checkpoint
Mathematics
Practice Book
8
CAMBRIDGE UNIVERSITY PRESS
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Cambridge University Press
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© Cambridge University Press 2013
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permission of Cambridge University Press.
First published 2013
Printed in the United Kingdom by Latimer Trend
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Contents
Introduction
1
Integers, powers and roots
1.1 Arithmetic with integers
1.2 Multiples, factors and primes
1.3 More about prime numbers
1.4 Powers and roots
5
7
7
8
9
10
2
2.1
2.2
2.3
2.4
2.5
2.6
Sequences, expressions and formulae
Generating sequences
Finding rules for sequences
Using the nth term
Using functions and mappings
Constructing linear expressions
Deriving and using formulae
11
11
12
13
14
15
16
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Place value, ordering and rounding
Multiplying and dividing by 0.1 and 0.01
Ordering decimals
Rounding
Adding and subtracting decimals
Dividing decimals
Multiplying by decimals
Dividing by decimals
Estimating and approximating
17
17
18
19
20
21
22
23
24
4
4.1
4.2
Length, mass and capacity
Choosing suitable units
Kilometres and miles
25
25
26
5
5.1
5.2
5.3
Angles
Parallel lines
Explaining angle properties
Solving angle problems
27
27
29
30
6
6.1
6.2
6.3
Planning and collecting data
Collecting data
Types of data
Using frequency tables
31
31
33
34
7
7.1
36
7.2
7.3
7.4
7.5
7.6
7.7
7.8
Fractions
Finding equivalent fractions, decimals
and percentages
Converting fractions to decimals
Ordering fractions
Adding and subtracting fractions
Finding fractions of a quantity
Multiplying an integer by a fraction
Dividing an integer by a fraction
Multiplying and dividing fractions
8
8.1
8.2
Shapes and geometric reasoning
Recognising congruent shapes
Identifying symmetry of 2D shapes
43
43
44
36
37
38
39
40
41
41
42
8.3
8.4
8.5
Classifying quadrilaterals
Drawing nets of solids
Making scale drawings
45
46
47
9
Simplifying expressions and
solving equations
Collecting like terms
Expanding brackets
Constructing and solving equations
49
49
50
52
9.1
9.2
9.3
10 Processing and presenting data
10.1 Calculating statistics from discrete data
10.2 Calculating statistics from grouped
or continuous data
10.3 Using statistics to compare two distributions
53
53
11
11.1
11.2
11.3
11.4
Percentages
Calculating percentages
Percentage increases and decreases
Finding percentages
Using percentages
56
56
57
58
59
12
12.1
12.2
12.3
12.4
Constructions
Drawing circles and arcs
Drawing a perpendicular bisector
Drawing an angle bisector
Constructing triangles
60
60
61
62
64
13
13.1
13.2
13.3
13.4
Graphs
Drawing graphs of equations
Equations of the form y = mx + c
The midpoint of a line segment
Graphs in real-life contexts
65
65
66
67
68
14
14.1
14.2
14.3
Ratio and proportion
Simplifying ratios
Sharing in a ratio
Solving problems
70
70
71
73
54
55
15 Probability
15.1 The probability that an outcome
does not happen
15.2 Equally likely outcomes
15.3 Listing all possible outcomes
15.4 Experimental and theoretical
probabilities
74
16 Position and movement
16.1 Transforming shapes
16.2 Enlarging shapes
79
79
81
17 Area, perimeter and volume
17.1 The area of a triangle
17.2 The areas of a parallelogram and trapezium
84
84
84
74
75
76
77
3
17.3
17.4
17.5
17.6
The area and circumference of a circle
The areas of compound shapes
The volumes and surface areas of cuboids
Using nets of solids to work out surface areas
18 Interpreting and discussing results
18.1 Interpreting and drawing frequency
diagrams
18.2 Interpreting and drawing pie charts
18.3 Interpreting and drawing line graphs
18.4 Interpreting and drawing stem-and-leaf
diagrams
18.5 Drawing conclusions
4
86
87
88
89
90
90
91
93
94
95
Introduction
Welcome to Cambridge Checkpoint Mathematics Practice Book 8
The Cambridge Checkpoint Mathematics course covers the Cambridge Secondary 1 Mathematics
framework.
The course is divided into three stages: 7, 8 and 9. This Practice Book can be used with Coursebook 8. It
is intended to give you extra practice in all the topics covered in the Coursebook.
Like the Coursebook, the Practice Book is divided into 18 units. In each unit you will find an exercise
for every topic. These exercises contain similar questions to the corresponding exercises in the
Coursebook.
This Practice Book gives you a chance to try further questions on your own. This will improve your
understanding of the subject. It will also help you to feel confident about working on your own when
there is no teacher available to help you.
There are no explanations or worked examples in this book. If you are not sure what to do or need to
remind yourself about something, look at the explanations and worked examples in the Coursebook.
5
1 Integers, powers and roots
) Exercise 1.1 Arithmetic with integers
1 Add these numbers.
a 6 + −3
b −6 + −4
c −2 + −8
2 Find the missing integer in each case.
b 4 + = −6
a 5+ =2
e 7 + = −6
d −12 + = −8
d −1 + 6
c −3 +
3 Subtract.
a 3−7
b −3 − 7
c −20 − 30
4 Subtract.
a 4 − −6
d −6 − −12
b 10 − −3
e 15 − −10
c −10 − −5
e −10 + 4
=3
d 5 − 15
e −9 − 4
Add the inverse.
5 In each wall diagram, add the two numbers above to get the number below.
For example, 3 + −5 = −2. Find the bottom number in each diagram.
b
c
a
–5
3
4
–4
2
–1
–1
4
–6
–2
6 Copy this multiplication table.
Fill in the missing numbers.
×
−3
−1
2
5
−3
−1
2
5
7 Complete these divisions.
a 20 ÷ −2
b −24 ÷ 3
25
c −44 ÷ −4
d 28 ÷ −4
8 Look at the multiplication in the box.
Use the same integers to write down two divisions.
9 Xavier has made a mistake.
Correct it.
e −12 ÷ −6
−5 × 6 = −30
5 times 5 is 25.
So −5 times −5 is −25.
10 The product of two different integers is −16. What could they be?
11 Find the missing numbers.
b 4×
a −2 × = 20
= −12
c
× 9 = −45
d
× −5 = −35
1 Integers, powers and roots
7
) Exercise 1.2 Multiples, factors and primes
1 Find the first three multiples of each number.
a 12
b 15
c 32
2 From the numbers in the box, find:
a a multiple of 10
c a common factor of 27 and 36
d 50
b two factors of 24
d a prime number.
8
9
12
23
32
40
95
96
97
98
99
100
3 List all the prime numbers between 40 and 50.
4 Which of the numbers in the box is:
a a multiple of 2
b a multiple of 5
c a common multiple of 2 and 5
d a factor of 500
e a prime number
f a common multiple of 2 and 3?
You may use some numbers more than once.
5 Is Mia correct?
17, 37 and 47 end in 7 and are prime numbers,
so 57 and 67 must also be prime numbers.
6 Write true (T) or false (F) for each statement.
a 7 is a factor of 84.
b 80 is a multiple of 15.
c There is only one prime number between 90 and 100.
d 36 is the lowest common multiple (LCM) of 6 and 9.
e 5 is the highest common factor (HCF) of 25 and 50.
7 Find the LCM of each pair of numbers.
a 4 and 6
b 15 and 20
c 20 and 50
d 6 and 7
8 Find the factors of each number.
a 27
b 28
c 72
d 82
e 31
9 Find the prime factors of each number.
a 32
b 18
c 70
d 99
e 19
10 Find the HCF of each pair.
a 12 and 15 b 12 and 18
d 12 and 25
c 12 and 24
11 The HCF of 221 and 391 is 17.
Explain why 221 and 391 cannot be prime numbers.
12 Find two numbers that are not prime and have a HCF of 1.
8
1 Integers, powers and roots
) Exercise 1.3 More about prime numbers
1 Copy and complete these factor trees.
b
c
a
88
135
8
11
9
15
260
26
10
2 a Draw two different factor trees for 80.
b Write 80 as a product of primes.
3 Write down each number.
b 24 × 33
a 2 × 32 × 52
c 22 × 112
4 84 = 22 × 3 × 7 and 90 = 2 × 32 × 5
a Write the HCF of 84 and 90 as a product of primes.
b Write the LCM of 84 and 90 as a product of primes.
5 a Write each number as a product of primes.
i 120
ii 160
b Find the LCM of 120 and 160.
c Find the HCF of 120 and 160.
6 a Find the HCF of 84 and 96.
b Find the LCM of 84 and 96.
7 a Find the HCF of 104 and 156.
b Find the LCM of 104 and 156.
1000 = 23 × 53
8 10 = 2 × 5
100 = 22 × 52
Write 10 000 as a product of primes.
9
I am thinking of two
prime numbers.
I can tell you
their HCF.
I can tell you how
to find their LCM.
a How can Sasha do that?
b What will Razi tell Jake?
10 a Write 81 as a product of primes.
b Write 154 as a product of primes.
c Explain why the HCF of 81 and 154 must be 1.
1 Integers, powers and roots
9
) Exercise 1.4 Powers and roots
1 Find the value of each of these.
b 33
a 23
c 43
d 53
2 Find the value of each of these.
b 34
a 24
c 44
d 104
e 10³
3 a 44 is equal to 2N. What number is N ?
b 93 is equal to 3M. What number is M ?
4 The number 100 has two square roots.
a What is their sum?
b What is their product?
5 Find the square roots of each number.
a 1
b 36
c 169
d 256
e 361
6 a Show that 3 −1 = 32 + 3 + 1.
2
3
4
b Show that −1 = 42 + 4 + 1.
3
c Write a similar expression involving 53.
3
7 The numbers in the box are all identical in value.
Use this fact to write down:
b 3 4096 .
a 4096
8 Find the value of:
b
a 121
9 Find the value of:
b
a 38
3
289
c
125
c
3
212
400
d
27
d
10 113 = 1331. Use this fact to work out:
b 3 1331 .
a 114
11 Explain why Alicia is correct.
A square root of 25 could be less than a
square root of 16.
10
1 Integers, powers and roots
1.
3
1000
46
163
642
4096