Greg Byrd, Lynn Byrd and Chris Pearce
Cambridge Checkpoint
Mathematics Practice Book
9
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK www.cambridge.org Information on this title: www.cambridge.org/9781107698994 © Cambridge University Press 2013 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the w ritten permission of Cambridge University Press. First published 2013 Printed and bound in the United Kingdom by the MPG Books Group A catalogue record for this publication is available from the British Library ISBN 978-1-107-69899-4 Paperback Cover image © Cosmo Condina concepts / Alamy Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
Contents
Introduction 1 Integers, powers and roots 1.1 Directed numbers 1.2 Square roots and cube roots 1.3 Indices 1.4 Working with indices
5 7 7 8 9 10
9.6 9.7
10 Processing and presenting data 10.1 Calculating statistics 10.2 Using statistics
48 48 50
2 2.1 2.2 2.3
Sequences and functions Generating sequences Finding the n th term Finding the inverse of a function
11 11 12 13
3 3.1 3.2 3.3 3.4
Place value, ordering and rounding Multiplying and dividing decimals mentally Multiplying and dividing by powers of 10 Rounding Order of operations
14 14 15 16 17
11 11.1 11.2 11.3 11.4
Percentages Using mental methods Comparing different quantities Percentage changes Practical examples
52 52 53 54 55
4 4.1 4.2 4.3
Length, mass, capacity and time Solving problems involving measurements Solving problems involving average speed Using compound measures
18 18 19 20
12 12.1 12.2 12.3 12.4 12.5
Tessellations, transformations and loci Tessellating shapes Solving transformation problems Transforming shapes Enlarging shapes Drawing a locus
56 56 57 59 60 61
5 5.1 5.2 5.3 5.4 5.5 5.6
Shapes Regular polygons More polygons Solving angle problems Isometric drawings Plans and elevations Symmetry in three-dimensional shapes
21 21 22 23 25 26 27
13 13.1 13.2 13.3 13.4 13.5 13.6
Equations and inequalities Solving linear equations Solving problems Simultaneous equations 1 Simultaneous equations 2 Trial and improvement Inequalities
62 62 63 64 65 66 67
6 6.1 6.2 6.3 6.4
Planning and collecting data Identifying data Types of data Designing data-collection sheets Collecting data
28 28 29 30 31
14 Ratio and proportion 14.1 Comparing and using ratios 14.2 Solving problems
68 68 70
7 7.1 7.2 7.3 7.4 7.5
Fractions Writing a fraction in its simplest form Adding and subtracting fractions Multiplying fractions Dividing fractions Working with fractions mentally
32 32 33 34 35 36
15 15.1 15.2 15.3 15.4
Area, perimeter and volume Converting units of area and volume Using hectares Solving circle problems Calculating with prisms and cylinders
72 72 73 74 75
16 16.1 16.2 16.3
Probability Calculating probabilities Sample space diagrams Using relative frequency
76 76 77 78
8 8.1 8.2 8.3
Constructions and Pythagoras’ theorem Constructing perpendicular lines Inscribing shapes in circles Using Pythagoras' theorem
37 37 38 39
17 Bearings and scale drawings 17.1 Using bearings 17.2 Making scale drawings
80 80 82
9 9.1 9.2 9.3 9.4 9.5
Expressions and formulae Simplifying algebraic expressions Constructing algebraic expressions Substituting into expressions Deriving and using formulae Factorising
40 40 41 43 44 45
18 18.1 18.2 18.3 18.4 18.5 18.6
83 83 85 86 87 89 90
Adding and subtracting algebraic fractions Expanding the product of two linear expressions
Graphs Gradient of a graph The graph of y = mx + c Drawing graphs Simultaneous equations Direct proportion Practical graphs
46 47
3
19 Interpreting and discussing results 19.1 Interpreting and drawing frequency diagrams 19.2 Interpreting and drawing line graphs 19.3 Interpreting and drawing scatter graphs 19.4 Interpreting and drawing stem-andleaf diagrams 19.5 Comparing distributions and drawing conclusions
4
91 91 92 93 94 95
Introduction
Welcome to Cambridge Checkpoint Mathematics Practice Book 9
Cambridge Checkpoint Mathematics course covers the Cambridge Secondary 1 Mathematics framework. e
e course is divided into three stages: 7,
8 and 9. is Practice Book can be used with Coursebook 9. 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 19 units. In each unit you will find an exercise for every topic. ese exercises contain similar questions to the corresponding exercises in the Coursebook. is Practice Book gives you a chance to try further questions on your own. is
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. ere
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
Directed numbers
1 Work these out. a −6 + 2.7 c 16 + −2.7
b −6 + −2.7 d 2.7 + −16
2 Work these out. a 7 − −5 c −7.1 − −5.2
b 7.1 − −5.2 d −5.2 − −7.1
3 Work these out. a −8.4 + 12.1 c 8.4 − −12.1
b d
8.4 − 12.1 −12.1 − −8.4 −
4 These are five temperatures, in degrees Celsius (°C). 1.5
3.5
−
7
−
10
3
−
−
Find the mean temperature.
5 Solve these equations. a N + 2.3 = −4.7 b 2N + 6.8 = −10.2 c N ÷ 4 = −2.7 6 Work these out. a −2 × 3.4 c −3 × 9.2
b −4.8 ÷ −4 d 14 ÷ −4
7 Copy and complete this multiplication table. ×
1.2
3
−
1.1
−
1.5
−
8 Use the information in the box to work out the value of each expression. a r + s + t b (r − s ) − t r = 8.4 s = 6.4 t = 7.4 c (s − r ) × t d t ÷ (r − s ) e (r + s ) ÷ t −
9
A + B = 0 and AB =
36.
−
What is the value of A − B ?
1
Integers, powers and roots
7
Exercise 1.2
Square roots and cube roots
1 Estimate each root, to the nearest whole number. a 50 b 150 c
d
350
3
350
2 Explain why: a
95 3
b 3
3
must be between 9 and 10.
95 must
<
10.5
<
be between 4 and 5.
4
Write a similar statement for each of these roots. a 385 b 3 500
c 4 a
d
69.8
144
<
3
55.5
N < 225
What can you say about
b
100
<
N ?
M < 400
What can you say about
c
0
<
R < 125
What can you say about
5
M ?
25.52 = 650.25
3
R ?
26.52 = 702.25
a Estimate
690 to
the nearest whole number.
b Estimate
650 to
one decimal place.
c Estimate
700 to
one decimal place.
6 Show that 3
200 is
7 a Show that
less than half
7500 is
200 .
more than 80.
b Show that 3 7500 is less than 20. 8 Use a calculator to find the following square roots. a
3025 .
b
441
c
841
d
5476 .
e
174.24
9 Use a calculator to find the following square roots. Round your answers to two decimal places.
8
a
6
b
60
c e
600
d
4265 .
2.43
1 Integers, powers and roots
Do not use a calculator in this exercise, except for questions 8 and 9.
Exercise 1.3
Indices
1 Write each number as an integer or a fraction. a 54 b 35 c 62 d 23 e 40 − −
2 Write each number as a decimal. a 81 b 22 c 41 d 31 e 10 3 − − − −
−
3 Write these numbers in order of size, smallest first. 112
26
34
43
62
121
4 Write these numbers in order of size, smallest first. 1
5
24
−
−
33 −
4
2
5
−
1
−
5 Write each number as a power of 4. a 16 b 256 c 1 d
1 4
e
1 64
6 Write each of the numbers in question 5 as a power of 2. 7 3N = 9 2 Work out the value of −
N .
8 Write each expression as a single number. a 3 1 + 6 1 b 42 + 41 + 40 + 4 1 + 4 2 −
−
−
−
1
Integers, powers and roots
9
Exercise 1.4
Working with indices
1 Simplify each expression. Write the answers in index form. a 83 × 82 b 7 × 73 c 22 × 22 × 22 d r 2 × r 4 e s 3 × s 2 × s 2 Simplify each expression. a 42 × 41 b 6 × 60 c c 2 × c 2 d
1 5 × 2 2
e
e × e 0
3 Simplify each expression in the box. One is different from the other four. Which one? a 4
×
a 2
a 0
×
a 5
a 5
×
a
a 6
×
a 0
a 3 × a 3
Give a reason for your answer.
4 This table shows powers of 9. 91 9
92 81
93 729
94 6561
95 59 049
Use the table to find the value of each expression.
a
b
531441
3
531441
5 Simplify each expression, writing it as a single power. a a 5 ÷ a 3 b 6 ÷ 63 c 82 ÷ 8 d d 2 ÷ d 2 e e ÷ e 2 6 Write each of these as a fraction. a 32 ÷ 34 b k 2 ÷ k 3 c 10 4 × 10 × 10 d 42 ÷ 25 −
7 Simplify each expression. a c
a
3
2
× a a
f
5
d
10
2
f f ×
3
b
×
5
3
5 3
10
× 10
2
4
× 10
8 Find the value of n in each equation. a 5n × 53 = 625 b 10n ÷ 10 = 0.1 c n 0 × n 2 × n = 64
10
1 Integers, powers and roots
96 531 441
