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Cambridge University Press978-1-107-69787-4 – Cambridge Checkpoint MathematicsGreg Byrd Lynn Byrd and Chris PearceFrontmatterMore information
© in this web service Cambridge University Press www.cambridge.org
Greg Byrd, Lynn Byrd and Chris Pearce
Coursebook
Cambridge Checkpoint
Mathematics
8
Cambridge University Press978-1-107-69787-4 – Cambridge Checkpoint MathematicsGreg Byrd Lynn Byrd and Chris PearceFrontmatterMore information
© in this web service Cambridge University Press www.cambridge.org
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/9781107697874
© 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 written 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 978-1-107-69787-4 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.
Cambridge University Press978-1-107-69787-4 – Cambridge Checkpoint MathematicsGreg Byrd Lynn Byrd and Chris PearceFrontmatterMore information
© in this web service Cambridge University Press www.cambridge.org
3
Introduction
Welcome to Cambridge Checkpoint Mathematics stage 8
Th e Cambridge Checkpoint Mathematics course covers the Cambridge Secondary 1 mathematics framework and is divided into three stages: 7, 8 and 9. Th is book covers all you need to know for stage 8.Th ere are two more books in the series to cover stages 7 and 9. Together they will give you a fi rm foundation in mathematics. At the end of the year, your teacher may ask you to take a Progression test to fi nd out how well you have done. Th is book will help you to learn how to apply your mathematical knowledge and to do well in the test.Th e curriculum is presented in six content areas: • Number • Measure • Geometry• Algebra • Handling data • Problem solving.
Th is book has 18 units, each related to one of the fi rst fi ve content areas. Problem solving is included in all units. Th ere are no clear dividing lines between the fi ve areas of mathematics; skills learned in one unit are oft en used in other units. Each unit starts with an introduction, with key words listed in a blue box. Th is will prepare you for what you will learn in the unit. At the end of each unit is a summary box, to remind you what you’ve learned.Each unit is divided into several topics. Each topic has an introduction explaining the topic content, usually with worked examples. Helpful hints are given in blue rounded boxes. At the end of each topic there is an exercise. Each unit ends with a review exercise. Th e questions in the exercises encourage you to apply your mathematical knowledge and develop your understanding of the subject. As well as learning mathematical skills you need to learn when and how to use them. One of the most important mathematical skills you must learn is how to solve problems.When you see this symbol, it means that the question will help you to develop your problem-solving skills.During your course, you will learn a lot of facts, information and techniques. You will start to think like a mathematician. You will discuss ideas and methods with other students as well as your teacher. Th ese discussions are an important part of developing your mathematical skills and understanding.Look out for these students, who will be asking questions, making suggestions and taking part in the activities throughout the units.
Hassan
Dakarai
Shen
Xavier
Jake
Anders
Razi
Sasha
Maha
Mia
Alicia
Harsha
Zalika
Oditi
Tanesha
Ahmad
Cambridge University Press978-1-107-69787-4 – Cambridge Checkpoint MathematicsGreg Byrd Lynn Byrd and Chris PearceFrontmatterMore information
© in this web service Cambridge University Press www.cambridge.org
4
Contents
Introduction 3Acknowledgements 6
Unit 1 Integers, powers and roots 7
1.1 Arithmetic with integers 81.2 Multiples, factors and primes 111.3 More about prime numbers 131.4 Powers and roots 15End-of-unit review 17
Unit 2 Sequences, expressions and formulae 18
2.1 Generating sequences 192.2 Finding rules for sequences 212.3 Using the nth term 232.4 Using functions and mappings 242.5 Constructing linear expressions 262.6 Deriving and using formulae 27End-of-unit review 30
Unit 3 Place value, ordering and rounding 31
3.1 Multiplying and dividing by 0.1 and 0.01 323.2 Ordering decimals 343.3 Rounding 363.4 Adding and subtracting decimals 373.5 Dividing decimals 383.6 Multiplying by decimals 393.7 Dividing by decimals 403.8 Estimating and approximating 41End-of-unit review 43
Unit 4 Length, mass and capacity 44
4.1 Choosing suitable units 454.2 Kilometres and miles 47End-of-unit review 49
Unit 5 Angles 50
5.1 Parallel lines 515.2 Explaining angle properties 545.3 Solving angle problems 57End-of-unit review 60
Unit 6 Planning and collecting data 61
6.1 Collecting data 626.2 Types of data 656.3 Using frequency tables 66End-of-unit review 69
Unit 7 Fractions 70
7.1 Finding equivalent fractions, decimals and percentages 71
7.2 Converting fractions to decimals 737.3 Ordering fractions 747.4 Adding and subtracting fractions 757.5 Finding fractions of a quantity 777.6 Multiplying an integer by a fraction 787.7 Dividing an integer by a fraction 797.8 Multiplying and dividing fractions 80End-of-unit review 82
Unit 8 Shapes and geometric reasoning 83
8.1 Recognising congruent shapes 848.2 Identifying symmetry of 2D shapes 868.3 Classifying quadrilaterals 888.4 Drawing nets of solids 908.5 Making scale drawings 92End-of-unit review 94
Unit 9 Simplifying expressions and solving equations 95
9.1 Collecting like terms 969.2 Expanding brackets 989.3 Constructing and solving equations 99End-of-unit review 101
Unit 10 Processing and presenting data 102
10.1 Calculating statistics from discrete data 10310.2 Calculating statistics from grouped or
continuous data 10510.3 Using statistics to compare two distributions 107End-of-unit review 109
Cambridge University Press978-1-107-69787-4 – Cambridge Checkpoint MathematicsGreg Byrd Lynn Byrd and Chris PearceFrontmatterMore information
© in this web service Cambridge University Press www.cambridge.org
5
Unit 11 Percentages 110
11.1 Calculating percentages 11111.2 Percentage increases and decreases 11311.3 Finding percentages 11511.4 Using percentages 117End-of-unit review 119
Unit 12 Constructions 120
12.1 Drawing circles and arcs 12112.2 Drawing a perpendicular bisector 12212.3 Drawing an angle bisector 12412.4 Constructing triangles 126End-of-unit review 128
Unit 13 Graphs 129
13.1 Drawing graphs of equations 13013.2 Equations of the form y = mx + c 13213.3 The midpoint of a line segment 13413.4 Graphs in real-life contexts 136End-of-unit review 139
Unit 14 Ratio and proportion 140
14.1 Simplifying ratios 14114.2 Sharing in a ratio 14314.3 Solving problems 145End-of-unit review 147
Unit 15 Probability 148
15.1 The probability that an outcome does not happen 149
15.2 Equally likely outcomes 15015.3 Listing all possible outcomes 15215.4 Experimental and theoretical probabilities 154End-of-unit review 157
Unit 16 Position and movement 158
16.1 Transforming shapes 15916.2 Enlarging shapes 161End-of-unit review 164
Unit 17 Area, perimeter and volume 165
17.1 The area of a triangle 16617.2 The areas of a parallelogram
and trapezium 16717.3 The area and circumference
of a circle 16917.4 The areas of compound shapes 17117.5 The volumes and surface
areas of cuboids 17317.6 Using nets of solids to work out
surface areas 175End-of-unit review 177
Unit 18 Interpreting and discussing results 178
18.1 Interpreting and drawing frequency diagrams 179
18.2 Interpreting and drawing pie charts 18218.3 Interpreting and drawing line graphs 18418.4 Interpreting and drawing stem-and-
leaf diagrams 18618.5 Drawing conclusions 188End-of-unit review 191
End-of-year review 192Glossary and index 196
Contents
Cambridge University Press978-1-107-69787-4 – Cambridge Checkpoint MathematicsGreg Byrd Lynn Byrd and Chris PearceFrontmatterMore information
© in this web service Cambridge University Press www.cambridge.org
6
Acknowledgements
Th e publisher would like to thank Ángel Cubero of the International School Santo Tomás de Aquino, Madrid, for reviewing the language level. Cover image © Cosmo Condina concepts/Alamyp. 7b pressureUA /iStock; p. 18tl Jon Arnold Images Ltd/Alamy; p. 18mr Maksim Toome / Shutterstock;p. 18br forestpath/ Shutterstock; p. 26b ilyast/ iStock; p. 31b Antonio Mo/Iconica/Getty Images; p. 37b Christopher Steer/ iStock; p.38b DAJ/ Getty Images; p. 44mr Chris Ryan/OJO Images/Getty Images;p. 44b NASA; p. 46tr Lynn Byrd; 46mr Aspen Photo/Shutterstock; p. 63m dundanim/Shutterstock; p. 83t Diego Cervo/Shutterstock; p. 83mr Francesco Dazzi/Shutterstock;p. 83br Peter Kirillov/Shutterstock; p. 93mr mbbirdy/iStock; p. 95tr pidjoe/iStock;p. 95mr Liz Van Steenburgh/Shutterstock; p. 95br Aleksandar Petrovic/iStock; p. 114ml a40757/ Shutterstock;p. 114bl Pakhnyushcha/ Shutterstock; p. 129tr Portrait Essentials / Alamy; p. 140mr RosetteJordaan/ iStock; p. 140br Mark Bowden/iStock; p. 143b Ferenc Szelepcsenyi/ Shutterstock; p. 146tr kryczka/ iStock; p. 147br design56/ Shutterstock; p. 158br Geoff Brightling / Peter Minister/Dorling Kindersley
l = left , r = right, t = top, b = bottom, m = middle