EDEXCEL INTERNATIONAL GCSE (9 –1) Student Book 1
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EDEXCEL INTERNATIONAL GCSE (9 –1) MATHEMATICS A Student Book 1 David Turner, Ian Potts eBook included 1 Online access to your ActiveBook Thank you for buying this Edexcel International GCSE (9-1) Mathematics A Student Book 1. It comes with three years’ access* to ActiveBook – an online, digital version of your textbook. You can personalise your ActiveBook with notes, highlights and links to your wider reading. It is perfect for supporting your coursework and revision activities. * For new purchases only. If this access code has already been revealed, it may no longer be valid. If you have bought this textbook second hand, the code may already have been used by the fi rst owner of the book. How to access your ActiveBook Scratch the panel off with a coin to reveal your unique access code. 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This process confirms that this resource fully covers the Copies of official specifications for all Edexcel qualifications may be found teaching and learning content of the specification or part of a specification at on the website: www.qualifications.pearson.com which it is aimed. It also confirms that it demonstrates an appropriate balance between the development of subject skills, knowledge and understanding, in Text © Pearson Education Limited 2016 addition to preparation for assessment. Edited by Lyn Imeson Answers checked by Laurice Suess Endorsement does not cover any guidance on assessment activities or Designed by Cobalt id processes (e.g. practice questions or advice on how to answer assessment Typeset by Cobalt id questions), included in the resource nor does it prescribe any particular Original illustrations © Pearson Education Limited 2016 approach to the teaching or delivery of a related course. Illustrated by © Cobalt id Cover design by Pearson Education Limited While the publishers have made every attempt to ensure that advice on the Picture research by Ann Thomson qualification and its assessment is accurate, the official specification and Cover photo/illustration © Shutterstock.com: Filip Fuxa associated assessment guidance materials are the only authoritative source of information and should always be referred to for definitive guidance. The rights of David Turner and Ian Potts to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Pearson examiners have not contributed to any sections in this resource Patents Act 1988. relevant to examination papers for which they have responsibility. First published 2016 Examiners will not use endorsed resources as a source of material for any assessment set by Pearson. Endorsement of a resource does not mean that 19 18 17 16 the resource is required to achieve this Pearson qualification, nor does it mean 10 9 8 7 6 5 4 3 2 1 that it is the only suitable material available to support the qualification, and any resource lists produced by the awarding body shall include this and other British Library Cataloguing in Publication Data appropriate resources. A catalogue record for this book is available from the British Library ISBN 978 0 435 18144 4 Copyright notice All rights reserved. No part of this publication may be reproduced in any form or by any means (including photocopying or storing it in any medium by electronic means and whether or not transiently or incidentally to some other use of this publication) without the written permission of the copyright owner, except in accordance with the provisions of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency, Saffron House, 6–10 Kirby Street, London EC1N 8TS (www.cla.co.uk). Applications for the copyright owner’s written permission should be addressed to the publisher. Printed by Neografia in Slovakia Dedicated to Viv Hony who started the whole project. Grateful for contributions from Jack Barraclough, Chris Baston, Ian Bettison, Sharon Bolger, Phil Boor, Ian Boote, Judith Chadwick, Tony Cushen, Tara Doyle, Kath Hipkiss, Ian Jacques, Catherine Murphy, Su Nicholson, Naomi Norman, Diane Oliver, Katherine Pate, Glyn Payne, Jenny Roach, Carol Roberts, Peter Sherran, Robert Ward-Penny and our Development Editor: Gwen Burns. Websites There are links to relevant websites in this book. In order to ensure that the links are up to date and that the links work we have made the links available on our website at www.pearsonhotlinks.co.uk. Search for ISBN 978 0 435 18144 4. CONTENTS iii COURSE STRUCTURE IV PREFACE VI UNIT 1 2 UNIT 2 96 UNIT 3 174 UNIT 4 236 UNIT 5 298 FACT FINDERS 372 CHALLENGES 382 GLOSSARY 384 ANSWERS 388 INDEX 446 ACKNOWLEDGEMENTS 454 iv COURSE STRUCTURE UNIT 1 UNIT 2 UNIT 3 NUMBER 1 3 NUMBER 2 97 NUMBER 3 175 ◼ WORKING WITH FRACTIONS ◼ STANDARD FORM ◼ PRIME FACTORS ◼ ORDER OF OPERATIONS ◼ PERCENTAGES ◼ HCF AND LCM (BIDMAS) ◼ PERCENTAGE INCREASE ◼ RATIO ◼ SIGNIFICANT FIGURES AND DECREASE ◼ EXAM PRACTICE 183 AND DECIMAL PLACES ◼ EXAM PRACTICE 111 ◼ SUMMARY 184 ◼ EXAM PRACTICE 17 ◼ SUMMARY 112 ◼ SUMMARY 18 ALGEBRA 1 19 ALGEBRA 2 113 ALGEBRA 3 185 ◼ SIMPLIFYING ALGEBRAIC ◼ SIMPLIFYING ALGEBRAIC ◼ SIMPLE FACTORISING EXPRESSIONS FRACTIONS ◼ SIMPLIFYING FRACTIONS ◼ SIMPLIFYING ALGEBRAIC ◼ SOLVING EQUATIONS ◼ EQUATIONS WITH EXPRESSIONS WITH WITH ROOTS AND POWERS FRACTIONS BRACKETS ◼ POSITIVE INTEGER INDICES ◼ SIMULTANEOUS ◼ SOLVING EQUATIONS ◼ INEQUALITIES EQUATIONS ◼ EXAM PRACTICE 30 ◼ EXAM PRACTICE 124 ◼ EXAM PRACTICE 199 ◼ SUMMARY 31 ◼ SUMMARY 125 ◼ SUMMARY 200 GRAPHS 1 32 GRAPHS 2 126 GRAPHS 3 201 ◼ GRADIENT OF A ◼ STRAIGHT-LINE GRAPHS ◼ DISTANCE–TIME GRAPHS STRAIGHT LINE ◼ SKETCHING STRAIGHT-LINE ◼ SPEED–TIME GRAPHS ◼ PLOTTING STRAIGHT-LINE GRAPHS ◼ EXAM PRACTICE 211 GRAPHS ◼ SIMULTANEOUS EQUATIONS ◼ SUMMARY 212 ◼ STRAIGHT-LINE ◼ EXAM PRACTICE 135 CONVERSION GRAPHS ◼ SUMMARY 136 ◼ EXAM PRACTICE 48 ◼ SUMMARY 49 SHAPE AND SPACE 1 50 SHAPE AND SPACE 2 137 SHAPE AND SPACE 3 213 ◼ TRIANGLES ◼ PYTHAGORAS' THEOREM ◼ TANGENT RATIO ◼ QUADRILATERALS ◼ CIRCLE THEOREMS ◼ CALCULATING SIDES ◼ POLYGONS ◼ EXAM PRACTICE 148 ◼ CALCULATING ANGLES ◼ CONSTRUCTIONS ◼ SUMMARY 149 ◼ EXAM PRACTICE 222 ◼ SIMILAR TRIANGLES ◼ SUMMARY 223 ◼ EXAM PRACTICE 81 ◼ SUMMARY 82 SETS 84 HANDLING DATA 1 150 HANDLING DATA 2 224 ◼ SET NOTATION ◼ STATISTICAL INVESTIGATION ◼ FREQUENCY TABLES ◼ VENN DIAGRAMS ◼ PRESENTING DATA ◼ DISCRETE DATA ◼ EXAM PRACTICE 94 ◼ MISLEADING DATA PRESENTATION ◼ CONTINUOUS DATA ◼ SUMMARY 95 ◼ AVERAGES FOR DISCRETE DATA ◼ EXAM PRACTICE 234 ◼ EXAM PRACTICE 170 ◼ SUMMARY 235 ◼ SUMMARY 172 COURSE STRUCTURE v UNIT 4 UNIT 5 NUMBER 4 237 NUMBER 5 299 FACT FINDERS 372 ◼ COMPOUND ◼ CALCULATORS ◼ ANTS PERCENTAGES ◼ ESTIMATING ◼ FRAGILE EARTH ◼ INVERSE PERCENTAGES ◼ ROUNDING, UPPER AND ◼ GREAT WHITE SHARK ◼ EXAM PRACTICE 245 LOWER BOUNDS ◼ LONDON 2012 OLYMPIC ◼ SUMMARY 246 ◼ EXAM PRACTICE 309 GAMES ◼ SUMMARY 310 ◼ THE INCREDIBLE HUMAN BODY ALGEBRA 4 247 ALGEBRA 5 311 CHALLENGES 382 ◼ USING FORMULAE ◼ MULTIPLYING BRACKETS ◼ CHANGE OF SUBJECT ◼ FACTORISING QUADRATIC ◼ FURTHER FORMULAE EXPRESSIONS ◼ EXAM PRACTICE 257 ◼ SOLVING QUADRATIC EQUATIONS ◼ SUMMARY 258 BY FACTORISATION ◼ PROBLEMS LEADING TO QUADRATIC EQUATIONS ◼ EXAM PRACTICE 324 ◼ SUMMARY 325 GRAPHS 4 259 GRAPHS 5 326 ◼ QUADRATIC GRAPHS ◼ REPRESENTING y = ax ² + bx + c INEQUALITIES GRAPHICALLY ◼ SOLUTION OF 0 = ax ² + bx + c ◼ PERPENDICULAR LINES ◼ EXAM PRACTICE 269 ◼ MID-POINTS ◼ SUMMARY 270 ◼ USING PYTHAGORAS' THEOREM ◼ EXAM PRACTICE 336 ◼ SUMMARY 337 SHAPE AND SPACE 4 271 SHAPE AND SPACE 5 338 ◼ SINE AND COSINE RATIOS ◼ TRANSFORMATIONS ◼ CALCULATING SIDES ◼ TRANSLATIONS ◼ CALCULATING ANGLES ◼ REFLECTIONS AND ROTATIONS ◼ MIXED QUESTIONS ◼ ENLARGEMENTS ◼ EXAM PRACTICE 283 ◼ COMBINED TRANSFORMATIONS ◼ SUMMARY 284 ◼ EXAM PRACTICE 355 ◼ SUMMARY 356 HANDLING DATA 3 285 HANDLING DATA 4 357 ◼ MEASURES OF ◼ PROBABLILITY – DISPERSION SINGLE EVENTS ◼ QUARTILES ◼ EXPERIMENTAL ◼ CUMULATIVE FREQUENCY PROBABILITY ◼ EXAM PRACTICE 296 ◼ THEORETICAL ◼ SUMMARY 297 PROBABILITY ◼ EXAM PRACTICE 370 ◼ SUMMARY 371 vi PREFACE ABOUT THIS BOOK This two-book