Cambridge AssessmentCollinsInternational EducationEndorsed for Paper 1Cambridge InternationalAS A Level Further MathematicsFurther Pure Mathematics 1STUDENT'S BOOKTom Andrews,Helen Ball,Chris Chisholm,Michael KentSeries Editor:Dr Adam BoddisonCollinsCambridge InternationalAs A Level Further MathematicsFurther Pure Mathematics 1STUDENT'S BOOKTom Andrews,Helen Ball,Chris Chisholm,Michael KentSeries Editor:Dr Adam BoddisonWilliam Collins'dream of knowledge for all began with the publication of hisfirst book in 1819.A self-educated mill worker,he not only enriched millions of lives,but alsofounded a flourishing publishing house.Today,staying true to this spirit,Collins books are packed with inspiration,innovation and practical expertise.They place you at the centre of a world of possibility and give you exactlywhat you need to explore it.Collins.Freedom to teach.Published by CollinsThe News Building1 London Bridge StreetLondonSE1 9GFAcknowledgementsBrowse the complete Collins catalogue atThe publishers wish to thank Cambridge AssessmentInternational Education for permission to reproducequestions from past AS &A Level Mathematics andFurther Mathematics papers.Cambridge Assessment10987654321International Education bears no responsibility for978-0-00-834032-2the example answers to questions taken from itspast papers.These have been written by the authors.All rights reserved.No part of this publication may be reproduced,Exam-style questions and sample answers havestored in a retrieval system,or transmitted in any form by any means,been written by the authors.electronic,mechanical,photocopying,recording or otherwise,withoutThe publishers wish to thank the following forthe prior written permission of the Publisher or a licence permittingpermission to reproduce photographs.Every effortrestricted copying in the United Kingdom issued by the CopyrightLicensing Agency Ltd.,Barnard's Inn,86 Fetter Lane,London,has been made to trace copyright holders and toEC4A 1EN.obtain their permission for the use of copyrightmaterial.The publishers will gladly receive anyBritish Library Cataloguing in Publication Datainformation enabling them to rectify any error orA catalogue record for this publication is available from theomission at the first opportunity.British Library.pvi Dusit/Shutterstock,p1 Dusit/Shutterstock,p20Granger,NYC./Granger Historical Picture Archive/Commissioning editor:Jennifer HalAlamy Stock Photo,p55 Juice Images329/JuiceIn-house editor:Lara McMurrayImages/Alamy Stock Photo,p76 Syda Productions/Authors:Tom Andrews/Helen Ball/Chris Chisholm/Michael KentShutterstock,p115 Sergiy Tryapitsyn/Alamy StockSeries editor:Dr Adam BoddisonPhoto,p149 Jacob Lund/Shutterstock,p189 HeroDevelopment editor:Tim MajorProject manager:Emily HootonCopyeditor:Julie BondReviewer:Adele SearleProofreaders:Gwynneth Drabble/Joan MillerAnswer checkers:David Hemsley/Alice YewCover designer:Gordon MacGilpCover illustrator:Maria Herbert-LiewTypesetter:Jouve India Private LtdProduction controller:Sarah BurkePrinted and bound by CPI Group(UK)Ltd,Croydon,CRO 4YYFull worked solutions for all exercises,exam-style questions and past paper questions in this book are available toteachers by emailing international.schools@harpercollins.co.uk and stating the book title