Cambridge AssessmentCollinsInternational EducationEndorsed for Paper 2Cambridge InternationalAS A Level Further MathematicsFurther Pure Mathematics 2STUDENT'S BOOKTom Andrews,Helen Ball,Jonny Griffiths,Chris PearceSeries Editor:Dr Adam BoddisonCollinsCambridge InternationalAs A Level Further MathematicsFurther Pure Mathematics 2STUDENT'S BOOKTom Andrews,Helen Ball,Jonny Griffiths,Chris PearceSeries Editor:Dr Adam BoddisonWilliam Collins'dream of knowledge for all began with thepublication of his first book in 1819.A self-educated mill worker,he not only enriched millions of lives,but also founded a flourishing publishing house.Today,staying trueto this spirit,Collins books are packed with inspiration,innovationand practical expertise.They place you at the centre of a world ofpossibility and give you exactly what you need to explore it.Collins.Freedom to teach.Published by CollinsAn imprint of HarperCollinsPublishersThe News BuildingAcknowledgements1 London Bridge StreetThe publishers wish to thank Cambridge AssessmentLondonInternational Education for permission to reproduceSE1 9GFquestions from past AS &A Level Mathematics papers.Cambridge Assessment International Education bearsBrowse the complete Collins catalogue atno responsibility for the example answers to questionswww.collins.co.uktaken from its past papers.These have been written bythe authors.Exam-style questions and sample answershave been written by the authors.10987654321The publishers wish to thank the following for permission978-0-00-834031-5to reproduce photographs.Every effort has been madeAll rights reserved.No part of this publication may be reproduced,to trace copyright holders and to obtain their permissionstored in a retrieval system,or transmitted in any form by anyfor the use of copyright material.The publishers willmeans,electronic,mechanical,photocopying,recording orgladly receive any information enabling them to rectifyotherwise,without the prior written permission of the Publisher or aany error or omission at the first opportunity.licence permitting restricted copying in the United Kingdom issuedpvi Solis Images/Shutterstock,p1 Solis Images/by the Copyright Licensing Agency Ltd.,Barnard's Inn,86 FetterShutterstock,p19 Rawpixel.com/Shutterstock,p57Lane,London,EC4A 1EN.indukas/Shutterstock,p77 Monty Rakusen/CulturaCreative(RF)/Alamy Stock Photo,p102 Joho/CulturaBritish Library Cataloguing in Publication DataCreative(RF)/Alamy Stock Photo,p122 Rocketclips,A catalogue record for this publication is available from theInc./Shutterstock.British Library.Commissioning editor:Jennifer HallIn-house editor:Lara McMurrayAuthors:Tom Andrews/Helen Ball/Jonny Griffiths/Chris PearceSeries editor:Dr Adam BoddisonDevelopment editor:Tim MajorProject manager:Emily HootonCopyeditor:Julie BondReviewer:Adele SearleProofreaders:Gwynneth Drabble/Joan MillerAnswer checkers:Jason Davison/Amanda DicksonCover designer:Gordon MacGilpCover illustrator:Maria Herbert-LiewTypesetter:Jouve India Private Ltdlllustrators:Jouve India Private Ltd/Ken Vail Graphic Design 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 available toteachers by emailing international.schools@harpercollins.co.uk and stating the book title