PEARSON EDEXCEL INTERNATIONAL A LEVEL PURE MATHEMATICS 2 A LEVEL PEARSON EDEXCEL INTERNATIONAL STUDENT BOOK Pearson Edexcel International A Level Pure Mathematics 2 Student Book provides comprehensive coverage of the Pure Mathematics 2 unit. This book is designed to provide students with the best preparation possible for the examination: MATHEMATICS • Content is fully mapped to the specifi cation to provide comprehensive coverage and easy reference • Engaging and relevant international content in a real-world context • Exam-style questions at the end of each chapter, and an exam practice paper at the end of the book, provide practice for exam writing technique eBook • Signposted transferable skills prepare for further education and employment included • Reviewed by a language specialist to ensure the book is written in a clear and accessible style • Glossary of key Mathematics terminology, and full answers, included at the back of the book • Interactive practice activities also included An Online Teacher Resource Pack (9781292244907) provides further planning, teaching and assessment support. This Student Book supports the following qualifications: Pearson Edexcel International Advanced Subsidiary in Mathematics (XMA01) PEARSON EDEXCEL INTERNATIONAL A LEVEL Pearson Edexcel International Advanced Subsidiary in Pure Mathematics (XPM01) 2 PURE MATHEMATICS Pearson Edexcel International Advanced Level in Mathematics (YMA01) Pearson Edexcel International Advanced Level in Pure Mathematics (YPM01) For fi rst teaching September 2018 PURE MATHEMATICS 2 STUDENT BOOK STUDENT BOOK IAL PURE MATHS 1 IAL PURE MATHS 3 IAL PURE MATHS 4 Student Book Student Book Student Book ISBN: 9781292244792 ISBN: 9781292244921 ISBN: 9781292245126 www.pearsonglobalschools.com SAMPLE iAL_MathsPure2_Cover.indd 1-3 23/05/2018 12:23 F01_IASL_PM2_44853_PRE_i-x.indd 1 Student Book 2 PURE MATHEMATICS ALEVEL INTERNATIONAL PEARSON EDEXCEL Robert Ward-Penny, Dave Wilkins Robert Ward-Penny, Harry JoeSkrakowski, CongSan, Smith,Geoff Pledger, Staley, Keith Joe Petran, Oliver, Diane Moran, SuNicholson, Bronwen Alistair Macpherson, AnneMcAteer, Authors: Barraclough, Gallick, Greg Goldberg, Jack Daniel Attwood, IanBettison,Keith Series Editors: Harry and JoeSkrakowski Smith 2020. Pearson © part. in or whole in distribution or circulation resale, for Not material. 23/05/2018 12:20 Sample Published by Pearson Education Limited, 80 Strand, London, WC2R 0RL. Endorsement Statement In order to ensure that this resource offers high-quality support for the associated www.pearsonglobalschools.com Pearson qualification, it has been through a review process by the awarding body. This process confirms that this resource fully covers the teaching and learning Copies of official specifications for all Pearson qualifications may be found on the content of the specification or part of a specification at which it is aimed. It also website: https://qualifications.pearson.com confirms that it demonstrates an appropriate balance between the development of subject skills, knowledge and understanding, in addition to preparation for Text © Pearson Education Limited 2018 assessment. Edited by Richard Hutchinson Typeset by Tech-Set Ltd, Gateshead, UK Endorsement does not cover any guidance on assessment activities or processes Original illustrations © Pearson Education Limited 2018 (e.g. practice questions or advice on how to answer assessment questions) Illustrated by © Tech-Set Ltd, Gateshead, UK included in the resource, nor does it prescribe any particular approach to the Cover design by © Pearson Education Limited teaching or delivery of a related course. The rights of Greg Attwood, Jack Barraclough, Ian Bettison, Keith Gallick, While the publishers have made every attempt to ensure that advice on the Daniel Goldberg, Alistair Macpherson, Anne McAteer, Bronwen Moran, qualification and its assessment is accurate, the official specification and Su Nicholson, Diane Oliver, Joe Petran, Keith Pledger, Cong San, Joe Skrakowski, associated assessment guidance materials are the only authoritative source of Harry Smith, Geoff Staley, Robert Ward-Penny and Dave Wilkins to be identified information and should always be referred to for definitive guidance. as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Pearson examiners have not contributed to any sections in this resource relevant to examination papers for which they have responsibility. First published 2018 Examiners will not use endorsed resources as a source of material for any 21 20 19 18 assessment set by Pearson. Endorsement of a resource does not mean that the 10 9 8 7 6 5 4 3 2 1 resource is required to achieve this Pearson qualification, nor does it mean that it is the only suitable material available to support the qualification, and any resource British Library Cataloguing in Publication Data lists produced by the awarding body shall include this and other appropriate A catalogue record for this book is available from the British Library resources. ISBN 978 1 292244 85 3 Copyright notice All rights reserved. No part of this 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, Barnard's Inn, 86 Fetter Lane, London, EC4A 1EN (www.cla.co.uk). Applications for the copyright owner’s 2020. written permission should be addressed to the publisher. Printed in Slovakia by Neografia Pearson © Picture Credits The authors and publisher would like to thank the following individuals and part. organisations for permission to reproduce photographs: in Alamy Images: Utah Images 25, ZUMA Press, Inc 49; Fotolia.com: Kajano 1, or Thaut Images 112; Getty Images: Steve Dunwell 62; Shutterstock.com: Michel angelus 81, ssguy 136; 123RF.com: David Acosta Allely 152 whole in Cover images: Front: Getty Images: Werner Van Steen Inside front cover: Shutterstock.com: Dmitry Lobanov All other images © Pearson Education Limited 2018 All artwork © Pearson Education Limited 2018 distribution or circulation resale, for Not material. Sample F01_IASL_PM2_44853_PRE_i-x.indd 2 23/05/2018 12:20 CONTENTS iii COURSE STRUCTURE iv ABOUT THIS BOOK vi QUALIFICATION AND ASSESSMENT OVERVIEW viii EXTRA ONLINE CONTENT x 1 ALGEBRAIC METHODS 1 2 COORDINATE GEOMETRY IN THE (x, y) PLANE 25 3 EXPONENTIALS AND LOGARITHMS 49 4 THE BINOMIAL EXPANSION 62 REVIEW EXERCISE 1 77 5 SEQUENCES AND SERIES 80 2020. 6 TRIGONOMETRIC IDENTITIES AND EQUATIONS 112 Pearson © part. 7 DIFFERENTIATION 137 in or 8 INTEGRATION 152 whole in REVIEW EXERCISE 2 174 distribution or EXAM PRACTICE 178 GLOSSARY 181 circulation resale, ANSWERS 184 for Not INDEX 204 material. Sample F01_IASL_PM2_44853_PRE_i-x.indd 3 23/05/2018 12:20 iv COURSE STRUCTURE CHAPTER 1 ALGEBRAIC CHAPTER 4 THE BINOMIAL METHODS 1 EXPANSION 62 1.1 ALGEBRAIC FRACTIONS 2 4.1 PASCAL’S TRIANGLE 63 1.2 DIVIDING POLYNOMIALS 3 4.2 FACTORIAL NOTATION 65 1.3 THE FACTOR THEOREM 7 4.3 THE BINOMIAL EXPANSION 67 1.4 THE REMAINDER THEOREM 11 4.4 SOLVING BINOMIAL PROBLEMS 69 1.5 MATHEMATICAL PROOF 13 4.5 BINOMIAL ESTIMATION 71 1.6 METHODS OF PROOF 17 CHAPTER REVIEW 4 73 CHAPTER REVIEW 1 21 REVIEW EXERCISE 1 77 CHAPTER 2 COORDINATE GEOMETRY IN THE (x, y) CHAPTER 5 SEQUENCES AND PLANE 25 SERIES 80 2.1 MIDPOINTS AND 5.1 ARITHMETIC SEQUENCES 81 PERPENDICULAR BISECTORS 26 5.2 ARITHMETIC SERIES 84 2.2 EQUATION OF A CIRCLE 29 5.3 GEOMETRIC SEQUENCES 87 2.3 INTERSEC TIONS OF STRAIGHT 5.4 GEOMETRIC SERIES 91 LINES AND CIRCLES 33 2020. 5.5 SUM TO INFINITY 94 2.4 USE TANGENT AND CHORD 5.6 SIGMA NOTATION 97 Pearson PROPERTIES 35 5.7 RECURRENCE RELATIONS 100 © 2.5 CIRCLES AND TRIANGLES 40 5.8 MODELLING WITH SERIES 104 part. CHAPTER REVIEW 2 44 in CHAPTER REVIEW 5 107 or whole in CHAPTER 3 EXPONENTIALS AND LOGARITHMS 49 3.1 EXPONENTIAL FUNCTIONS 50 distribution 3.2 LOGARITHMS 52 or 3.3 LAWS OF LOGARITHMS 54 3.4 SOLVING EQUATIONS USING circulation LOGARITHMS 57 resale, 3.5 CHANGING THE BASE OF A for LOGARITHM 58 Not CHAPTER REVIEW 3 60 material. Sample F01_IASL_PM2_44853_PRE_i-x.indd 4 23/05/2018 12:20 COURSE STRUCTURE v CHAPTER 6 TRIGONOMETRIC CHAPTER 8 INTEGRATION 152 IDENTITIES AND 8.1 DEFINITE INTEGRALS 153 EQUATIONS 112 8.2 AREAS UNDER CURVES 155 6.1 ANGLES IN ALL FOUR 8.3 AREAS UNDER THE x-AXIS 157 QUADRANTS 113 8.4 AREAS BETWEEN CURVES 6.2 EXACT VALUES OF AND LINES 160 TRIGONOMETRICAL RATIOS 119 8.5 AREAS BETWEEN TWO CURVES 163 6.3 TRIGONOMETRIC IDENTITIES 120 8.6 THE TRAPEZIUM RULE 166 6.4 SOLVE SIMPLE CHAPTER REVIEW 8 169 TRIGONOMETRIC EQUATIONS 124 6.5 HARDER TRIGONOMETRIC REVIEW EXERCISE 2 174 EQUATIONS 128 6.6 EQUATIONS AND IDENTITIES 130 CHAPTER REVIEW 6 133 EXAM PRACTICE 178 CHAPTER 7 GLOSSARY 181 DIFFERENTIATION 137 7.1 INCREASING AND ANSWERS 184 2020. DECREASING FUNCTIONS 138 Pearson 7.2 STATIONARY POINTS 139 © INDEX 204 7.3 SKET CHING GRADIENT part. FUNCTIONS 143 in or 7.4 MODELLING WITH whole DIFFERENTIATION 145 in CHAPTER REVIEW 7 148 distribution or circulation resale, for Not material. Sample F01_IASL_PM2_44853_PRE_i-x.indd 5 23/05/2018 12:20 vi ABOUT THIS BOOK ABOUT THIS BOOK The following three themes have been fully integrated throughout the Pearson Edexcel International Advanced Level in Mathematics series, so they can be applied