Edexcel International GCSE Further Pure Mathematics ...

1 Edexcel International GCSE (9 1) Further PURE Mathematics Student Book Ali Datoo eBookincludedEDEXCEL International GCSE (9 1) Further PURE MATHEMATICSS tudent BookAli Datoo Pearson Edexcel International GCSE (9 1) Further Pure Mathematics provides comprehensive coverage of the specifi cation and is designed to supply students with the best preparation possible for the examination: Written by a highly-experienced International GCSE Mathematics teacher and author Content is mapped to the specifi cation to provide comprehensive coverage Exam practice throughout, with full answers included in the back of the book Signposted transferable skills Reviewed by a language specialist to ensure the book is written in a clear and accessible style Glossary of key Mathematics terminology eBook included Online Teacher Resource Pack (ISBN 9780435191214) also available, providing Further planning, teaching and assessment supportFor Pearson Edexcel International GCSE (9 1) Further Pure Mathematics (4PM1) higher tier for fi rst teaching AStudent Book 1 ISBN: 9780435181444 Mathematics AStudent Book 2 ISBN: International GCSE (9 1) Further PURE Mathematics Student 1-307/09/2017 16:27 Uncorrected proof, all content subject to change at publisher discretion.

2 Not for resale, circulation or distribution in whole or in part. Pearson 2019 Online access to your ActiveBookThank you for buying this Edexcel International GCSE (9 1) Further Pure Mathematics Student comes with three years access* to your 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 to access your ActiveBook1 Scratch off panel with a coin to reveal your unique access code. Do not use a knife or other sharp object as it may damage the to you already have an ActiveLearn Digital Services account (ActiveTeach or ActiveLearn), log in and click I have a new access code in the top right of the screen.

3 Type in the code above and select Activate .4If you do not have an ActiveLearn Digital Services account, click Register . It is free to do this. Type in the code above and select Activate . Simply follow the instructions on screen to information The access code can only be used once. Please activate your access code as soon as possible, as it does have a use by date . If your code has expired when you enter it, please contact our ActiveLearn support site at The ActiveBook will be valid for three years upon help To check that you will be able to access an ActiveBook, go to and choose Will ActiveLearn Digital Service work on my computer? If you have any questions about accessing your ActiveBook, please contact our ActiveLearn support site at 407/09/2017 16:27 Uncorrected proof, all content subject to change at publisher discretion. Not for resale, circulation or distribution in whole or in part.

4 Pearson 2019 Edexcel International GCSE (9 1) Further PURE MATHEMATICSS tudent BookAli DatooGreg Attwood, Keith Pledger, David Wilkins, Alistair Macpherson, Bronwen Moran, Joseph Petran and Geoff 107/09/2017 14:35 Uncorrected proof, all content subject to change at publisher discretion. Not for resale, circulation or distribution in whole or in part. Pearson 2019 Published by Pearson Education Limited, 80 Strand, London, WC2R of official specifications for all Pearson qualifications may be found on the website: Pearson Education Limited 2017 Edited by Linnet Bruce, Keith Gallick and Susan Lyons Designed by Cobalt id Typeset by Tech-Set Ltd, Gateshead, UK Cover design by Pearson Education Limited Picture research by Debbie Gallagher Cover photo Getty Images: Naahushi Kavuri / EyeEmInside front cover: : Dmitry LobanovThe rights of Ali Datoo, Greg Attwood, Keith Pledger, David Wilkins, Alistair Macpherson, Bronwen Moran, Joseph Petran and Geoff Staley to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act published 201720 19 18 1710 9 8 7 6 5 4 3 2 1 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British LibraryISBN 978 0 435 18854 2 Copyright notice All rights reserved.

5 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, Barnard s Inn, 86 Fetter Lane, London EC4A 1EN ( ). Applications for the copyright owner s written permission should be addressed to the in Slovakia by NeografiaAcknowledgements The publisher would like to thank the following for their kind permission to reproduce their photographs:(Key: b-bottom; c-centre; l-left; r-right; t-top) : ealisa 143; Alamy Stock Photo: Ammit 3; Getty Images: Christoph Hetzmannseder 2, David Crunelle / EyeEm 160, Ditto 24, EyeEm 136, hohl 74, Julia Antonio / EyeEm 60, Krzysztof Dydynski 106, Martin Barraud 124, Ozgur Donmaz 36, sebastian-julian 96, View Pictures / UIG 182.

6 : Africa Studio 75, Akhenaton Images 90, Aleksandr Markin 128, andrea crisante 107t, Anette Holmberg 37, Brian Kinney 161, cigdem 148, IM_photo 123, Jacques Durocher 49t, jordache 180, Maridav 83, Miami2you 130, migrean 107b, Mikael Damkier 160, Nando 11, Nattawadee Supchapo 137, Neil Lockhart 61, Nicku 80, oksmit 125, Ondrej Prosicky 183, Patricia Hofmeester 131, Pavel L Photo and Video 154, photofriday 77t, 9, Sergey Edentod 47, Steve Noakes 25, Svetlana Privezentseva 49b, Syda Productions 77b, Viacheslav Nikolaenko 92, wavebreakmedia 121, worradirek 10, Zhukov Oleg 5 All other images Pearson EducationEndorsement statement In order to ensure that this resource offers high-quality support for the associated 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 content of the specification or part of a specification at which it is aimed.

7 It also confirms that it demonstrates an appropriate balance between the development of subject skills, knowledge and understanding, in addition to preparation for does not cover any guidance on assessment activities or processes ( practice questions or advice on how to answer assessment questions), included in the resource nor does it prescribe any particular approach to the teaching or delivery of a related the publishers have made every attempt to ensure that advice on the qualification and its assessment is accurate, the official specification and associated assessment guidance materials are the only authoritative source of information and should always be referred to for definitive examiners have not contributed to any sections in this resource relevant to examination papers for which they have will not use endorsed resources as a source of material for any assessment set by Pearson. Endorsement of a resource does not mean that the 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 lists produced by the awarding body shall include this and other appropriate TO BE 207/09/2017 14:35 Uncorrected proof, all content subject to change at publisher discretion.

8 Not for resale, circulation or distribution in whole or in part. Pearson 2019 CONTENTSiiiPREFACECHAPTER 1: SURDS AND LOGARITHMIC FUNCTIONSCHAPTER 2: THE QUADRATIC FUNCTIONCHAPTER 3: INEQUALITIES AND IDENTITIESCHAPTER 4: SKETCHING POLYNOMIALSCHAPTER 5: SEQUENCES AND SERIESCHAPTER 6: THE BINOMIAL SERIESCHAPTER 7: SCALAR AND VECTOR QUANTITIESCHAPTER 8: RECTANGULAR CARTESIAN COORDINATESCHAPTER 9: DIFFERENTIATIONCHAPTER 10: INTEGRATIONCHAPTER 11: 307/09/2017 14:35 Uncorrected proof, all content subject to change at publisher discretion. Not for resale, circulation or distribution in whole or in part. Pearson 2019 COURSE STRUCTUREivCHAPTER 1 WRITE A NUMBER EXACTLY USING A SURD 4 RATIONALISE THE DENOMINATOR OF A SURD 5BE FAMILIAR WITH THE FUNCTIONS ax AND LOGbx AND RECOGNISE THE SHAPES OF THEIR GRAPHS 7BE FAMILIAR WITH EXPRESSIONS OF THE TYPE ex AND USE THEM IN GRAPHS 9BE ABLE TO USE GRAPHS OF FUNCTIONS TO SOLVE EQUATIONS 12 WRITING AN EXPRESSION AS A LOGARITHM 14 UNDERSTAND AND USE THE LAWS OF LOGARITHMS 15 CHANGE THE BASE OF A LOGARITHM 17 SOLVE EQUATIONS OF THE FORM ax 5 b 18 EXAM PRACTICE QUESTIONS 21 CHAPTER SUMMARY 23 CHAPTER 2 FACTORISE QUADRATIC EXPRESSIONS WHERE THE COEFFICIENT OF x2 IS GREATER THAN 1 26 COMPLETE THE SQUARE AND USE THIS TO SOLVE QUADRATIC EQUATIONS 27 SOLVE QUADRATIC EQUATIONS USING THE QUADRATIC FORMULA 28

9 UNDERSTAND AND USE THE DISCRIMINANT TO IDENTIFY WHETHER THE ROOTS ARE (i) EQUAL AND REAL, (ii) UNEQUAL AND REAL OR (iii) NOT REAL 29 UNDERSTAND THE ROOTS a AND b AND HOW TO USE THEM 31 EXAM PRACTICE QUESTIONS 34 CHAPTER SUMMARY 35 CHAPTER 3 SOLVE SIMULTANEOUS EQUATIONS, ONE LINEAR AND ONE QUADRATIC 38 SOLVE LINEAR INEQUALITIES 39 SOLVE QUADRATIC INEQUALITIES 41 GRAPH LINEAR INEQUALITIES IN TWO VARIABLES 44 DIVIDE A POLYNOMIAL BY (x 6 p) 50 FACTORISE A POLYNOMIAL BY USING THE FACTOR THEOREM 52 USING THE REMAINDER THEOREM, FIND THE REMAINDER WHEN A POLYNOMIAL IS DIVIDED BY (ax 2 b) 54 EXAM PRACTICE QUESTIONS 56 CHAPTER SUMMARY 58 CHAPTER 4 SKETCH CUBIC CURVES OF THE FORM y 5 ax3 1 bx2 1 cx 1 d OR y 5 (x 1 a)(x 1 b)(x 1 c) 62 SKETCH AND INTERPRET GRAPHS OF CUBIC FUNCTIONS OF THE FORM y 5 x3 64 SKETCH THE RECIPROCAL FUNCTION y 5 k __ x WHERE k IS A CONSTANT 65 SKETCH CURVES OF DIFFERENT FUNCTIONS TO SHOW POINTS OF INTERSECTION AND SOLUTIONS TO EQUATIONS 67 APPLY TRANSFORMATIONS TO CURVES 69 EXAM PRACTICE QUESTIONS 71 CHAPTER SUMMARY 73 CHAPTER 5 IDENTIFY AN ARITHMETIC SEQUENCE 76 FIND THE COMMON DIFFERENCE, FIRST TERM AND nth TERM OF AN ARITHMETIC SERIES 78 FIND THE SUM OF AN ARITHMETIC SERIES AND BE ABLE TO USE NOTATION 80 IDENTIFY A GEOMETRIC SEQUENCE 84 FIND THE COMMON RATIO, FIRST TERM AND nth TERM OF A GEOMETRIC SEQUENCE 85 FIND THE SUM OF A GEOMETRIC SERIES 87 FIND THE SUM TO INFINITY OF A CONVERGENT GEOMETRIC SERIES 90 EXAM PRACTICE QUESTIONS 93 CHAPTER SUMMARY 95 CHAPTER 6 USE ( n r )

10 TO WORK OUT THE COEFFICIENTS IN THE BINOMIAL EXPANSION 407/09/2017 14:35 Uncorrected proof, all content subject to change at publisher discretion. Not for resale, circulation or distribution in whole or in part. Pearson 2019 COURSE STRUCTUREvUSE THE BINOMIAL EXPANSION TO EXPAND (1 1 x)n 100 DETERMINE THE RANGE OF VALUES FOR WHICH x IS TRUE AND VALID FOR AN EXPANSION 101 EXAM PRACTICE QUESTIONS 104 CHAPTER SUMMARY 105 CHAPTER 7 VECTOR NOTATION AND HOW TO DRAW VECTOR DIAGRAMS 108 PERFORM SIMPLE VECTOR ARITHMETIC AND UNDERSTAND THE DEFINITION OF A UNIT VECTOR 110 USE VECTORS TO DESCRIBE THE POSITION OF A POINT IN TWO DIMENSIONS 113 USE VECTORS TO DEMONSTRATE SIMPLE PROPERTIES OF GEOMETRICAL FIGURES 114 WRITE DOWN AND USE CARTESIAN COMPONENTS OF A VECTOR IN TWO DIMENSIONS 117 EXAM PRACTICE QUESTIONS 120 CHAPTER SUMMARY 123 CHAPTER 8 WORK OUT THE GRADIENT OF A STRAIGHT LINE 125 FIND THE EQUATION OF A STRAIGHT LINE 127 UNDERSTAND THE RELATIONSHIP BETWEEN PERPENDICULAR LINES 128 FIND THE DISTANCE BETWEEN TWO POINTS ON A LINE 131 FIND THE COORDINATES OF A POINT THAT DIVIDES A LINE IN A GIVEN RATIO 132 EXAM PRACTICE