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'O>,6 XO) iB) UNIVERSITY PRESS ASPIRE SUCCEED PROGRESS Mathematic - Cambridge | IG l all al = (6) ms U SE‘ ( 060 7) Extended | David Rayner oe ys % wr - - cal Jim Fensomaa ‘ ; — —— < ¥ : > -=——_ eay OXFORD UNIVERSITY PRESS ‘ASPIRE SUCCEED PROGRESS Maineimatice Cambridge IGCSE® (0607) Extended | WN 7, David Rayner — ~ - al Jim Fensomaa on — , 4 ¥ ’ OXFORD UNIVERSITY PRESS Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford, It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dares Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Oxford University Press 2013 ‘The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2013, All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose this sme condition on any acquirer British Library Cataloguing in Publication Data Data available ISBN: 978-0-19-841690-6 10987654321 Printed in Great Britain by Bell and Bain Ltd., Glasgow © IGCSE is the registered trademark of Cambridge International Examinations. ‘The publisher would like to thank Cambridge International Examinations for their kind permission to reproduce past paper questions. Cambridge International Examinations bears no responsibility for the example answers to questions taken from its past question papers which are contained in this publication. Acknowledgements ‘The publisher would like to thank the following for their permission to reproduce photographs P1: Texas Instruments; P1: Texas Instruments; P1: Casio Electronics Co. Ltd; P38: LapoojShut- terstock; P46: Grzym/Shutterstock; PSS: FloridastockjShutterstock; PSS: Rodho{Shutterstock; Leonello Calvetti/Shutterstock; P59: Fstop/Alamy; P61: Dean BertoncelijShutterstock; P61: Milovad/Shutterstock; P63: M. Unal Ozmen/Shutterstock; P63: IkongraphicAlamy, P64: Serg64/Shutterstock; P67: Mike Flippo/Shutterstock; P68: Miroslav Hlavko/Shutterstock; P69: Oleksiy MarkjShutterstock; P72: Alexussk/Shutterstock; P73: Gorilla/Shutterstock; P74: Maxim PetrichukjShutterstock; P75: Musicman/Shutterstock; P76: Joerg Beuge/Shutterstock; P81: Fedor Selivanoy/Shutterstock; P84: Nicku/Shutterstock.Com; P85: Rich Carey/Shutterstock; P11 ‘Aleksei Ruzhin/Shutterstock; P13: Michael WesemanjShutterstock; P127: Classic Image/Alamy; P129: Sandys/Shutterstock; P135: Brocreative|Shutterstock; P144: Temiropix/Shutterstock; P149: Pichugin Dmitry/Shutterstock; P154: Evgeny Atamanenko/Shutterstock; P154: Clearview- stock/Shutterstock; P156: Geomgios Kollidas/Shutterstock; P177: Emilio Segre Visual Archives} American Institute Of Physics)Science Photo Library; P186: Offscreen|Shutterstock; P204: Turtix) Shutterstock; P204: Images.Ftc/Shutterstock; P205: Lee Yiu Tung/Shutterstock; P205: Lee Yiu ‘Tung/Shutterstock; P206: Dan Breckwoldt/Shutterstock; P214: Volodymyr Goinyk/Shutter- stock; P27: Science Source/Science Photo Library; P228: Robert Kneschke/Shutterstock; P23 Alexander Tolstykh/Shutterstock; P230: TV/Shutterstock; P239: Mopic/Shutterstock; P239: Mat- thew Benoit/Shutterstock; P260: Artsilense/Shutterstock; P267: Anatolym|Shutterstock; P269: Khoroshunova Olga/Shutterstock; P269: Andrey Pavlov/Shutterstock; P276: Antonio Abrignani Shutterstock; P308: New York Public Library/Science Photo Library; P8320: DanielbothaShut- terstock; P321: Manuel Fernandes/Shutterstock; P32: CopridjShutterstock; P342: David Fowler) Shutterstock.Com; P374: Bettmann|Corbis; P385: Georgios KollidasShutterstock; P388: Pedro Nogueira/Shutterstock; P399: Leventegyori/Shutterstock; P402: Pictorial Press Ltd/Alamy; P413: Ljupco Smokovskij/Shutterstock; P435: Zoran Vukmanov Simokov/Shutterstock; P44: Tatiana PopovajShutterstock; P449: Professor Peter Goddard/Science Photo Library; P45S: Katatonia82/ Shutterstock.Com Cover image: Oksix/Dreamstime.com Contents Introduction | a Using your graphic display calculator 1 Using templates in basic calculations 1.1 Fractions 1.2 Square roots 1.3 nth roots ._. 1.4 Exponents .,... 1.5 Absolute value 1.6 Logarithms 2 ~ Working with graphs 2.1 Entering a function and choosing a window 2.2 Producing a table of values for a function 14 2.3. Finding zeros (roots) 16 2.4 Finding a local minimum 18 2.5 Finding a local maximum 2.6 Finding the intersection point of two graphs ._. 3 Working with data 3.1 Calculation of basic statistics froma list , 26 3.2. Calculation of basic statistics from a frequency table 30 3.3. Finding a linear regression equation ,,. 3.4 Drawing a scatter graph and the graph of the equation of linear regression , Number . 2.1 Vocabulary and notation for sets of numbers . 2.2 Arithmetic 2.3. Number facts and sequences 2.4 Approximations and estimation 2.5 Standard form 2.6 Ratio and proportion 2.7 Percentages 2.8 Speed, distance and time Revision exercise 2A Revision exercise 2B Revision exercise 2C Examination exercise 2D Algebra 1 84-126 3.1 Negative numbers ., 3.2 Directed numbers ., 3.3 Formulae and expressions 3.4. Brackets and simplifying . 3.5 Linear equations __. 3.6 3.7 3.8 3.9 3.10 3.11 Revision exercise 3A .,. Examination exercise 3B Problems solved by linear equations ., Simultaneous equations .., Problems solved by simultaneous equations .. Factorising Quadratic equations ,, Problems solved by quadratic equations . Mensuration ... . 127-155 4.1 Area _ 128 4.2 ‘Thecircle , 4.3. Arc length and sector area . 4.4 Chord ofacircle ... _ 140 4.5 Volume . . 142 4.6 Surface area 151 Revision exercise 4A Examination exercise 4B Functions 4 5.1 5.2 5.3 5.4 5.5 5.6 Revision exercise 5A Examination 5B 156-176 _ 157 161 Function notation ,, Inverse function, ‘The absolute value function (modulus function) Sketch graphs . Interpreting graphs .., ‘The quadratic function _ 175 10 Investigations and mathematical modelling .. 6.1 Investigations , 6.2 Mathematical modelling .. 177-185 177 Geometry ... 7.1 Fundamental results 7.2. Pythagoras’ theorem 7.3 Symmetry 7.4 Similarity 7.5 Circle properties Revision exercise 7A Examination exercise 7B _ 187 215 Algebra 2 8.1 Inequalities 8.2 Indices ,,, 8.3 Rearrangement and evaluation of formulae 8.4 Algebraic fractions .,, 8.5 Difference method, nth term of a 227-275 aw 228 sequence 8.6 Geometric series 8.7 Variance, direct and inverse Revision exercise 8A .,, Examination exercise 8B Functions 2 9.1 Drawing and using graphs 9.2. Gradient of aline ., 9.3. ‘the forms y = mx + ¢, and ax + by=d 9.4 Curved graphs 9.5 Graphical solution of equations 9.6 Transformations of the graph of y= fe) .. _ 9.7 Logarithm function , Revision exercise 9A Examination exercise 9B Trigonometry... ; 10.1 Right-angled triangles . 10.2. Sine, cosine and tangent for 0°, 30°, 45°, 60°, 90° 10.3 Three-dimensional problems . 308-341 wa 308 323 a4 12 13 14 15 Answers |. Index | 10.4 Sine, cosine, tangent for any angle 327 10.5 The sine rule , _ 330 10.6 The cosine rule , _ 333 Revision exercise 10A .. | 338 Examination exercise 10B . 340 Vectors and transformations 342-373 11.1 Vectors .... 343 11.2. Column vectors _ 349 11.3. Simple transformations 11.4 Combined transformations Revision exercise 11A ... Examination exercise 11B Sets 12.1 Set notation 12.2 Logical problems . Revision exercise 12A Examination exercise 12B 374-384 374 . 380 _ 383 383 Probability 13.1 Probability 13.2. Mutually exclusive and independent 385-401 . 386 events 13.3. ‘Tree diagrams Revision exercise 13A ... Examination exercise 13B _ 392 _ 394 399 _ 400 Statistics _ _ . .. 402-448 14.1 Reading and interpretation of data or graphs _ 401 14.2 Averages, range and quartiles... 416 14.3. Histograms 424 14.4 Cumulative frequency 438 . 444 14.5 Scatter diagrams . Revision exercise 14A Examination exercise 14B .., Investigations and mathematical modelling | 15.1 Investigations 15.2 Mathematical modelling ._ About this book This book has been written to cover the Cambridge IGCSE” International Mathematics (0607) course, and is fully aligned to the syllabus. In addition to the main curriculum content, you will find: © Two chapters devoted entirely to investigations and mathematical modelling, which will help you develop fundamental techniques for solving problems and open-ended questions. © Comprehensive support for the use of a graphic display calculator, an integral part of the course. Chapter 1 will show you the basic skills you need to learn, and there are examples throughout the rest of the book of how to put these into practice. Throughout the book, you will encounter worked examples and a host of rigorous exercises. The examples show you the important techniques required to tackle questions. The exercises are carefully graded, starting from a basic level and going up to exam standard, allowing you plenty of opportunities to practise your skills. ‘Together, the examples and exercises put maths in a real-world context, with a truly international focus. At the start of each chapter, you will see a list of objectives that are covered in that chapter. These objectives are drawn from the Cambridge IGCSE syllabus. About the authors David Rayner is a highly experienced author. He has taught and examined mathematics for over thirty years and has published a number of leading textbooks on the subject. Jim Fensom has many years of experience teaching and examining mathematics at secondary level. He is currently Mathematics Coordinator at Nexus International School in Singapore. Special thanks to James Nicholson for his contribution to the resources on the support website. What’s on the website? ‘The website that accompanies the book contains a wealth of material to help solidify your understanding of the Cambridge IGCSE International Mathematics course, and to aid revision for your examinations: Worksheets are provided for further practice, They accompany each of the main chapters in the book, and some questions are intended to be more difficult, to challenge you. Revision check will help you track your progress as you consolidate your knowledge of the topic: on the Cambridge IGCSE International Mathematics course. Full worked solutions to each of the examination exercises in the book. Access your support website at www.oxfordsecondary.com/9780198416906 A glossary offers detailed overage of mathematical terminology, and can be edited to include your own notes and definitions ~orpmeememaae Worked solutions a available for selected questions from the examination é in the book. These are in the form of PowerPoint how to approach exam-style questions Fe coelers Rs egted esto shew [overpass Fer exanie,tyoanae teh ta ‘eet you mart the ut ofan eruntet oe Exam preparation is given ina range of materials, covering advice for re the language used in question papers, and tips for avoiding commonly-made errors. ‘To get the most out of the International Mathematics course and the examination, you will need to use a graphic display calculator (GDC). Instructions in this book have been written for the TI-Nspire™ CX Handheld (but will work with any of the Tl-Nspire™ family), for the TI-84 Plus Pocket SE (but will work with any other TI-84 Plus) and for the Casio PRIZM fx-CG10/20 (but will also work with the fx-9860 Gll and other similar models). However, there are a number of popular manufactures and models available, which may be used for your Cambridge IGCSE course. Allleading brands of calculator are capable of performing the same mathematical functions, although their menu structures and the exact name of a function may vary from one to another. Other existing in-built applications should not be used and will gain no credit. Any other applications and programs from external sources are not permitted. ‘This chapter is split into three sections and covers the use of a GDC for each of the above. Instructions are given side-by-side for each of the models shown. Being an efficient user of your GDC is very important in the examination. The GDC will not do the mathematics for you; it will help you to do your mathematics. If you use it resourcefully, it will give you more time in the examination to do other things. As well as the instructions in this chapter, you will also find examples throughout the textbook of applications where you can use the GDC. 1 Using templates in basic calculations GDCs use a method known as MathPrint” or Natural Input and Display” to show mathematics on their screens. The most efficient way to use the calculator is to enter a calculation in the same way that you see it written on paper. By using expression templates, you can do this easily. You can move around templates using the arrow keys on your GDC. 1.1 Fractions . x 4241.75 Consider the calculation 22175 3.63—2.14 Here are the instructions for doing this with a scientific calculator from a textbook written in 2000: Find the bottom line first: 38 (Jaa 6 W949 G19 IAW So, after you calculated the bottom line, you had to store it in the calculator’s memory (M), clear the screen (C), calculate the top line and finally divide the result by the value that you stored in the memory (MR). There was another way you could do the same thing, but using brackets. This was to type: GadeWueCwswua Neither of these methods looks much like the original. ‘Ihe use of templates for things like fractions, exponents and roots has made a huge difference to the use of the calculator. In mathematics examinations in the past, the questions on the quadratic formula and the cosine rule (both fairly complicated formulas) were very often answered incorrectly. This was due to the difficulty of entering the calculation. Now with a template and your GDC, you have no excuse for getting the answer wrong. Example 1 4.24175 3.63 —2.14 Calculate TI-Nspire TI84-Plus Open anew calculator page and | Press atpHa) F1 FRAC and select Enter Run. Matrix mode press (ari) I:n/d and press (#a) > Using your graphic display calculator