Haese Mathematicsspecialists in mathematics publishingEndorsed by Cambridge International ExaminationsCambridgeAdditionalMathematicsO Level (4037)Michael HaeseSandra HaeseMark HumphriesChris SangwinCAMBRIDGE ADDITIONAL MATHEMATICS(0606)(4037)Michael HaeseB.Sc.(Hons.),Ph.D.Sandra HaeseB.Sc.Mark HumphriesB.Sc.(Hons.)Chris SangwinM.A.,M.Sc.,Ph.D.Haese Mathematics152 Richmond Road,Marleston,SA 5033,AUSTRALIATelephone:+61882104666,Fax:+61883541238Email:info@haesemathematics.com.auWeb:www.haesemathematics.com.auNational Library of Australia Card Number ISBN 978-1-921972-42-3C Haese Harris Publications 2014Published by Haese Mathematics152 Richmond Road,Marleston,SA 5033,AUSTRALIAFirst Edition2014Cartoon artwork by John Martin.Cover design by Brian Houston.Artwork by Brian Houston and Gregory Olesinski.Fractal artwork on the cover generated using ChaosPro,http://www.chaospro.de/Computer software by Adrian Blackburn,Ashvin Narayanan,Tim Lee,Linden May,Seth Pink,WilliamPietsch,and Nicole Szymanczyk.Production work by Katie Richer,Gregory Olesinski,and Anna Rijken.Typeset in Australia by Deanne Gallasch and Charlotte Frost.Typeset in Times Roman 10.This textbook and its accompanying CD have beenendorsed by Cambridge International Examinations.Printedin Chinaby Prolong Press Limited.This book is copyright.Except as permitted by the Copyright Act (any fair dealing for the purposes ofprivate study,research,criticism or review),no part of this publication may be reproduced,stored in aretrieval system,or transmitted in any form or by any means,electronic,mechanical,photocopying,recording or otherwise,without the prior permission of the publisher.Enquiries to be made to HaeseMathematics.Copying for educational purposes:Where copies of part or the whole of the book are made under Part VBof the Copyright Act,the law requires that the educational institution or the body that administers it has givena remuneration notice to Copyright Agency Limited (CAL).For information,contact the Copyright AgencyLimited.Acknowledgements:The publishers acknowledge the cooperation of Oxford University Press,Australia,for the reproduction of material originally published in textbooks produced in association withHaese Mathematics.While every attempt has been made to trace and acknowledge copyright,the authors and publishers apologise forany accidental infringement where copyright has proved untraceable.They would be pleased to come to asuitable agreement with the rightful owner.Disclaimer:All the internet addresses (URLs)given in this book were valid at the time of printing.While theauthors and publisher regret any inconvenience that changes of address may cause readers,no responsibilityfor any such changes can be accepted by either the authors or the publisher.FOREWORDThis book has been written to cover the 'Cambridge O Level Additional Mathematics (4037)'and theCambridge IGCSER Additional Mathematics (0606)'courses over a one-year period.These syllabuses enable learners to extend the mathematics skills,knowledge,and understanding developedin the Cambridge IGCSE or O Level Mathematics courses,and use skills in the context of more advancedtechniques.The syllabuses have a Pure Mathematics only content which enables learners to acquire a suitable foundationin mathematics for further study in the subject.Knowledge of the content of the Cambridge IGCSE or OLevel Mathematics syllabus (or an equivalent syllabus)is assumed.Learners who successfully complete these courses gain lifelong skills,including:the further development of mathematical concepts and principlesan ability to solve problems,present solutions logically,and interpret results.This book is an attempt to cover,in one volume,the content outlined in the Cambridge O Level AdditionalMathematics (4037)and Cambridge IGCSE Additional Mathematics (0606)syllabuses.The book can beused as a preparation for GCE Advanced Level Mathematics.The book has been endorsed by Cambridge.To reflect the principles on which the course is based,we have attempted to produce a book and CD packagethat embraces understanding and problem solving in order to give students different learning experiences.Review exercises appear at the end of each chapter.Answers are given at the end of the book,followed by anindex.The interactive CD contains Self Tutor software (see p.5),geometry and graphics software,demonstrations and simulations.The CD also contains the text of the book so that students can load it on ahome computer and keep the textbook at school.The examinations for Cambridge Additional Mathematics are in the form of two papers.Many of theproblems in this textbook have been written to reflect the style of the examination questions.The questions,worked solutions and comments that appear in the book and CD were written by the authors.The book can be used as a scheme of work but it is expected that the teacher will choose the order of topics.Exercises in the book range from routine practice and consolidation of basic skills,to problem solvingexercises that are quite demanding.In this changing world of mathematics education,we believe that the contextual approach shown in this bookwill enhance the students'understanding,knowledge and appreciation of mathematics,and its universalapplication.We welcome your feedback.Email:info(@haesemathematics.com.auWeb:www.haesemathematics.com.auPMH,SHH,MH,CS