mathematics for year 12 specialist mathematics Robert Haese Sandra Haese Michael Haese Roger Dixon Jon Roberts Michael Teubner Anthony Thompson Haese & Harris Publications SPECIALIST MATHEMATICS MATHEMATICS FOR YEAR 12 Robert Haese Sandra Haese Michael Haese Roger Dixon Jon Roberts Michel Teubner Anthony Thompson B.Sc. B.Sc. B.Sc.Hons. B.Ed. B.Sc.Hons.(Ma.Sc.), Dip.Ed. B.Sc., Ph.D. B.Sc., Dip.T, Dip.Ed., Grad.Dip.Ed.Admin. Haese & Harris Publications 3 Frank Collopy Court, Adelaide Airport SA 5950 Telephone: (08) 8355 9444, Fax: (08) 8355 9471 email:
[email protected] National Library of Australia Card Number & ISBN 1 876543 79 5 © Haese & Harris Publications Published by Raksar Nominees Pty Ltd, 3 Frank Collopy Court, Adelaide Airport SA 5950 First Edition 2002 Cartoon artwork by John Martin. Artwork by Piotr Poturaj, Joanna Poturaj and David Purton Cover design by Piotr Poturaj. Cover photography Piotr Poturaj Computer software by David Purton and Mark Foreman Typeset in Australia by Susan Haese (Raksar Nominees). Typeset in Times Roman 10\Qw_ /11\Qw_ This book is copyright. Except as permitted by the Copyright Act (any fair dealing for the purposes of private study, research, criticism or review), no part of this publication may be reproduced, stored in a retrieval 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 Haese & Harris Publications. Copying for educational purposes: Where copies of part or the whole of the book are made under Part VB of the Copyright Act, the law requires that the educational institution or the body that administers it has given a remuneration notice to Copyright Agency Limited (CAL). For information, contact the Copyright Agency Limited. While every attempt has been made to trace and acknowledge copyright, the author and publishers apologise for any accidental infringement where copyright has proved untraceable. They would be pleased to come to a suitable agreement with the rightful owner. Disclaimer: All the internet addresses (URL’s) given in this book were valid at the time of printing. While the authors and publisher regret any inconvenience that changes of address may cause readers, no responsibility for any such changes can be accepted by either the authors or the publisher. FOREWORD Mathematics for Year 12 Specialist Mathematics is our interpretation of the concepts outlined in the Stage 2 Mathematics Curriculum Statement. It is not our intention to define the course, and teachers are encouraged to use other resources. Our package is a textbook with an interactive CD. The CD displays the contents of the textbook plus many interactive features such as simulations, computer demonstrations, video clips, graphing packages, spreadsheets etc to stimulate the interest of students and assist their teachers. The book is language rich and technology rich. Some exercises are simply designed to build skills, but every effort has been made to contextualise problems to help students see the everyday uses and practical application of the mathematics they are studying. The book contains many problems, from basic to the advanced, to cater for a wide range of student abilities and interests. Much emphasis has been placed on the gradual development of concepts with appropriate worked examples. However, we have provided material for those who look towards further studies or applications of mathematics for their career choices. It is not our intention that each chapter should be worked through in full. Time constraints will not allow for this. Consequently, teachers mus