MATHEMATICS STANDARD LEVEL

3RD EDITION 3rd Imprint

Series editor: Fabio Cirrito Contributing author

Patrick Tobin

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MATHEMATICS Standard Level

Copyright ©Patrick Tobin, Key-Strokes Pty Ltd, Mifasa Pty Ltd. First published in 1997 by IBID Press 2nd Edition published in 1999 by IBID Press, 3rd Edition published in 2004 (2nd Imprint published in 2005) by IBID Press. Reprinted 2007 Published by IBID Press, Victoria. Library Catalogue:

Cirrito Fabio Editor., Tobin 1. Mathematics, 2. International Baccalaureate. Series Title: International Baccalaureate in Detail ISBN: 1 876659 17 3 (10-digit) 978 1 876659 17 2 (13-digit) All rights reserved except under the conditions described in the Copyright Act 1968 of Australia and subsequent amendments. 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 of the publishers. While every care has been taken to trace and acknowledge copyright, the publishers tender their apologies for any accidental infringement where copyright has proved untraceable. They would be pleased to come to a suitable arrangement with the rightful owner in each case. This book has been developed independently of the International Baccalaureate Organisation (IBO). The text is in no way connected with, or endorsed by, the IBO. “This publication is independently produced for use by teachers and students. Although references have been reproduced with permission of the VCAA the publication is in no way connected or endorsed by the VCAA.” We also wish to thank the Incorporated Association of Registered Teachers of Victoria for granting us permission to reproduced questions from their October Examination Papers. Cover design by Adcore Creative. Published by IBID Press, at www.ibid.com.au For further information contact fabio@ibid.com.au Printed by SHANNON Books, Australia.

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PREFACE TO 3RD EDITION

The 3rd edition of the Mathematics Standard Level text has been completely revised and updated. Sections of the previous two editions are still present, but much has happened to improve the text both in content and accuracy. In response to the many requests and suggestions from teachers worldwide the text was extensively revised. There are more examples for students to refer to when learning the subject matter for the ﬁrst time or during their revision period. There is an abundance of well-graded exercises for students to hone their skills. Of course, it is not expected that any one student work through every question in this text - such a task would be quite a feat. It is hoped then that teachers will guide the students as to which questions to attempt. The questions serve to develop routine skills, reinforce concepts introduced in the topic and develop skills in making appropriate use of the graphics calculator. The text has been written in a conversational style so that students will ﬁnd that they are not simply making reference to an encyclopedia ﬁlled with mathematical facts, but rather ﬁnd that they are in some way participating in or listening in on a discussion of the subject matter. Throughout the text the subject matter is presented using graphical, numerical, algebraic and verbal means whenever appropriate. Classical approaches have been judiciously combined with modern approaches reﬂecting new technology - in particular the use of the graphics calculator. The book has been speciﬁcally written to meet the demands of the Mathematics Standard Level course and has been pitched at a level that is appropriate for students studying this subject. The book presents an extensive coverage of the syllabus and in some areas goes beyond what is required of the student. Again, this is for the teacher to decide how best to use these sections. Sets of revision exercises are included in the text. Many of the questions in these sets have been aimed at a level that is on par with what...