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  • for the international student Mathematics

    Specialists in mathematics publishing

    HAESE HARRIS PUBLICATIONS&

    Pre-Diploma SL and HL (MYP 5 Plus)

    Presumed Knowledge for SL and HL courses

    Pamela Vollmar

    Edward Kemp

    Robert Haese

    Sandra Haese

    Mark Humphries

    Chris Sangwin

    Michael Haese

    for use with IB Middle Years

    Programme

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    symbol_pp s meswti

    second edition

    IB10 plus 2nd ed

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  • MATHEMATICS FOR THE INTERNATIONAL STUDENT Pre-Diploma SL and HL (MYP 5 Plus) second edition

    Presumed Knowledge for SL and HL courses

    Pamela Vollmar B.Sc.(Hons.), PGCE.

    Edward Kemp B.Sc., M.A.

    Michael Haese B.Sc.(Hons.), Ph.D.

    Robert Haese B.Sc.

    Sandra Haese B.Sc.

    Mark Humphries B.Sc.(Hons.)

    Chris Sangwin M.A., M.Sc., Ph.D.

    Haese & Harris Publications

    3 Frank Collopy Court, Adelaide Airport, SA 5950, AUSTRALIA

    Telephone: +61 8 8355 9444, Fax: + 61 8 8355 9471

    Email:

    National Library of Australia Card Number & ISBN 978-1-876543-89-1

    © Haese & Harris Publications 2008

    Published by Raksar Nominees Pty Ltd

    3 Frank Collopy Court, Adelaide Airport, SA 5950, AUSTRALIA

    First Edition 2006

    Second Edition 2008 2008, 2010, 2011

    Cartoon artwork by John Martin. Artwork by Piotr Poturaj and David Purton.

    Cover design by Piotr Poturaj.

    Computer software by David Purton, Thomas Jansson and Troy Cruickshank.

    Typeset in Australia by Susan Haese (Raksar Nominees). Typeset in Times Roman 10 /11

    The textbook and its accompanying CD have been developed independently of the International

    Baccalaureate Organization (IBO). The textbook and CD are in no way connected with, or endorsed by,

    the IBO.

    . 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.

    : 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.

    : The publishers acknowledge the cooperation of Oxford University Press, Australia,

    for the reproduction of material originally published in textbooks produced in association with

    Haese & Harris Publications.

    While every attempt has been made to trace and acknowledge copyright, the authors 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.

    : 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.

    Reprinted

    \Qw_ \Qw_

    This book is copyright

    Copying for educational purposes

    Acknowledgements

    Disclaimer

    info@haesemathematics.com.au

    www.haesemathematics.com.auWeb:

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  • Pre-Diploma SL and HL (MYP 5 Plus) second edition is an attempt to cover, in one volume, the Presumed Knowledge required for the IB Diploma courses ‘Mathematics SL’ and ‘Mathematics HL’. This book may

    also be used as a general textbook at about 10 Grade level in classes where students complete a rigorous

    course in preparation for the study of mathematics at a high level in their final two years of high school.

    Feedback from teachers using the first edition suggested that while it provided satisfactory preparation for

    prospective Mathematics SL students, several sections needed to be more rigorous to prepare students

    thoroughly for Mathematics HL. The first edition has been revised throughout and the highlighted topics in

    the table of contents show at a glance the main areas that have been substantially revised and extended.

    In terms of the IB Middle Years Programme (MYP), this book does not pretend to be a definitive course. In

    response to requests from teachers who use ‘Mathematics for the International Student’ at IB Diploma level,

    we have endeavoured to interpret their requirements, as expressed to us, for a book that will prepare students

    for Mathematics SL and Mathematics HL. We have developed this book independently of the International

    Baccalaureate Organization (IBO) in consultation with experienced teachers of IB Mathematics. The text is

    not endorsed by the IBO.

    It is not our intention that each chapter be worked through in full. Teachers must select carefully, according to

    the abilities and prior knowledge of their students, to make the most efficient use of time and give as

    thorough coverage of content as possible.

    Three additional chapters appear on the CD as printable pages:

    Chapter 23: Counting and probability

    Chapter 24: Locus

    Chapter 25: Networks

    These chapters were selected because the content could be regarded as extension beyond what might be seen

    as an essential prerequisite for IB Diploma mathematics.

    We understand the emphasis that the IB MYP places on the five Areas of Interaction and in response there

    are links on the CD to printable pages which offer ideas for projects and investigations to help busy teachers

    (see p. 5).

    Frequent use of the interactive features on the CD should nurture a much deeper understanding and

    appreciation of mathematical concepts. The inclusion of our new software (see p. 4) is intended to

    help students who have been absent from classes or who experience difficulty understanding the material.

    The book contains many problems to cater for a range of student abilities and interests, and efforts have been

    made to contextualise problems so that students can see the practical applications of the mathematics they are

    studying.

    We welcome your feedback.

    th

    PV, EK, PMH, RCH, SHH, MH, CS

    Acknowledgements

    The authors and publishers would like to thank all those teachers who have read proofs and offered advice

    and encouragement.

    Among those who submitted courses of study for Middle Years Mathematics and who offered to read and

    comment on the proofs of the textbook are: Margie Karbassioun, Kerstin Mockrish, Todd Sharpe, Tamara

    Jannink, Yang Zhaohui, Cameron Hall, Brendan Watson, Daniel Fosbenner, Rob DeAbreu, Philip E.

    Hedemann, Alessandra Pecoraro, Jeanne-Mari Neefs, Ray Wiens, John Bush, Jane Forrest, Dr Andrzej Cichy,

    William Larson, Wendy Farden, Chris Wieland, Kenneth Capp, Sara Locke, Rae Deeley, Val Frost, Mal

    Coad, Pia Jeppesen, Wissam Malaeb, Eduardo Betti, Robb Kitcher, Catherine Krylova, Julie Tan, Rosheen

    Gray, Jan-Mark Seewald, Nicola Cardwell, Tony Halsey, Ros McCabe, Alison Ryan, Mark Bethune, Keith

    Black, Vivienne Verschuren, Mark Willis, Curtis Wood, Ufuk Genc, Fran O’Connor. Special thanks to

    Heather Farish. To anyone we may have missed, we offer our apologies.

    The publishers wish to make it clear that acknowledging these individuals does not imply any endorsement of

    this book by any of them, and all responsibility for the content rests with the authors and publishers.

    Email: info@haesemathematics.com.au

    Web: www.haesemathematics.com.au

    Self Tutor

    FOREWORD

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  • Simply ‘click’ on the (or anywhere in the example box) to access the worked

    example, with a teacher’s voice explaining each step necessary to reach the answer.

    Play any line as often as you like. See how the basic processes come alive using

    movement and colour on the scree

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