11

Ross Brodie Stephen Swift NewQMaths

B

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New QMaths 11B

3rd Edition

Ross Brodie

Stephen Swift

Publishing editor: Kirstie Pickett

Developmental editor: Roger Walter

Editor: Anna Beth McCormack

Senior designer: Sue Dani and Santiago Villamizar

Cover designer: Sue Dani

Cover: Corbis / O. Alamany & E. Vicens

Text designer: Sue Dani

Text illustrator: Paulene Meyer

Photo research: Corrina Tauschke

Production controller: Jo Vraca

Typeset in 11/14pt Esperanto by Phillip Idczak and Amanda

Griffin

Any URLs contained in this publication were checked for

currency during the production process. Note, however,

that the publisher cannot vouch for the ongoing currency

of URLs.

© 2008 R Brodie, S Swift

ALL RIGHTS RESERVED. No part of this work covered by the

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For permission to use material from this text

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National Library of Australia Cataloguing-in-Publication Data

Ross Brodie, Stephen Swift

New QMaths 11B

For secondary school age.

ISBN 9780170136570

Mathematics - Textbooks.

510

Cengage Learning Australia

Level 7, 80 Dorcas Street

South Melbourne, Victoria Australia 3205

Cengage Learning New Zealand

Unit 4B Rosedale Office Park

331 Rosedale Road, Albany, North Shore 0632, NZ

For learning solutions, visit cengage.com.au

Printed in China by C&C Offset Printing Co Ltd.

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iii

Contents

Contents

Introduction vi

Symbols and abbreviations viii

1 Triangle applications 11.1 Using right-angled triangles 21.2 Applying directions and bearings 91.3 The sine rule 121.4 The cosine rule 161.5 Trig applications 201.6 Working in three dimensions 28Chapter summary 34Chapter review 35

2 Working with data 372.1 Collecting statistical data 382.2 Organising and displaying information 512.3 Finding data positions and centres 632.4 Measuring spread 732.5 Analysing data 79Chapter summary 87Chapter review 89

3 Straight line functions 933.1 Review of linear equations 943.2 Functions and relations 1023.3 Sequences and progressions 1093.4 Gradient and intercepts of a linear function 1173.5 Equations of linear functions 1263.6 Distances and midpoints 1383.7 Finding simultaneous solutions of linear functions 143Chapter summary 149Chapter review 151

4 Waves and functions 155

4.1 Features of periodic functions 1564.2 Predictions using periodic functions 1624.3 Models of periodic functions 166Chapter summary 170Chapter review 171

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iv New QMaths 11B

5 Gradients of curves 1735.1 Finding average rates of change 1745.2 Finding instantaneous rates of change 1885.3 Practical applications of rates of change 1945.4 Mathematical applications of rates of change 199Chapter summary 208Chapter review 210

6 Parabolic functions 2156.1 Solving quadratic equations 2166.2 Algebraic solution of quadratics 2236.3 Sketching quadratic functions 2326.4 Finding simultaneous solutions 241Chapter summary 246Chapter review 247

7 Differential calculus 2517.1 Finding derivatives as limits 2527.2 Rules for fi nding derivatives 2637.3 Practical applications of derivatives 2717.4 Mathematical applications of derivatives 276Chapter summary 285Chapter review 286

8 Applying trigonometric functions 2898.1 Degrees and radians 2908.2 Trigonometric ratios and the unit circle 2958.3 Trigonometric graphs 3068.4 Trigonometric functions and applications 309Chapter summary 320Chapter review 322

9 Growth, decay and logarithms 3259.1 Exponential functions 3269.2 Solving exponential equations 3409.3 Logarithms 3469.4 Modelling using exponential functions 350Chapter summary 354Chapter review 355

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Chapter Review

vContents

10 Working with probability 35910.1 Review of probability 36010.2 Finding probabilities 36710.3 Using binomial probability 374Chapter summary 381Chapter review 382

11 Reversing derivatives 38511.1 Finding indefi nite integrals 38611.2 Graphing indefi nite integrals 39011.3 Applying indefi nite integrals 393Chapter summary 396Chapter review 397

Appendix 398

Answers 402

Index 438

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vi New QMaths 11B

Introduction

The New QMaths B textbooks are designed to assist students to build competence in the advanced computational and algebraic methods and procedures they need for further study and lifelong learning, to increase mathematical modelling and problem-solving skills, and to provide a basis for sound mathematical arguments and decisions. Students are encouraged to further develop key competencies in contexts that arise naturally from the general objectives and learning experiences of the subject.

New QMaths 11B provides ample opportunity for students to develop skills and demonstrate performance in the dimensions of communication and justifi cation, knowledge and procedures, use of technology, use of mathematical instruments and modelling and problem solving. It is a gender-inclusive and culturally inclusive text that accommodates a variety of student learning styles through a modern approach that will engage students and provide impetus for the affective objectives of the Mathematics B syllabus. The Mathematics B texts are sequenced to allow for the systematic development of mathematical concepts through the course and are designed to complement the sequencing in the New QMaths C textbooks for those students studying both subjects.

The New QMaths B textbooks provide considerable support for the use of appropriate technologies and application of concepts in a variety of situations from life-related to purely abstract tasks. Students are provided with opportunities to demonstrate initiative and there is variation from simple, single-step tasks to ones that are complex in nature.

What you will fi nd in New QMaths 11B and the CD-ROMThe textbook includes:

■ modern full-colour layout to help you to distinguish between examples, exercises, defi nitions and investigations

■ clear defi nitions and explanations of important terms and methods

■ artwork, photographs and maps in colour for maximum clarity and appeal

■ new content and exercises to improve development of concepts and skills

■ extensive explanations to help you to get the most from graphics calculators

■ detailed instructions in the text for the Casio and Texas Instruments graphics calculators and on the CD-ROM for the Sharp graphics calculator; the authors have assumed that calculators are in default settings—different results may be obtained if this is not the case

■ explanations of the use of spreadsheets and other technology

■ modelling and problem-solving practice within exercises to develop concepts beyond basic knowledge and procedures

■ a chapter summary and chapter review at the end of each chapter to assist in revision for end-of-term and end-of-semester assessment; the review questions are labelled to indicate the exercises where concepts were introduced

■ a clear linkage from the text to the syllabus at the beginning of each chapter.

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viiIntroduction

The CD-ROM includes:The entire student text with hot-link icons from the text to the additional features shown below.

■ Additional exercises (with answers) for every exercise to give opportunities for extra practice of concepts

■ Graphics calculator programs in downloadable form

■ Graphics calculator instructions for the Sharp graphics calculator

■ Extra material as background or extension for interested students and their teachers

■ Alternative solutions to some examples

■ Detailed proofs of important theorems

■ Spreadsheets for investigations and exercises, including interactive spreadsheets

■ A complete syllabus guide for Years 11 and 12 with appropriate sections linked to chapter openings

■ Teacher notes and copy masters

■ Hot-links from individual review questions back to the exercise where the concept was introduced

■ An extensive glossary explaining important terms with examples

Additional Exercise

Calculator Program

Extra Material

Spreadsheet

Syllabus Guide

Chapter 3.0

Ex 3.11

Teacher Notes

Calculator Instructions

Alternative Method

Detailed Proof

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viii New QMaths 11B

Symbols and abbreviations

While every effort has been made to ensure that calculator instructions are accurate, results may vary when graphics calculators are not set in default mode or as a result of manufacturers’ changes.

= is equal to

≠ is not equal to

≈ is approximately equal to

√ square root

% percentage

� is less than

� is greater than

� is less than or equal to

� is greater than or equal to

� plus or minus

� summation

Q3 3rd quartile

P87 87th percentile

D4 4th decile

1 : 650 000 at a scale of 1 to 650 000

π pi (approximately 3.141 592 7)

52°15′42′′ 52 degrees 15 minutes 42 seconds

∠ angle

� triangle

x mean of x values

σ standard deviation

5 : 8 ratio of 5 to 8

/ per

157°M magnetic bearing of 157°

123°T true bearing of 123°

LHS left-hand side

RHS right-hand side

� is a member of

AcknowledgementsWe would like to thank the following for permission to reproduce copyright material:

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Every effort has been made to trace and acknowledge copyright. However, if any infringement has occurred the publishers tender their apologies and invite the copyright holders to contact them.

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