11
Ross
Brodie
Stephen
Swift
NewQMaths
B
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00 NQM11B SB TXT.prelim.indd 1
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
copyright herein may be reproduced, transmitted, stored or used in any form or by any means graphic, electronic, or mechanical,
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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.
1 2 3 4 5 6 7 12 11 10 09 08
00 NQM11B SB TXT.prelim.indd 2
iii
Contents
Contents
Introduction vi
Symbols and abbreviations
viii
1
Triangle applications
1
1.1 Using right-angled triangles 2
1.2 Applying directions and bearings 9
1.3 The sine rule 12
1.4 The cosine rule 16
1.5 Trig applications 20
1.6 Working in three dimensions 28
Chapter summary 34
Chapter review 35
2
Working with data
37
2.1 Collecting statistical data 38
2.2 Organising and displaying information 51 2.3 Finding data positions and centres 63
2.4 Measuring spread 73
2.5 Analysing data 79
Chapter summary 87
Chapter review 89
3
Straight line functions
93
3.1 Review of linear equations 94
3.2 Functions and relations 102
3.3 Sequences and progressions 109
3.4 Gradient and intercepts of a linear function 117 3.5 Equations of linear functions 126
3.6 Distances and midpoints 138
3.7 Finding simultaneous solutions of linear functions 143
Chapter summary 149
Chapter review 151
4
Waves and functions
155
4.1 Features of periodic functions 156 4.2 Predictions using periodic functions 162 4.3 Models of periodic functions 166
Chapter summary 170
Chapter review 171
00 NQM11B SB TXT.prelim.indd iii
iv New QMaths 11B
5
Gradients of curves
173
5.1 Finding average rates of change 174 5.2 Finding instantaneous rates of change 188 5.3 Practical applications of rates of change 194 5.4 Mathematical applications of rates of change 199
Chapter summary 208
Chapter review 210
6
Parabolic functions
215
6.1 Solving quadratic equations 216 6.2 Algebraic solution of quadratics 223 6.3 Sketching quadratic functions 232 6.4 Finding simultaneous solutions 241
Chapter summary 246
Chapter review 247
7
Differential calculus
251
7.1 Finding derivatives as limits 252 7.2 Rules for fi nding derivatives 263 7.3 Practical applications of derivatives 271 7.4 Mathematical applications of derivatives 276
Chapter summary 285
Chapter review 286
8
Applying trigonometric functions
289
8.1 Degrees and radians 290
8.2 Trigonometric ratios and the unit circle 295
8.3 Trigonometric graphs 306
8.4 Trigonometric functions and applications 309
Chapter summary 320
Chapter review 322
9
Growth, decay and logarithms
325
9.1 Exponential functions 326
9.2 Solving exponential equations 340
9.3 Logarithms 346
9.4 Modelling using exponential functions 350
Chapter summary 354
Chapter review 355
00 NQM11B SB TXT.prelim.indd iv
Chapter Review
v Contents
10
Working with probability
359
10.1 Review of probability 360
10.2 Finding probabilities 367
10.3 Using binomial probability 374
Chapter summary 381
Chapter review 382
11
Reversing derivatives
385
11.1 Finding indefi nite integrals 386 11.2 Graphing indefi nite integrals 390 11.3 Applying indefi nite integrals 393
Chapter summary 396
Chapter review 397
Appendix
398
Answers
402
Index 438
00 NQM11B SB TXT.prelim.indd v
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-ROM
The 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.
00 NQM11B SB TXT.prelim.indd vi
vii Introduction
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
00 NQM11B SB TXT.prelim.indd vii
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
兺 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
䉭 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
僆 is a member of
Acknowledgements
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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.
00 NQM11B SB TXT.prelim.indd viii
