Maths Quest 11 Mathematical Methods CAS Prelims
Content
VCE MATHEMATICS UNITS 1 & 2
M ATHS QUEST QU EST 11 Mathematical Methods Metho ds CAS C AS TI-NSPIRE 2.0 EDITION
N O I T I D E D N 2
VCE MATHEMATICS UNITS 1 & 2
MATHS QUEST 11 Mathematical Methods CAS TI-NSPIRE 2.0 EDITION ROBYN WILLIAMS
NICOLAOS KARANIKOLAS
GAYLE ROBERTS
JENNIFER NOLAN
KYLIE BOUCHER
GEOFF PHILLIPS
CONTRIBUTING AUTHORS ROGER WANDER | DOUGLAS SCOTT | MARK BARNES HOWARD LISTON
|
ANDREW MENTLIKOWSKI
|
SUE STOCKDALE
SUPPORT MATERIAL JOHN DOWSEY
|
DENNIS FITZGERALD | EMILY HUI | CAROLINE MEWS | VINOD NARAYAN
PETER SWAIN | DAVID TYNAN
|
IAN YOUNGER | WAYNE YOUNGS
SIMONE RICHARDSON | DINA ANTONIOU | NORRENE HILL
N O I T I D E D N 2
Second revised edition published 2010 by John Wiley & Sons Australia, Ltd 42 McDougall Street, Milton, Qld 4064 First edition published 2009 Typeset in 10/12pt Times LT © John Wiley & Sons Australia, Ltd 2009, 2010 The moral rights of the authors have been asserted. National Library of Australia Cataloguing-in-Publication data
Title:
Edition: ISBN:
Notes: Target Audience: Subjects: Other Authors/ Contributors: Dewey Number:
Maths quest 11 mathematical methods CAS TI-Nspire 2.0 edition / Robyn Williams . . . [et al.]. 2nd ed. 978 1 7424 6447 3 (student pbk.) 978 1 7424 6448 0 (student ebook) 978 1 7424 6450 3 (teacher pbk.) 978 1 7424 6451 0 (teacher ebook) Includes index. For secondary school age. Mathematics — Textbooks. Mathematics — Problems exercises, etc. Williams, Robyn (Robyn Ellen) 1967– 510
Reproduction and communication for educational purposes The Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10% of the pages of this work, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that the educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL). Reproduction and communication for other purposes Except as permitted under the Act (for example, a fair dealing for the purposes of study, research, criticism or review), no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher.
Screenshots from TI-Nspire reproduced with permission of Texas Instruments Illustrated by Aptara Typeset in India by Aptara Printed in Singapore by Craft Print International Ltd 10 9 8 7 6 5 4 3 2
Contents 2H
Introduction ix About eBookPLUS xi Acknowledgements xii
2I
CHAPTER 1
Linear functions 1A
1B
1C
1D
1E
1F
1G
1H
2J
1
Solving linear equations and inequations 1 Exercise 1A 5 Rearrangement and substitution 6 Exercise 1B 9 Gradient of a straight line 11 Exercise 1C 13 Sketching linear functions 16 Exercise 1D 19 Simultaneous equations 21 Exercise 1E 24 Finding the equation of a straight line 25 Exercise 1F 27 Distance between two points and midpoint of a segment 29 Exercise 1G 30 Linear modelling 32 Exercise 1H 34
Summary 36 Chapter review 37 eBookPLUS activities
42
Quadratic functions
2B
2C
2D
2E
2F
2G
2L
Summary 102 Chapter review 104 eBookPLUS activities 108 CHAPTER 3
Cubic and quartic functions 3A
3B
3C
3D
CHAPTER 2
2A
2K
3E
43
Polynomials 43 Exercise 2A 45 Expanding quadratic expressions 46 Exercise 2B 48 Factorising quadratic expressions 49 Exercise 2C 52 Factorising by completing the square 53 Exercise 2D 56 Solving quadratic equations — Null Factor Law 56 Exercise 2E 59 Solving quadratic equations — completing the square 61 Exercise 2F 64 The quadratic formula 65 Exercise 2G 68
The discriminant 70 Exercise 2H 74 Graphs of quadratic functions as power functions (turning point form) 75 Exercise 2I 78 Graphs of quadratic functions (intercepts method) 80 Exercise 2J 89 Using technology to solve quadratic equations 91 Exercise 2K 94 Simultaneous quadratic and linear equations 95 Exercise 2L 100
3F
3G
3H
3I
3J
3K
3L
109
Expanding 109 Exercise 3A 111 Long division of polynomials 111 Exercise 3B 114 Polynomial values 115 Exercise 3C 117 The remainder and factor theorems 118 Exercise 3D 120 Factorising polynomials 121 Exercise 3E 123 Sum and difference of two cubes 124 Exercise 3F 125 Solving polynomial equations 126 Exercise 3G 129 Cubic graphs — intercepts method 129 Exercise 3H 134 Quartic graphs — intercepts method 136 Exercise 3I 138 Graphs of cubic functions in power function form 139 Exercise 3J 142 Domain, range, maximums and minimums 143 Exercise 3K 146 Modelling using technology 148 Exercise 3L 150
Acknowledgements The authors and publisher would like to thank the following copyright holders, organisations and individuals for their assistance and for permission to reproduce copyright material in this book.
Images • Coo-ee Picture Library: p. 309 • Corbis Australia: p. 35 (left)/© Corbis/John & Loraine Carnemolla; p. 35 (right)/Corbis/Robert Landau; p. 149/© Corbis/Gary Bell; p. 321/© Corbis; p. 529/Corbis/David Woods • Corbis Royalty Free: p. 70/© Corbis Corporation; p. 491/© Corbis Images; p. 547/© Jack Hollingsworth/Corbis • Digital Stock: pp. 11 (right), 214; pp. 11 (left), 95, 148 (bottom), 360, 449 (right), 472, 558 (bottom)/© Digital Stock/ Corbis Corporation • ImageState: p. 465; p. 507/© John Foxx Images • Image 100, p. 270 (bottom) • Image Source: p. 256 (bottom) • iStockphoto: p. 170 (bottom left)/© iStockphoto.com/ Adnan Ahmad; p. 173/© iStockphoto.com/Tim McCaig • John Wiley & Sons Australia: pp. 335, 554 (left bottom, left top, right bottom, right centre)/© John Wiley & Sons Australia/ Photo by Renee Bryon; pp. 454, 495, 558 (top)© John Wiley & Sons Australia/Malcolm Cross; p. 537 (bottom)/© John Wiley & Sons Australia /Taken by Jo Patterson • Newspix, p. 327/ Newspix/Robert McKell; p. 410/Newspix/Lannon Harley; p. 449 (left)/Newspix/AFP • Photodisc: pp. 31 (top), 41, 44, 46, 94, 100, 148 (top), 170 (bottom centre), 170 (bottom right), 175, 212, 213, 254, 255, 256 (top), 258, 270 (top), 312, 313, 383, 387, 394, 451, 452, 471, 475, 476, 490, 512, 525, 530, 538, 544, 559, 575 • Photolibrary: p. 31 (bottom); p. 34/ © photolibrary.com/Edward Cross; p. 226/© photolibrary.com/ Sydney/SPL/CNRI • Photolibrary Royalty Free: p. 15/© Huntstock/Photolibrary Inc. • Shutterstock, p. 170 (top left)/© 2009 Used under license from Shutterstock.com; p. 320/© Patricia Hofmeester, 2009 Used under license from Shutterstock.com; p. 377/© Kalim, 2009 Used under license from Shutterstock.com; p. 485/© Andrejs Pidjass, 2009 Used under license from Shutterstock.com; p. 537 (top)/© ronfromyork, 2009 Used under license from Shutterstock.com; p. 554 (right top)/© Lincoln Rogers, 2009 Used under license from Shutterstock.com; p. 571/© Lario Tus, 2009 Used under license from Shutterstock.com • Stockbyte: pp. 170 (top right), 496 • Viewnder Australia Photo Library: p. 215
Text © VCAA All Victorian Curriculum and Assessment Authority material has been used with permission. For more information go to www.vcaa.vic.edu.au./ Every effort has been made to trace the ownership of copyright material. Information that will enable the publisher to rectify any error or omission in subsequent editions will be welcome. In such cases, please contact the Permissions Section of John Wiley & Sons Australia, Ltd.
M ATHS QUEST QU EST 11 Mathematical Methods Metho ds CAS C AS TI-NSPIRE 2.0 EDITION
N O I T I D E D N 2
VCE MATHEMATICS UNITS 1 & 2
MATHS QUEST 11 Mathematical Methods CAS TI-NSPIRE 2.0 EDITION ROBYN WILLIAMS
NICOLAOS KARANIKOLAS
GAYLE ROBERTS
JENNIFER NOLAN
KYLIE BOUCHER
GEOFF PHILLIPS
CONTRIBUTING AUTHORS ROGER WANDER | DOUGLAS SCOTT | MARK BARNES HOWARD LISTON
|
ANDREW MENTLIKOWSKI
|
SUE STOCKDALE
SUPPORT MATERIAL JOHN DOWSEY
|
DENNIS FITZGERALD | EMILY HUI | CAROLINE MEWS | VINOD NARAYAN
PETER SWAIN | DAVID TYNAN
|
IAN YOUNGER | WAYNE YOUNGS
SIMONE RICHARDSON | DINA ANTONIOU | NORRENE HILL
N O I T I D E D N 2
Second revised edition published 2010 by John Wiley & Sons Australia, Ltd 42 McDougall Street, Milton, Qld 4064 First edition published 2009 Typeset in 10/12pt Times LT © John Wiley & Sons Australia, Ltd 2009, 2010 The moral rights of the authors have been asserted. National Library of Australia Cataloguing-in-Publication data
Title:
Edition: ISBN:
Notes: Target Audience: Subjects: Other Authors/ Contributors: Dewey Number:
Maths quest 11 mathematical methods CAS TI-Nspire 2.0 edition / Robyn Williams . . . [et al.]. 2nd ed. 978 1 7424 6447 3 (student pbk.) 978 1 7424 6448 0 (student ebook) 978 1 7424 6450 3 (teacher pbk.) 978 1 7424 6451 0 (teacher ebook) Includes index. For secondary school age. Mathematics — Textbooks. Mathematics — Problems exercises, etc. Williams, Robyn (Robyn Ellen) 1967– 510
Reproduction and communication for educational purposes The Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10% of the pages of this work, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that the educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL). Reproduction and communication for other purposes Except as permitted under the Act (for example, a fair dealing for the purposes of study, research, criticism or review), no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher.
Screenshots from TI-Nspire reproduced with permission of Texas Instruments Illustrated by Aptara Typeset in India by Aptara Printed in Singapore by Craft Print International Ltd 10 9 8 7 6 5 4 3 2
Contents 2H
Introduction ix About eBookPLUS xi Acknowledgements xii
2I
CHAPTER 1
Linear functions 1A
1B
1C
1D
1E
1F
1G
1H
2J
1
Solving linear equations and inequations 1 Exercise 1A 5 Rearrangement and substitution 6 Exercise 1B 9 Gradient of a straight line 11 Exercise 1C 13 Sketching linear functions 16 Exercise 1D 19 Simultaneous equations 21 Exercise 1E 24 Finding the equation of a straight line 25 Exercise 1F 27 Distance between two points and midpoint of a segment 29 Exercise 1G 30 Linear modelling 32 Exercise 1H 34
Summary 36 Chapter review 37 eBookPLUS activities
42
Quadratic functions
2B
2C
2D
2E
2F
2G
2L
Summary 102 Chapter review 104 eBookPLUS activities 108 CHAPTER 3
Cubic and quartic functions 3A
3B
3C
3D
CHAPTER 2
2A
2K
3E
43
Polynomials 43 Exercise 2A 45 Expanding quadratic expressions 46 Exercise 2B 48 Factorising quadratic expressions 49 Exercise 2C 52 Factorising by completing the square 53 Exercise 2D 56 Solving quadratic equations — Null Factor Law 56 Exercise 2E 59 Solving quadratic equations — completing the square 61 Exercise 2F 64 The quadratic formula 65 Exercise 2G 68
The discriminant 70 Exercise 2H 74 Graphs of quadratic functions as power functions (turning point form) 75 Exercise 2I 78 Graphs of quadratic functions (intercepts method) 80 Exercise 2J 89 Using technology to solve quadratic equations 91 Exercise 2K 94 Simultaneous quadratic and linear equations 95 Exercise 2L 100
3F
3G
3H
3I
3J
3K
3L
109
Expanding 109 Exercise 3A 111 Long division of polynomials 111 Exercise 3B 114 Polynomial values 115 Exercise 3C 117 The remainder and factor theorems 118 Exercise 3D 120 Factorising polynomials 121 Exercise 3E 123 Sum and difference of two cubes 124 Exercise 3F 125 Solving polynomial equations 126 Exercise 3G 129 Cubic graphs — intercepts method 129 Exercise 3H 134 Quartic graphs — intercepts method 136 Exercise 3I 138 Graphs of cubic functions in power function form 139 Exercise 3J 142 Domain, range, maximums and minimums 143 Exercise 3K 146 Modelling using technology 148 Exercise 3L 150
Acknowledgements The authors and publisher would like to thank the following copyright holders, organisations and individuals for their assistance and for permission to reproduce copyright material in this book.
Images • Coo-ee Picture Library: p. 309 • Corbis Australia: p. 35 (left)/© Corbis/John & Loraine Carnemolla; p. 35 (right)/Corbis/Robert Landau; p. 149/© Corbis/Gary Bell; p. 321/© Corbis; p. 529/Corbis/David Woods • Corbis Royalty Free: p. 70/© Corbis Corporation; p. 491/© Corbis Images; p. 547/© Jack Hollingsworth/Corbis • Digital Stock: pp. 11 (right), 214; pp. 11 (left), 95, 148 (bottom), 360, 449 (right), 472, 558 (bottom)/© Digital Stock/ Corbis Corporation • ImageState: p. 465; p. 507/© John Foxx Images • Image 100, p. 270 (bottom) • Image Source: p. 256 (bottom) • iStockphoto: p. 170 (bottom left)/© iStockphoto.com/ Adnan Ahmad; p. 173/© iStockphoto.com/Tim McCaig • John Wiley & Sons Australia: pp. 335, 554 (left bottom, left top, right bottom, right centre)/© John Wiley & Sons Australia/ Photo by Renee Bryon; pp. 454, 495, 558 (top)© John Wiley & Sons Australia/Malcolm Cross; p. 537 (bottom)/© John Wiley & Sons Australia /Taken by Jo Patterson • Newspix, p. 327/ Newspix/Robert McKell; p. 410/Newspix/Lannon Harley; p. 449 (left)/Newspix/AFP • Photodisc: pp. 31 (top), 41, 44, 46, 94, 100, 148 (top), 170 (bottom centre), 170 (bottom right), 175, 212, 213, 254, 255, 256 (top), 258, 270 (top), 312, 313, 383, 387, 394, 451, 452, 471, 475, 476, 490, 512, 525, 530, 538, 544, 559, 575 • Photolibrary: p. 31 (bottom); p. 34/ © photolibrary.com/Edward Cross; p. 226/© photolibrary.com/ Sydney/SPL/CNRI • Photolibrary Royalty Free: p. 15/© Huntstock/Photolibrary Inc. • Shutterstock, p. 170 (top left)/© 2009 Used under license from Shutterstock.com; p. 320/© Patricia Hofmeester, 2009 Used under license from Shutterstock.com; p. 377/© Kalim, 2009 Used under license from Shutterstock.com; p. 485/© Andrejs Pidjass, 2009 Used under license from Shutterstock.com; p. 537 (top)/© ronfromyork, 2009 Used under license from Shutterstock.com; p. 554 (right top)/© Lincoln Rogers, 2009 Used under license from Shutterstock.com; p. 571/© Lario Tus, 2009 Used under license from Shutterstock.com • Stockbyte: pp. 170 (top right), 496 • Viewnder Australia Photo Library: p. 215
Text © VCAA All Victorian Curriculum and Assessment Authority material has been used with permission. For more information go to www.vcaa.vic.edu.au./ Every effort has been made to trace the ownership of copyright material. Information that will enable the publisher to rectify any error or omission in subsequent editions will be welcome. In such cases, please contact the Permissions Section of John Wiley & Sons Australia, Ltd.
