MATHS QUEST for the AustralianCurriculum
KYLIE BOUCHER DEBBIE KEMPFF LYN ELMS RUTH BAKOGIANISDOUGLAS SCOTT CORAL CONNOR TOBIAS COOPER
CONTRIBUTING AUTHORSCAROL PATTERSON

ROBERT CAHN

ANITA CANN

JACINTA DEYLANBRENDAN OWEN

IRENE KIROFF

ROSETTA BATSAKIS

ELENA IAMPOLSKY
10
+
10A
T E A C H E R E D I T I O N
First published 2012 byJohn Wiley & Sons Australia, Ltd42 McDougall Street, Milton, Qld 4064Typeset in 10/12pt Times LT© John Wiley & Sons Australia, Ltd 2012The moral rights of the authors have been asserted.National Library of AustraliaCataloguinginPublication dataTitle: Maths quest 10+10A for the Australian curriculum/ Kylie Boucher [et al.]ISBN: 978 0 7303 4178 9 (student ed. : pbk) 978 0 7303 4179 6 (student ed. : ebook) 978 0 7303 4181 9 (teacher ed. : pbk) 978 0 7303 4182 6 (teacher ed. : ebook)Series: Maths quest series.Notes: Includes indexTarget Audience: For secondary school age.Subjects: Mathematics—Textbooks. Mathematics—Study and teaching (Secondary)Other Authors/ Contributors: Boucher, Kylie.Dewey Number: 510
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Contents
Introduction viii About eBookPLUS x Acknowledgements xi
CHAPTER 1
NUMBER AND ALGEBRAPATTERNS AND ALGEBRA
Indices 1
Are you ready? 2
1A
Review of index laws 3
Exercise 1A 5
1B
Negative indices 7
Exercise 1B 10
1C
Fractional indices 12
Exercise 1C 14
1D
Combining index laws 17
Exercise 1D 20
Summary 23Chapter review 24eBookPLUS activities 26
CHAPTER 2
NUMBER AND ALGEBRAPATTERNS AND ALGEBRA
Linear algebra 27
Are you ready? 28
2A
Substitution 29
Exercise 2A 31
2B
Adding and subtracting algebraic fractions 33
Exercise 2B 36
2C
Multiplying and dividing algebraic fractions 37
Exercise 2C 39
2D
Solving linear equations 40
Exercise 2D 43
2E
Solving equations with algebraic fractions and multiple brackets 45
Exercise 2E 48
Summary 50Chapter review 52eBookPLUS activities 54
CHAPTER 3
NUMBER AND ALGEBRALINEAR AND NONLINEAR RELATIONSHIPS
Coordinate geometry 55
Are you ready? 56
3A
Sketching linear graphs 57
Exercise 3A 62
3B
Determining linear equations 64
Exercise 3B 67
3C
The distance between two points on a straight line 68
Exercise 3C 70
3D
The midpoint of a line segment 71
Exercise 3D 73
3E
Parallel and perpendicular lines 74
Exercise 3E 79
Summary 83Chapter review 85eBookPLUS activities 88
CHAPTER 4
NUMBER AND ALGEBRALINEAR AND NONLINEAR RELATIONSHIPS
Simultaneous linear equations and inequations 89
Are you ready? 90
4A
Graphical solution of simultaneous linear equations 91
Exercise 4A 94
4B
Solving simultaneous linear equations using substitution 96
Exercise 4B 98
4C
Solving simultaneous linear equations using elimination 99
Exercise 4C 101
4D
Problem solving using simultaneous linear equations
103Exercise 4D 105
4E
Solving linear inequations 106
Exercise 4E 108
4F
Sketching linear inequations 110
Exercise 4F 113
4G
Solving simultaneous linear inequations 116
Exercise 4G 118
Summary 123Chapter review 125eBookPLUS activities 130
CHAPTER 5
MEASUREMENT AND GEOMETRYPYTHAGORAS AND TRIGONOMETRY
Trigonometry
I
131
Are you ready? 132
5A
Pythagoras’ theorem 133
Exercise 5A 137
iv
Contents
5B
Pythagoras’ theorem in three dimensions 140
Exercise 5B 143
5C
Trigonometric ratios 145
Exercise 5C 149
5D
Using trigonometry to calculate side lengths 151
Exercise 5D 154
5E
Using trigonometry to calculate angle size 156
Exercise 5E 158
5F
Angles of elevation and depression 161
Exercise 5F 163
5G
Bearings and compass directions 165
Exercise 5G 169
5H
Applications 172
Exercise 5H 173
Summary 177Chapter review 179eBookPLUS activities 182
CHAPTER 6
MEASUREMENT AND GEOMETRYUSING UNITS OF MEASUREMENT
Surface area and volume 183
Are you ready? 184
6A
Area 185
Exercise 6A 189
6B
Total surface area 193
Exercise 6B 199
6C
Volume 203
Exercise 6C 208
Summary 213Chapter review 214eBookPLUS activities 218
CHAPTER 7
NUMBER AND ALGEBRAPATTERNS AND ALGEBRA
Quadratic expressions 219
Are you ready? 220
7A
Expanding algebraic expressions 221
Exercise 7A 225
7B
Factorising expressions with three terms 227
Exercise 7B 229
7C
Factorising expressions with two or four terms 231
Exercise 7C 234
7D
Factorising by completing the square 236
Exercise 7D 239
7E
Mixed factorisation 240
Exercise 7E 240
Summary 242Chapter review 244eBookPLUS activities 246
CHAPTER 8
NUMBER AND ALGEBRALINEAR AND NONLINEAR RELATIONSHIPS
Quadratic equations 247
Are you ready? 248
8A
Solving quadratic equations 249
Exercise 8A 253
8B
The quadratic formula 255
Exercise 8B 257
8C
Solving quadratic equations by inspecting graphs 258
Exercise 8C 261
8D
Finding solutions to quadratic equations by interpolation and using the discriminant 263
Exercise 8D 267
8E
Solving a quadratic equation and a linear equation simultaneously 269
Exercise 8E 272
Summary 274Chapter review 276eBookPLUS activities 278
CHAPTER 9
NUMBER AND ALGEBRALINEAR AND NONLINEAR RELATIONSHIPS
Functions 279
Are you ready? 280
9A
Plotting parabolas 281
Exercise 9A 284
9B
Sketching parabolas using the basic graph of
y
=
x
2
287
Exercise 9B 291
9C
Sketching parabolas in turning point form 292
Exercise 9C 296
9D
Sketching parabolas of the form
y
=
ax
2
+
bx
+
c
298
Exercise 9D 302
9E
Exponential functions and their graphs 306
Exercise 9E 309
9F
The hyperbola 312
Exercise 9F 314
9G
The circle 315
Exercise 9G 317
Summary 319Chapter review 321eBookPLUS activities 324