Learning with learnON ix
Teaching with learnON xv
Acknowledgements xvi
Problem-solving and modelling task guide
Unit 1 Surds, Algebra, Functions and Probability 01
Topic 1 Surds and Quadratic Functions
1 Surds 03
1.1 Overview 04
1.2 The real number system and surds 05
1.3 Simplifying surds 10
1.4 Operations with surds and rationalising the denominator 16
1.5 Review 23
Answers 26
2 Quadratic functions 29
2.1 Overview 30
2.2 Solving quadratic equations with rational roots 31
2.3 Solving quadratic equations over R 37
2.4 Graphs of quadratic functions 44
2.5 The discriminant 58
2.6 Modelling with quadratic functions 67
2.7 Review 77
Answers 81
Topic 2 Binomial Expansion and Cubic Functions
3 Binomial expansions and cubic functions 89
3.1 Overview 90
3.2 Pascalâs triangle and binomial expansions 91
3.3 The binomial theorem 101
3.4 Polynomials and cubic functions 105
3.5 Graphing cubic functions 111
3.6 Solving cubic equations 124
3.7 Modelling cubic functions 130
3.8 Review 137
Answers 141
Topic 3 Functions and Relations
4 Introduction to functions and relations 153
4.1 Overview 154
4.2 Functions and relations 155
4.3 Function notation 166
4.4 Piece-wise functions 176
4.5 Review 189
Answers 194
5 Graphs of relations and reciprocal functions 201
5.1 Overview 202
5.2 The circle 203
5.3 The sideways parabola and square root function 211
5.4 The reciprocal function 219
5.5 Review 231
Answers 235
Topic 4 Trigonometric Functions
6 Trigonometric functions 243
6.1 Overview 244
6.2 Trigonometry review 245
6.3 Radian measure 253
6.4 Unit circle definitions 262
6.5 Exact values and symmetry properties 273
6.6 Graphs of the sine, cosine and tangent functions 285
6.7 Solving trigonometric equations 295
6.8 Transformations of the sine and cosine functions 307
6.9 Modelling with trigonometric functions 321
6.10 Review 331
Answers 335
Topic 5 Probability
7 Probability 351
7.1 Overview 352
7.2 Concepts of probability 353
7.3 Relative frequency 365
7.4 Conditional probability 371
7.5 Independence 379
7.6 Review 387
Answers 392
Practice Assessment 1
Problem-solving and modelling task
Practice Assessment 2
Unit 1 Examination
Unit 2 Calculus and Further Functions 397
Topic 1 Exponential Functions
8 Indices and index laws 399
8.1 Overview 400
8.2 Index laws 401
8.3 Negative and fractional indices 408
8.4 Scientific notation 415
8.5 Review 420
Answers 423
9 Introduction to exponential functions 425
9.1 Overview 426
9.2 Solving exponential equations 427
9.3 Graphs of exponential functions 431
9.4 Modelling with exponential functions 441
9.5 Review 448
Answers 452
Topic 2 Logarithms and Logarithmic Functions
10 Logarithms and logarithmic functions 457
10.1 Overview 458
10.2 Logarithms and logarithmic laws 459
10.3 Indicial equations and logarithms 466
10.4 Graphs of logarithmic functions 473
10.5 Modelling with logarithmic functions 481
10.6 Review 491
Answers 494
Topic 3 Introduction to Differential Calculus
11 Rates of change and the concept of derivatives 499
11.1 Overview 500
11.2 Average rates of change 501
11.3 Differentiation from first principles 508
11.4 Differentiation by rule 517
11.5 Interpreting the derivative 526
11.6 Differentiation of power functions 532
11.7 Review 539
Answers 542
Topic 4 Applications of Differential Calculus
12 Graphical applications of derivatives 549
12.1 Overview 550
12.2 Instantaneous rates of change 551
12.3 Tangents and normals of a graph 556
12.4 Kinematics 566
12.5 Curve sketching 577
12.6 Review 591
Answers 594
Topic 5 Further Differentiation
13 Differentiation rules 601
13.1 Overview 602
13.2 The chain rule 603
13.3 The product rule 610
13.4 The quotient rule 614
13.5 Combinations of the chain rule, product rule and quotient rule 620
13.6 Review 623
Answers 626
Practice Assessment 3
Unit 2 Examination
Practice Assessment 4
Units 1&2 Examination
Glossary 631
