About this resource ix
About eBookPLUS and studyON xii
Acknowledgements xiii
Unit 1 Algebra, Statistics and Functions 1
Topic 1 Arithmetic and geometric sequences and series 1
1 Arithmetic sequences 1
1.1 Overview 1
1.2 Arithmetic sequences 2
1.3 The general form of an arithmetic sequence 8
1.4 The sum of an arithmetic sequence 15
1.5 Applications of arithmetic sequences 19
1.6 Review: exam practice 26
Answers 29
Revision Unit 1 Topic 1 Chapter 1 31
Topic 2 Functions and graphs
2 Functions 32
2.1 Overview 32
2.2 Functions and relations 33
2.3 Function notation 44
2.4 Transformations of functions 53
2.5 Piece-wise functions 62
2.6 Review: exam practice 74
Answers 80
3 Quadratic relationships 89
3.1 Overview 89
3.2 Graphs of quadratic functions 90
3.3 Solving quadratic equations with rational roots 103
3.4 Factorising and solving quadratics over R 109
3.5 The discriminant 116
3.6 Modelling with quadratic functions 126
3.7 Review: exam practice 134
Answers 138
4 Inverse proportions and graphs of relations 145
4.1 Overview 145
4.2 The hyperbola 146
4.3 Inverse proportion 157
4.4 The circle 162
4.5 The sideways parabola 170
4.6 Review: exam practice 178
Answers 182
5 Powers and polynomials 191
5.1 Overview 191
5.2 Polynomials 192
5.3 Graphs of cubic polynomials 203
5.4 The factor and remainder theorems 217
5.5 Solving cubic equations 224
5.6 Cubic models and applications 229
5.7 Graphs of quartic polynomials 235
5.8 Solving polynomial equations 242
5.9 Review: exam practice 250
Answers 254
Revision Unit 1 Topic 2 Chapters 2 to 5 270
Practice Assessment 1 Problem solving and modelling task: Functions and graphs 271
Topic 3 Counting and probability
6 Counting and probability 274
6.1 Overview 274
6.2 Fundamentals of probability 275
6.3 Relative frequency 286
6.4 Conditional probability 290
6.5 Independence 299
6.6 Permutations and combinations 305
6.7 Pascalâs triangle and binomial expansions 319
6.8 Review: exam practice 329
Answers 332
Revision Unit 1 Topic 3 Chapter 6 336
Topic 4 Exponential functions 1
7 Indices 337
7.1 Overview 337
7.2 Index laws 338
7.3 Negative and rational indices 343
7.4 Indicial equations and scientific notation 348
7.5 Review: exam practice 354
Answers 356
Revision Unit 1 Topic 4 Chapter 7 358
Topic 5 Arithmetic and geometric sequences and series 2
8 Geometric sequences 359
8.1 Overview 359
8.2 Recursive definition and the general term of geometric sequences 360
8.3 The sum of a geometric sequence 371
8.4 Geometric sequences in context 378
8.5 Review: exam practice 384
Answers 387
Revision Unit 1 Topic 5 Chapter 8 389
Practice Assessment 2 Unit 1 internal examination 390
Unit 2 Calculus and Further Functions
Topic 1 The logarithmic function 1
Topic 2 Exponential functions 2
9 Exponential and logarithmic functions 399
9.1 Overview 399
9.2 Exponential functions 400
9.3 functions 410
9.4 Modelling with exponential functions 423
9.5 Solving equations with indices 432
9.6 Review: exam practice 438
Answers 442
Revision Unit 2 Topic 1 AND 2 Chapter 9 449
Topic 3 Trigonometric functions 1
10 Trigonometric functions 450
10.1 Overview 450
10.2 Trigonometry review 451
10.3 Radian measure 459
10.4 Unit circle definitions 469
10.5 Exact values and symmetry properties 480
10.6 Graphs of the sine, cosine and tangent functions 490
10.7 Transformations of sine and cosine graphs 499
10.8 Solving trigonometric equations 513
10.9 Modelling with trigonometric functions 524
10.10 Review: exam practice 531
Answers 536
Revision Unit 2 Topic 3 Chapter 10 550
Topic 4 Introduction to differential calculus
11 Rates of change 551
11.1 Overview 551
11.2 Exploring rates of change 552
11.3 The difference quotient 561
11.4 Differentiating simple functions 567
11.5 Interpreting the derivative 570
11.6 Review: exam practice 576
Answers 580
12 Properties and applications of derivatives 584
12.1 Overview 584
12.2 Differentiation by formula 585
12.3 The derivative as a function 589
12.4 Properties of the derivative 595
12.5 Differentiation of power and polynomial functions 599
12.6 Review: exam practice 604
Answers 607
13 Applications of derivatives 611
13.1 Overview 611
13.2 Gradient and equation of a tangent 612
13.3 Displacementâ"time graphs 620
13.4 Sketching curves using derivatives 629
13.5 Modelling optimisation problems 643
13.6 Review: exam practice 648
Answers 651
Revision Unit 2 Topic 4 Chapters 11 to 13 656
Topic 5 Further differentiation and applications 1
14 Differentiation rules 657
14.1 Overview 657
14.2 The product rule 658
14.3 The quotient rule 660
14.4 The chain rule 666
14.5 Applications of the product, quotient and chain rules 672
14.6 Review: exam practice 674
Answers 677
Revision Unit 2 Topic 5 Chapter 14 682
Topic 6 Discrete random variables 1
15 Discrete random variables 1 683
15.1 Overview 683
15.2 Discrete random variables 684
15.3 Expected values 695
15.4 Variance and standard deviation 704
15.5 Applications of discrete random variables 712
15.6 Review: exam practice 718
Answers 723
Revision Unit 2 Topic 6 Chapter 15 727
Practice Assessment 3 Unit 2 internal examination 728
Practice Assessment 4 Units 1 and 2 internal examination 735
Glossary 743
Index 750
