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Publisher | John Wiley & Sons Australia |
Author(s) | Sue Michell |
Edition | 2 |
Published | 19th November 2018 |
Related course codes |
About this resource vii
About eBookPLUS and studyON x
Acknowledgements xi
1 Lines and linear relationships 1
1.1 Overview 1
1.2 Linearly related variables, linear equations and inequations 3
1.3 Systems of 3 × 3 simultaneous linear equations 16
1.4 Linear graphs and their equations 21
1.5 Intersections of lines and their applications 34
1.6 Coordinate geometry of the straight line 40
1.7 Bisection and lengths of line segments 47
1.8 Review: exam practice 53
Answers 56
2 Algebraic foundations 63
2.1 Overview 63
2.2 Algebraic skills 65
2.3 Pascal’s triangle and binomial expansions 73
2.4 The binomial theorem 77
2.5 Sets of real numbers 85
2.6 Surds 91
2.7 Review: exam practice 102
Answers 106
3 Quadratic relationships 110
3.1 Overview 110
3.2 Quadratic equations with rational roots 112
3.3 Quadratics over R 117
3.4 Applications of quadratic equations 130
3.5 Graphs of quadratic polynomials 134
3.6 Determining the rule of a quadratic polynomial from a graph 146
3.7 Quadratic inequations 152
3.8 Quadratic models and applications 159
3.9 Review: exam practice 163
Answers 167
4 Cubic polynomials 178
4.1 Overview 178
4.2 Polynomials 180
4.3 The remainder and factor theorems 192
4.4 Graphs of cubic polynomials 201
4.5 Equations of cubic polynomials 212
4.6 Cubic models and applications 223
4.7 Review: exam practice 228
Answers 232
5 Higher-degree polynomials 247
5.1 Overview 247
5.2 Quartic polynomials 249
5.3 Families of polynomials 258
5.4 Numerical approximations to roots of polynomial equations 267
5.5 Review: exam practice 276
Answers 280
6 Functions and relations 289
6.1 Overview 289
6.2 Functions and relations 291
6.3 The circle 301
6.4 The rectangular hyperbola and the truncus 312
6.5 The relation y2 = x 330
6.6 Other functions and relations 343
6.7 Transformations of functions 356
6.8 Review: exam practice 366
Answers 371
Revision Topics 1 to 6 393
7 Matrices and applications to transformations 394
7.1 Overview 394
7.2 Addition, subtraction and scalar multiplication of matrices 396
7.3 Matrix multiplication 403
7.4 Determinants and inverses of 2 × 2 matrices 408
7.5 Matrix equations and solving 2 × 2 linear simultaneous equations 414
7.6 Translations 424
7.7 Reflections 431
7.8 Dilations 438
7.9 Combinations of transformations 443
7.10 Review: exam practice 446
Answers 451
Revision Topic 7 458
8 Probability 459
8.1 Overview 459
8.2 Probability review 461
8.3 Conditional probability 472
8.4 Independence 481
8.5 Counting techniques 487
8.6 Binomial coefficients and Pascal’s triangle 500
8.7 Review: exam practice 509
Answers 513
Revision Topic 8 517
9 Trigonometric functions 1 518
9.1 Overview 518
9.2 Trigonometric ratios 519
9.3 Circular measure 529
9.4 Unit circle definitions 538
9.5 Symmetry properties 548
9.6 Graphs of the sine and cosine functions 559
9.7 Review: exam practice 570
Answers 573
10 Trigonometric functions 2 580
10.1 Overview 580
10.2 Trigonometric equations 582
10.3 Transformations of sine and cosine graphs 591
10.4 Applications of sine and cosine functions 605
10.5 The tangent function 612
10.6 Trigonometric relationships 622
10.7 Review: exam practice 629
Answers 634
11 Exponential functions 648
11.1 Overview 648
11.2 Indices as exponents 650
11.3 Indices as logarithms 658
11.4 Graphs of exponential functions 668
11.5 Applications of exponential functions 677
11.6 Inverses of exponential functions 684
11.7 Review: exam practice 697
Answers 701
Revision Topics 9 to 11 712
12 Introduction to differential calculus 713
12.1 Overview 713
12.2 Rates of change 715
12.3 Gradients of secants 723
12.4 The derivative function 728
12.5 Differentiation of polynomials by rule 735
12.6 Review: exam practice 746
Answers 750
13 Differentiation and applications 757
13.1 Overview 757
13.2 Limits, continuity and differentiability 759
13.3 Derivatives of power functions 769
13.4 Coordinate geometry applications of differentiation 777
13.5 Curve sketching 786
13.6 Optimisation problems 796
13.7 Rates of change and kinematics 803
13.8 Review: exam practice 812
Answers 815
14 Anti-differentiation and introduction to integral calculus 824
14.1 Overview 824
14.2 Anti-derivatives 826
14.3 Anti-derivative functions and graphs 833
14.4 Application of anti-differentiation 841
14.5 The definite integral 847
14.6 Review: exam practice 858
Answers 862
Revision Topics 12 to 14 868
Glossary 869
Index 878