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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
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.