| Introduction |
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vii | |
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1 | (8) |
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2 | (2) |
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1.2 Choosing from groups when order does not matter |
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4 | (1) |
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1.3 Choosing from groups when order does matter |
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5 | (1) |
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1.4 Solving equations with binomial coefficients and factorials |
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6 | (3) |
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2 Exponents and logarithms |
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9 | (8) |
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2.1 Solving exponential equations |
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11 | (1) |
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2.2 Solving disguised quadratic equations |
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12 | (1) |
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13 | (1) |
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2.4 Solving equations involving logarithms |
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14 | (1) |
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2.5 Problems involving exponential functions |
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15 | (2) |
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17 | (10) |
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3.1 Using the discriminant |
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19 | (1) |
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3.2 Sketching polynomial functions |
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20 | (1) |
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21 | (1) |
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3.4 Finding the coefficients of a polynomial |
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22 | (1) |
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3.5 Linking equations via their roots |
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23 | (1) |
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3.6 Applying the binomial theorem |
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24 | (3) |
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4 Functions, graphs and equations |
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27 | (13) |
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30 | (1) |
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4.2 Inverse and composite functions |
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31 | (1) |
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4.3 Transformations of graphs |
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32 | (2) |
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4.4 Reciprocal functions and transformations |
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34 | (2) |
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36 | (1) |
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4.6 Systems of linear equations |
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37 | (3) |
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40 | (6) |
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5.1 Arithmetic sequences and series |
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41 | (1) |
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5.2 Geometric sequences and series |
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42 | (1) |
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43 | (3) |
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46 | (12) |
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6.1 Transformations of trigonometric graphs |
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49 | (1) |
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6.2 Proving trigonometric identities |
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50 | (1) |
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6.3 Using identities to find exact values of trigonometric functions |
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51 | (1) |
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6.4 Solving trigonometric equations |
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52 | (1) |
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6.5 Using identities to solve trigonometric equations |
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53 | (1) |
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6.6 Functions of the form a sin x + b cos x |
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54 | (1) |
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6.7 Geometry of triangles and circles |
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55 | (3) |
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58 | (14) |
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7.1 Proving geometrical properties using vectors |
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61 | (1) |
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7.2 Applications of the vector product |
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62 | (1) |
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7.3 Equation of a line and the intersection of lines |
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63 | (1) |
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64 | (1) |
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7.5 Intersections involving planes |
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65 | (1) |
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7.6 Angles between lines and planes |
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66 | (1) |
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7.7 Distances from lines and planes |
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67 | (1) |
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7.8 Applying vectors to motion |
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68 | (4) |
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72 | (11) |
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8.1 Solving equations involving complex numbers |
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75 | (1) |
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8.2 Evaluating expressions involving complex numbers |
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76 | (1) |
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8.3 Finding solutions to polynomial equations |
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77 | (1) |
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8.4 Finding multiple angle formulae for trigonometric functions |
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78 | (1) |
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8.5 Finding formulae for powers of trigonometric functions |
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79 | (1) |
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8.6 Finding roots of complex numbers |
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80 | (3) |
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83 | (16) |
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9.1 Differentiation from first principles |
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86 | (1) |
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9.2 The product, quotient and chain rules |
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87 | (1) |
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88 | (1) |
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9.4 Implicit differentiation |
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89 | (1) |
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90 | (1) |
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9.6 Optimisation with constraints |
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91 | (1) |
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92 | (1) |
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93 | (2) |
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9.9 Related rates of change |
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95 | (1) |
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96 | (3) |
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99 | (10) |
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10.1 Integrating expressions |
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102 | (1) |
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103 | (1) |
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10.3 Volumes of revolution |
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104 | (1) |
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105 | (4) |
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11 Probability and statistics |
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109 | (14) |
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11.1 Calculating the mean and standard deviation from summary statistics |
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111 | (1) |
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11.2 Frequency tables and grouped data |
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112 | (1) |
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11.3 Calculating probabilities by considering possible outcomes |
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113 | (1) |
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114 | (1) |
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11.5 Bayes' theorem and tree diagrams |
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115 | (1) |
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11.6 Expectation and variance of discrete random variables |
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116 | (1) |
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11.7 The binomial and Poisson distributions |
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117 | (1) |
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11.8 Expectation and variance of continuous random variables |
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118 | (1) |
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11.9 The normal and inverse normal distributions |
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119 | (1) |
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11.10 Using the standard normal distribution when μ or σ are unknown |
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120 | (3) |
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12 Mathematical induction |
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123 | (7) |
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12.1 Series and sequences |
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124 | (2) |
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126 | (1) |
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127 | (1) |
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128 | (2) |
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130 | (3) |
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130 | (1) |
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How to check your answers |
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131 | (2) |
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14 Things you need to know how to do on your calculator |
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133 | (8) |
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133 | (4) |
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137 | (4) |
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141 | (44) |
| Answers to practice questions |
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185 | |
