| Introduction |
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v | |
| How to use this book |
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vi | |
| Working with the large data set |
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viii | |
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1 Proof and mathematical communication |
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1 | (15) |
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Section 1 Mathematical structures and arguments |
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1 | (6) |
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Section 2 Inequality notation |
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7 | (2) |
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Section 3 Disproof by counter example |
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9 | (1) |
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Section 4 Proof by deduction |
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10 | (2) |
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Section 5 Proof by exhaustion |
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12 | (4) |
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16 | (11) |
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Section 1 Using the laws of indices |
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17 | (5) |
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Section 2 Working with surds |
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22 | (5) |
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27 | (28) |
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Section 1 Review of quadratic equations |
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28 | (2) |
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Section 2 Graphs of quadratic functions |
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30 | (4) |
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Section 3 Completing the square |
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34 | (8) |
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Section 4 Quadratic inequalities |
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42 | (3) |
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Section 5 The discriminant |
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45 | (4) |
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Section 6 Disguised quadratics |
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49 | (6) |
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55 | (15) |
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Section 1 Working with polynomials |
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56 | (1) |
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Section 2 Polynomial division |
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57 | (2) |
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Section 3 The factor theorem |
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59 | (3) |
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Section 4 Sketching polynomial functions |
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62 | (8) |
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70 | (17) |
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Section 1 Intersections of graphs |
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70 | (2) |
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Section 2 The discriminant revisited |
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72 | (2) |
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Section 3 Transforming graphs |
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74 | (4) |
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Section 4 Graphs of a/x and a/x2 |
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78 | (1) |
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Section 5 Direct and inverse proportion |
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79 | (2) |
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Section 6 Sketching inequalities in two variables |
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81 | (6) |
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87 | (26) |
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Section 1 Midpoint and distance between two points |
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89 | (2) |
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Section 2 Equation of a straight line |
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91 | (5) |
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Section 3 Parallel and perpendicular lines |
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96 | (4) |
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Section 4 Equation of a circle |
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100 | (3) |
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Section 5 Solving problems with lines and circles |
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103 | (10) |
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113 | (15) |
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Section 1 Introducing logarithms |
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114 | (4) |
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Section 2 Laws of logarithms |
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118 | (4) |
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Section 3 Solving exponential equations |
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122 | (2) |
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Section 4 Disguised quadratics |
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124 | (4) |
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128 | (21) |
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Section 1 Graphs of exponential functions |
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129 | (5) |
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Section 2 Graphs of logarithms |
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134 | (1) |
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Section 3 Exponential functions and mathematical modelling |
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135 | (6) |
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Section 4 Fitting models to data |
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141 | (8) |
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149 | (20) |
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Section 1 The binomial theorem |
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149 | (5) |
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Section 2 Calculating the binomial coefficients |
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154 | (3) |
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Section 3 Applications of the binomial theorem |
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157 | (12) |
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161 | (1) |
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Focus on... Problem solving 1 |
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162 | (3) |
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165 | (2) |
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Cross-topic review exercise 1 |
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167 | (2) |
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10 Trigonometric functions and equations |
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169 | (34) |
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Section 1 Definitions and graphs of the sine and cosine functions |
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170 | (6) |
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Section 2 Definition and graph of the tangent function |
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176 | (1) |
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Section 3 Exact values of trigonometric functions |
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177 | (2) |
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Section 4 Trigonometric identities |
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179 | (5) |
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Section 5 Introducing trigonometric equations |
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184 | (5) |
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Section 6 Transformations of trigonometric graphs |
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189 | (4) |
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Section 7 More complex trigonometric equations |
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193 | (10) |
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203 | (17) |
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204 | (5) |
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Section 2 The cosine rule |
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209 | (5) |
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Section 3 Area of a triangle |
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214 | (6) |
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220 | (27) |
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Section 1 Describing vectors |
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221 | (5) |
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Section 2 Operations with vectors |
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226 | (6) |
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Section 3 Position and displacement vectors |
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232 | (5) |
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Section 4 Using vectors to solve geometrical problems |
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237 | (10) |
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247 | (23) |
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Section 1 Sketching derivatives |
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247 | (4) |
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Section 2 Differentiation from first principles |
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251 | (3) |
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Section 3 Rules of differentiation |
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254 | (4) |
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Section 4 Simplifying into terms of the form axn |
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258 | (3) |
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Section 5 Interpreting derivatives and second derivatives |
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261 | (9) |
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14 Applications of differentiation |
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270 | (20) |
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Section 1 Tangents and normals |
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270 | (5) |
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Section 2 Stationary points |
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275 | (4) |
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279 | (11) |
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290 | (33) |
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Section 1 Rules for integration |
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291 | (3) |
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Section 2 Simplifying into terms of the form axn |
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294 | (3) |
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Section 3 Finding the equation of a curve |
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297 | (3) |
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Section 4 Definite integration |
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300 | (2) |
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Section 5 Geometrical significance of definite integration |
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302 | (21) |
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315 | (1) |
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Focus on... Problem solving 2 |
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316 | (2) |
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318 | (2) |
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Cross-topic review exercise 2 |
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320 | (3) |
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323 | (36) |
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Section 1 A reminder of statistical diagrams |
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324 | (9) |
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Section 2 Standard deviation |
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333 | (4) |
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Section 3 Calculations from frequency tables |
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337 | (6) |
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Section 4 Scatter diagrams and correlation |
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343 | (5) |
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Section 5 Outliers and cleaning data |
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348 | (11) |
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359 | (25) |
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Section 1 Combining probabilities |
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360 | (6) |
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Section 2 Probability distributions |
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366 | (4) |
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Section 3 The binomial distribution |
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370 | (14) |
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18 Statistical hypothesis testing |
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384 | (36) |
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Section 1 Populations and samples |
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385 | (10) |
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Section 2 Introduction to hypothesis testing |
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395 | (8) |
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Section 3 Critical region for a hypothesis test |
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403 | (17) |
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411 | (2) |
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Focus on... Problem solving 3 |
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413 | (1) |
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414 | (2) |
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Cross-topic review exercise 3 |
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416 | (4) |
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19 Introduction to kinematics |
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420 | (35) |
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Section 1 Mathematical models in mechanics |
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421 | (2) |
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Section 2 Displacement, velocity and acceleration |
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423 | (5) |
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Section 3 Kinematics and calculus |
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428 | (4) |
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Section 4 Using travel graphs |
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432 | (13) |
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Section 5 Solving problems in kinematics |
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445 | (10) |
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20 Motion with constant acceleration |
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455 | (24) |
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Section 1 Deriving the constant acceleration formulae |
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455 | (5) |
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Section 2 Using the constant acceleration formulae |
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460 | (3) |
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Section 3 Vertical motion under gravity |
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463 | (7) |
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Section 4 Multi-stage problems |
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470 | (9) |
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479 | (27) |
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Section 1 Newton's laws of motion |
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479 | (5) |
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Section 2 Combining forces |
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484 | (5) |
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Section 3 Types of forces |
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489 | (5) |
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Section 4 Gravity and weight |
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494 | (4) |
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Section 5 Forces in equilibrium |
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498 | (8) |
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506 | (38) |
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Section 1 Newton's third law |
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507 | (1) |
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Section 2 Normal reaction force |
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508 | (7) |
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Section 3 Further equilibrium problems |
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515 | (4) |
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Section 4 Connected particles |
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519 | (4) |
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523 | (21) |
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536 | (1) |
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Focus on... Problem solving 4 |
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537 | (2) |
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539 | (2) |
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Cross-topic review exercise 4 |
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541 | (3) |
| AS practice paper 1 |
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544 | (2) |
| AS practice paper 2 |
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546 | (2) |
| Formulae |
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548 | (1) |
| Answers |
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549 | (53) |
| Glossary |
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602 | (4) |
| Index |
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606 | (5) |
| Acknowledgements |
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611 | |
