Mathematics for Australia 12 Mathematical Methods
| 1 | FUNCTIONS | 9 | |
| A | Exponential functions | 10 | |
| B | Logarithms | 12 | |
| C | Logarithmic functions | 16 | |
| D | Trigonometric functions | 22 | |
| Review set 1A | 24 | ||
| Review set 1B | 25 | ||
| 2 | DIFFERENTIAL CALCULUS | 27 | |
| A | First principles | 28 | |
| B | Simple rules of differentiation | 32 | |
| C | The chain rule | 35 | |
| D | The product rule | 39 | |
| E | The quotient rule | 41 | |
| F | Derivatives of exponential functions | 44 | |
| G | Derivatives of logarithmic functions | 48 | |
| H | Derivatives of trigonometric functions | 51 | |
| I | Second derivatives | 54 | |
| Review set 2A | 55 | ||
| Review set 2B | 57 | ||
| 3 | APPLICATIONS OF DIFFERENTIAL CALCULUS | 59 | |
| A | Equations of tangents | 61 | |
| B | Increasing and decreasing functions | 64 | |
| C | Stationary points | 67 | |
| D | Inflections and shape | 69 | |
| E | Kinematics | 79 | |
| F | Rates of change | 83 | |
| G | Optimisation | 87 | |
| Review set 3A | 92 | ||
| Review set 3B | 94 | ||
| 4 | INTEGRATION | 97 | |
| A | The area under a curve | 98 | |
| B | Antidifferentiation | 104 | |
| C | The Fundamental Theorem of Calculus | 106 | |
| D | Integration | 112 | |
| E | Rules for integration | 114 | |
| F | Integrating f(ax + b) | 119 | |
| G | Definite integrals | 122 | |
| Review set 4A | 124 | ||
| Review set 4B | 125 | ||
| 5 | APPLICATIONS OF INTEGRATION | 127 | |
| A | The area under a curve | 128 | |
| B | The area between two functions | 133 | |
| C | Kinematics | 138 | |
| D | Problem solving by integration | 145 | |
| Review set 5A | 148 | ||
| Review set 5B | 151 | ||
| 6 | STATISTICS | 153 | |
| A | Key statistical concepts | 154 | |
| B | Measuring the centre of data | 160 | |
| C | Variance and standard deviation | 172 | |
| Review set 6A | 180 | ||
| Review set 6B | 181 | ||
| 7 | DISCRETE RANDOM VARIABLES | 183 | |
| A | Random variables | 184 | |
| B | Discrete probability distributions | 187 | |
| C | Expected value | 192 | |
| D | Variance and standard deviation | 199 | |
| E | Properties of aX + b | 202 | |
| F | The Bernoulli distribution | 204 | |
| G | The binomial distribution | 207 | |
| Review set 7A | 217 | ||
| Review set 7B | 219 | ||
| 8 | CONTINUOUS RANDOM VARIABLES | 221 | |
| A | Continuous random variables | 222 | |
| B | Probability density functions | 225 | |
| C | The normal distribution | 231 | |
| D | Probabilities using a calculator | 236 | |
| E | The standard normal distribution (Z-distribution) | 240 | |
| F | Quantiles | 244 | |
| Review set 8A | 249 | ||
| Review set 8B | 251 | ||
| 9 | SAMPLING AND CONFIDENCE INTERVALS | 253 | |
| A | Sampling distributions | 254 | |
| B | Distributions of sample means | 258 | |
| C | The Central Limit Theorem | 263 | |
| D | Confidence intervals for means | 268 | |
| E | Sample proportions | 280 | |
| F | Confidence intervals for proportions | 283 | |
| Review set 9A | 291 | ||
| Review set 9B | 293 | ||
| ANSWERS | 297 | ||
| INDEX | 334 | ||
