# Mathematics for Australia 12 Mathematical Methods

### 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