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