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# Maths Quest 12 Mathematical Methods VCE Units 3 and 4 Solutions Manual & eBookPLUS

Author/s Swale 9780730323129 November 2015 264 \$44.95

Maths Quest 12 Mathematical Methods VCE Units 3 and 4 Solutions Manual with eBookPLUS contains fully worked solutions to every question in the Maths Quest 12 Mathematical Methods VCE Units 3 and 4 student text.

This resource is a printed student text that includes Maths Quest 12 Mathematical Methods VCE Units 3 and 4 Solutions Manual eBookPLUS.

Topic 1 — Solving equations 1

Exercise 1.2 — Polynomials 1

Exercise 1.3 — Trigonometric symmetry properties 5

Exercise 1.4 — Trigonometric equations and general solutions 8

Exercise 1.5 — Literal and simultaneous equations 14

Topic 2 — Functions and graphs 19

Exercise 2.2 — Polynomial functions 19

Exercise 2.3 — Other algebraic functions 25

Exercise 2.4 — Combinations of functions 33

Exercise 2.5 — Non-algebraic functions 38

Exercise 2.6 — Modelling and applications 49

Topic 3 — Composite functions, transformations and inverses 53

Exercise 3.2 — Composite functions and functional equations 53

Exercise 3.3 — Transformations 56

Exercise 3.4 — Transformations using matrices 59

Exercise 3.5 — Inverse graphs and relations 62

Exercise 3.6 — Inverse functions 64

Topic 4 — Logarithmic functions 69

Exercise 4.2 — Logarithm laws and equations 69

Exercise 4.3 — Logarithmic scales 72

Exercise 4.4 — Indicial equations 74

Exercise 4.5 — Logarithmic graphs 78

Exercise 4.6 — Applications 83

Topic 5 — Differentiation 87

Exercise 5.2 — Review of differentiation 87

Exercise 5.3 — Differentiation of exponential functions 94

Exercise 5.4 — Applications of exponential functions 97

Exercise 5.5 — Differentiation of trigonometric functions 100

Exercise 5.6 — Applications of trigonometric functions 103

Topic 6 — Further differentiation and applications 107

Exercise 6.2 — The chain rule 107

Exercise 6.3 — The product rule 111

Exercise 6.4 — The quotient rule 116

Exercise 6.5 — Curve sketching 121

Exercise 6.6 — Maximum and minimum problems 133

Exercise 6.7 — Rates of change 137

Topic 7 — Antidifferentiation 143

Exercise 7.2 — Antidifferentiation 143

Exercise 7.3 — Antiderivatives of exponential and trigonometric functions 145

Exercise 7.4 — Families of curves and applications 147

Topic 8 — Integration 153

Exercise 8.2 — The fundamental theorem of integral calculus 153

Exercise 8.3 — Areas under curves 159

Exercise 8.4 — Applications 162

Topic 9 — Logarithmic functions using calculus 171

Exercise 9.2 — The derivative of f(x) = loge(x) 171

Exercise 9.3 — The antiderivative of f(x) = x 1 177

Exercise 9.4 — Applications 182

Topic 10 — Discrete random variables 189

Exercise 10.2 — Discrete random variables 189

Exercise 10.3 — Measures of centre and spread 196

Exercise 10.4 — Applications 204

Topic 11 — The binomial distribution 211

Exercise 11.2 — Bernoulli trials 211

Exercise 11.3 — The binomial distribution 212

Exercise 11.4 — Applications 216

Topic 12 — Continuous probability distributions 219

Exercise 12.2 — Continuous random variables and probability functions 219

Exercise 12.3 — The continuous probability density function 223

Exercise 12.4 — Measures of centre and spread 229

Exercise 12.5 — Linear transformations 237

Topic 13 — The normal distribution 243

Exercise 13.2 — The normal distribution 243

Exercise 13.3 — Calculating probabilities and the standard normal distribution 245

Exercise 13.4 — The inverse normal distribution 246

Exercise 13.5 — Mixed probability application problems 247

Topic 14 — Statistical inference 253

Exercise 14.2 — Population parameters and sample statistics 253

Exercise 14.3 — The distribution of ­p 253

Exercise 14.4 — Confidence intervals 255

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