Learning with Learnon ix
Teaching with learnON xv
Acknowledgements xvi
Problem-solving and modelling task guide
Unit 3 Further Calculus and Introduction to Statistics 1
Topic 1 Differentiation of Exponential and Logarithmic Functions
1 Calculus of exponential and logarithmic functions 3
1.1 Overview 4
1.2 Limits 5
1.3 The exponential function 11
1.4 Differentiation of exponential functions 20
1.5 The logarithmic function 25
1.6 Solving equations 34
1.7 Differentiation of logarithmic functions 39
1.8 Modelling and solving with exponential and logarithmic functions 44
1.9 Review 56
Topic 2 Differentiation of Trigonometric Functions and Differentiation Rules
2 Calculus of trigonometric functions 71
2.1 Overview 72
2.2 Review of the unit circle 73
2.3 Review of the trigonometric functions 87
2.4 Differentiation of trigonometric functions 97
2.5 Modelling and solving with trigonometric functions 104
2.6 Review 116
3 Differentiation rules 129
3.1 Overview 130
3.2 The chain rule 131
3.3 The product rule 139
3.4 The quotient rule 144
3.5 Modelling and solving using the differentiation rules 150
3.6 Review 166
Topic 3 Further Applications of Differentiation
4 The second derivative and applications of differentiation 177
4.1 Overview 178
4.2 Second derivatives 179
4.3 Concavity and points of inflection 185
4.4 Curve sketching 191
4.5 Modelling and solving optimisation problems 201
4.6 Review 208
Topic 4 Introduction to Integration
5 Anti-differentiation 219
5.1 Overview 220
5.2 Anti-differentiation of rational functions 221
5.3 Anti-differentiation of exponential functions 228
5.4 Anti-differentiation of logarithmic functions 232
5.5 Anti-differentiation of trigonometric functions 236
5.6 Further integration 240
5.7 Modelling and solving using indefinite integrals 247
5.8 Review 255
Topic 5 Discrete Random Variables
6 General discrete random variables 265
6.1 Overview 266
6.2 Discrete random variables 267
6.3 Expected values 279
6.4 Variance and standard deviation 289
6.5 Modelling and solving with discrete random variables 298
6.6 Review 304
7 Bernoulli and binomial distributions 315
7.1 Overview 316
7.2 Bernoulli distributions 317
7.3 Binomial distributions 323
7.4 The mean and variance of a binomial distribution 333
7.5 Modelling and solving with Bernoulli and binomial distributions 337
7.6 Review 342
Practice Assessment 1
Problem-solving and modelling task
Practice Assessment 2
Unit 3 Examination
Unit 4 Further Calculus, Trigonometry and Statistics 349
Topic 1 Further Integration
8 Further integration 351
8.1 Overview 352
8.2 Estimating the area under a curve 353
8.3 The fundamental theorem of calculus 365
8.4 Areas under a curve 374
8.5 Areas between curves 385
8.6 Modelling and solving with definite integrals 395
8.7 Review 408
Topic 2 Trigonometry
9 Cosine and sine rules 421
9.1 Overview 422
9.2 The sine rule 423
9.3 The cosine rule 432
9.4 Area of a triangle 440
9.5 Modelling and solving with the sine and cosine rules 445
9.6 Review 453
Topic 3 Continuous Random Variables and the Normal Distribution
10 General continuous random variables 461
10.1 Overview 462
10.2 Continuous random variables and the probability density function 463
10.3 Cumulative distribution functions 479
10.4 Measures of centre and spread 490
10.5 Review 499
11 Normal distributions 511
11.1 Overview 512
11.2 The normal distribution 513
11.3 Standardised normal variables 521
11.4 The inverse normal distribution 526
11.5 Modelling and solving with normal distributions 531
1.6 Review 538
Topic 4 Sampling and Proportions
Topic 5 Interval Estimates for Proportions
12 Sampling, proportions and interval estimates 547
12.1 Overview 548
12.2 Random sampling 550
12.3 Sample proportions 557
12.4 Confidence intervals for proportions 562
12.5 Review 568
Answers 573
Practice Assessment 3
Unit 4 Examination
Practice Assessment 4
Units 3 & 4 Examination
Glossary (online only)
