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MathsQuest 12: Mathematical Methods VCE Units 3 and 4 & eBookPLUS + StudyOn VCE Mathematical Methods Units 3 and 4

MathsQuest 12: Mathematical Methods VCE Units 3 and 4 & eBookPLUS + StudyOn VCE Mathematical Methods Units 3 and 4

Margaret Swale, Sue Michell, Steven Morris, Raymond Rozen

ISBN: 978-0-730-32313-6

Dec 2015, Jacaranda

560 pages

Introduction vii

About eBookPLUS and studyON x

Acknowledgements xi

TOPIC 1 Solving equations 2

1.1 Kick off with CAS 3

1.2 Polynomials 4

1.3 Trigonometric symmetry properties 12

1.4 Trigonometric equations and general solutions 24

1.5 Literal and simultaneous equations 33

1.6 Review 42

Answers 43

TOPIC 2 Functions and graphs 46

2.1 Kick off with CAS 47

2.2 Polynomial functions 48

2.3 Other algebraic functions 68

2.4 Combinations of functions 82

2.5 Non-algebraic functions 90

2.6 Modelling and applications 111

2.7 Review 118

Answers 119

TOPIC 3 Composite functions, transformations and inverses 136

3.1 Kick off with CAS 137

3.2 Composite functions and functional equations 138

3.3 Transformations 142

3.4 Transformations using matrices 148

3.5 Inverse graphs and relations 153

3.6 Inverse functions 159

3.7 Review 165

Answers 166

TOPIC 4 Logarithmic functions 174

4.1 Kick off with CAS 175

4.2 Logarithm laws and equations 176

4.3 Logarithmic scales 183

4.4 Indicial equations 186

4.5 Logarithmic graphs 189

4.6 Applications 195

4.7 Review 200

Answers 201

TOPIC 5 Differentiation 206

5.1 Kick off with CAS 207

5.2 Review of differentiation 208

5.3 Differentiation of exponential functions 219

5.4 Applications of exponential functions 223

5.5 Differentiation of trigonometric functions 228

5.6 Applications of trigonometric functions 233

5.7 Review 241

Answers 242

TOPIC 6 Further differentiation and applications 248

6.1 Kick off with CAS 249

6.2 The chain rule 250

6.3 The product rule 256

6.4 The quotient rule 262

6.5 Curve sketching 266

6.6 Maximum and minimum problems 274

6.7 Rates of change 281

6.8 Review 290

Answers 291

TOPIC 7 Antidifferentiation 300

7.1 Kick off with CAS 301

7.2 Antidifferentiation 302

7.3 Antiderivatives of exponential and trigonometric functions 308

7.4 Families of curves and applications 312

7.5 Review 322

Answers 323

TOPIC 8 Integration 326

8.1 Kick off with CAS 327

8.2 The fundamental theorem of integral calculus 328

8.3 Areas under curves 340

8.4 Applications 349

8.5 Review 361

Answers 362

TOPIC 9 Logarithmic functions using calculus 366

9.1 Kick off with CAS 367

9.2 The derivative of f (x) = loge(x) 368

9.3 The antiderivative of f (x) = 1 x 375

9.4 Applications 382

9.5 Review 391

Answers 392

TOPIC 10 Discrete random variables 396

10.1 Kick off with CAS 397

10.2 Discrete random variables 398

10.3 Measures of centre and spread 408

10.4 Applications 417

10.5 Review 424

Answers 425

TOPIC 11 The binomial distribution 428

11.1 Kick off with CAS 429

11.2 Bernoulli trials 430

11.3 The binomial distribution 434

11.4 Applications 445

11.5 Review 448

Answers 449

TOPIC 12 Continuous probability distributions 452

12.1 Kick off with CAS 453

12.2 Continuous random variables and probability functions 454

12.3 The continuous probability density function 464

12.4 Measures of centre and spread 470

12.5 Linear transformations 482

12.6 Review 489

Answers 490

TOPIC 13 The normal distribution 496

13.1 Kick off with CAS 497

13.2 The normal distribution 498

13.3 Calculating probabilities and the standard normal distribution 505

13.4 The inverse normal distribution 509

13.5 Mixed probability application problems 512

13.6 Review 519

Answers 520

TOPIC 14 Statistical inference 522

14.1 Kick off with CAS 523

14.2 Population parameters and sample statistics 524

14.3 The distribution of p^ 529

14.4 Confidence intervals 535

14.5 Review 540

Answers 541

Index 543