Jacaranda Maths Quest 12 Mathematical Methods VCE Units 3&4 Third Edition (learnON & Print)

Part of the series Maths Quest VCE.

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Jacaranda Maths Quest 12 Mathematical Methods VCE Units 3 and 4

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The best Mathematics series for the new VCE Study Design. Developed by expert Victorian teachers for VCE students.

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Table of Contents

About This Resource v

Acknowledgements xii

1 Functions and graphs 1

1.1 Overview 2

1.2 Linear functions 3

1.3 Solving systems of equations 11

1.4 Quadratic functions 18

1.5 Cubic functions 28

1.6 Higher degree polynomials 40

1.7 Other algebraic functions 50

1.8 Combinations of functions 66

1.9 Modelling and applications 77

1.10 Review 82

Answers 87

2 Trigonometric (circular) functions 103

2.1 Overview 104

2.2 Trigonometric symmetry properties 105

2.3 Trigonometric equations 118

2.4 General solutions of trigonometric equations 125

2.5 The sine and cosine functions 130

2.6 The tangent function 139

2.7 Modelling and applications 148

2.8 Review 154

Answers 159

3 Composite functions, transformations and inverses 167

3.1 Overview 168

3.2 Composite functions 169

3.3 Transformations 174

3.4 Inverse graphs 182

3.5 Inverse functions 192

3.6 Literal equations 201

3.7 Review 206

Answers 211

4 Exponential and logarithmic functions 223

4.1 Overview 224

4.2 Logarithm laws and equations 225

4.3 Logarithmic scales 234

4.4 Indicial equations 238

4.5 Logarithmic graphs 242

4.6 Exponential graphs 250

4.7 Applications 262

4.8 Review 270

Answers 276

5 Differentiation 287

5.1 Overview 288

5.2 Review of differentiation 289

5.3 Differentiation of exponential functions 304

5.4 Applications of exponential functions 310

5.5 Differentiation of trigonometric functions 316

5.6 Applications of trigonometric functions 322

5.7 Differentiation and application of logarithmic functions 330

5.8 Review 338

Answers 345

6 Further differentiation and applications 353

6.1 Overview 354

6.2 The chain rule 355

6.3 The product rule 363

6.4 The quotient rule 370

6.5 Curve sketching 375

6.6 Maximum and minimum problems 387

6.7 Rates of change 394

6.8 Newton’s method 403

6.9 Review 408

Answers 415

7 Anti-differentiation 425

7.1 Overview 426

7.2 Anti-differentiation 427

7.3 Anti-derivatives of exponential and trigonometric functions 435

7.4 The anti-derivative of f(x) = 1 /x 440

7.5 Families of curves 444

7.6 Applications 452

7.7 Review 458

Answers 464

8 Integral calculus 471

8.1 Overview 472

8.2 The fundamental theorem of integral calculus 473

8.3 Areas under curves 484

8.4 Areas between curves and average values 497

8.5 Applications 507

8.6 Review 522

Answers 529

9 Discrete random variables 535

9.1 Overview 536

9.2 Probability review 537

9.3 Discrete random variables 544

9.4 Measures of centre and spread 554

9.5 Applications 565

9.6 Review 572

Answers 577

10 The binomial distribution 583

10.1 Overview 584

10.2 Bernoulli trials 585

10.3 The binomial distribution 590

10.4 Applications 604

10.5 Review 608

Answers 614

11 Continuous probability distributions 617

11.1 Overview 618

11.2 Continuous random variables and probability functions 619

11.3 The continuous probability density function 631

11.4 Measures of centre and spread 638

11.5 Linear transformations 651

11.6 Review 657

Answers 664

12 The normal distribution 671

12.1 Overview 672

12.2 The normal distribution 673

12.3 Calculating probabilities and the standard normal distribution 681

12.4 The inverse normal distribution 688

12.5 Mixed probability applications 693

12.6 Review 702

Answers 709

13 Statistical inference 713

13.1 Overview 714

13.2 Population parameters and sample statistics 715

13.3 The distribution of the sample proportion 721

13.4 Confidence intervals 729

13.5 Review 736

Answers 744

Algorithms and Pseudocode

Glossary 747

Index 751