Jacaranda Maths Quest 12 Mathematical Methods VCE Units 3&4 2E eBookPLUS & Print + StudyOn VCE Mathematical Methods CAS Units 3&4 2E (Book Code) Image

Jacaranda Maths Quest 12 Mathematical Methods VCE Units 3&4 2E eBookPLUS & Print + StudyOn VCE Mathematical Methods CAS Units 3&4 2E (Book Code)

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ISBN: 9780730365563
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Jacaranda Maths Quest 12 Mathematical Methods VCE Units 3 & 4 2e Print & eBookPLUS + studyON
This combined print and digital title has been designed to help students at the point of learning, so every student can experience success in VCE Mathematics – in the classroom, at home and thus ultimately in the exam.

The latest editions from the Jacaranda Maths Quest VCE series include these key updates:
• Features in-depth coverage of the Study Design, plus support resources to assist teachers’ implementation of the curriculum
• Jacaranda’s unique exam preparation tool, studyON, is now included free and fully integrated to help prepare students for their exams
• 1000s of new questions written for the series to expand students’ understanding and improve learning outcomes
• Exercises ensure that all students can experience success through the gradation of questions from easier through to more challenging
• Exciting new HTML5 interactivities and videos have been optimised for all devices

An access code for the eBookPLUS comes free on the inside cover of your printed text, so you can make the most of both the print and digital formats.

About this resource ix

About eBookPLUS and studyON xii

Acknowledgements xiii

1 Functions and graphs 1

1.1 Overview 1

1.2 Linear functions 3

1.3 Solving systems of equations 10

1.4 Quadratic functions 17

1.5 Cubic functions 26

1.6 Higher degree polynomials 36

1.7 Other algebraic functions 47

1.8 Combinations of functions 61

1.9 Modelling and applications 71

1.10 Review: exam practice 75

Answers 79

2 Trigonometric functions 94

2.1 Overview 94

2.2 Trigonometric symmetry properties 96

2.3 Trigonometric equations 108

2.4 General solution of trigonometric equations 115

2.5 Circular functions 120

2.6 The tangent function 127

2.7 Modelling and applications 135

2.8 Review: exam practice 138

Answers 142

3 Composite functions, transformations and inverses 148

3.1 Overview 148

3.2 Composite functions 150

3.3 Functional equations 154

3.4 Transformations 156

3.5 Transformations using matrices 164

3.6 Inverse graphs and relations 171

3.7 Inverse functions 178

3.8 Literal equations 187

3.9 Review: exam practice 190

Answers 194

Revision Topics 1 to 3 205

4 Exponential and logarithmic functions 206

4.1 Overview 206

4.2 Logarithm laws and equations 207

4.3 Logarithmic scales 214

4.4 Indicial equations 217

4.5 Logarithmic graphs 220

4.6 Exponential graphs 228

4.7 Applications 237

4.8 Review: exam practice 242

Answers 247

Revision Topic 4 257

5 Differentiation 258

5.1 Overview 258

5.2 Review of differentiation 260

5.3 Differentiation of exponential functions 275

5.4 Applications of exponential functions 280

5.5 Differentiation of trigonometric functions 285

5.6 Applications of trigonometric functions 290

5.7 Review: exam practice 297

Answers 301

6 Further differentiation and applications 306

6.1 Overview 306

6.2 The chain rule 308

6.3 The product rule 315

6.4 The quotient rule 321

6.5 Curve sketching 325

6.6 Maximum and minimum problems 336

6.7 Rates of change 342

6.8 Review: exam practice 351

Answers 355

7 Anti-differentiation 363

7.1 Overview 363

7.2 Anti-differentiation 365

7.3 Anti-derivatives of exponential and trigonometric functions 372

7.4 Families of curves 376

7.5 Applications 382

7.6 Review: exam practice 388

Answers 392

8 Integration 396

8.1 Overview 396

8.2 The fundamental theorem of integral calculus 398

8.3 Areas under curves 411

8.4 Areas between curves and average values 420

8.5 Applications 427

8.6 Review: exam practice 433

Answers 439

9 Logarithmic functions using calculus 442

9.1 Overview 442

9.2 The derivative of f(x) = loge(x) 444

9.3 The anti-derivative of f(x) =1/X 452

9.4 Applications 464

9.5 Review: exam practice 471

Answers 474

Revision Topics 5 to 9 478

10 Discrete random variables 479

10.1 Overview 479

10.2 Discrete random variables 481

10.3 Measures of centre and spread 491

10.4 Applications 502

10.5 Review: exam practice 509

Answers 513

11 The binomial distribution 517

11.1 Overview 517

11.2 Bernoulli trials 519

11.3 The binomial distribution 523

11.4 Applications 537

11.5 Review: exam practice 540

Answers 544

12 Continuous probability distributions 547

12.1 Overview 547

12.2 Continuous random variables and probability functions 549

12.3 The continuous probability density function 560

12.4 Measures of centre and spread 566

12.5 Linear transformations 580

12.6 Review: exam practice 587

Answers 592

13 The normal distribution 597

13.1 Overview 597

13.2 The normal distribution 599

13.3 Calculating probabilities and the standard normal distribution 606

13.4 The inverse normal distribution 613

13.5 Mixed probability application problems 616

13.6 Review: exam practice 622

Answers 627

14 Statistical inference 629

14.1 Overview 629

14.2 Population parameters and sample statistics 631

14.3 The distribution of 637

14.4 Confidence intervals 644

14.5 Review: exam practice 650

Answers 653

Revision Topics 10 to 14 655

Glossary 657

Index 661