Jacaranda Maths Quest 12 Mathematical Methods Units 3&4 for Queensland eBookPLUS & Print + StudyOn Mathematical Methods Units 3&4 for Qld (Book Code) Image

Jacaranda Maths Quest 12 Mathematical Methods Units 3&4 for Queensland eBookPLUS & Print + StudyOn Mathematical Methods Units 3&4 for Qld (Book Code)

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ISBN: 9780730379959
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Jacaranda Maths Quest 12 Mathematical Methods Units 3 & 4 for Queensland Print & eBookPLUS + studyON
This combined print and digital title is designed to help teachers unpack the new curriculum and help students at the point of learning, so that every student can experience success in the classroom, at home and thus ultimately in the exam.

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About this resource ix

About eBookPLUS and studyON xii

Acknowledgements xiii

Unit 3 Further Calculus 1

Topic 1 The Logarithmic Function 2

1 The logarithmic function 2 1

1.1 Overview 1

1.2 Review of the index laws 2

1.3 Logarithmic laws and equations 7

1.4 Logarithmic scales 17

1.5 Indicial equations 21

1.6 Logarithmic graphs 25

1.7 Applications 32

1.8 Review: exam practice 37

Answers 41

Revision Unit 3 Topic 1

Chapter 1 47

Topic 2 Further Differentiation and Applications 2

2 Calculus of exponential functions 48

2.1 Overview 48

2.2 Review of limits and differentiation 49

2.3 The exponential function 54

2.4 Differentiation of exponential functions 61

2.5 Applications of exponential functions 64

2.6 Review: exam practice 74

Answers 78

3 Calculus of logarithmic functions 83

3.1 Overview 83

3.2 The natural logarithm and the function y = loge (x) 84

3.3 The derivative of y = loge (x) 91

3.4 Applications of logarithmic functions 94

3.5 Review: exam practice 97

Answers 100

4 Calculus of trigonometric functions 107

4.1 Overview 107

4.2 Review of the unit circle, symmetry and exact values 108

4.3 Review of solving trigonometric equations with and without the use of technology 117

4.4 Review of graphs of trigonometric functions of the form y = A sin(B (x + C)) + D and y = A cos(B (x + C)) + D 122

4.5 Derivatives of the sine and cosine functions 130

4.6 Applications of trigonometric functions 136

4.7 Review: exam practice 145

Answers 148

5 Further differentiation and applications 156

5.1 Overview 156

5.2 The chain rule 157

5.3 The product rule 162

5.4 The quotient rule 165

5.5 Applications of differentiation 170

5.6 Review: exam practice 188

Answers 191

Revision Unit 3 Topic 2

Chapters 2, 3, 4 and 5 196

Topic 3 Integrals

6 Antidifferentiation 197

6.1 Overview 197

6.2 Antidifferentiation of rational functions 198

6.3 Antidifferentiation of exponential functions 202

6.4 Antidifferentiation of logarithmic functions 205

6.5 Antidifferentiation of sine and cosine functions 208

6.6 Further integration 211

6.7 Review: exam practice 220

Answers 224

7 Integration 228

7.1 Overview 228

7.2 Estimating the area under a curve 229

7.3 The fundamental theorem of calculus and definite integrals 240

7.4 Areas under curves 247

7.5 Areas between curves 257

7.6 Applications of integration 265

7.7 Review: exam practice 275

Answers 280

Revision Unit 3 Topic 3

Chapters 6 and 7 285

Practice Assessment 1

Mathematical Methods: Problem solving and modelling task 286

Practice Assessment 2

Mathematical Methods: Unit 3 examination 290

Unit 4 Further Functions and Statistics 302

Topic 1 Further Differentiation and Applications 3

8 The second derivative and applications of differentiation 302

8.1 Overview 302

8.2 Second derivatives 303

8.3 Concavity and points of inflection 306

8.4 Curve sketching 311

8.5 Applications of the second derivative 321

8.6 Review: exam practice 327

Answers 332

Revision Unit 4 Topic 1

Chapter 8 337

Topic 2 Trigonometric Functions 2

9 Cosine and sine rules 338

9.1 Overview 338

9.2 Review of trigonometric ratios and the unit circle 339

9.3 The sine rule 347

9.4 The cosine rule 355

9.5 Area of a triangle 362

9.6 Applications of the sine and cosine rules 367

9.7 Review: exam practice 372

Answers 375

Revision Unit 4 Topic 2

Chapter 9 377

Topic 3 Discrete Random variables 2

10 Discrete random variables 378

10.1 Overview 378

10.2 Bernoulli distributions 379

10.3 Bernoulli random variables 380

10.4 Binomial distributions 385

10.5 The mean and variance of a binomial distribution 393

10.6 Applications 398

10.7 Review: exam practice 401

Answers 404

Revision Unit 4 Topic 3

Chapter 10 406

Topic 4 Continuous Random Variables and the Normal Distribution

11 General continuous random variables 407

11.1 Overview 407

11.2 Continuous random variables and the probability density function 408

11.3 Cumulative distribution functions 419

11.4 Measures of centre and spread 429

11.5 Review: exam practice 441

Answers 446

12 The normal distribution 449

12.1 Overview 449

12.2 The normal distribution 450

12.3 Standardised normal variables 457

12.4 The inverse normal distribution 468

12.5 Applications of the normal distribution 473

12.6 Review: exam practice 479

Answers 482

Revision Unit 4 Topic 4

Chapters 11 and 12 484

Topic 5 Interval Estimates For Proportions

13 Sampling and confidence intervals 485

13.1 Overview 485

13.2 Sample statistics 486

13.3 The distribution of p 491

13.4 Confidence intervals 499

13.5 Review: exam practice 504

Answers 508

Revision Unit 4 Topic 5

Chapter 13 510

Practice Assessment 3

Mathematical Methods: Unit 4 examination 511

Practice Assessment 4

Mathematical Methods: Units 3 & 4 examination 522

Glossary 532

Index 535