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

Author(s): |
Michell |

ISBN: |
9780730379959 |

Pub date: |
September 2019 |

RRP: |
$89.95 |

**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.

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.

The latest editions from the

*Jacaranda Maths Quest for Queensland*series include these key updates:

- Inclusion of important language to help frame question sets such as Simple Familiar, Complex Familiar and Complex Unfamiliar
- New assessment practice sections designed as per QCAA guidelines and samples, including Problem Solving and Modelling Tasks
- New chapter questions and activities are aligned with Marzano and Kendall’s new taxonomy: 4 levels of cognitive process – retrieval, comprehension, analysis and knowledge
- Jacaranda’s unique exam preparation tool, studyON, is now included free and fully integrated to help prepare students for their exams
- Provides an unmatched interactive learning experience, through a variety of new interactivities to help students understand challenging concepts
- Free online Fully Worked Solutions with every student text
- Exam practice questions included in every chapter

EXCLUSIVE OFFER: Get four eBookPLUS and four studyON activation codes free in every print text!

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 *= log* _{e} *(

*x*) 84

3.3 The derivative of *y *= log* _{e} *(

*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