Jacaranda Maths Quest 11 Mathematical Methods Units 1&2 for Queensland eBookPLUS & Print + StudyOn Mathematical Methods Units 1&2 for Qld (Book Code)

About this resource ix

About eBookPLUS and studyON xii

Acknowledgements xiii

Unit 1 Algebra, Statistics and Functions 1

Topic 1 Arithmetic and geometric sequences and series 1

1 Arithmetic sequences 1

1.1 Overview 1

1.2 Arithmetic sequences 2

1.3 The general form of an arithmetic sequence 8

1.4 The sum of an arithmetic sequence 15

1.5 Applications of arithmetic sequences 19

1.6 Review: exam practice 26

Answers 29

Revision Unit 1 Topic 1 Chapter 1 31

Topic 2 Functions and graphs

2 Functions 32

2.1 Overview 32

2.2 Functions and relations 33

2.3 Function notation 44

2.4 Transformations of functions 53

2.5 Piece-wise functions 62

2.6 Review: exam practice 74

Answers 80

3 Quadratic relationships 89

3.1 Overview 89

3.2 Graphs of quadratic functions 90

3.3 Solving quadratic equations with rational roots 103

3.4 Factorising and solving quadratics over R 109

3.5 The discriminant 116

3.6 Modelling with quadratic functions 126

3.7 Review: exam practice 134

Answers 138

4 Inverse proportions and graphs of relations 145

4.1 Overview 145

4.2 The hyperbola 146

4.3 Inverse proportion 157

4.4 The circle 162

4.5 The sideways parabola 170

4.6 Review: exam practice 178

Answers 182

5 Powers and polynomials 191

5.1 Overview 191

5.2 Polynomials 192

5.3 Graphs of cubic polynomials 203

5.4 The factor and remainder theorems 217

5.5 Solving cubic equations 224

5.6 Cubic models and applications 229

5.7 Graphs of quartic polynomials 235

5.8 Solving polynomial equations 242

5.9 Review: exam practice 250

Answers 254

Revision Unit 1 Topic 2 Chapters 2 to 5 270

Practice Assessment 1 Problem solving and modelling task: Functions and graphs 271

Topic 3 Counting and probability

6 Counting and probability 274

6.1 Overview 274

6.2 Fundamentals of probability 275

6.3 Relative frequency 286

6.4 Conditional probability 290

6.5 Independence 299

6.6 Permutations and combinations 305

6.7 Pascal’s triangle and binomial expansions 319

6.8 Review: exam practice 329

Answers 332

Revision Unit 1 Topic 3 Chapter 6 336

Topic 4 Exponential functions 1

7 Indices 337

7.1 Overview 337

7.2 Index laws 338

7.3 Negative and rational indices 343

7.4 Indicial equations and scientific notation 348

7.5 Review: exam practice 354

Answers 356

Revision Unit 1 Topic 4 Chapter 7 358

Topic 5 Arithmetic and geometric sequences and series 2

8 Geometric sequences 359

8.1 Overview 359

8.2 Recursive definition and the general term of geometric sequences 360

8.3 The sum of a geometric sequence 371

8.4 Geometric sequences in context 378

8.5 Review: exam practice 384

Answers 387

Revision Unit 1 Topic 5 Chapter 8 389

Practice Assessment 2 Unit 1 internal examination 390

Unit 2 Calculus and Further Functions

Topic 1 The logarithmic function 1

Topic 2 Exponential functions 2

9 Exponential and logarithmic functions 399

9.1 Overview 399

9.2 Exponential functions 400

9.3 functions 410

9.4 Modelling with exponential functions 423

9.5 Solving equations with indices 432

9.6 Review: exam practice 438

Answers 442

Revision Unit 2 Topic 1 AND 2 Chapter 9 449

Topic 3 Trigonometric functions 1

10 Trigonometric functions 450

10.1 Overview 450

10.2 Trigonometry review 451

10.3 Radian measure 459

10.4 Unit circle definitions 469

10.5 Exact values and symmetry properties 480

10.6 Graphs of the sine, cosine and tangent functions 490

10.7 Transformations of sine and cosine graphs 499

10.8 Solving trigonometric equations 513

10.9 Modelling with trigonometric functions 524

10.10 Review: exam practice 531

Answers 536

Revision Unit 2 Topic 3 Chapter 10 550

Topic 4 Introduction to differential calculus

11 Rates of change 551

11.1 Overview 551

11.2 Exploring rates of change 552

11.3 The difference quotient 561

11.4 Differentiating simple functions 567

11.5 Interpreting the derivative 570

11.6 Review: exam practice 576

Answers 580

12 Properties and applications of derivatives 584

12.1 Overview 584

12.2 Differentiation by formula 585

12.3 The derivative as a function 589

12.4 Properties of the derivative 595

12.5 Differentiation of power and polynomial functions 599

12.6 Review: exam practice 604

Answers 607

13 Applications of derivatives 611

13.1 Overview 611

13.2 Gradient and equation of a tangent 612

13.3 Displacement–time graphs 620

13.4 Sketching curves using derivatives 629

13.5 Modelling optimisation problems 643

13.6 Review: exam practice 648

Answers 651

Revision Unit 2 Topic 4 Chapters 11 to 13 656

Topic 5 Further differentiation and applications 1

14 Differentiation rules 657

14.1 Overview 657

14.2 The product rule 658

14.3 The quotient rule 660

14.4 The chain rule 666

14.5 Applications of the product, quotient and chain rules 672

14.6 Review: exam practice 674

Answers 677

Revision Unit 2 Topic 5 Chapter 14 682

Topic 6 Discrete random variables 1

15 Discrete random variables 1 683

15.1 Overview 683

15.2 Discrete random variables 684

15.3 Expected values 695

15.4 Variance and standard deviation 704

15.5 Applications of discrete random variables 712

15.6 Review: exam practice 718

Answers 723

Revision Unit 2 Topic 6 Chapter 15 727

Practice Assessment 3 Unit 2 internal examination 728

Practice Assessment 4 Units 1 and 2 internal examination 735

Glossary 743

Index 750