Jacaranda Maths Quest 11 Mathematical Methods Units 1 and 2 for Queensland, 2e learnON & Print

Learning with learnON ix

Teaching with learnON xv

Acknowledgements xvi

Problem-solving and modelling task guide

Unit 1 Surds, Algebra, Functions and Probability 01

Topic 1 Surds and Quadratic Functions

1 Surds 03

1.1 Overview 04

1.2 The real number system and surds 05

1.3 Simplifying surds 10

1.4 Operations with surds and rationalising the denominator 16

1.5 Review 23

Answers 26

2 Quadratic functions 29

2.1 Overview 30

2.2 Solving quadratic equations with rational roots 31

2.3 Solving quadratic equations over R 37

2.4 Graphs of quadratic functions 44

2.5 The discriminant 58

2.6 Modelling with quadratic functions 67

2.7 Review 77

Answers 81

Topic 2 Binomial Expansion and Cubic Functions

3 Binomial expansions and cubic functions 89

3.1 Overview 90

3.2 Pascal’s triangle and binomial expansions 91

3.3 The binomial theorem 101

3.4 Polynomials and cubic functions 105

3.5 Graphing cubic functions 111

3.6 Solving cubic equations 124

3.7 Modelling cubic functions 130

3.8 Review 137

Answers 141

Topic 3 Functions and Relations

4 Introduction to functions and relations 153

4.1 Overview 154

4.2 Functions and relations 155

4.3 Function notation 166

4.4 Piece-wise functions 176

4.5 Review 189

Answers 194

5 Graphs of relations and reciprocal functions 201

5.1 Overview 202

5.2 The circle 203

5.3 The sideways parabola and square root function 211

5.4 The reciprocal function 219

5.5 Review 231

Answers 235

Topic 4 Trigonometric Functions

6 Trigonometric functions 243

6.1 Overview 244

6.2 Trigonometry review 245

6.3 Radian measure 253

6.4 Unit circle definitions 262

6.5 Exact values and symmetry properties 273

6.6 Graphs of the sine, cosine and tangent functions 285

6.7 Solving trigonometric equations 295

6.8 Transformations of the sine and cosine functions 307

6.9 Modelling with trigonometric functions 321

6.10 Review 331

Answers 335

Topic 5 Probability

7 Probability 351

7.1 Overview 352

7.2 Concepts of probability 353

7.3 Relative frequency 365

7.4 Conditional probability 371

7.5 Independence 379

7.6 Review 387

Answers 392

Practice Assessment 1

Problem-solving and modelling task

Practice Assessment 2

Unit 1 Examination

Unit 2 Calculus and Further Functions 397

Topic 1 Exponential Functions

8 Indices and index laws 399

8.1 Overview 400

8.2 Index laws 401

8.3 Negative and fractional indices 408

8.4 Scientific notation 415

8.5 Review 420

Answers 423

9 Introduction to exponential functions 425

9.1 Overview 426

9.2 Solving exponential equations 427

9.3 Graphs of exponential functions 431

9.4 Modelling with exponential functions 441

9.5 Review 448

Answers 452

Topic 2 Logarithms and Logarithmic Functions

10 Logarithms and logarithmic functions 457

10.1 Overview 458

10.2 Logarithms and logarithmic laws 459

10.3 Indicial equations and logarithms 466

10.4 Graphs of logarithmic functions 473

10.5 Modelling with logarithmic functions 481

10.6 Review 491

Answers 494

Topic 3 Introduction to Differential Calculus

11 Rates of change and the concept of derivatives 499

11.1 Overview 500

11.2 Average rates of change 501

11.3 Differentiation from first principles 508

11.4 Differentiation by rule 517

11.5 Interpreting the derivative 526

11.6 Differentiation of power functions 532

11.7 Review 539

Answers 542

Topic 4 Applications of Differential Calculus

12 Graphical applications of derivatives 549

12.1 Overview 550

12.2 Instantaneous rates of change 551

12.3 Tangents and normals of a graph 556

12.4 Kinematics 566

12.5 Curve sketching 577

12.6 Review 591

Answers 594

Topic 5 Further Differentiation

13 Differentiation rules 601

13.1 Overview 602

13.2 The chain rule 603

13.3 The product rule 610

13.4 The quotient rule 614

13.5 Combinations of the chain rule, product rule and quotient rule 620

13.6 Review 623

Answers 626

Practice Assessment 3

Unit 2 Examination

Practice Assessment 4

Units 1&2 Examination

Glossary 631