# Maths Quest 11 Mathematical Methods VCE Units 1 and 2 & eBookPLUS + StudyOn VCE Mathematical Methods Units 1 and 2

Author/s |
Michell |
---|---|

ISBN13 | 9780730322986 |

Pub date | November 2015 |

Pages | 784 |

RRP | $89.95 |

Introduction vii

About eBookPLUS and studyON x

Acknowledgements xi

**Topic 1 Lines and linear relationships 2**

1.1 Kick off with CAS 3

1.2 Linearly related variables, linear equations and inequations 4

1.3 Systems of 3 × 3 simultaneous linear equations 16

1.4 Linear graphs and their equations 21

1.5 Intersections of lines and their applications 33

1.6 Coordinate geometry of the straight line 40

1.7 Review 52

Answers 53

**Topic 2 Algebraic foundations 58**

2.1 Kick off with CAS 59

2.2 Algebraic skills 60

2.3 Pascal’s triangle and binomial expansions 67

2.4 The binomial theorem 72

2.5 Sets of real numbers 80

2.6 Surds 86

2.7 Review 97

Answers 98

**Topic 3 Quadratic relationships 104**

3.1 Kick off with CAS 105

3.2 Quadratic equations with rational roots 106

3.3 Quadratics over R 110

3.4 Applications of quadratic equations 122

3.5 Graphs of quadratic polynomials 127

3.6 Determining the rule of a quadratic polynomial from a graph 138

3.7 Quadratic inequations 142

3.8 Quadratic models and applications 149

3.9 Review 154

Answers 155

**Topic 4 Cubic polynomials 164**

4.1 Kick off with CAS 165

4.2 Polynomials 166

4.3 The remainder and factor theorems 177

4.4 Graphs of cubic polynomials 185

4.5 Equations of cubic polynomials 195

4.6 Cubic models and applications 202

4.7 Review 209

Answers 210

**Topic 5 Higher-degree polynomials 222**

5.1 Kick off with CAS 223

5.2 Quartic polynomials 224

5.3 Families of polynomials 231

5.4 Numerical approximations to roots of polynomial equations 240

5.5 Review 250

Answers 251

**Topic 6 Functions and relations 258**

6.1 Kick off with CAS 259

6.2 Functions and relations 260

6.3 The circle 269

6.4 The rectangular hyperbola and the truncus 278

6.5 The relation y2 = x 294

6.6 Other functions and relations 305

6.7 Transformations of functions 319

6.8 Review 328

Answers 329

**Topic 7 Matrices and applications to**

transformations 348

7.1 Kick off with CAS 349

7.2 Addition, subtraction and scalar multiplication of matrices 350

7.3 Matrix multiplication 357

7.4 Determinants and inverses of 2 × 2 matrices 362

7.5 Matrix equations and solving 2 × 2 linear simultaneous equations 367

7.6 Translations 376

7.7 Reflections 383

7.8 Dilations 389

7.9 Combinations of transformations 394

7.10 Review 397

Answers 398

**Topic 8 Probability 404**

8.1 Kick off with CAS 405

8.2 Probability review 406

8.3 Conditional probability 417

8.4 Independence 425

8.5 Counting techniques 430

8.6 Binomial coefficients and Pascal’s triangle 443

8.7 Review 451

Answers 452

**Topic 9 Trigonometric functions 1 456**

9.1 Kick off with CAS 457

9.2 Trigonometric ratios 458

9.3 Circular measure 465

9.4 Unit circle definitions 473

9.5 Symmetry properties 482

9.6 Graphs of the sine and cosine functions 493

9.7 Review 503

Answers 504

**Topic 10 Trigonometric functions 2 510**

10.1 Kick off with CAS 511

10.2 Trigonometric equations 512

10.3 Transformations of sine and cosine graphs 521

10.4 Applications of sine and cosine functions 533

10.5 The tangent function 540

10.6 Trigonometric relationships 550

10.7 Review 558

Answers 559

**Topic 11 Exponential functions 570**

11.1 Kick off with CAS 571

11.2 Indices as exponents 572

11.3 Indices as logarithms 579

11.4 Graphs of exponential functions 587

11.5 Applications of exponential functions 596

11.6 Inverses of exponential functions 604

11.7 Review 618

Answers 619

**Topic 12 Introduction to differential calculus 630**

12.1 Kick off with CAS 631

12.2 Rates of change 632

12.3 Gradients of secants 640

12.4 The derivative function 645

12.5 Differentiation of polynomials by rule 652

12.6 Review 662

Answers 663

**Topic 13 Differentiation and applications 668**

13.1 Kick off with CAS 669

13.2 Limits, continuity and differentiability 670

13.3 Derivatives of power functions 679

13.4 Coordinate geometry applications of differentiation 686

13.5 Curve sketching 695

13.6 Optimisation problems 704

13.7 Rates of change and kinematics 710

13.8 Review 720

Answers 721

**Topic 14 Anti-differentiation and introduction to integral calculus 728**

14.1 Kick off with CAS 729

14.2 Anti-derivatives 730

14.3 Anti-derivative functions and graphs 736

14.4 Applications of anti-differentiation 742

14.5 The definite integral 748

14.6 Review 758

Answers 759

Index 765