# Jacaranda Maths Quest 11 Specialist Mathematics VCE Units 1 and 2 2E LearnON and Print

 Author(s): Rozen ISBN: 9781119876656 Pub date: October 2022 RRP: \$85

Jacaranda Maths Quest 11 Specialist Mathematics VCE Units 1 and 2

Everything your students need to succeed.

The best Mathematics series for the new VCE Study Design. Developed by expert Victorian teachers for, VCE students.

Get exam ready: past VCAA exam questions (all since 2013)

Students can start preparing from lesson one, with past VCAA exam questions embedded in every lesson.  Practice, customisable SACs available for all Units to build student competence and confidence.

Learn online with Australia’s most powerful learning platform, learnON

Be confident your students can get unstuck and progress, in class or at home. For every question online they receive immediate feedback and fully worked solutions. Teacher-led videos to learn and re-learn. Instant reports make tracking progress simple.

Combine units flexibly with the Jacaranda Supercourse

An Australian first, build the course you’ve always wanted with the Jacaranda Supercourse. You can combine all Methods Units 1 to 4, so students can move backwards and forwards freely. Or Methods and General Units 1 & 2 for when students switch courses. The possibilities are endless!

Acknowledgements xiv

1 Combinatorics 1

1.1 Overview 2

1.2 Counting techniques 3

1.3 Factorials and permutations 15

1.4 Permutations with restrictions 23

1.5 Combinations 31

1.6 Applications of permutations and combinations 40

1.7 Pascal’s triangle and the pigeon-hole principle 47

1.8 Review 55

2 Sequences and series 63

2.1 Overview 64

2.2 Describing sequences 65

2.3 Arithmetic sequences 69

2.4 Arithmetic series 75

2.5 Geometric sequences 78

2.6 Geometric series 86

2.7 Applications of sequences and series 92

2.8 Review 101

3 Logic and algorithms 111

3.1 Overview 112

3.2 Statements (propositions), connectives and truth tables 113

3.3 Valid and invalid arguments 120

3.4 Boolean algebra and digital logic 131

3.5 Sets and Boolean algebra 139

3.6 Algorithms and pseudocode 149

3.7 Review 166

4 Proof and number 189

4.1 Overview 190

4.2 Number systems and mathematical statements 191

4.3 Direct and indirect methods of proof 206

4.4 Proofs with rational and irrational numbers 212

4.5 Proof by mathematical induction 218

4.6 Proof of divisibility using induction 223

4.7 Review 227

5 Matrices 233

5.1 Overview 234

5.2 Addition, subtraction and scalar multiplication of matrices 235

5.3 Matrix multiplication 243

5.4 Determinants and inverses 251

5.5 Matrix equations 260

5.6 Review 271

6 Graph theory 279

6.1 Overview 280

6.2 Introduction to graph theory 281

6.3 Planar graphs and Euler’s formula 300

6.4 Eulerian and Hamiltonian graphs 311

6.5 Weighted graphs and trees 321

6.6 Bipartite graphs and the Hungarian algorithm 331

6.7 Review 343

7 Trigonometric ratios and applications 367

7.1 Overview 368

7.2 Review of trigonometry 369

7.3 The sine rule 379

7.4 The cosine rule 385

7.5 Arc length, sectors and segments 390

7.6 Review 398

8 Trigonometric identities 405

8.1 Overview 406

8.2 Pythagorean identities 407

8.3 Compound angle formulas 416

8.4 Double and half angle formulas 426

8.5 Converting a cos(x) + b sin(x) to r cos(x ± α) or r sin(x ± α) 435

8.6 Review 441

9 Vectors in the plane 449

9.1 Overview 450

9.2 Vectors and scalars 451

9.3 Position vectors in the plane 459

9.4 Scalar multiplication of vectors 470

9.5 The scalar (dot) product 475

9.6 Projections of vectors—scalar and vector resolutes 483

9.7 Review 489

10 Complex numbers 497

10.1 Overview 498

10.2 Introduction to complex numbers 499

10.3 Basic operations on complex numbers 504

10.4 Complex conjugates and division of complex numbers 510

10.5 The complex plane (the Argand plane) 517

10.6 Complex numbers in polar form 524

10.7 Basic operations on complex numbers in polar form 536

10.8 Solving quadratic equations with complex roots 546

10.9 Lines, rays, circles, ellipses and regions in the complex plane 550

10.10 Review 562

11 Transformations 577

11.1 Overview 578

11.2 Translations 579

11.3 Reflections and rotations 588

11.4 Dilations 603

11.5 Combinations of transformations 610

11.6 Review 619

12 Functions, relations and graphs 627

12.1 Overview 628

12.2 The absolute value function 629

12.3 Partial fractions 636

12.4 Reciprocal graphs 645

12.5 The reciprocal trigonometric functions 654

12.6 Inverse trigonometric functions 669

12.7 Circles and ellipses 683

12.8 Hyperbolas 695

12.9 Polar coordinates, equations and graphs 703

12.10 Parametric equations 712

12.11 Review 717

13 Simulation, sampling and sampling distributions 745

13.1 Overview 746

13.2 Random experiments, events and event spaces 747

13.3 Simulation 750

13.4 Discrete random variables 757

13.5 Sampling 768

13.6 Sampling distribution of sample means 774

13.7 Review 786