# Maths Quest 12 Specialist Mathematics VCE Units 3 and 4 & eBookPLUS + StudyOn VCE Specialist Mathematics Units 3 and 4

Author/s |
Rozen |
---|---|

ISBN13 | 9780730323037 |

Pub date | November 2015 |

Pages | 752 |

RRP | $89.95 |

* Maths Quest 12 Specialist Mathematics VCE Units 3 and 4 with eBookPLUS and studyON VCE Specialist Mathematics Units 3 and 4* provides comprehensive coverage of the new VCE Study Design for 2016-2019. It includes Jacaranda’s unique exam preparation tool,

**studyON**, which has been fully integrated with the text to maximise every student’s opportunity for exam success.

**Features and benefits**

• Many HTML5 interactivities are available. These are designed to engage, excite and enhance understanding by bringing difficult concepts to life.

• The theory is written by highly experienced and successful teachers with a proven and fundamental understanding of how students learn mathematics and succeed in exams.

• Every exercise contains three levels of carefully graded questions which allow students to practise, consolidate and master their knowledge independently.

• Thousands of new questions have been written exclusively for this series, including many higher level questions that stretch students’ understanding of mathematics for improved learning outcomes.

• CAS support is provided within the student text through activities and questions. Additionally, students can obtain detailed step-by-step instructions by accessing the TI-Nspire CAS or the Casio ClassPad II Calculator Manuals in the Prelim section of their eBookPLUS.

•

**studyON VCE Specialist Mathematics Units 3 and 4**is fully integrated with the student text. studyON is Jacaranda’s unique study, revision and exam preparation tool, containing all past VCAA exam questions from 2006.

**Students can rely on Jacaranda’s dedicated customer service and support.**

This resource is a hard-copy student text that includes the

**eBookPLUS**and

**studyON VCE Specialist Mathematics Units 3 and 4**.

**studyON**for Units 3 and 4 is a comprehensive study, revision and exam preparation tool that delivers proven learning outcomes through a range of interactivities, videos and past VCAA exam questions.

**Features and benefits**

•

**Sit exams:**VCAA exam questions from 2006 onwards, along with marking guides and examiner comments. Students receive instant feedback and can track their results at a concept, topic or whole-course level.

•

**Concepts:**Concept summary screens provide concise, in-depth explanations supported by relevant examples.

•

**Read more:**Hyperlinks direct students to more information in the Jacaranda eBookPLUS.

•

**See more:**Videos and animations bring concepts to life.

•

**Do more:**Hands-on interactivities enhance understanding of on-screen concepts and provide instant feedback.

Introduction vii

About eBookPLUS and studyON x

Acknowledgements xi

**Topic 1 Sketching graphs 2**

1.1 Kick off with CAS 3

1.2 An introduction to the modulus function 4

1.3 Sketching graphs of reciprocal functions 7

1.4 Sketching graphs of rational functions 13

1.5 Sketching graphs of y = |f (x )| and y = f (|x |) from y = f (x ) 27

1.6 Circles, ellipses and hyperbolas 34

1.7 Review 43

Answers 44

**Topic 2 Trigonometry 56**

2.1 Kick off with CAS 57

2.2 Reciprocal trigonometric functions 58

2.3 Trigonometric identities using reciprocal trigonometric functions 66

2.4 Compound-angle formulas 69

2.5 Double-angle formulas 76

2.6 Inverse trigonometric functions 85

2.7 General solutions of trigonometric equations 97

2.8 Graphs of reciprocal trigonometric functions 106

2.9 Graphs of inverse trigonometric functions 115

2.10 Review 122

Answers 123

**Topic 3 Complex numbers 130**

3.1 Kick off with CAS 131

3.2 Complex numbers in rectangular form 132

3.3 Complex numbers in polar form 142

3.4 Polynomial equations 156

3.5 Subsets of the complex plane: circles, lines and rays 162

3.6 Roots of complex numbers 170

3.7 Review 177

Answers 178

**Topic 4 Kinematics 184**

4.1 Kick off with CAS 185

4.2 Constant acceleration 186

4.3 Motion under gravity 190

4.4 Velocity–time graphs 193

4.5 Variable acceleration 197

4.6 Review 204

Answers 205

**Topic 5 Vectors in three dimensions 208**

5.1 Kick off with CAS 209

5.2 Vectors 210

5.3 i∼ j∼k∼notation 215

5.4 Scalar product and applications 228

5.5 Vector proofs using the scalar product 237

5.6 Parametric equations 242

5.7 Review 248

Answers 249

**Topic 6 Mechanics 256**

6.1 Kick off with CAS 257

6.2 Statics of a particle 258

6.3 Inclined planes and connected particles 272

6.4 Dynamics 279

6.5 Dynamics with connected particles 289

6.6 Review 299

Answers 300

**Topic 7 Differential calculus 302**

7.1 Kick off with CAS 303

7.2 Review of differentiation techniques 304

7.3 Applications of differentiation 314

7.4 Implicit and parametric differentiation 324

7.5 Second derivatives 331

7.6 Curve sketching 338

7.7 Derivatives of inverse trigonometric functions 351

7.8 Related rate problems 360

7.9 Review 368

Answers 369

**Topic 8 integral calculus 378**

8.1 Kick off with cas 379

8.2 areas under and between curves 380

8.3 Linear substitutions 391

8.4 other substitutions 402

8.5 integrals of powers of trigonometric functions 411

8.6 integrals involving inverse trigonometric functions 418

8.7 integrals involving partial fractions 428

8.8 Review 439

answers 440

**Topic 9 Differential equations 446**

9.1 Kick off with cas 447

9.2 verifying solutions to a differential equation 448

9.3 solving type 1 differential equations, dy dx = f (x) 454

9.4 solving type 2 differential equations, dy dx = f (y) 461

9.5 solving type 3 differential equations, dy dx = f (x )g(y ) 468

9.6 solving type 4 differential equations, d2y dx2 = f (x) 472

9.7 Review 480

answers 481

**Topic 10 Further applications of integration 484**

10.1 Kick off with cas 485

10.2 integration by recognition 486

10.3 solids of revolution 494

10.4 volumes 504

10.5 arc length, numerical integration and graphs of antiderivatives 512

10.6 Water flow 524

10.7 Review 533

answers 534

**Topic 11 Applications of first-order differential equations 538**

11.1 Kick off with cas 539

11.2 Growth and decay 540

11.3 other applications of first-order differential equations 546

11.4 Bounded growth and newton’s Law of cooling 553

11.5 chemical reactions and dilution problems 560

11.6 the logistic equation 572

11.7 euler’s method 584

11.8 slope fields 593

11.9 Review 604

answers 605

**Topic 12 Variable forces 612**

12.1 Kick off with cas 613

12.2 Forces that depend on time 614

12.3 Forces that depend on velocity 621

12.4 Forces that depend on displacement 634

12.5 Review 641

answers 642

**Topic 13 Vector calculus 644**

13.1 Kick off with cas 645

13.2 Position vectors as functions of time 646

13.3 differentiation of vectors 651

13.4 special parametric curves 662

13.5 integration of vectors 675

13.6 Projectile motion 681

13.7 Review 696

answers 697

**Topic 14 Statistical inference 704**

14.1 Kick off with cas 705

14.2 Linear combinations of random variables 706

14.3 sample means 713

14.4 confidence intervals 719

14.5 Hypothesis testing 724

14.6 Review 730

answers 731

Index 733