# Maths Quest 11 Specialist Mathematics VCE Units 1 and 2 & eBookPLUS + StudyOn VCE Specialist Mathematics Units 1 and 2

Author(s): |
Evans |

ISBN: |
9780730323082 |

Pub date: |
November 2015 |

RRP: |
$80 |

* Maths Quest 11 Specialist Mathematics VCE Units 1 and 2 with eBookPLUS and studyON VCE* provides comprehensive coverage of the new VCE Study Design for 2016-2022. 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 1 and 2**is fully integrated with the student text. studyON is Jacaranda’s unique study, revision and exam preparation tool.

**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 1 and 2**.

**studyON**for Units 1 and 2 is a comprehensive study, revision and exam preparation tool that delivers proven learning outcomes.

**Features and benefits**

•

**Sit exams:**VCAA exam-style questions along with marking guides. 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.

Introduction v

About eBookPLUS and studyON viii

Acknowledgements ix

**Topic 1 Number systems: real and complex 2**

1.1 Kick off with CAS 3

1.2 Review of set notation 4

1.3 Properties of surds 17

1.4 The set of complex numbers 24

1.5 Multiplication and division of complex numbers 27

1.6 Representing complex numbers on an Argand diagram 31

1.7 Factorising quadratic expressions and solving quadratic equations over the complex number field 33

1.8 Review 39

Answers 40

**Topic 2 Algebra and logic 46**

2.1 Kick off with CAS 47

2.2 Statements (propositions), connectives and truth tables 48

2.3 Valid and invalid arguments 54

2.4 Techniques of proof 65

2.5 Sets and Boolean algebra 72

2.6 Digital logic 81

2.7 Review 88

Answers 89

**Topic 3 Sequences and series 98**

3.1 Kick off with CAS 99

3.2 Describing sequences 100

3.3 Arithmetic sequences 106

3.4 Arithmetic series 111

3.5 Geometric sequences 114

3.6 Geometric series 120

3.7 Applications of sequences and series 124

3.8 Review 129

Answers 130

**Topic 4 Geometry in the plane 134**

4.1 Kick off with CAS 135

4.2 Review of basic geometry 136

4.3 Congruence and similarity 141

4.4 Geometric constructions 149

4.5 Polygons 154

4.6 Circle geometry 161

4.7 Tangents, chords and circles 166

4.8 Review 174

Answers 175

**Topic 5 Trigonometric ratios and their applications 178**

5.1 Kick off with CAS 179

5.2 Trigonometry of right-angled triangles 180

5.3 Elevation, depression and bearings 185

5.4 The sine rule 190

5.5 The cosine rule 195

5.6 Arcs, sectors and segments 199

5.7 Review 206

Answers 207

**Topic 6 Simulation, sampling and sampling distributions 210**

6.1 Kick off with CAS 211

6.2 Random experiments, events and event spaces 212

6.3 Simulation 215

6.4 Populations and samples 221

6.5 Distribution of sample proportions and means 228

6.6 Measuring central tendency and spread of sample distributions 237

6.7 Review 244

Answers 245

**Topic 7 Coordinate geometry 248**

7.1 Kick off with CAS 249

7.2 Distance between two points 250

7.3 Midpoint of a line segment 253

7.4 Parallel lines and perpendicular lines 256

7.5 Applications 261

7.6 Review 268

Answers 269

**Topic 8 Vectors 272**

8.1 Kick off with CAS 273

8.2 Introduction to vectors 274

8.3 Operations on vectors 279

8.4 Magnitude, direction and components of vectors 284

8.5 i~, j ~ notation 289

8.6 Applications of vectors 296

8.7 Review 304

Answers 305

**Topic 9 Kinematics 310**

9.1 Kick off with CAS 311

9.2 Introduction to kinematics 312

9.3 Velocity–time graphs and acceleration–time graphs 322

9.4 Constant acceleration formulas 335

9.5 Instantaneous rates of change 342

9.6 Review 351

Answers 352

**Topic 10 Circular functions 358**

10.1 Kick off with CAS 359

10.2 Modelling with trigonometric functions 360

10.3 Reciprocal trigonometric functions 366

10.4 Graphs of reciprocal trigonometric functions 372

10.5 Trigonometric identities 381

10.6 Compound- and double-angle formulas 386

10.7 Other identities 394

10.8 Review 400

Answers 401

**Topic 11 Linear and non-linear relationships 408**

11.1 Kick off with CAS 409

11.2 Reciprocal graphs 410

11.3 The circle and the ellipse 419

11.4 The hyperbola 431

11.5 Polar coordinates, equations and graphs 437

11.6 Parametric equations 445

11.7 Review 449

Answers 450

**Topic 12 Transformations 462**

12.1 Kick off with CAS 463

12.2 Translations of points and graphs 464

12.3 Reflections and dilations 470

12.4 Successive transformations 476

12.5 Matrices and transformations 479

12.6 Review 484

Answers 485

Index 492