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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