 # Maths Quest 11 Specialist Mathematics VCE Units 1 and 2 Solutions Manual & eBookPLUS

 Author(s): Crammond ISBN: 9780730323075 Pub date: November 2015 RRP: \$44.95

Maths Quest 11 Specialist Mathematics VCE Units 1 and 2 Solutions Manual with eBookPLUS contains fully worked solutions to every question in the Maths Quest 11 Specialist Mathematics VCE Units 1 and 2 student text.

This resource is a printed student text that includes Maths Quest 11 Specialist Mathematics VCE Units 1 and 2 Solutions Manual eBookPLUS.

Topic 1 — Number systems: real and complex 1

Exercise 1.2 — Review of set notation 1

Exercise 1.3 — Properties of surds 5

Exercise 1.4 — The set of complex numbers 10

Exercise 1.5 — Multiplication and division of complex numbers 12

Exercise 1.6 — Representing complex numbers on an Argand diagram 15

Exercise 1.7 — Factorising quadratic expressions and solving quadratic equations over the complex number field 17

Topic 2 — Algebra and logic 23

Exercise 2.2 — Statements (propositions), connectives and truth tables 23

Exercise 2.3 — Valid and invalid arguments 27

Exercise 2.4 — Techniques of proof 30

Exercise 2.5 — Sets and Boolean algebra 36

Exercise 2.6 — Digital logic 39

Topic 3 — Sequences and series 43

Exercise 3.2 — Describing sequences 43

Exercise 3.3 — Arithmetic sequences 46

Exercise 3.4 — Arithmetic series 49

Exercise 3.5 — Geometric sequences 51

Exercise 3.6 — Geometric series 56

Exercise 3.7 — Applications of sequences and series 60

Topic 4 — Geometry in the plane 63

Exercise 4.2 — Review of basic geometry 63

Exercise 4.3 — Congruence and similarity 66

Exercise 4.4 — Geometric constructions 69

Exercise 4.5 — Polygons 72

Exercise 4.6 — Circle geometry 76

Exercise 4.7 — Tangents, chords and circles 78

Topic 5 — Trigonometric ratios and their applications 83

Exercise 5.2 — Trigonometry of right-angled triangles 83

Exercise 5.3 — Elevation, depression and bearings 89

Exercise 5.4 — The sine rule 93

Exercise 5.5 — The cosine rule 98

Exercise 5.6 — Arcs, sectors and segments 103

Topic 6 — Simulation, sampling and sampling distributions 109

Exercise 6.2 — Random experiments, events and event spaces 109

Exercise 6.3 — Simulation 109

Exercise 6.4 — Populations and samples 111

Exercise 6.5 — Distribution of sample proportions and means 112

Exercise 6.6 — Measuring central tendency and spread of sample distributions 120

Topic 7 — Coordinate geometry 123

Exercise 7.2 — Distance between two points 123

Exercise 7.3 — Midpoint of a line segment 125

Exercise 7.4 — Parallel lines and perpendicular lines 128

Exercise 7.5 — Applications 134

Topic 8 — Vectors 141

Exercise 8.2 — Introduction to vectors 141

Exercise 8.3 — Operations on vectors 143

Exercise 8.4 — Magnitude, direction and components of vectors 147

Exercise 8.5 — i, j notation 154

Exercise 8.6 — Applications of vectors 160

Topic 9 — Kinematics 167

Exercise 9.2 — Introduction to kinematics 167

Exercise 9.3 — Velocity–time graphs and acceleration–time graphs 170

Exercise 9.4 — Constant acceleration formulas 175

Exercise 9.5 — Instantaneous rates of change 178

Topic 10 — Circular functions 181

Exercise 10.2 — Modelling with trigonometric functions 181

Exercise 10.3 — Reciprocal trigonometric functions 185

Exercise 10.4 — Graphs of reciprocal trigonometric functions 191

Exercise 10.5 — Trigonometric identities 199

Exercise 10.6 — Compound- and double-angle formulas 203

Exercise 10.7 — Other identities 211

Topic 11 — Linear and non-linear relationships 215

Exercise 11.2 — Reciprocal graphs 215

Exercise 11.3 — The circle and the ellipse 219

Exercise 11.4 — The hyperbola 225

Exercise 11.5 — Polar coordinates, equations and graphs 234

Exercise 11.6 — Parametric equations 243

Topic 12 — Transformations 247

Exercise 12.2 — Translations of points and graphs 247

Exercise 12.3 — Reflections and dilations 249

Exercise 12.4 — Successive transformations 254

Exercise 12.5 — Matrices and transformations 259