# Maths Quest 12 Further Mathematics 5E VCE Units 3 and 4 Solutions Manual & eBookPLUS

Author/s |
Barnes |
---|---|

ISBN13 | 9780730321743 |

Pub date | October 2015 |

Pages | 320 |

RRP | $44.95 |

**Topic 1 — Univariate data 1**

Exercise 1.2 — Types of data 1

Exercise 1.3 — Stem plots 1

Exercise 1.4 — Dot plots, frequency tables and histograms, and bar charts 3

Exercise 1.5 — Describing the shape of stem plots and histograms 6

Exercise 1.6 — The median, the interquartile range, the range and the mode 8

Exercise 1.7 — Boxplots 11

Exercise 1.8 — The mean of a sample 14

Exercise 1.9 — Standard deviation of a sample 17

Exercise 1.10 — Populations and simple random samples 17

Exercise 1.11 — The 68−95−99.7% rule and z-scores 18

**Topic 2 — Comparing data sets 23**

Exercise 2.2 — Back-to-back stem plots 23

Exercise 2.3 — Parallel boxplots and dot plots 26

Exercise 2.4 — Two-way (contingency) frequency tables and segmented bar charts 28

**Topic 3 — Introduction to regression 33**

Exercise 3.2 — Response (dependent) and explanatory (independent) variables 33

Exercise 3.3 — Scatterplots 33

Exercise 3.4 — Pearson’s product–moment correlation coefficient 35

Exercise 3.5 — Calculating r and the coefficient of determination 36

Exercise 3.6 — Fitting a straight line — least-squares regression 38

Exercise 3.7 — Interpretation, interpolation and extrapolation 40

Exercise 3.8 — Residual analysis 43

Exercise 3.9 — Transforming to linearity 46

**Topic 4 — Time series 51**

Exercise 4.2 — Time series and trend lines 51

Exercise 4.3 — Fitting trend lines and forecasting 53

Exercise 4.4 — Smoothing time series 58

Exercise 4.5 — Smoothing with an even number of points 63

Exercise 4.6 — Median smoothing from a graph 67

Exercise 4.7 — Seasonal adjustment 69

**Topic 5 — Recurrence relations 77**

Exercise 5.2 — Generating the terms of a first-order recurrence relation 77

Exercise 5.3 — First-order linear recurrence relations 79

Exercise 5.4 — Graphs of first-order recurrence relations 82

**Topic 6 — Interest and depreciation 87**

Exercise 6.2 — Simple interest 87

Exercise 6.3 — Compound interest tables 90

Exercise 6.4 — Compound interest formula 92

Exercise 6.5 — Finding rate or time for compound interest 96

Exercise 6.6 — Flat rate depreciation 100

Exercise 6.7 — Reducing balance depreciation 103

Exercise 6.8 — Unit cost depreciation 106

**Topic 7 — Loans, investments and asset value 111**

Exercise 7.2 — Reducing balance loans I 111

Exercise 7.3 — Reducing balance loans II 115

Exercise 7.4 — Reducing balance loans III 118

Exercise 7.5 — Reducing balance and flat rate loan comparisons 125

Exercise 7.6 — Effective annual interest rate 127

Exercise 7.7 — Perpetuities 129

Exercise 7.8 — Annuity investments 132

**Topic 8 — Matrices 137**

Exercise 8.2 — Matrix representation 137

Exercise 8.3 — Addition, subtraction and scalar operations with matrices 138

Exercise 8.4 — Multiplying matrices 141

Exercise 8.5 — Multiplicative inverse and solving matrix equations 147

Exercise 8.6 — Dominance and communication matrices 149

Exercise 8.7 — Application of matrices to simultaneous equations 151

Exercise 8.8 — Transition matrices 153

**Topic 9 — Undirected graphs and networks 159**

Exercise 9.2 — Basic concepts of a network 159

Exercise 9.3 — Planar graphs and Euler’s formula 161

Exercise 9.4 — Walks, trails, paths, cycles and circuits 162

Exercise 9.5 — Trees and their applications 164

**Topic 10 — Directed graphs and networks 169**

Exercise 10.2 — Critical path analysis 169

Exercise 10.3 — Critical path analysis with backward scanning and crashing 173

Exercise 10.4 — Network flow 180

Exercise 10.5 — Assignment problems and bipartite graphs 184

**Topic 11 — Geometry: similarity and mensuration 191**

Exercise 11.2 — Properties of angles, triangles and polygons 191

Exercise 11.3 — Area and perimeter I 193

Exercise 11.4 — Area and perimeter II 196

Exercise 11.5 — Great circles 198

Exercise 11.6 — Total surface area 200

Exercise 11.7 — Volume of prisms, pyramids and spheres 203

Exercise 11.8 — Similar figures 207

Exercise 11.9 — Similar triangles 208

Exercise 11.10 — Triangulation — similarity 212

Exercise 11.11 — Area and volume scale factors 215

Exercise 11.12 — Time zones 221

**Topic 12 — Trigonometry 223**

Exercise 12.2 — Trigonometry 223

Exercise 12.3 — Pythagorean triads 225

Exercise 12.4 — Three-dimensional Pythagoras’ theorem 227

Exercise 12.5 — Trigonometric ratios 229

Exercise 12.6 — The sine rule 232

Exercise 12.7 — Ambiguous case of the sine rule 235

Exercise 12.8 — The cosine rule 237

Exercise 12.9 — Special triangles 239

Exercise 12.10 — Area of triangles 241

**Topic 13 — Applications of geometry and trigonometry 245**

Exercise 13.2 — Angles 245

Exercise 13.3 — Angles of elevation and depression 247

Exercise 13.4 — Bearings 250

Exercise 13.5 — Navigation and specification of locations 254

Exercise 13.6 — Triangulation — cosine and sine rules 259

**Topic 14 — Construction and interpretation of graphs 267**

Exercise 14.2 — Constructing and interpreting straight-line graphs 267

Exercise 14.3 — Line segments and step functions 273

Exercise 14.4 — Simultaneous equations and break-even point 278

Exercise 14.5 — Interpreting non-linear graphs 282

Exercise 14.6 — Constructing non-linear relations and graphs 285

**Topic 15 — Linear inequalities and linear programming 291**

Exercise 15.2 — Linear inequalities 291

Exercise 15.3 — Simultaneous linear inequalities 293

Exercise 15.4 — Linear programming 298

Exercise 15.5 — Applications 304