About this resource vi
About eBookPLUS viii
Acknowledgements ix
Unit 3 Measurement, Scales and Data 1
1 Calculations 1
1.1 Overview 1
1.2 Number operations 2
1.3 Order of operations 4
1.4 Rounding 9
1.5 Estimation and approximation strategies 12
1.6 Decimal fractions 15
1.7 Review: exam practice 23
Answers 27
2 Geometry 29
2.1 Overview 29
2.2 Review of angles 30
2.3 Two-dimensional geometric shapes 39
2.4 Three-dimensional objects 52
2.5 Two-dimensional representations of three-dimensional objects 55
2.6 Review: exam practice 61
Answers 69
3 Linear and area measure 73
3.1 Overview 73
3.2 Units of length and estimation 74
3.3 Perimeters of familiar and composite shapes 78
3.4 Units of area and estimation 87
3.5 Areas of regular shapes 92
3.6 Areas of composite figures 100
3.7 Surface areas of familiar prisms 105
3.8 Surface areas of familiar pyramids and irregular solids 111
3.9 Review: exam practice 117
Answers 126
4 Volume, capacity and mass 128
4.1 Overview 128
4.2 Units of volume and capacity 129
4.3 Volume and capacity of prisms and cylinders 134
4.4 Volume and capacity of pyramids and spheres 141
4.5 Problems involving mass 145
4.6 Review: exam practice 150
Answers 156
5 Scales, plans and models 158
5.1 Overview 158
5.2 Reading and interpreting scale drawings 159
5.3 Calculating measurements from scale drawings 163
5.4 Creating scale drawings 173
5.5 Review: exam practice 182
Answers 187
6 Right-angled triangles 189
6.1 Overview 189
6.2 Pythagoras’ theorem 190
6.3 Trigonometric ratios: sine, cosine and tangent 195
6.4 Calculating unknown side lengths of right-angled triangles 201
6.5 Calculating unknown angles in right-angled triangles 207
6.6 Angles of elevation and depression 212
6.7 Review: exam practice 217
Answers 223
7 Summarising and interpreting data 225
7.1 Overview 225
7.2 Measures of central tendency and mode 226
7.3 Measures of spread 238
7.4 Outliers 251
7.5 Applications of measures of centre and spread 256
7.6 Review: exam practice 261
Answers 267
8 Comparing data sets 270
8.1 Overview 270
8.2 Constructing box plots 271
8.3 Comparing parallel box plots 277
8.4 Comparing back-to-back stem plots 281
8.5 Comparing histograms 288
8.6 Review: exam practice 295
Answers 304
Practice Assessment 1
Essential Mathematics: Problem solving and modelling task 314
Practice Assessment 2
Essential Mathematics: Unit 3 examination 317
Unit 4 Graphs, Chance and Loans 324
9 Cartesian plane 324
9.1 Overview 324
9.2 Plotting points on a Cartesian plane 325
9.3 Generating tables of values for linear functions 328
9.4 Graphing linear functions 335
9.5 Review: exam practice 347
Answers 350
10 Scatterplots and lines of best fit 357
10.1 Overview 357
10.2 Interpreting scatterplots 358
10.3 The line of best fit 368
10.4 Making predictions using a line of best fit 378
10.5 Causality and correlation 387
10.6 Review: exam practice 393
Answers 401
11 Simulations and simple probability 407
11.1 Overview 407
11.2 Theoretical probability and sample spaces 408
11.3 Multi-stage experiments (arrays and tree diagrams) 414
11.4 Relative frequency and simulations 421
11.5 Review: exam practice 431
Answers 435
12 Loans and compound interest 441
12.1 Overview 441
12.2 Simple interest 442
12.3 Simple interest as a recurrence relation 449
12.4 Compound interest 454
12.5 Comparing simple and compound interest 462
12.6 Review: exam practice 476
Answers 481
13 Reducing balance loans 486
13.1 Overview 486
13.2 Modelling reducing balance loans with technology 487
13.3 The effect of interest rate and repayment amount on reducing balance loans 496
13.4 Review: exam practice 503
Answers 507
Practice Assessment 3
Essential Mathematics: Problem solving and modelling task 508
Practice Assessment 4
Essential Mathematics: Unit 4 examination 512
Appendix Maths Skills Workbook 519
Key skill 1 Fractions 520
Key skill 2 Equivalent fractions 521
Key skill 3 Multiplying fractions 522
Key skill 4 Percentage skills 524
Key skill 5 Percentages 525
Key skill 6 Fractions into percentages 526
Key skill 7 Ratios 527
Key skill 8 Using ratios 528
Key skill 9 Simplifying ratios 529
Investigation Crash statistics 530
Answers 532
Glossary 534
Index 539
