Jacaranda Maths Quest 12 Essential Mathematics Units 3 and 4 for Queensland, 2e learnON & Print

Learning with learnON  vii
Teaching with Learnon xiii
Acknowledgements xiv

Unit 3 Measurement, Scales And Chance 1

Topic Fundamental Topic

1 Calculations 3

1.1 Overview 4
1.2 Number operations 5
1.3 Order of operations and reasonableness 15
1.4 Estimation 21
1.5 Decimal significance 26
1.6 Calculator skills 32
1.7 Approximation 36
1.8 Review 43

Topic 1 Measurement

2 Geometry 51

2.1 Overview 52
2.2 Review of angles 53
2.3 Two-dimensional geometric shapes 63
2.4 Three-dimensional objects 76
2.5 Two-dimensional representations of three-dimensional objects [complex] 82
2.6 Review 92

3 Linear and area measure 101

3.1 Overview 102
3.2 Units of length and estimation 104
3.3 Perimeters of familiar and composite shapes 109
3.4 Units of area and estimation 119
3.5 Areas of standard shapes 125
3.6 Areas of composite figures [complex] 133
3.7 Surface areas of prisms and cylinders [complex] 140
3.8 Surface areas of pyramids and cones [complex] 145
3.9 Surface areas of composite shapes and spheres [complex] 150
3.10 Review 155

4 Volume, capacity, time and mass 163

4.1 Overview 164
4.2 Units of volume and capacity 166
4.3 Volumes and capacities of prisms and cylinders 172
4.4 Volumes and capacities of pyramids and cones 180
4.5 Volumes and capacities of composite shapes and spheres [complex] 186
4.6 Units of time 192
4.7 Units of mass 199
4.8 Review 205

Topic 2 Scales, Plans and Models

5 Interpreting and creating scale drawings 213

5.1 Overview 214
5.2 Reading and interpreting scale drawings 215
5.3 Calculating, costing and comparing using measurements from scale drawings 220
5.4 Creating scale drawings [complex] 230
5.5 Review 239

6 Right-angled triangles 247

6.1 Overview 248
6.2 Pythagoras’ theorem 250
6.3 Trigonometric ratios — sine, cosine and tangent 256
6.4 Calculating unknown side lengths of right-angled triangles [complex] 263
6.5 Calculating unknown angles in right-angled triangles [complex] 272
6.6 Angles of elevation and depression [complex] 278
6.7 Review 285

Topic 3 Probability and Relative Frequencies

7 Simulations and simple probabilities 293

7.1 Overview 294
7.2 Theoretical probability and sample spaces 295
7.3 Multi-stage experiments (arrays and tree diagrams) 303
7.4 Relative frequency and simulations 311
7.5 Review 322

Practice Assessment 1
Unit 3 Problem-solving and modelling task

PRACTICE ASSESSMENT 2
Unit 3 Practice examination

Unit 4 Graphs, Data and Loans 333

Topic 1 Bivariate Graphs

8 Cartesian plane 335

8.1 Overview 336
8.2 Plotting points on a Cartesian plane 337
8.3 Generating tables of values for linear functions 341
8.4 Graphing linear functions 348
8.5 Review 360

9 Bivariate scatterplots and lines of best fit 371

9.1 Overview 372
9.2 Interpreting scatterplots 373
9.3 The line of best fit 383
9.4 Making predictions using a line of best fit [complex] 396
9.5 Causality and correlation [complex] 407
9.6 Review 414

Topic 2 Summarising and Comparing Data

10 Summarising and interpreting data 429

10.1 Overview 430
10.2 Measures of central tendency and mode 431
10.3 Measures of spread 444
10.4 Outliers [complex] 460
10.5 Applications of measures of centre and spread [complex] 468
10.6 Review 475

11 Comparing datasets 485

11.1 Overview 486
11.2 Constructing box plots 487
11.3 Comparing parallel box plots [complex] 494
11.4 Comparing back-to-back stem plots [complex] 500
11.5 Comparing histograms [complex] 508
11.6 Review 521

TOPIC 3 LOANS AND COMPOUND INTEREST

12 Compound interest 541

12.1 Overview 542
12.2 Simple interest 543
12.3 Using formulas to calculate the future value 555
12.4 Using technology to determine the future value of compound investments or loans 559
12.5 Comparing simple and compound interest [complex] 569
12.6 Review 582

13 Reducing balance loans 591

13.1 Overview 592
13.2 Modelling reducing balance loans with technology 593
13.3 The effect of repayment amounts, the interest rate and compounding periods on reducing balance loans [complex] 601
13.4 Review 611

Practice Assessment 3 (online only)
Unit 4 Problem-solving and modelling task

Practice Assessment 4 (online only)
Unit 4 Practice examination

Glossary (online only)