Jacaranda Maths Quest 8 for Western Australia (learnON & Print)

Part of the series Maths Quest for Western Australia.

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Jacaranda Maths Quest For Western Australia

Developed by expert Australian teachers for ALL students

Tried, tested and trusted. The Maths Quest series focuses on helping teachers achieve learning success for every student - ensuring no student is left behind and no student is held back.

Because both what and how students learn matter

Table of Contents

About this resource vii
The new jacTUTOR xiv
Acknowledgements xv

NAPLAN practice

Set A Calculator allowed
Set B Non-calculator
Set C Calculator allowed
Set D Non-calculator
Set E Calculator allowed
Set F Non-calculator

STRAND Number and algebra 1

1 Integers 1

Sub-strands
Understanding number | Calculating with number

1.1 Overview 2
1.2 Adding and subtracting integers 4
1.3 Multiplying integers 11
1.4 Dividing integers 15
1.5 Order of operations with integers 19
1.6 Review 23

2 Real numbers 33

Sub-strands
Understanding number | Calculating with number

2.1 Overview 34
2.2 The real number system 36
2.3 Adding and subtracting fractions 42
2.4 Multiplying and dividing fractions 50
2.5 Terminating and recurring decimals 55
2.6 Adding and subtracting decimals 59
2.7 Multiplying and dividing decimals 64
2.8 Estimation 69
2.9 Review 76

3 Ratios and rates 89

Sub-strand
Understanding number

3.1 Overview 90
3.2 Introduction to ratios 92
3.3 Simplifying ratios 99
3.4 Proportion 107
3.5 Comparing ratios 113
3.6 Dividing in a given ratio 116
3.7 Rates 122
3.8 Interpreting graphs 127
3.9 Review 136

4 Applications of percentages 149

Sub-strand
Calculating with number

4.1 Overview 150
4.2 Percentages 152
4.3 Calculating percentages of an amount 158
4.4 Discount 164
4.5 Profit and loss 170
4.6 Goods and Services Tax (GST) 177
4.7 Review 182

5 Index laws 191

Sub-strand
Algebraic techniques

5.1 Overview 192
5.2 Review of index form 194
5.3 Multiplying powers 199
5.4 Dividing powers 203
5.5 The zero index 207
5.6 Raising powers 211
5.7 Review 216

6 Algebraic techniques 227

Sub-strand
Algebraic techniques

6.1 Overview 228
6.2 Using pronumerals 230
6.3 Substitution 235
6.4 Substituting positive and negative numbers 240
6.5 Number laws 243
6.6 Adding and subtracting terms 249
6.7 Multiplying and dividing terms 254
6.8 Expanding brackets 260
6.9 Factorising 265
6.10 Review 269

7 Linear and non-linear equations 281

Sub-strand
Linear and non-linear equations and inequalities

7.1 Overview 282
7.2 Backtracking and inverse operations 284
7.3 Keeping equations balanced 289
7.4 Solving linear equations and simple quadratic equations 293
7.5 Equations with the unknown on both sides 304
7.6 Review 310

8 Coordinates and linear graphs 321

Sub-strand
Linear and non-linear patterns and relationships

8.1 Overview 322
8.2 The Cartesian plane 325
8.3 Linear patterns 332
8.4 Plotting linear graphs 339
8.5 Determining the rule for a linear relationship 345
8.6 Sketching linear graphs (extending) 360
8.7 Solving equations graphically 365
8.8 Review 374

9 Financial mathematics 399

Sub-strand
Financial mathematics

9.1 Overview 400
9.2 Payment forms and methods 402
9.3 Surcharges and transaction costs 407
9.4 Penalties 413
9.5 Review 419

Modelling with number and algebra 427

STRAND Measurement and geometry 431

10 Pythagoras’ theorem 431

Sub-strand
Two-dimensional space and structures

10.1 Overview 432
10.2 Pythagoras’ theorem 435
10.3 Calculating shorter side lengths 442
10.4 Applying Pythagoras’ theorem 446
10.5 Pythagorean triads 452
10.6 Review 456

11 Measurement 463

Sub-strands
Two-dimensional space and structures | Three-dimensional

space and structures | Non-spatia measurement

11.1 Overview 464
11.2 Length and perimeter 467
11.3 Circumference 475
11.4 Areas of rectangles, triangles, parallelograms, rhombuses and kites 484
11.5 Areas of circles 497
11.6 Areas of trapeziums 503
11.7 Volumes of prisms and other solids 508
11.8 Time 515
11.9 24-hour clocks and time zones 521
11.10 Review 530

12 Congruence 545

Sub-strand
Two-dimensional space and structures

12.1 Overview 546
12.2 Transformations and tessellations 550
12.3 Congruent figures 568
12.4 Congruent triangles 576
12.5 Quadrilaterals 583
12.6 Review 591

Modelling with measurement and geometry 607

STRAND Probability and statistics 611

13 Probability 611

Sub-strand
Probability and statistics

13.1 Overview 612
13.2 Experimental probability 615
13.3 Probability scale 623
13.4 Sample spaces and theoretical probability 627
13.5 Complementary events 635
13.6 Venn diagrams and two-way tables 640
13.7 Tree diagrams 653
13.8 Review 662

14 Statistics 677

Sub-strand
Probability and statistics

14.1 Overview 678
14.2 Data collection methods 681
14.3 Primary and secondary data 692
14.4 Organising and displaying data 701
14.5 Measures of centre and spread 711
14.6 Analysing data 725
14.7 Review 734

Modelling with probability and statistics 749

Glossary