Jacaranda Maths Quest 8 Stage 4 NSW Syllabus Third Edition (learnON & Print)

Part of the series Jacaranda Core Science NSW.

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Jacaranda Maths Quest 8 Stage 4 NSW Syllabus (for the NSW Syllabus)

NSW's most supportive Maths resource

Developed by expert teachers, every lesson is carefully designed to support learning online, offline, in class, and at home.

Supporting students
Whether students need a challenge or a helping hand, they have the tools to help them take the next step, in class and at home:

• concepts brought to life with rich multi-media
• easy navigation
• differentiated pathways
• immediate corrective feedback
• Worked solutions for every question
• personalised pathways that also allow for social learning
• opportunities for remediation, extension, acceleration
• tracking progress and growth

Supporting teachers
Teachers are empowered to teach their class, their way with flexible resources perfect for teaching and learning:

• 100's of ready-made and customisable lessons
• comprehensive Syllabus coverage and planning documentation
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• marking, tracking, monitoring and reporting capabilities
• ability to add own materials

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Table of Contents

About this resource vii
Acknowledgements xiv

NAPLAN practice online only

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

1 Computation with integers 1

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 24
Answers 30

2 Index laws 33

2.1 Overview 34
2.2 Review of index form 36
2.3 Multiplying powers 41
2.4 Dividing powers 45
2.5 The zero index 50
2.6 Raising powers 54
2.7 Review 60
Answers 66

3 Real numbers 71

3.1 Overview 72
3.2 The real number system 74
3.3 Adding and subtracting fractions 79
3.4 Multiplying and dividing fractions 87
3.5 Terminating and recurring decimals 93
3.6 Adding and subtracting decimals 99
3.7 Multiplying and dividing decimals 103
3.8 Estimation 108
3.9 Review 115
Answers 121

4 Percentages 127

4.1 Overview 128
4.2 Percentages 130
4.3 Finding percentages of an amount 136
4.4 Discount 141
4.5 Profit and loss 147
4.6 Goods and Services Tax (GST) 154
4.7 Review 159
Answers 164

5 Ratios and rates 167

5.1 Overview 168
5.2 Ratios 170
5.3 Simplifying ratios 176
5.4 Proportion 184
5.5 Comparing ratios 191
5.6 Dividing in a given ratio 195
5.7 Rates 201
5.8 Interpreting graphs 207
5.9 Review 216
Answers 222

6 Algebraic techniques 229

6.1 Overview 230
6.2 Using pronumerals 232
6.3 Substitution 237
6.4 Substituting positive and negative numbers 242
6.5 Number laws 245
6.6 Adding and subtracting terms 251
6.7 Multiplying and dividing terms 255
6.8 Expanding brackets 262
6.9 Factorising 267
6.10 Review 272
Answers 278

Semester review 1 284

7 Equations 287

7.1 Overview 288
7.2 Backtracking and inverse operations 290
7.3 Keeping equations balanced 296
7.4 Solving linear equations and simple quadratic equations 300
7.5 Equations with an unknown on both sides 310
7.6 Review 317
Answers 322

8 Length, area and volume 327

8.1 Overview 328
8.2 Length and perimeter 331
8.3 Circumference 339
8.4 Areas of rectangles, triangles, parallelograms, rhombuses and kites 349
8.5 Areas of circles 362
8.6 Areas of trapeziums 368
8.7 Volumes of prisms and other solids 373
8.8 Review 381
Answers 389

9 Linear relationships 393

9.1 Overview 394
9.2 The Cartesian plane 398
9.3 Linear patterns 406
9.4 Linear graphs 412
9.5 Solving equations graphically 423
9.6 Review 431
Answers 438

10 Data 455

10.1 Overview 456
10.2 Data collection methods (Foundational) 459
10.3 Primary and secondary data (Foundational) 471
10.4 Organising and displaying data 479
10.5 Measures of centre and spread 492
10.6 Analysing data 507
10.7 Review 516
Answers 522

11 Probability 531

11.1 Overview 532
11.2 Observed probability 535
11.3 Probability scale 543
11.4 Sample space and theoretical probability 547
11.5 Complementary events 555
11.6 Review 560
Answers 565

12 Right-angled triangles (Pythagoras' theorem) 571

12.1 Overview 572
12.2 Pythagoras' theorem 575
12.3 Calculating shorter side lengths 582
12.4 Applying Pythagoras' theorem 586
12.5 Pythagorean triads 592
12.6 Review 596
Answers 601

Semester review 2 604
Glossary607
Index 612