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# Jacaranda Maths Quest 8 Stage 4 NSW Australian curriculum 2e learnON & print

ISBN 9780730347316
Edition 2
Publication Date
Publisher Jacaranda
Overview

Overview ix

Acknowledgements xi

1 NAPLAN Practice 1

1.1 Overview 1

1.2 NAPLAN Practice 1 1

1.3 NAPLAN Practice 2 10

1.4 NAPLAN Practice 3 18

1.5 Review 25

2 Computation with Integers 27

2.1 Overview 27

2.2 Adding and Subtracting Integers 28

2.3 Multiplying Integers 33

2.4 Dividing Integers 36

2.5 Combined Operations on Integers 39

2.6 Review 43

3 Fractions, Decimals and Percentages 51

3.1 Overview 51

3.2 Addition and Subtraction of Fractions 52

3.3 Multiplication and Division of Fractions 59

3.4 Terminating and Recurring Decimals 63

3.5 Addition and Subtraction of Decimals 67

3.6 Multiplication and Division of Decimals 70

3.7 Estimation 74

3.8 Percentages, fractions and decimals 79

3.9 Finding percentages of an amount 84

3.10 Review 89

4 Financial Mathematics 101

4.1 Overview 101

4.2 Discount 102

4.3 The Unitary Method 108

4.4 Profit and Loss 112

4.5 Goods and Services Tax (GST) 118

4.6 Review 120

5 Ratios and Rates 129

5.1 Overview 129

5.2 Introduction to Ratios 130

5.3 Simplifying Ratios 134

5.4 Proportion 139

5.5 Comparing Ratios 143

5.6 Dividing in a Given Ratio 145

5.7 Rates 149

5.8 Interpreting Graphs 153

5.9 Review 158

6 Congruence 169

6.1 Overview 169

6.2 Congruent Figures 170

6.3 Congruent Triangles 174

6.5 Review 184

7 Algebraic Techniques 191

7.1 Overview 191

7.2 Using Variables 192

7.3 Substitution 196

7.4 Working with Brackets 199

7.5 Substituting Positive and Negative Numbers 201

7.6 Number Laws and Variables 203

7.7 Simplifying Expressions 208

7.8 Multiplying and Dividing Expressions with Variables 211

7.9 Expanding Brackets 217

7.10 Factorising 221

7.11 Review 224

8 Indices 237

8.1 Overview 237

8.2 Review of Index Form 238

8.3 First Index Law (multiplying numbers in index form with the same base) 241

8.4 Second Index Law (dividing numbers in index form with the same base) 244

8.5 Third Index Law (the power of zero) 248

8.6 Fourth Index Law (raising a power to another power) 250

8.7 Review 254

9 Measurement 265

9.1 Overview 265

9.2 Perimeter 266

9.3 Circumference 272

9.4 Area of Rectangles, Triangles, Parallelograms, Rhombuses and Kites 279

9.5 Area of a Circle 287

9.6 Area of Trapeziums 292

9.7 Volume of Prisms and other Solids 295

9.8 Time 301

9.9 24-hour Clock and Time Zones 307

9.10 Review 313

10 Equations 327

10.1 Overview 327

10.2 Keeping Equations Balanced 328

10.3 Using Algebra to Solve Problems 330

10.4 Equations with the Unknown on Both Sides 336

10.6 Review 344

11 Linear Relationships 353

11.1 Overview 353

11.2 The Cartesian plane 354

11.3 Translations in the Cartesian plane 359

11.4 Identifying Patterns 370

11.5 Linear Patterns 375

11.6 Linear Graphs 380

11.7 Graphing with Technology 388

11.8 Solving Equations Graphically 391

11.9 Review 397

12 Probability 421

12.1 Overview 421

12.2 Probability Scale 422

12.3 Sample Spaces and Theoretical Probability 426

12.4 Complementary Events 433

12.5 Mutually Exclusive and Compound Events 436

12.6 Venn diagrams and Two-Way Tables 442

12.7 Review 453

13 Data Analysis 465

13.1 Overview 465

13.2 Samples and Populations 466

13.3 Primary and Secondary Data 473

13.4 Organising and Displaying Data 482

13.5 Measures of Centre and Spread 492

13.6 Analysing Data 505

13.7 Review 512

14 Pythagoras Theorem 529

14.1 Overview 529

14.2 Right-angled Triangles 530

14.3 Finding the Hypotenuse 532

14.4 Finding a Shorter Side 536

14.5 Working with Different Units 539

14.6 Composite Shapes 543

14.8 Review 551

Glossary 557

Index 561

Overview

Overview ix

Acknowledgements xi

1 NAPLAN Practice 1

1.1 Overview 1

1.2 NAPLAN Practice 1 1

1.3 NAPLAN Practice 2 10

1.4 NAPLAN Practice 3 18

1.5 Review 25

2 Computation with Integers 27

2.1 Overview 27

2.2 Adding and Subtracting Integers 28

2.3 Multiplying Integers 33

2.4 Dividing Integers 36

2.5 Combined Operations on Integers 39

2.6 Review 43

3 Fractions, Decimals and Percentages 51

3.1 Overview 51

3.2 Addition and Subtraction of Fractions 52

3.3 Multiplication and Division of Fractions 59

3.4 Terminating and Recurring Decimals 63

3.5 Addition and Subtraction of Decimals 67

3.6 Multiplication and Division of Decimals 70

3.7 Estimation 74

3.8 Percentages, fractions and decimals 79

3.9 Finding percentages of an amount 84

3.10 Review 89

4 Financial Mathematics 101

4.1 Overview 101

4.2 Discount 102

4.3 The Unitary Method 108

4.4 Profit and Loss 112

4.5 Goods and Services Tax (GST) 118

4.6 Review 120

5 Ratios and Rates 129

5.1 Overview 129

5.2 Introduction to Ratios 130

5.3 Simplifying Ratios 134

5.4 Proportion 139

5.5 Comparing Ratios 143

5.6 Dividing in a Given Ratio 145

5.7 Rates 149

5.8 Interpreting Graphs 153

5.9 Review 158

6 Congruence 169

6.1 Overview 169

6.2 Congruent Figures 170

6.3 Congruent Triangles 174

6.5 Review 184

7 Algebraic Techniques 191

7.1 Overview 191

7.2 Using Variables 192

7.3 Substitution 196

7.4 Working with Brackets 199

7.5 Substituting Positive and Negative Numbers 201

7.6 Number Laws and Variables 203

7.7 Simplifying Expressions 208

7.8 Multiplying and Dividing Expressions with Variables 211

7.9 Expanding Brackets 217

7.10 Factorising 221

7.11 Review 224

8 Indices 237

8.1 Overview 237

8.2 Review of Index Form 238

8.3 First Index Law (multiplying numbers in index form with the same base) 241

8.4 Second Index Law (dividing numbers in index form with the same base) 244

8.5 Third Index Law (the power of zero) 248

8.6 Fourth Index Law (raising a power to another power) 250

8.7 Review 254

9 Measurement 265

9.1 Overview 265

9.2 Perimeter 266

9.3 Circumference 272

9.4 Area of Rectangles, Triangles, Parallelograms, Rhombuses and Kites 279

9.5 Area of a Circle 287

9.6 Area of Trapeziums 292

9.7 Volume of Prisms and other Solids 295

9.8 Time 301

9.9 24-hour Clock and Time Zones 307

9.10 Review 313

10 Equations 327

10.1 Overview 327

10.2 Keeping Equations Balanced 328

10.3 Using Algebra to Solve Problems 330

10.4 Equations with the Unknown on Both Sides 336

10.6 Review 344

11 Linear Relationships 353

11.1 Overview 353

11.2 The Cartesian plane 354

11.3 Translations in the Cartesian plane 359

11.4 Identifying Patterns 370

11.5 Linear Patterns 375

11.6 Linear Graphs 380

11.7 Graphing with Technology 388

11.8 Solving Equations Graphically 391

11.9 Review 397

12 Probability 421

12.1 Overview 421

12.2 Probability Scale 422

12.3 Sample Spaces and Theoretical Probability 426

12.4 Complementary Events 433

12.5 Mutually Exclusive and Compound Events 436

12.6 Venn diagrams and Two-Way Tables 442

12.7 Review 453

13 Data Analysis 465

13.1 Overview 465

13.2 Samples and Populations 466

13.3 Primary and Secondary Data 473

13.4 Organising and Displaying Data 482

13.5 Measures of Centre and Spread 492

13.6 Analysing Data 505

13.7 Review 512

14 Pythagoras Theorem 529

14.1 Overview 529

14.2 Right-angled Triangles 530

14.3 Finding the Hypotenuse 532

14.4 Finding a Shorter Side 536

14.5 Working with Different Units 539

14.6 Composite Shapes 543

14.8 Review 551