Naplan Practice vii
About This Resource viii
Acknowledgements .xiv
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
1 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 23
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 68
3 Real numbers 73
3.1 Overview 74
3.2 The real number system 76
3.3 Adding and subtracting fractions 82
3.4 Multiplying and dividing fractions 89
3.5 Terminating and recurring decimals 94
3.6 Adding and subtracting decimals 99
3.7 Multiplying and dividing decimals 104
3.8 Estimation 109
3.9 Review 116
Answers 124
4 Applications of percentages 129
4.1 Overview 130
4.2 Percentages 132
4.3 Finding percentages of an amount 138
4.4 Discount 144
4.5 Profit and loss 150
4.6 Goods and Services Tax (GST) 157
4.7 Review 162
Answers 169
5 Ratios and rates 173
5.1 Overview 174
5.2 Introduction to ratios 176
5.3 Simplifying ratios 183
5.4 Proportion 191
5.5 Comparing ratios 197
5.6 Dividing in a given ratio 200
5.7 Rates 206
5.8 Interpreting graphs 210
5.9 Review 219
Answers 226
6 Congruence 233
6.1 Overview 234
6.2 Transformations and tessellations 238
6.3 Congruent figures 256
6.4 Triangle constructions 263
6.5 Congruent triangles 268
6.6 Quadrilaterals 276
6.7 Review 283
Answers 291
Semester review 1 302
7 Algebra 305
7.1 Overview 306
7.2 Using pronumerals 308
7.3 Substitution 313
7.4 Substituting positive and negative numbers 318
7.5 Number laws 321
7.6 Adding and subtracting terms 327
7.7 Multiplying and dividing terms 331
7.8 Expanding brackets 338
7.9 Factorising 343
7.10 Review 347
Answers 354
8 Measurement 359
8.1 Overview 360
8.2 Length and perimeter 363
8.3 Circumference 371
8.4 Areas of rectangles, triangles, parallelograms, rhombuses and kites 380
8.5 Areas of circles 391
8.6 Areas of trapeziums 397
8.7 Volumes of prisms and other solids 402
8.8 Time 408
8.9 24-hour clocks and time zones 414
8.10 Review 423
Answers 433
9 Linear equations 439
9.1 Overview 440
9.2 Backtracking and inverse operations 442
9.3 Keeping equations balanced 447
9.4 Solving linear equations 451
9.5 Equations with the unknown on both sides 460
9.6 Review 466
Answers 473
10 Representing and interpreting data 477
10.1 Overview 478
10.2 Samples and populations 481
10.3 Primary and secondary data 490
10.4 Organising and displaying data 499
10.5 Measures of centre and spread 509
10.6 Analysing data 524
10.7 Review 532
Answers 539
11 Probability 547
11.1 Overview 548
11.2 Experimental probability 551
11.3 Probability scale 559
11.4 Sample spaces and theoretical probability 563
11.5 Complementary events 571
11.6 Venn diagrams and two-way tables 576
11.7 Tree diagrams (extending) 589
11.8 Review 596
Answers 603
12 Coordinates and linear graphs 611
12.1 Overview 612
12.2 The Cartesian plane 615
12.3 Linear patterns 622
12.4 Plotting linear graphs 628
12.5 Determining the rule for a linear relationship 635
12.6 Sketching linear graphs (extending) 649
12.7 Solving equations graphically 654
12.8 Non-linear graphs 661
12.9 Review 669
Answers 677
13 Pythagoras’ theorem 697
13.1 Overview 698
13.2 Pythagoras’ theorem 701
13.3 Calculating shorter side lengths 708
13.4 Applying Pythagoras’ theorem 712
13.5 Pythagorean triads 718
13.6 Review 722
Answers 728
Semester review 2 730
14 Algorithmic thinking
14.1 Overview
14.2 Expressions
14.3 Decisions
14.4 Functions
14.5 Testing
14.6 Debugging
14.7 Review
Answers
Glossary 732
Index 737