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 Number skills and index laws 1
1.1 Overview 2
1.2 Real numbers 4
1.3 Rounding numbers and significant figures 10
1.4 Review of index laws 15
1.5 Raising powers 22
1.6 Negative indices 27
1.7 Scientific notation 32
1.8 Square roots and cube roots 38
1.9 Surds (extending) 41
1.10 Review 52
Answers 61
2 Algebra 67
2.1 Overview 68
2.2 Using pronumerals 70
2.3 Algebra in worded problems 79
2.4 Simplification of algebraic expressions 84
2.5 Expanding brackets 90
2.6 Difference of two squares and perfect squares 99
2.7 Further expansions 104
2.8 The highest common factor 107
2.9 The highest common binomial factor 113
2.10 Solving worded problems 117
2.11 Review 126
Answers 134
3 Linear equations 143
3.1 Overview 144
3.2 Solving linear equations 146
3.3 Solving linear equations with brackets 155
3.4 Solving linear equations with pronumerals on both sides 158
3.5 Solving problems with linear equations 162
3.6 Rearranging formulas 168
3.7 Review 173
Answers 180
4 Congruence and similarity 185
4.1 Overview 186
4.2 Ratio and scale 189
4.3 Congruent figures 198
4.4 Nets, polyhedra and Euler’s formula 206
4.5 Similar figures 211
4.6 Area and volume of similar figures 220
4.7 Review 229
Answers 239
5 Pythagoras and trigonometry 245
5.1 Overview 246
5.2 Pythagoras’ theorem 250
5.3 Applications of Pythagoras’ theorem 258
5.4 Trigonometric ratios 265
5.5 Calculating unknown side lengths 273
5.6 Calculating unknown angles 282
5.7 Angles of elevation and depression 289
5.8 Review 295
Answers 305
6 Linear and non-linear graphs 311
6.1 Overview 312
6.2 Plotting linear graphs 314
6.3 Features of linear graphs 320
6.4 The equation of a straight line 328
6.5 Sketching linear graphs 336
6.6 Technology and linear graphs 344
6.7 Practical applications of linear graphs 348
6.8 Midpoint of a line segment and distance between two points 353
6.9 Non-linear relations (parabolas, hyperbolas, circles) 359
6.10 Review 370
Answers 379
Semester review 1 394
7 Proportion and rates 397
7.1 Overview 398
7.2 Direct linear proportion 400
7.3 Proportionality 405
7.4 Introduction to rates 409
7.5 Constant and variable rates 412
7.6 Review 419
Answers 428
8 Financial mathematics 431
8.1 Overview 432
8.2 Salaries and wages 435
8.3 Penalty rates 439
8.4 Simple interest 445
8.5 Compound interest 453
8.6 Review 462
Answers 468
9 Measurement 471
9.1 Overview 472
9.2 Measurement 476
9.3 Area 485
9.4 Area and perimeter of a sector 495
9.5 Surface area of rectangular and triangular prisms 501
9.6 Surface area of a cylinder 508
9.7 Volume of prisms and cylinders 512
9.8 Review 523
Answers 533
10 Probability 537
10.1 Overview 538
10.2 Theoretical probability 544
10.3 Experimental probability 551
10.4 Venn diagrams and two-way tables 559
10.5 Two-step experiments 576
10.6 Review 588
Answers 596
11 Statistics 603
11.1 Overview 604
11.2 Sampling 608
11.3 Collecting data 616
11.4 Displaying data 626
11.5 Measures of centre 639
11.6 Measures of spread 650
11.7 Review 661
Answers 668
12 Quadratic equations and graphs 681
12.1 Overview 682
12.2 Quadratic equations 684
12.3 The Null Factor Law 689
12.4 Solving quadratic equations with two terms 693
12.5 Factorising and solving monic quadratic equations 697
12.6 Graphs of quadratic functions 703
12.7 Sketching parabolas of the form y = ax 2 712
12.8 Sketching parabolas of the form y =(x − h) 2 + k 718
12.9 Sketching parabolas of the form y =(x + a)(x + b) 730
12.10 Applications 735
12.11 Review 740
Answers 750
Semester review 2 776
13 Algorithmic thinking
13.1 Overview
13.2 Programs
13.3 Arrays
13.4 Loops
13.5 Set structures
13.6 Sorting algorithms
13.7 The Monte Carlo method
13.8 Review
Answers
Glossary 778
Index 784