About this resource vii
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 exponent laws 1
1.1 Overview 2
1.2 Real numbers 4
1.3 Rounding numbers and significant figures 11
1.4 Review of exponent laws 16
1.5 Raising powers 24
1.6 Negative exponents 28
1.7 Scientific notation 34
1.8 Square roots and cube roots 41
1.9 Surds (extending) 44
1.10 Review 56
Answers 64
2 Algebra 71
2.1 Overview 72
2.2 Using variables 74
2.3 Algebra in worded problems 83
2.4 Simplification of algebraic expressions 88
2.5 Expanding brackets 95
2.6 Difference of two squares and perfect squares 104
2.7 Further expansions 109
2.8 The highest common factor 112
2.9 The highest common binomial factor 118
2.10 Solving worded problems 122
2.11 Review 131
Answers 138
3 Linear equations 147
3.1 Overview 148
3.2 Solving linear equations and inequations 150
3.3 Solving linear equations with brackets 161
3.4 Solving linear equations with variables on both sides 165
3.5 Solving problems with linear equations 169
3.6 Rearranging formulas 175
3.7 Review 181
Answers 187
4 Congruence and similarity 191
4.1 Overview 192
4.2 Ratio and scale 195
4.3 Congruent figures 204
4.4 Nets, polyhedra and Euler’s formula 212
4.5 Similar figures 217
4.6 Area and volume of similar figures 229
4.7 Review 238
Answers 247
5 Pythagoras and trigonometry 253
5.1 Overview 254
5.2 Pythagoras’ theorem 258
5.3 Applications of Pythagoras’ theorem 267
5.4 Trigonometric ratios 274
5.5 Calculating unknown side lengths 282
5.6 Calculating unknown angles 291
5.7 Angles of elevation and depression 299
5.8 Review 305
Answers 315
6 Linear and non-linear graphs 321
6.1 Overview 322
6.2 Plotting linear graphs 325
6.3 Features of linear graphs 331
6.4 The equation of a straight line 339
6.5 Sketching linear graphs 348
6.6 Technology and linear graphs 356
6.7 Practical applications of linear graphs 360
6.8 Midpoint of a line segment and distance between two points 365
6.9 Non-linear relations 371
6.10 Review 385
Answers 393
Semester review 1 410
7 Proportion and rates 413
7.1 Overview 414
7.2 Direct linear proportion 416
7.3 Proportionality 421
7.4 Introduction to rates 426
7.5 Constant and variable rates 429
7.6 Review 436
Answers 444
8 Financial mathematics (extending) 447
8.1 Overview 448
8.2 Salaries and wages 451
8.3 Penalty rates 455
8.4 Simple interest 461
8.5 Compound interest 469
8.6 Review 478
Answers 483
9 Measurement 487
9.1 Overview 488
9.2 Absolute, relative and percentage error 492
9.3 Perimeter and circumference 498
9.4 Area 508
9.5 Area and perimeter of a sector 518
9.6 Surface area of rectangular and triangular prisms 525
9.7 Surface area of a cylinder 531
9.8 Volume of prisms and cylinders 536
9.9 Review 549
Answers 559
10 Probability 565
10.1 Overview 566
10.2 Theoretical probability 572
10.3 Experimental probability 579
10.4 Venn diagrams and two-way tables 588
10.5 Compound events 605
10.6 Review 618
Answers 625
11 Statistics 633
11.1 Overview 634
11.2 Collecting data 638
11.3 Organising data 647
11.4 Displaying data 657
11.5 Measures of centre 672
11.6 Measures of spread 688
11.7 Review 697
Answers 703
12 Quadratic equations and graphs 715
12.1 Overview 716
12.2 Quadratic equations 718
12.3 The Null Factor Law 723
12.4 Solving quadratic equations with two terms 727
12.5 Factorising and solving monic quadratic equations 731
12.6 Graphs of quadratic functions 737
12.7 Sketching parabolas of the form y = ax2 746
12.8 Sketching parabolas of the form y = (x - h)2 + k 752
12.9 Sketching parabolas of the form y = (x + a)(x + b) 764
12.10 Applications 768
12.11 Review 774
Answers 783
Semester review 2 808
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
Algorithms and pseudocode (Optional) 810
Glossary 833
Index 840
