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Overview ix
Acknowledgments xi
1 NAPLAN practice 1
1.1 Overview 1
1.2 NAPLAN practice 1 2
1.3 NAPLAN practice 2 8
1.4 NAPLAN practice 3 15
1.5 Review 22
Answers 23
2 Financial mathematics [5.1] 25
2.1 Overview 25
NSW 2.2 [Stage 5.1] Salaries and wages 26
NSW 2.3 [Stage 5.1] Special rates 29
NSW 2.4 [Stage 5.1] Piecework 35
NSW 2.5 [Stage 5.1] Commissions and royalties 38
NSW 2.6 [Stage 5.1] Loadings and bonuses 41
NSW 2.7 [Stage 5.1] Taxation and net earnings 45
ACMNA211 2.8 [Stage 5.1] Simple interest 49
ACMNA229 2.9 [Stage 5.1] Compound interest 55
2.10 Review 61
Answers 65
3 Similar figures and scale drawings [5.1 and 5.3] 71
3.1 Overview 71
ACMMG201 3.2 [Stage 4] Congruent figures 72
ACMMG221 3.3 [Stage 5.1] Scale drawings 79
ACMMG220 | ACMMG221 3.4 [Stage 5.1] Similar figures 90
ACMMG244 3.5 [Stage 5.3] Area and volume of similar figures 102
3.6 Review 108
Answers 114
4 Right-angled triangles (trigonometry) [5.1] 119
4.1 Overview 119
ACMMG222 4.2 [Stage 4] Pythagoras’ theorem 120
ACMMG222 4.3 [Stage 4] Applications of Pythagoras’ theorem 129
ACMMG223 4.4 [Stage 5.1] Similarity and the sine, cosine and tangent ratios 136
ACMMG224 4.5 [Stage 5.1] Calculating unknown side lengths 144
ACMMG224 4.6 [Stage 5.1] Calculating unknown angles 152
ACMMG245 4.7 [Stage 5.1] Angles of elevation and depression 158
4.8 Review 164
Answers 171
5 Single variable data analysis [5.1 and 5.2] 177
5.1 Overview 177
ACMSP284 5.2 [Stage 4] Collecting data 178
ACMSP282 | ACMSP228 5.3 [Stage 5.1] Stem-and-leaf plots and dot plots 188
ACMSP282 5.4 [Stage 5.1] Comparing and displaying data 195
ACMSP283 5.5 [Stage 5.1] Mean, median and mode 206
ACMSP248 5.6 [Stage 5.2] Quartiles, interquartile range and distributions 214
5.7 Review 222
Answers 228
6 Indices, scientific notation and surds [5.1, 5.2 and 5.3] 241
6.1 Overview 241
ACMNA186 6.2 [Stage 5.3] Rational and irrational numbers 242
ACMMG219 6.3 [Stage 5.3] Simple operations with surds 248
ACMNA264 6.4 [Stage 5.1] Rounding and significant figures 254
ACMNA210 6.5 [Stage 5.1] Scientific notation 258
ACMNA212 6.6 [Stage 5.1] Applying the index laws to variables 264
ACMNA231 6.7 [Stage 5.1] Using index laws to simplify algebraic products and quotients 270
ACMNA209 | ACMNA231 6.8 [Stage 5.2] Applying index laws to algebraic expressions involving integer indices 273
ACMNA264 6.9 [Stage 5.3] Introduction to fractional indices 278
6.10 Review 281
Answers 287
7 Area, surface area and volume [5.1 and 5.2] 297
7.1 Overview 297
ACMMG219 7.2 [Stage 5.1] Time scales and units of measurement 298
ACMMG216 7.3 [Stage 5.1] Area of composite shapes 307
ACMMG216 7.4 [Stage 5.1] Area and perimeter of semicircles and sectors 318
ACMMG218 7.5 [Stage 5.1] Surface area of rectangular and triangular prisms 324
ACMMG217 | ACMMG242 7.6 [Stage 5.2] Surface area of cylinders and composite solids 330
ACMMG217 | ACMMG242 7.7 [Stage 5.2] Volume of prisms, cylinders and composite solids 335
7.8 Review 346
Answers 352
8 Algebraic techniques 1 [5.2] 359
8.1 Overview 359
ACMNA175 | ACMNA176 8.2 [Stage 4] Variables 360
ACMNA177 8.3 [Stage 4] Algebra in worded problems 366
ACMNA177 8.4 [Stage 4] Simplifying algebraic expressions 370
ACMNA232 8.5 [Stage 5.2] Simplifying algebraic fractions 1 375
ACMNA213 | ACMNA233 8.6 [Stage 5.2] Expanding algebraic expressions 380
ACMNA230 8.7 [Stage 5.2] The highest common factor 387
ACMNA233 8.8 [Stage 5.2] Factorising monic quadratics 390
8.9 Review 394
Answers 399
9 Probability [5.1 and 5.2] 407
9.1 Overview 407
ACMSP226 9.2 [Stage 5.1] Theoretical probability 408
ACMSP226 9.3 [Stage 5.1] Experimental probability 415
ACMSP226 9.4 [Stage 5.1] Venn diagrams and two-way tables 421
ACMSP225 9.5 [Stage 5.2] Two-step experiments 431
ACMSP246 9.6 [Stage 5.2] Mutually exclusive and independent events 439
ACMSP247 9.7 [Stage 5.2] Conditional probability 447
9.8 Review 454
Answers 459
10 Linear equations [5.2] 471
10.1 Overview 471
ACMNA215 | ACMNA240 10.2 [Stage 5.2] Solving linear equations 472
ACMNA215 10.3 [Stage 5.2] Solving linear equations with brackets 479
ACMNA215 10.4 [Stage 5.2] Solving linear equations with pronumerals on both sides 482
ACMNA235 10.5 [Stage 5.2] Solving problems with linear equations 486
ACMNA234 10.6 [Stage 5.2] Substituting values into formulas 490
10.7 Review 494
Answers 499
11 Linear and non-linear relationships [5.1 and 5.2] 503
11.1 Overview 503
ACMNA215 11.2 [Stage 5.1] Sketching linear graphs using the coordinates of two points 504
ACMNA294 | ACMNA214 11.3 [Stage 5.1] Midpoint of a line segment and distance between two points 509
ACMNA294 11.4 [Stage 5.1] The gradient of a straight line 514
ACMNA215 11.5 [Stage 5.2] Using the gradient–intercept form to graph linear relationships 522
ACMNA238 11.6 [Stages 5.1 and 5.2] Parallel and perpendicular lines 526
NSW 11.7 [Stage 5.2] Finding the equation of a straight line 529
NSW 11.8 [Going further] Practical applications of linear graphs 535
ACMNA296 | ACMNA239 11.9 [Stages 5.1 and 5.2] Non-linear relationships (parabolas, exponentials, circles) 540
11.10 Review 550
Answers 555
12 Quadratic equations [5.2] 571
12.1 Overview 571
ACMNA241 12.2 [Stage 5.2] Quadratic equations 572
ACMNA241 12.3 [Stage 5.2] The Null Factor Law 576
ACMNA241 12.4 [Stage 5.2] Solving the quadratic equation ax2 + bx + c = 0 579
ACMNA241 12.5 [Stage 5.2] Solving quadratic equations with two terms 582
ACMNA241 12.6 [Stage 5.2] Applications of quadratic equations 585
12.7 Review 589
Answers 592
13 Proportion and rates [5.2 and 5.3] 595
13.1 Overview 595
ACMNA208 13.2 [Stage 5.2] Direct proportion 596
ACMNA208 13.3 [Stage 5.2] Direct proportion and ratio 600
ACMNA208 13.4 [Stage 5.2] Inverse proportion 604
ACMNA208 13.5 [Stage 5.2] Simple rate problems 607
ACMNA208 13.6 [Stage 5.3] Constant and variable rates 610
ACMNA208 13.7 [Stage 5.3] Rates of change 616
13.8 Review 621
Answers 627
14 Algebraic techniques 2 [5.3] 635
14.1 Overview 635
ACMNA233 14.2 [Stage 5.3] Special binomial products 636
ACMNA233 14.3 [Stage 5.3] Further expansions 641
ACMNA269 14.4 [Stage 5.3] The highest common binomial factor 642
ACMNA269 14.5 [Stage 5.3] Factorisation patterns 645
ACMNA269 14.6 [Stage 5.3] Factorising non-monic quadratics 649
NSW 14.7 [Stage 5.3] Simplifying algebraic fractions 2 652
ACMNA233 14.8 [Stage 5.3] Applications of binomial products 657
14.9 Review 665
Answers 669
15 Quadratic relationships [5.3] 677
15.1 Overview 677
ACMNA267 15.2 [Stage 5.3] Graphs of quadratic functions 678
ACMNA267 15.3 [Stage 5.3] Plotting points to graph quadratic functions 683
ACMNA267 15.4 [Stage 5.3] Sketching parabolas of the form y = ax2 689
ACMNA267 15.5 [Stage 5.3] Sketching parabolas of the form y = ax2 + k 693
ACMNA267 15.6 [Stage 5.3] Sketching parabolas of the form y = (x − h)2 697
ACMNA267 15.7 [Stage 5.3] Sketching parabolas of the form y = (x − h)2 + k 701
ACMNA267 15.8 [Stage 5.3] Sketching parabolas of the form y = (x + a) (x + b) 705
ACMNA267 15.9 [Stage 5.3] Applications 709
15.10 Review 714
Answers 719
Glossary 739
Index 749