Table of Contents

About eBookPLUS vii Overview viii Acknowledgements x NUMERACY Topic 1 Numeracy 1 2 1.1 Overview 2 1.2 Set A 4 1.3 Set B 9 Answers 14 NUMBER AND ALGEBRA Topic 2 Integers 16 2.1 Overview 16 2.2 Adding and subtracting integers 18 Exercise 2.2 19 2.3 Multiplying integers 23 Exercise 2.3 24 2.4 Dividing integers 26 Exercise 2.4 27 2.5 Combined operations on integers 29 Exercise 2.5 30 2.6 Review ONLINE ONLY 33 eBookPLUS activities 37 Answers 38 NUMBER AND ALGEBRA Topic 3 Index laws 40 3.1 Overview 40 3.2 Review of index form 42 Exercise 3.2 43 3.3 First Index Law (multiplying numbers in index form with the same base) 45 Exercise 3.3 47 3.4 Second Index Law (dividing numbers in index form with the same base) 49 Exercise 3.4 50 3.5 Third Index Law (the power of zero) 52 Exercise 3.5 53 3.6 Fourth Index Law (raising a power to another power) 55 Exercise 3.6 56 3.7 Review ONLINE ONLY 59 eBookPLUS activities 63 Answers 64 ProjectsPLUS ICT ACTIVITY Attack of the killer balloons pro-0095 66 NUMBER AND ALGEBRA Topic 4 Real numbers 68 4.1 Overview 68 4.2 Addition and subtraction of fractions 70 Exercise 4.2 74 4.3 Multiplication and division of fractions 76 Exercise 4.3 78 4.4 Terminating and recurring decimals 80 Exercise 4.4 83 4.5 Addition and subtraction of decimals 85 Exercise 4.5 86 4.6 Multiplication and division of decimals 88 Exercise 4.6 91 4.7 Estimation 92 Exercise 4.7 96 4.8 Review ONLINE ONLY 99 eBookPLUS activities 103 Answers 104 NUMBER AND ALGEBRA Topic 5 Ratios and rates 108 5.1 Overview 108 5.2 Introduction to ratios 110 Exercise 5.2 110 5.3 Simplifying ratios 114 Exercise 5.3 116 5.4 Proportion 119 Exercise 5.4 120 5.5 Comparing ratios 123 Exercise 5.5 124 5.6 Dividing in a given ratio 126 Exercise 5.6 127 5.7 Rates 129 Exercise 5.7 130 5.8 Interpreting graphs 133 Exercise 5.8 136 5.9 Review ONLINE ONLY 139 eBookPLUS activities 143 Answers 144 FMPrelims.indd 3 04/08/14 10:09 AM iv Contents NUMBER AND ALGEBRA Topic 6 Application of percentages 148 6.1 Overview 148 6.2 Percentages, fractions and decimals 150 Exercise 6.2 152 6.3 Finding percentages of an amount 154 Exercise 6.3 155 6.4 Discount 158 Exercise 6.4 160 6.5 Profi t and loss 163 Exercise 6.5 165 6.6 Goods and Services Tax (GST) 168 Exercise 6.6 169 6.7 Review ONLINE ONLY 171 eBookPLUS activities 175 Answers 176 MEASUREMENT AND GEOMETRY Topic 7 Congruence 178 7.1 Overview 178 7.2 Congruent fi gures 180 Exercise 7.2 181 7.3 Triangle constructions 184 Exercise 7.3 186 7.4 Congruent triangles 188 Exercise 7.4 191 7.5 Quadrilaterals 193 Exercise 7.5 195 7.6 Nets, polyhedra and Euler?s rule 198 Exercise 7.6 200 7.7 Review ONLINE ONLY 203 eBookPLUS activities 207 Answers 208 NUMBER AND ALGEBRA Topic 8 Algebra 212 8.1 Overview 212 8.2 Using variables 214 Exercise 8.2 215 8.3 Substitution 219 Exercise 8.3 220 8.4 Working with brackets 221 Exercise 8.4 222 8.5 Substituting positive and negative numbers 224 Exercise 8.5 225 8.6 Number laws and variables 226 Exercise 8.6 231 8.7 Simplifying expressions 232 Exercise 8.7 234 8.8 Multiplying and dividing expressions with variables 236 Exercise 8.8 239 8.9 Expanding brackets 242 Exercise 8.9 243 8.10 Factorising 245 Exercise 8.10 247 8.11 Review ONLINE ONLY 249 eBookPLUS activities 253 Answers 254 NUMERACY Topic 9 Numeracy 2 258 9.1 Overview 258 9.2 Set C 260 9.3 Set D 266 Answers 272 MEASUREMENT AND GEOMETRY Topic 10 Measurement 274 10.1 Overview 274 10.2 Perimeter 276 Exercise 10.2 279 10.3 Circumference 281 Exercise 10.3 283 10.4 Area of rectangles, triangles, parallelograms, rhombuses and kites 287 Exercise 10.4 291 10.5 Area of a circle 295 Exercise 10.5 296 10.6 Area of trapeziums 299 Exercise 10.6 300 10.7 Volume of prisms and other solids 302 Exercise 10.7 305 10.8 Time 308 Exercise 10.8 311 10.9 24-hour clock and time zones 314 Exercise 10.9 317 10.10 Review ONLINE ONLY 321 eBookPLUS activities 325 Answers 326 FMPrelims.indd 4 04/08/14 10:09 AM NUMBER AND ALGEBRA Topic 11 Linear equations 330 11.1 Overview 330 11.2 Identifying patterns 332 Exercise 11.2 335 11.3 Backtracking and inverse operations 336 Exercise 11.3 338 11.4 Keeping equations balanced 340 Exercise 11.4 341 11.5 Using algebra to solve problems 344 Exercise 11.5 347 11.6 Equations with the unknown on both sides 350 Exercise 11.6 353 11.7 Review ONLINE ONLY 357 eBookPLUS activities 361 Answers 362 STATISTICS AND PROBABILITY Topic 12 Representing and interpreting data 366 12.1 Overview 366 12.2 Samples and populations 368 Exercise 12.2 372 12.3 Primary and secondary data 376 Exercise 12.3 381 12.4 Organising and displaying data 384 Exercise 12.4 389 12.5 Measures of centre 393 Exercise 12.5 398 12.6 Measures of spread 402 Exercise 12.6 405 12.7 Analysing data 408 Exercise 12.7 411 12.8 Review ONLINE ONLY 415 eBookPLUS activities 419 Answers 420 ProjectsPLUS ICT ACTIVITY How to burglar-proof your bedroom pro-0097 428 STATISTICS AND PROBABILITY Topic 13 Probability 430 13.1 Overview 430 13.2 Probability scale 432 Exercise 13.2 434 13.3 Experimental probability 436 Exercise 13.3 438 13.4 Sample spaces and theoretical probability 443 Exercise 13.4 446 13.5 Complementary events 451 Exercise 13.5 452 13.6 Venn diagrams 454 Exercise 13.6 458 13.7 Tree diagrams and two-way tables 461 Exercise 13.7 465 13.8 Review ONLINE ONLY 471 eBookPLUS activities 475 Answers 476 NUMBER AND ALGEBRA Topic 14 Coordinates and linear graphs 482 14.1 Overview 482 14.2 The Cartesian plane 484 Exercise 14.2 486 14.3 Linear patterns 488 Exercise 14.3 490 14.4 Plotting linear graphs 492 Exercise 14.4 494 14.5 The y-intercept and gradient 497 Exercise 14.5 501 14.6 Sketching linear graphs 506 Exercise 14.6 508 14.7 Solving equations graphically 509 Exercise 14.7 512 14.8 Review ONLINE ONLY 515 eBookPLUS activities 519 Answers 520 MEASUREMENT AND GEOMETRY Topic 15 Pythagoras? theorem 528 15.1 Overview 528 15.2 Right-angled triangles 530 Exercise 15.2 530 15.3 Finding the hypotenuse 532 Exercise 15.3 534 15.4 Finding a shorter side 536 Exercise 15.4 537 15.5 Working with different units 540 Exercise 15.5 541 Contents v FMPrelims.indd 5 04/08/14 10:09 AM 15.6 Composite shapes 543 Exercise 15.6 545 15.7 Pythagorean triads 548 Exercise 15.7 550 15.8 Pythagoras in 3-D 551 Exercise 15.8 553 15.9 Review ONLINE ONLY 555 eBookPLUS activities 559 Answers 560 NUMERACY Topic 16 Numeracy 3 562 16.1 Overview 562 16.2 Set E 564 16.3 Set F 568 Answers 573 Glossary 575 Index