iii Contents About the authors ix Introduction x Guide to the working programs xi Guide to this resource xii Acknowledgements xvi Working with unfamiliar problems: Part 1 xvii Working with unfamiliar problems: Part 2 xix 1 Reviewing number and financial mathematics 2 1A Integer operations CONSOLIDATING 4 1B Decimals and significant figures 9 1C Rational numbers CONSOLIDATING 14 1D Operations with fractions CONSOLIDATING 20 1E Ratios, rates and best buys CONSOLIDATING 26 1F Percentages and money CONSOLIDATING 32 1G Percentage increase and decrease CONSOLIDATING 38 Progr ess quiz 43 1H Profits and discounts 44 1I Income and taxation 49 Applications and problem-solving 57 1J Simple interest 59 1K Compound interest EXTENDING 64 Modelling 69 Technology and computational thinking 70 Investigation 72 Problems and challenges 73 Chapter checklist and success criteria 75 Chapter review 78 2 Linear and simultaneous equations 84 2A Algebraic expressions CONSOLIDATING 86 2B Simplifying algebraic expressions CONSOLIDATING 92 2C Expanding algebraic expressions 97 2D Solving linear equations 102 2E Equations with brackets and pronumerals on both sides 107 2F Solving word problems 111 Progr ess quiz 116 2G Inequalities 117 Strand: Algebra Strand: Algebra UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37303-6 • Ph 03 8671 1400
iv Contents 2H Using formulas 122 2I Simultaneous equations using substitution EXTENDING 128 Applications and problem-solving 133 2J Simultaneous equations using elimination EXTENDING 135 2K Applications of simultaneous equations EXTENDING 141 Modelling 146 Technology and computational thinking 147 Investigation 149 Problems and challenges 150 Chapter checklist and success criteria 152 Chapter review 154 3 Pythagoras’ theorem and trigonometry 158 3A Pythagoras’ theorem 160 3B Finding the length of the shorter sides 167 3C Applying Pythagoras’ theorem 172 3D Pythagoras in three dimensions EXTENDING 177 3E Trigonometric ratios 182 3F Finding side lengths 189 Progr ess quiz 195 3G Solving for the denominator 196 3H Finding an angle 201 Applications and problem-solving 206 3I Applying trigonometry EXTENDING 208 3J Bearings EXTENDING 215 Modelling 222 Technology and computational thinking 223 Investigation 225 Problems and challenges 226 Chapter checklist and success criteria 228 Chapter review 230 4 Linear relations 234 4A Introduction to linear relations CONSOLIDATING 236 4B Graphing straight lines using intercepts 243 4C Lines with one intercept 247 4D Gradient 254 4E Gradient and direct proportion 263 4F Gradient–intercept form 268 Progr ess quiz 274 4G Finding the equation of a line 276 4H Midpoint and length of a line segment 281 Strand: Algebra Strand: Measurement Algebra UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37303-6 • Ph 03 8671 1400
v Contents 4I Perpendicular and parallel lines EXTENDING 286 Applications and problem-solving 290 4J Linear modelling 292 4K Graphical solutions to simultaneous equations 297 Modelling 303 Technology and computational thinking 304 Investigation 306 Problems and challenges 308 Chapter checklist and success criteria 310 Chapter review 312 5 Measurement 318 5A Errors and accuracy in measurement 320 5B Length and perimeter CONSOLIDATING 326 5C Circle circumference and perimeter of a sector 333 5D Area 339 5E Composite shapes 348 Progr ess quiz 355 5F Surface area of prisms and pyramids 356 5G Surface area of a cylinder 362 Applications and problem-solving 367 5H Volume of a prism 369 5I Volume of a cylinder 376 Modelling 381 Technology and computational thinking 382 Investigation 384 Problems and challenges 385 Chapter checklist and success criteria 387 Chapter review 390 Semester review 1 394 6 Indices and surds 394 6A Index notation CONSOLIDATING 396 6B Index laws 1 and 2 402 6C Index law 3 and the zero power 408 6D Index laws 4 and 5 413 6E Negative indices 418 Progr ess quiz 424 6F Scientific notation 425 6G Scientific notation using significant figures 430 Strand: Algebra Strand: Measurement Algebra UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37303-6 • Ph 03 8671 1400
vi Contents Applications and problem-solving 435 6H Fractional indices and surds EXTENDING 437 6I Simple operations with surds EXTENDING 443 Modelling 447 Technology and computational thinking 448 Investigation 450 Problems and challenges 451 Chapter checklist and success criteria 453 Chapter review 455 7 Geometry 460 7A Angles and triangles CONSOLIDATING 462 7B Parallel lines CONSOLIDATING 470 7C Quadrilaterals and other polygons 478 7D Congruent triangles 485 7E Using congruence in proof EXTENDING 493 Progr ess quiz 499 7F Enlargement and similar figures 501 Applications and problem-solving 509 7G Similar triangles 511 7H Proving and applying similar triangles 519 Modelling 525 Technology and computational thinking 526 Investigation 528 Problems and challenges 529 Chapter checklist and success criteria 531 Chapter review 534 8 Algebraic techniques 540 8A Expanding binomial products 542 8B Perfect squares and difference of per fect squares 546 8C Factorising algebraic expressions 552 8D Factorising the difference of perfect squares 557 8E Factorising by grouping 561 8F Factorising monic quadratic trinomials 565 Progr ess quiz 569 8G Factorising trinomials of the form a x 2 + bx + c EXTENDING 570 8H Simplifying algebraic fractions: Multiplication and division 575 8I Simplifying algebraic fractions: Addition and subtraction 580 Strand: Algebra Strand: Space UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37303-6 • Ph 03 8671 1400
vii Contents Applications and problem-solving 585 8J Further simplification of algebraic fractions EXTENDING 587 8K Equations with algebraic fractions EXTENDING 592 Modelling 598 Technology and computational thinking 599 Investigation 601 Problems and challenges 602 Chapter checklist and success criteria 604 Chapter review 605 9 Probability and statistics 608 9A Review of probability CONSOLIDATING 610 9B Venn diagrams and two-way tables 617 9C Using set notation 624 9D Using arrays for two-step experiments 630 9E Tree diagrams 636 9F Experimental probability 642 Progr ess quiz 647 9G Data and sampling 648 9H Summarising data: Measures of centre 654 9I Stem-and-leaf plots 660 Applications and problem-solving 667 9J Grouped data 670 9K Measures of spread 677 9L Box plots EXTENDING 683 Modelling 690 Technology and computational thinking 691 Investigation 693 Problems and challenges 694 Chapter checklist and success criteria 696 Chapter review 699 10 Introduction to quadratic equations and graphs 704 10A Quadratic equations EXTENDING 706 10B Solving a x 2 + bx = 0 and x 2 = d EXTENDING 711 10C Solving x 2 + bx + c = 0 EXTENDING 715 10D Applications of quadratic equations EXTENDING 719 Progr ess quiz 723 10E The parabola 724 10F Sketching y = a x 2 with dilations and reflections 734 Strand: Algebra Strand: Statistics UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37303-6 • Ph 03 8671 1400
viii Contents Applications and problem-solving 742 10G Sketching translations of y = x 2 745 10H Sketching parabolas using intercept form EXTENDING 754 Modelling 762 Technology and computational thinking 763 Investigation 765 Problems and challenges 766 Chapter checklist and success criteria 768 Chapter review 770 Semester review 2 403 11 Algorithmic thinking 1271 Introduction 1273 Activity 1: Algorithms for number patterns and financial maths 1274 Activity 2: Minimising and maximising 1278 Activity 3: Sorting, simulations and sampling 1280 Index xxx Answers xxx Digital only UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37303-6 • Ph 03 8671 1400