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 xviii Working with unfamiliar problems: Part 2 xx 1 Linear relations 2 1A Review of algebra CONSOLIDATING 4 1B Solving linear equations 11 1C Linear inequalities 18 1D Linear equations involving more complex algebraic fractions OPTIONAL 24 1E Graphing straight lines CONSOLIDATING 29 1F Finding an equation of a line 38 Progress quiz 45 1G Length and midpoint of a line segment 46 1H Perpendicular and parallel lines 52 Applications and problem-solving 58 1I Simultaneous equations using substitution 60 1J Simultaneous equations using elimination 67 1K Further applications of simultaneous equations 71 1L Half planes 75 Modelling 83 Technology and algorithms 84 Investigation 86 Problems and challenges 87 Chapter checklist and success criteria 89 Chapter review 92 2 Geometry and networks 9 8 2A Review of geometry CONSOLIDATING 100 2B Congruent triangles 109 2C Investigating parallelograms using congruence 116 2D Similar figures CONSOLIDATING 122 2E Proving and applying similar triangles 128 Progress quiz 136 2F Circles and chord properties OPTIONAL 138 Strand: Algebra Strand: Space UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37312-8 • Ph 03 8671 1400
iv 2G Angle properties of circles: Theorems 1 and 2 OPTIONAL 146 2H Angle properties of circles: Theorems 3 and 4 OPTIONAL 154 Applications and problem-solving 160 2I Tangents to a circle OPTIONAL 162 2J Intersecting chords, secants and tangents EXTENDING 169 2K Introduction to networks 174 2L Isomorphic and planar graphs 181 2M Trails, paths and Eulerian circuits 189 2N Shortest path problems 198 Modelling 205 Technology and algorithms 206 Investigation 208 Problems and challenges 209 Chapter checklist and success criteria 212 Chapter review 219 3 Exponentials and logarithms 22 2 3A Review of index laws CONSOLIDATING 224 3B Negative indices 230 3C Scientific notation CONSOLIDATING 236 3D Rational indices OPTIONAL 241 3E Exponential equations OPTIONAL 247 3F Graphs of exponentials 251 Progress quiz 257 3G Exponential growth and decay 258 3H Compound interest 264 Applications and problem-solving 269 3I Introducing logarithms 271 3J Logarithmic scales 276 3K Laws of logarithms OPTIONAL 286 3L Solving exponential equations using logarithms OPTIONAL 291 Modelling 295 Technology and algorithms 296 Investigation 298 Problems and challenges 299 Chapter checklist and success criteria 301 Chapter review 304
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v 4 Measurement and surds 31 2 4A Irrational numbers including surds OPTIONAL 314 4B Adding and subtracting surds OPTIONAL 321 4C Multiplying and dividing surds OPTIONAL 325 4D Rationalising the denominator OPTIONAL 331 4E Review of length CONSOLIDATING 335 4F Pythagoras’ theorem 342 4G Review of area CONSOLIDATING 350 Progress quiz 359 4H Errors and accuracy 361 4I Surface area of prisms and cylinders 368 4J Surface area of pyramids and cones EXTENDING 376 4K Volume of prisms and cylinders 382 Applications and problem-solving 389 4L Volume of pyramids and cones EXTENDING 391 4M Surface area and volume of spheres EXTENDING 397 Modelling 404 Technology and algorithms 405 Investigation 407 Problems and challenges 408 Chapter checklist and success criteria 411 Chapter review 415 5 Quadratic expressions and equations 4 22 5A Expanding expressions CONSOLIDATING 424 5B Factorising expressions 430 5C Multiplying and dividing algebraic fractions 436 5D Factorising monic quadratic trinomials 441 5E Factorising non-monic quadratic trinomials OPTIONAL 446 Progress quiz 450 5F Factorising by completing the square 451 5G Solving quadratic equations using factorisation 456 5H Applications of quadratics 462 Applications and problem-solving 466 5I Solving quadratic equations by completing the square 468 5J Solving quadratic equations using the quadratic formula OPTIONAL 473 Modelling 479 Technology and algorithms 480 Investigation 482 Strand: Measurement Algebra Strand: Algebra Contents UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37312-8 • Ph 03 8671 1400
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vi Problems and challenges 483 Chapter checklist and success criteria 485 Chapter review 487 Semester review 1 484 6 Trigonometry 49 6 6A Trigonometric ratios 498 6B Finding unknown angles 506 6C Applications using angles of elevation and depression 512 6D Bearings 518 6E Applications in three dimensions 525 Progress quiz 531 6F The sine rule EXTENDING 532 6G The cosine rule EXTENDING 538 Applications and problem-solving 543 6H Area of a triangle EXTENDING 545 6I The unit circle OPTIONAL 550 6J Graphs of trigonometric functions OPTIONAL 559 6K Exact values and solving trigonometric equations OPTIONAL 571 Modelling 576 Technology and algorithms 577 Investigation 579 Problems and challenges 580 Chapter checklist and success criteria 582 Chapter review 585
5 92 7A Exploring parabolas 594 7B Sketching parabolas using transformations 603 7C Sketching parabolas using factorisation 611 7D Sketching parabolas by completing the square 619 7E Sketching parabolas using the quadratic formula OPTIONAL 627 Progress quiz 633 7F Applications of parabolas 635 7G Intersection of lines and parabolas OPTIONAL 641 Applications and problem-solving 650 7H Rates of change OPTIONAL 652 Strand: Measurement Strand: Algebra Contents UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37312-8 • Ph 03 8671 1400
Graphs of quadratic relations
vii 7I Average and instantaneous rates of change OPTIONAL 662 7J Direct and inverse proportion EXTENDING 669 Modelling 676 Technology and algorithms 677 Investigation 679 Problems and challenges 680 Chapter checklist and success criteria 683 Chapter review 686 8 Probability and counting techniques 69 0 8A Review of probability CONSOLIDATING 692 8B Unions and intersections 698 8C The addition rule 707 8D Conditional probability 713 8E Two-step experiments using tables 719 Progress quiz 726 8F Using tree diagrams 727 8G Independent events 736 Applications and problem-solving 741 8H Counting principles and factorial notation OPTIONAL 743 8I Arrangements OPTIONAL 747 8J Selections OPTIONAL 752 8K Applications of counting in probability OPTIONAL 756 Modelling 760 Technology and algorithms 761 Investigation 764 Problems and challenges 765 Chapter checklist and success criteria 767 Chapter review 769 9 Statistics 7 74 9A Collecting and using data 776 9B Review of statistical graphs CONSOLIDATING 782 9C Two-way tables 791 9D Summary statistics 799 9E Box plots 805 Progress quiz 812 9F Standard deviation OPTIONAL 814 9G Cumulative frequency curves and percentiles 821 9H Time-series data 832 9I Bivariate data and scatter plots 838 Strand: Probability Strand: Statistics Contents UNCORRECTEDSAMPLEPAGES Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37312-8 • Ph 03 8671 1400
(Digital only)
viii Applications and problem-solving 846 9J Line of best fit by eye 848 Modelling 857 Technology and algorithms 858 Investigation 860 Problems and challenges 861 Chapter checklist and success criteria 863 Chapter review 866 10 Polynomials and other graphs 87 2 10A Functions EXTENDING 874 10B Introducing polynomials EXTENDING 882 10C Expanding and simplifying polynomials EXTENDING 888 10D Division of polynomials EXTENDING 892 10E The remainder and factor theorems EXTENDING 895 Progress quiz 899 10F Solving polynomial equations EXTENDING 900 10G Graphs of polynomials EXTENDING 905 10H Graphs of circles EXTENDING 911 Applications and problem-solving 918 10I Graphs of hyperbolas EXTENDING 920 10J Further transformations of graphs EXTENDING 927 Modelling 933 Technology and algorithms 934 Investigation 936 Problems and challenges 937 Chapter checklist and success criteria 939 Chapter review 941 Semester review 2 944 11 Algorithmic thinking 956 Introduction 958 Activity 1: Using numerical methods to solve equations 959 Activity 2: Pythagorean triples 964 Activity 3: Using simulations to find probabilities 969 Index 000 Answers 000 Strand: Algebra Contents UNCORRECTEDSAMPLEPAGES
Uncorrected 2nd sample pages • Cambridge University Press and Assessment © Greenwood, et al 2023 • 978-1-009-37312-8 • Ph 03 8671 1400