Table Of ContentEE SS SS EE NN TT II AA LL
MMAATTHHEEMMAATTIICCSS
FOR THE AUSTRALIAN CURRICULUM
YEAR
10
Additional resources online
DAVID GREENWOOD | JENNY GOODMAN
JENNIFER VAUGHAN | SARA WOOLLEY
| MARGARET POWELL
ISBN: 9781107687028 © David Greenwood et al. 2012 Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party
EMGAC10title.indd 1 28/02/12 2:23 PM
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Information on this title: www.cambridge.org/9781107687028
© David Greenwood, Jenny Goodman, Jennifer Vaughan, Sara Woolley,
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ISBN: 9781107687028 © David Greenwood et al. 2012 Cambridge University Press
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Table of Contents
Contents
Strand and content description
About the authors viii
Introduction and how to use this book ix
Acknowledgements xiv
1 Measurement 1
Measurement and Geometry
Pre-test 2
Using units of measurement
1.1 Conversion of units 3
1.2 Perimeter 8
1.3 Circumference 14
1.4 Area 18
1.5 Area of a circle 23
1.6 Surface area of prisms 28
1.7 Surface area of a cylinder 33
1.8 Volume of solids 37
Puzzles and games 42
Review: Chapter summary 43
Multiple-choice questions 44
Short-answer questions 45
Extended-response questions 46
Consumer arithmetic 47
2
Number and Algebra
Pre-test 48
2.1 Review of percentages 49 Money and fi nancial mathematics
2.2 Applications of percentages 54
2.3 Income 60
2.4 Budgeting 66
2.5 Simple interest and applications 72
2.6 Compound interest 76
2.7 Investments and loans 80
2.8 Comparing interest using technology 87
Puzzles and games 90
Review: Chapter summary 91
Multiple-choice questions 92
Short-answer questions 92
Extended-response questions 94
iii
ISBN: 9781107687028 © David Greenwood et al. 2012 Cambridge University Press
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iv Contents
3 Algebra and indices 95
Number and Algebra
Pre-test 96
Patterns and algebra
3.1 Algebraic expressions 97
3.2 Simplifying algebraic expressions 102
3.3 Expanding algebraic expressions 107
3.4 Factorising algebraic expressions 111
3.5 Multiplying and dividing algebraic fractions 115
3.6 Adding and subtracting algebraic fractions 120
3.7 Index notation and index laws 1 and 2 124
3.8 More index laws and the zero power 130
3.9 Scientifi c notation 135
3.10 Exponential growth and decay 139
Puzzles and games 144
Review: Chapter summary 145
Multiple-choice questions 146
Short-answer questions 147
Extended-response questions 148
4 Probability 149
Statistics and Probability
Pre-test 150
4.1 Review of probability 151 Chance
4.2 Venn diagrams 157
4.3 Two-way tables 163
4.4 Conditional probability 167
4.5 Multiple events using tables 172
4.6 Using tree diagrams 178
4.7 Independent events 185
Puzzles and games 189
Review: Chapter summary 190
Multiple-choice questions 191
Short-answer questions 192
Extended-response questions 194
5 Statistics 195
Statistics and Probability
Pre-test 196
Data representation and
5.1 Sorting data: frequency tables, column
interpretation
graphs and histograms 197
5.2 Graphical forms: dot plots and stem-and-leaf plots 206
5.3 Range and measures of centre 213
5.4 Quartiles and outliers 219
5.5 Boxplots 224
5.6 Time series data 229
5.7 Bivariate data and scatter plots 234
ISBN: 9781107687028 © David Greenwood et al. 2012 Cambridge University Press
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Contents v
5.8 Line of best fi t by eye 239
Puzzles and games 245
Review: Chapter summary 246
Multiple-choice questions 247
Short-answer questions 248
Extended-response questions 250
Semester review 1 251
66 Straight line graphs 259
MNuemasbuerre amnedn At lagnedb rGaeometry
Pre-test 260
Linear and non-linear relationships
6.1 Interpretation of straight line graphs 262
6.2 Distance–time graphs 268
6.3 Plotting straight lines 274
6.4 Midpoint and length of a line segment 281
6.5 Exploring gradient 288
6.6 Rates from graphs 295
6.7 y = mx + c and special lines 300
6.8 Sketching with x- and y-intercepts 306
6.9 Linear modelling 311
Puzzles and games 318
Review: Chapter summary 319
Multiple-choice questions 320
Short-answer questions 320
Extended-response questions 323
7 Geometry 325
Measurement and Geometry
Pre-test 326
Geometric reasoning
7.1 Parallel lines 328
7.2 Triangles 333
7.3 Quadrilaterals 338
7.4 Polygons 343
7.5 Congruent triangles 347
7.6 Similar triangles 353
7.7 Applying similar triangles 358
7.8 Applications of similarity in measurement 363
Puzzles and games 369
Review: Chapter summary 370
Multiple-choice questions 371
Short-answer questions 371
Extended-response questions 374
ISBN: 9781107687028 © David Greenwood et al. 2012 Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party
vi Contents
8 Equations 375
Number and Algebra
Pre-test 376
Linear and non-linear relationships
8.1 Solving linear equations 377
8.2 Solving more diffi cult linear equations 384
8.3 Using formulas 390
8.4 Inequalities 394
8.5 Solving simultaneous equations graphically 400
8.6 Solving simultaneous equations using substitution 406
8.7 Solving simultaneous equations using elimination 411
Puzzles and games 418
Review: Chapter summary 420
Multiple-choice questions 421
Short-answer questions 422
Extended-response questions 424
9 Pythagoras’ theorem and
trigonometry 425
Measurement and Geometry
Pre-test 426
Pythagoras and trigonometry
9.1 Reviewing Pythagoras’ theorem 427
9.2 Finding the length of a shorter side 432
9.3 Applications of Pythagoras’ theorem 436
9.4 Trigonometric ratios 442
9.5 Finding side lengths 448
9.6 Finding more side lengths 453
9.7 Finding angles 458
9.8 Angles of elevation and depression 463
9.9 Direction and bearings 471
Puzzles and games 477
Review: Chapter summary 478
Multiple-choice questions 479
Short-answer questions 480
Extended-response questions 482
10 Quadratics and non-linear graphs 483
Number and Algebra
Pre-test 484
Patterns and algebra
10.1 Expanding binomial products 485
Linear and non-linear relationships
10.2 Factorising a difference of perfect squares 490
10.3 Factorising trinomials of the form x 2 + bx + c 493
10.4 Solving quadratic equations 497
10.5 Applications of quadratics 501
10.6 Exploring parabolas 504
10.7 Graphs of circles and exponentials 513
ISBN: 9781107687028 © David Greenwood et al. 2012 Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party
Contents vii
Puzzles and games 519
Review: Chapter summary 520
Multiple-choice questions 521
Short-answer questions 522
Extended-response questions 524
Semester review 2 525
Glossary 539
Answers 543
ISBN: 9781107687028 © David Greenwood et al. 2012 Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party
viii
About
the authors
David Greenwood is the head of Mathematics at Trinity Grammar
School in Melbourne and has 19 years’ experience teaching
mathematics from Years 7 to 12. He has run numerous workshops
within Australia and overseas regarding the implementation of the
Australian Curriculum and the use of technology for the teaching of
mathematics. He has written more than 20 mathematics titles and
has a particular interest in the sequencing of curriculum content and
working with the Australian Curriculum proficiency strands.
Sara Woolley was born and educated in Tasmania. She completed
an Honours degree in Mathematics at the University of Tasmania
before completing her education training at the University of
Melbourne. She has taught mathematics in Victoria from Years 7 to
12 since 2006 and has a keen interest in the creation of resources
that cater for a wide range of ability levels.
Jenny Goodman has worked for 20 years in comprehensive state
and selective high schools in NSW and has a keen interest in
teaching students of differing ability levels. She was awarded the
Jones medal for education at Sydney University and the Bourke
prize for Mathematics. She has written for Cambridge NSW and
was involved in the Spectrum and Spectrum Gold series.
Jennifer Vaughan has taught secondary mathematics for more
than 30 years in NSW, WA, QLD and New Zealand, and has
tutored and lectured in mathematics at Queensland University of
Technology. She is passionate about providing students of all ability
levels with opportunities to understand and to have success in
using mathematics. She has taught special needs students and
has had extensive experience in developing resources that make
mathematical concepts more accessible, hence facilitating student
confidence, achievement and an enjoyment of maths.
Consultant
Margaret Powell has 23 years of experience in teaching special
needs students in Sydney and London. She has been head
teacher of the support unit at a NSW comprehensive high school
for 12 years. She is one of the authors of Spectrum Maths Gold
Year 7 and Year 8. Margaret is passionate about ensuring that
students with learning difficulties are provided with learning
materials that are engaging and accessible, so as to give them
the best chance to achieve in their adademic careers.
viii
ISBN: 9781107687028 © David Greenwood et al. 2012 Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party
Contents ix
Introduction and
how to use this book
The Essential Mathematics Gold for the Australian Curriculum series has been developed
especially to cater for students who require additional support in mathematics. Using the
Essential Mathematics for the Australian Curriculum series as a starting point, the Gold
series heavily revises that material and adds a wealth of new content to help students
meet the Achievement Standards of the Australian Curriculum.
In addition to an author team of skilled teachers with experience teaching students at
all levels, the Gold series has been carefully reviewed by Special Education advisors to
make sure that the language and concepts are effective for struggling students.
The Gold series takes a practical interpretation of the Australian Curriculum that
focuses on the Understanding and Fluency proficiency strands in order to help students
learn core mathematical skills. These foundation abilities are developed through clear
explanations of concepts that are repeated and closely linked to carefully graded
exercises, which include linked examples and hints throughout. Questions for the
Problem-solving and Reasoning proficiency strands, along with Gold Star enrichment
problems, are provided to challenge students that want to improve their skills further.
Literacy and numeracy skills are the other major focus of the Gold series. Key words
are defined multiple times within the books to help students become fluent with
mathematical terms and concepts. Real-world contexts and applications of mathematics
help students connect these concepts to everyday life. Each chapter has a Puzzles and
games section for stimulus and motivation.
The Essential Mathematics Gold for the Australian Curriculum series complements the
full Essential Mathematics series and Cambridge HOTmaths to provide a choice of
mathematics resources that work well across all ranges of ability.
ix
ISBN: 9781107687028 © David Greenwood et al. 2012 Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party
x Introduction and how to use this book
How to use this book
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Australian Curriculum: strands and
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content descriptions for chapter 1 Measurement
(also available in a grid)
What you will learn
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Pre-test: establishes prior knowledge
(also available as a printable worksheet) 2 Chapter 1 Measurement
Pre-test 1 Nae ame thes e sh apes.bf gc hd
2 Wa ri1t ek tmh e= m issing m n umber.b 1 m = cm c 1 cm = mm
d 1 L = mL e 0.5 km = m f 2.5 cm = mm
3 Fa ind the perim eter of these sbh apes. 5 m c 2.5 mm
3 cm 11 m 1.3 mm 2.1 mm
4 Fa ind the a5re cam of these 2sh camp esb. 10 m 7 m c 6 km
5 Fa ind the area of t2h cemse trianglbe s u4s imng A = 12bh. c 4 km
6 tUwsoe dCe =ci m4π dca mla pnldac Aes =. π r 2 to fi nd the circumf7e rmence and area of this c3ir kclme. Round to
10 m
d = 10, r = 5
Topic introduction: use to relate the topic
to mathematics in the wider world Number and Algebra 49
2.1 Review of percentages
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(see next page for more) Choice A Choice B
Increase of $20 a week Increase of 2% on p.a. salary
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skills for the lesson (digital version also Exercise2A
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ISBN: 9781107687028 © David Greenwood et al. 2012 Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party
