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NEWCENTURYMATHS

australian curriculum

For the

Klaas BootsmaDavid BadgerSarah HamperRobert Yen Series EditorNelsonNet print resources by Megan Boltze

9NSW Stages 5.1/5.2

New Century Maths 9 for the Australian Curriculum: NSW Stages5.1/5.21st EditionKlaas BootsmaDavid BadgerSarah Hamper

Publishing editor: Robert YenProject editor: Alan StewartEditor: Anna PangSenior designer: Luana KeaysCover image: Shutterstock.com/Filip FuxaPermissions researcher: Miriam AllenProduction controller: Erin DowlingTypeset by: Cenveo Publisher Services

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Copyright NoticeThis Work is copyright. No part of this Work may be reproduced, stored in a retrievalsystem, or transmitted in any form or by any means without prior written permission ofthe Publisher. Except as permitted under the Copyright Act 1968, for example any fairdealing for the purposes of private study, research, criticism or review, subject to certainlimitations. These limitations include: Restricting the copying to a maximum of onechapter or 10% of this book, whichever is greater; providing an appropriate notice andwarning with the copies of the Work disseminated; taking all reasonable steps to limitaccess to these copies to people authorised to receive these copies; ensuring you holdthe appropriate Licences issued by the Copyright Agency Limited (“CAL”), supply a remuneration notice to CAL and pay any required fees. For details of CAL licences andremuneration notices please contact CAL at Level 15, 233 Castlereagh Street, Sydney NSW 2000, Tel: (02) 9394 7600, Fax: (02) 9394 7601Email: [email protected]: www.copyright.com.au

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National Library of Australia Cataloguing-in-Publication DataBootsma, Klaas, author.New Century Maths 9 for the Australian Curriculum : NSWStages 5.1/5.2 / Klaas Bootsma, David Badger, Sarah Hamper.

9780170193047 (paperback)Includes index.For secondary school age.

Mathematics--New South Wales--Textbooks.Mathematics--New South Wales--Study and teaching(Secondary)

510

Cengage Learning AustraliaLevel 7, 80 Dorcas StreetSouth Melbourne, Victoria Australia 3205

Cengage Learning New Zealand Unit 4B Rosedale Office Park 331 Rosedale Road, Albany, North Shore 0632, NZ

For learning solutions, visit cengage.com.au

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under the Copyright Act 1968 (Cth) and is owned by the AustralianCurriculum, Assessment and Reporting Authority 2013.

For all Australian Curriculum material except elaborations: This isan extract from the Australian Curriculum.

Elaborations: This may be a modified extract from the AustralianCurriculum and may include the work of other authors.

Disclaimer: ACARA neither endorses nor verifies the accuracy of theinformation provided and accepts no responsibility for incomplete orinaccurate information. In particular, ACARA does not endorse orverify that:• The content descriptions are solely for a particular year and subject;• All the content descriptions for that year and subject have been

used; and• The author’s material aligns with the Australian Curriculum content descriptions for the relevant year and subject.

You can find the unaltered and most up to date version of thismaterial at http://www.australiancurriculum.edu.au. This materialis reproduced with the permission of ACARA.

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Preface

First published in 1996, New Century Maths 9 Stages 5.1/5.2 has now been completely rewritten to reflect the spirit of the new Australian curriculum and the NSW syllabus. For Years 9 and 10, we publish two levels of mathematics books:

New Century Maths Stages 5.1/5.2 New Century Maths Advanced Stages 5.2/5.3

The NSW mathematics syllabus describes Stage 5 (Years 9–10) as a continuum with content classified into three sub-stages, Stage 5.1, Stage 5.2 and Stage 5.3, with each sub-stage including the content of the previous sub-stage. This book has been designed for students and classes progressing along Stages 5.1 or 5.2 of the continuum.We have retained those familiar features that have made New Century Maths a leading series: clear worked examples, graded exercises, multiple-choice questions, Investigation, Technology, Mental skills, SkillCheck pre-chapter exercise, Power Plus extension exercise, Language of Maths, Topic overview with mind map, glossary, video tutorials and worksheets.New features include:

GeoGebra activities in our Technology sections

NelsonNet student and teacher websites of print and multimedia resourcesNelsonNetBook digital version of this book with interactive features

We always aim to write textbooks to provide flexibility for teachers to plan and teach for a variety of pathways. We thank our families and teaching colleagues for their continued support and patience, and editors Anna Pang and Alan Stewart for transforming our manuscript into this fine text. Finally, we wish all teachers and students using this book every success in embracing the new Australian mathematics curriculum.

About the authorsKlaas Bootsma

students, and his interests are in curriculum and the use of technology (ICT) in learning.

David Badger is principal of Toongabbie Christian School, was deputy principal at Mt Annan Christian

passion is to make mathematics interesting, practical and accessible to all students.

Sarah Hamper teaches at Abbotsleigh School in Wahroonga and has taught at Meriden and Tara

expertise is in using modelling, problem solving and ICT for the effective learning of mathematics, and she has presented workshops for MANSW and nationally.

Series editor Robert Yen has New Century Maths Essentials 9–10 and Mathematics General 2,

writes and presents for MANSW, and has co-edited its journal, ReflectionsLearning as an associate publisher.

Contributing authorsMegan Boltze wrote and edited many of the NelsonNet print resources (blackline masters) and is head

iii9780170193047

Preface iiiAbout the authors iiiCurriculum grids viiiUser’s guide xii* ¼ STAGE 5.2

Chapter 1: Pythagoras’theorem 2

SkillCheck 48NA186 1-01 Squares, square roots

and surds 5Investigation: DiscoveringPythagoras’ theorem 7

9MG222 1-02 Pythagoras’ theorem 79MG222 1-03 Finding the hypotenuse 12

Technology: Finding thehypotenuse 15

9MG222 1-04 Finding a shorter side 16Mental skills 1A: Multiplyingand dividing by a power of 10 19Technology: Finding ashorter side 20

9MG222 1-05 Mixed problems 219MG222 1-06 Testing for right-angled

triangles 279MG222 1-07 Pythagorean triads 299MG222 1-08 Pythagoras’ theorem

problems 31Mental skills 1B: Multiplyingand dividing by a multipleof 10 36Power plus 37Chapter 1 review 39

Chapter 2: Working withnumbers 42

SkillCheck 448NA183 2-01 Integers 448NA183 2-02 Decimals 478NA184 2-03 Terminating and

recurring decimals 52Technology: Terminating andrecurring decimals 53

8NA183 2-04 Fractions 54Mental skills 2A: Squaring anumber ending in 5, 1 or 9 60

8NA183 2-05 Percentages 62Technology: Convertingfractions to percentages 65

8NA187 2-06 Operations withpercentages 66

Technology: Convertingmarks to percentages 70

8NA189 2-07 Percentages and money 70Technology: Profit or loss 74

9NA211 2-08 Simple interest 75Mental skills 2B: Estimatingsquare roots 78

8NA188 2-09 Ratios and rates 799NA208 2-10 Converting rates* 858MG199 2-11 Time differences 86

Power plus 88Chapter 2 review 89

Chapter 3: Algebra 92SkillCheck 94

7NA177 3-01 From words to algebraicexpressions 95

7NA176 3-02 Substitution 98Technology: Substitution 101

8NA192 3-03 Adding and subtractingterms 102

8NA192 3-04 Multiplying and dividingterms 104

Mental skills 3A: Multiplyingand dividing by 5, 15,25 and 50 108

10NA232 3-05 Adding and subtractingalgebraic fractions* 109

10NA232 3-06 Multiplying and dividingalgebraic fractions* 111

9NA213 3-07 Expanding expressions 1128NA191 3-08 Factorising expressions 115

Mental skills 3B: Multiplyingby 9, 11, 99 and 101 119

9NA213 3-09 Expanding binomialproducts* 120


Mixed revision 1 129

Chapter 4: Trigonometry 132SkillCheck 134

9MG223 4-01 The sides of a right-angled triangle 135

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Contents

9MG223 4-02 The trigonometric ratios 1389MG223 4-03 Similar right-angled

triangles 141Technology: Similar right-angled triangles 144

9MG223 4-04 Trigonometry on acalculator 146

Mental skills 4: Estimatinganswers 149

9MG224 4-05 Finding an unknown side 150Investigation: Calculating theheight of an object 156

9MG224 4-06 Finding more unknownsides 157

Investigation: Finding an angle,given a trigonometric ratio 162

9MG224 4-07 Finding an unknownangle 163


Chapter 5: Indices 172SkillCheck 174Investigation: Multiplying anddividing terms with powers 175

9NA212 5-01 Multiplying and dividingterms with the same base 175

Investigation: Powers ofpowers 178

9NA212 5-02 Power of a power 1799NA212 5-03 Powers of products and

quotients 180Investigation: The power ofzero 183

9NA212 5-04 The zero index 183Mental skills 5: Adding ormultiplying in any order 185Investigation: Negative powers 185Technology: Negative powers 187

9NA209 5-05 Negative indices 1889NA209 5-06 Summary of the index

laws 191NSW 5-07 Significant figures 1929NA210 5-08 Scientific notation 1959NA210 5-09 Scientific notation on a

calculator 199Investigation: A lifetime ofheartbeats 201Power plus 202Chapter 5 review 203

Chapter 6: Geometry 206SkillCheck 208

7MG163,

164

6-01 Angle geometry 210

Technology: Constructingtriangles 217Technology: Exterior angleof a triangle 217

7MG165,

166

6-02 Triangle geometry 218

Technology: Sketchingparallelograms and rectangles 224

7MG165,

166

6-03 Quadrilateral geometry 226

Investigation: Angle sum of apolygon* 234

NSW 6-04 Angle sum of a polygon* 235Mental skills 6: Dividingdecimals 239Investigation: Exterior anglesum of a convex polygon* 240

NSW 6-05 Exterior angle sum of aconvex polygon* 241


Chapter 7: Equations 248SkillCheck 250

8NA194 7-01 Two-step equations 2518NA194 7-02 Equations with variables

on both sides 2558NA194,

9NA215

7-03 Equations withbrackets 257

Investigation: Make your ownequation 259

8NA194 7-04 Equation problems 259Mental skills 7A: Fraction ofa quantity 264

10NA240 7-05 Equations with algebraicfractions* 265

Technology: Solving equationson a graphics calculator 267Investigation: Solving x 2 ¼ c 267

10NA241 7-06 Simple quadraticequations ax 2 ¼ c* 268

10NA234,

235

7-07 Equations and formulas* 270

Mental skills 7B: Percentageof a quantity 273Power plus 274Chapter 7 review 275

v9780170193047

NEW CENTURY MATHSfor the A u s t r a l i a n C u r r i c u l um9


Chapter 8: Earningmoney 282

SkillCheck 284NSW 8-01 Wages and salaries 284

Investigation: Positions vacant 288NSW 8-02 Overtime pay 289

Technology: Calculatingincomes 293

NSW 8-03 Commission, pieceworkand leave loading 294

NSW 8-04 Income tax 300Technology: Online incometax calculators 302Mental skills 8: Percentageincrease and decrease 303

NSW 8-05 PAYG tax and net pay 304Technology: Online PAYGtax calculator 307Power plus 308Chapter 8 review 309

Chapter 9: Investigatingdata 312

SkillCheck 3147SP171,

8SP207

9-01 The mean, median,mode and range 315

Investigation: The effect ofoutliers 324Technology: Most valuableplayer 324

9SP282,

228

9-02 Histograms andstem-and-leaf plots 325

Technology: Histograms 3329SP282 9-03 The shape of a

distribution 3349SP283 9-04 Comparing data sets 338

Technology: Comparingrelative humidities 341Mental skills 9: Finding apercentage of a multiple of 10 342

8SP284,

9SP228

9-05 Sampling and typesof data 343

Technology: Random numbers 346Investigation: AustralianBureau of Statistics 346

9SP227 9-06 Bias and questionnaires* 347Investigation: Media reportsof surveys 350

Investigation: Year 9 studentsurvey 351Power plus 352Chapter 9 review 353

Chapter 10: Surface area andvolume 358

SkillCheck 3609MG219 10-01 Metric units 362NSW 10-02 Limits of accuracy of

measuring instruments 3689MG216 10-03 Perimeters and areas

of composite shapes 370Investigation: Area of atrapezium, kite and rhombus 373

8MG196 10-04 Areas of quadrilaterals 374Mental skills 10A: Finding10%, 20% and 5% 378

9MG216 10-05 Circumferences andareas of circular shapes 379

Investigation: Nets of prisms 3869MG218 10-06 Surface area of a prism 387

Investigation: Surface areaof a cylinder 394

9MG217 10-07 Surface area of acylinder* 394

8MG198 10-08 Volumes of prisms andcylinders 397

Investigation: Volume vssurface area 402Technology: Drawing prismsand cylinders 403Mental skills 10B: Finding15%, 21

2%, 25% and 1212% 405



Chapter 11: Coordinategeometryand graphs 416

SkillCheck 4189NA214 11-01 The length of an

interval 419Investigation (optional): Thedistance formula 421Technology: The length of aninterval 423

vi 9780170193047

Contents

Investigation: The midpointof an interval 424Technology: The midpointof an interval 425

9NA294 11-02 The midpoint of aninterval 426

9NA294 11-03 The gradient of a line 428Technology: The gradient ofcollinear points 433

9NA215 11-04 Graphing linearequations 434

Technology: Graphing linearequations 439Mental skills 11: Divisibilitytests 440Investigation: Comparinggradients and y-intercepts 441

NSW 11-05 The gradient–interceptequation y ¼ mx þ b* 442

NSW 11-06 Finding the equationof a line* 445

8NA194 11-07 Solving linear equationsgraphically 447

Technology: Solving linearequations graphically 448

9NA208 11-08 Direct proportion* 450Investigation: Graphing y ¼ x 2

and y ¼ ax 2 453Technology: Graphing y ¼ ax 2 454Investigation: Graphingy ¼ ax 2 þ c 456

9NA296 11-09 Graphing quadraticequations 456

9NA296 11-10 Graphing circles 460Power plus 464Chapter 11 review 465

Chapter 12: Probability 468SkillCheck 470

8SP204 12-01 Probability 4719SP226 12-02 Relative frequency 476

Technology: Tossing a coin 481Technology: Rolling dice 482

9SP226 12-03 Venn diagrams 4839SP226 12-04 Two-way tables 489

Investigation: Using two-waytables 493Mental skills 12: The unitarymethod with percentages 493

Investigation: Are the Lottonumbers equally likely? 494

9SP225 12-05 Two-step experiments* 495Power plus 500Chapter 12 review 501

Chapter 13: Congruentand similarfigures 504

SkillCheck 5068MG200 13-01 Congruent figures 507

Technology: Tests forcongruent triangles 511Investigation: Congruenttriangles 512

8MG201 13-02 Tests for congruenttriangles 513

8MG202 13-03 Using congruence toprove geometricalproperties 519

Investigation: Same shape,different size 522

9MG220 13-04 Similar figures 523Mental skills 13: Simplifyingfractions and ratios 530Investigation: Properties ofsimilar figures 531

9MG220,

221

13-05 Properties of similarfigures 532

Investigation: Are all shapessimilar? 537

9MG221 13-06 Scale diagrams 537Investigation: Floor plans 542Investigation: Similar triangles 543

9MG220 13-07 Tests for similartriangles* 544

Investigation: Congruenceand similarity 548Power plus 550Chapter 13 review 551


General revision 560Glossary 566Answers 580Index 628

vii9780170193047

NEW CENTURY MATHSfor the A u s t r a l i a n C u r r i c u l um9

Curriculum grid: Australian curriculum

Strand and substrandNew Century Maths 9Stages 5.1/5.2chapter

New Century Maths 10Stages 5.1/5.2chapter

NUMBER AND ALGEBRA

Real numbers 2 Working with numbers 5 Indices11 Coordinate geometry and

graphs

7 Graphs

Money and financial mathematics 2 Working with numbers 1 Interest and depreciation

Patterns and algebra 3 Algebra 5 Indices

4 Algebra

Linear and non-linear relationships 7 Equations11 Coordinate geometry and

graphs

2 Coordinate geometry 6 Graphs 7 Equations and inequalities 9 Simultaneous equations

MEASUREMENT AND GEOMETRY

Using units of measurement 10 Surface area and volume 3 Surface area and volume

Geometric reasoning 6 Geometry13 Congruent and similar figures

11 Geometry

Pythagoras and trigonometry 1 Pythagoras theorem 4 Trigonometry

8 Trigonometry

STATISTICS AND PROBABILITY

Chance 12 Probability 10 Probability

Data representation and interpretation 5 Investigating data 5 Investigating data

viii 9780170193047

Strand and substrandNew Century Maths 9Stages 5.1/5.2chapter

New Century Maths 10Stages 5.1/5.2chapter

NUMBER AND ALGEBRA

Financial mathematics(Stages 5.1, 5.2)

2 Working with numbers 8 Earning money

1 Interest and depreciation

Indices(Stages 5.1, 5.2)

5 Indices 4 Algebra

Linear relationships(Stages 5.1, 5.2)

7 Equations11 Coordinate geometry and

graphs

2 Coordinate geometry

Non-linear relationships(Stages 5.1, 5.2)


graphs

2 Coordinate geometry 6 Graphs

Ratios and rates(Stage 5.2)

2 Working with numbers11 Coordinate geometry and

graphs

6 Graphs

Algebraic techniques(Stage 5.2)

3 Algebra 4 Algebra

Equations(Stage 5.2)

7 Equations 7 Equations and inequalities 9 Simultaneous equations


Area and surface area(Stages 5.1, 5.2)

10 Surface area and volume 3 Surface area and volume

Numbers of any magnitude(Stage 5.1)

5 Indices10 Surface area and volume

Right-angled triangles (Trigonometry)(Stages 5.1, 5.2)

1 Pythagoras theorem 4 Trigonometry

8 Trigonometry

Properties of geometrical figures(Stages 5.1, 5.2)

6 Geometry13 Congruent and similar figures

11 Geometry

Volume(Stage 5.2)

10 Surface area and volume 3 Surface area and volume


Single variable data analysis(Stages 5.1, 5.2)

9 Investigating data 5 Investigating data

Probability(Stages 5.1, 5.2)

12 Probability 10 Probability

Double variable data analysis(Stage 5.2)

5 Investigating data

Curriculum grid: NSW syllabus

ix9780170193047

Curriculum grid: Year 9 content descriptions

Content descriptionNew Century Maths 9 Stages 5.1/5.2chapter

NUMBER AND ALGEBRA

Real numbers

ACMNA208: Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems

11 Coordinate geometry and graphs

ACMNA209: Apply index laws to numerical expressions with integer indices 5 Indices

ACMNA210: Express numbers in scientific notation 5 Indices

Money and financial mathematics

ACMNA211: Solve problems involving simple interest 2 Working with numbers

NSW STAGE 5.1: Solve problems involving earning money 8 Earning money

Patterns and algebra

ACMNA212: Extend and apply the index laws to variables, using positive integer indices and the zero index

5 Indices

ACMNA213: Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate

3 Algebra

YEAR 10 ACMNA234: Substitute values into formulas to determine an unknown

7 Equations

Linear and non-linear relationships

ACMNA214: Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software


ACMNA215: Sketch linear graphs using the coordinates of two points and solve linear equations


graphs

YEAR 10 ACMNA235: Solve problems involving linear equations, including those derived from formulas

7 Equations

ACMNA294: Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software


NSW STAGE 5.2: Interpret and graph linear relationships using the gradient-intercept form of the equation of a straight line


ACMNA296: Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations


This is an extract from the Australian Curriculum.

x 9780170193047

Content descriptionNew Century Maths 9 Stages 5.1/5.2chapter


Using units of measurement

ACMMG216: Calculate the areas of composite shapes 10 Surface area and volume

ACMMG217: Calculate the surface area and volume of cylinders and solve related problems

10 Surface area and volume

ACMMG218: Solve problems involving the surface area and volume of right prisms


ACMMG219: Investigate very small and very large time scales and intervals 10 Surface area and volume

NSW STAGE 5.1: Round numbers to a specified number of significant figures, describe the limits of accuracy of measuring instruments


Geometric reasoning

ACMMG220: Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar

13 Congruent and similar figures

ACMMG221: Solve problems using ratio and scale factors in similar figures 13 Congruent and similar figures

NSW STAGE 5.2: Apply interior and exterior angle sum results for polygons to find the sizes of unknown angles

6 Geometry

Pythagoras and trigonometry

ACMMG222: Investigate Pythagoras theorem and its application to solving simple problems involving right-angled triangles

1 Pythagoras theorem

ACMMG223: Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles

4 Trigonometry

ACMMG224: Apply trigonometry to solve right-angled triangle problems 4 Trigonometry


Chance

ACMSP225: List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events

12 Probability

ACMSP226: Calculate relative frequencies from given or collected data to estimate probabilities of events involving ‘and or ‘or

12 Probability

ACMSP227: Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians

12 Probability

Data representation and interpretation

ACMSP228: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources


ACMSP282: Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed , ‘symmetric and ‘bi-modal


ACMSP283: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread


9NEW CENTURY MATHSAustral ian C urri culumfor the

xi9780170193047

New Century Maths User’s guide

Coverage of the Australian curriculum and NSW syllabus

New Century Maths 9 Stages 5.1/5.2

n Chapter outlineProficiency strands

1-01 Squares, square roots and

surds U C

1-02 Pythagoras’ theorem U F R C

1-03 Finding the hypotenuse U F

1-04 Finding a shorter side U F

1-05 Mixed problems F

1-06 Testing for right-angled

triangles U F C

1-07 Pythagorean triads U F C

1-08 Pythagoras’ theorem

problems F PS C

This is a Year 9 topic in the Australian Curriculum but a Stage 4

topic in the NSW syllabus, so this topic has also been covered in

Chapter 1 of New Century Maths 8 for the Australian Curriculum.

n

NAMGSP

chapter outline

UF PS RC

Working Mathematically explained

content strands Working Mathematically proficiencies

Understanding

Fluency

Problem solving

Reasoning

Communicating

Technology: Negative p

9NA209 5-05 Negative indices 190

9NA209 5-06 Summary of the index

laws 193

NSW 5-07 Significant figures194

9NA210 5-08 Scientific notation 197

5 09 Scientific notation on a

xii 9780170193047

9Austral ian C urri culumfor the

n In this chapter you will:

SkillCheck

1iiiiiia 84

b 48c h d h

2

Worksheet

StartUp assignment 5

MAT09NAWK10052

Worksheet

Powers review

Summary

When raising a quotient of terms to a power, raise each term to that power:

a

b

� n¼ an

bn

In each chapter

Wordbank is a sample glossary of 6–8 terms from the chapter.There is also a full glossary at the back of the book: in this book, all terms printed in red appear in the glossary.Content descriptions are listed at the beginning of each chapter, with the Australian Curriculum descriptions printed in blue with the symbol.SkillCheck and StartUp assignment review prerequisite skills and knowledge for the chapter.

Pages containing Stage 5.2 content are marked by a shaded margin.Graded exercises are linked to worked examples and include multiple-choice questions, exam-style problems and realistic applications.Worked solutions for selected exercise questions are provided.

Stage 5.2Exercise 3-06 Multiplying and dividing algebraicfractions

1 Simplify each product.

a w33 1

2 b s53 t

4 c 3h3 5

6kd 4

m3 3

n e l33 5

f f 1v3 2

3vg 2

x3 3

x h ab3 c

d i de3 e

gj 4ad

93 d

16a k 5p4

3 815p l 4

ak3 3a

5km 2

33 9u

10 n u33 3

u o 3zr

3 2r9dz2 Simplify each quotient.

a r24 r

5 b m64 n

3 c h24 h

8d q

44 3

4 e 3y5

42yd f 4t

94 3t

5g 3

e4 5

e h 32a

4 b6a i 5m

n4 2m

3nj h

k4 k

h k 8w3x

4 2w9x l 3s

44 6s

11m t

34 3t

5u n 3e7g

4 e14g o xh

54 3h

153 Simplify each expression.a 3p

24

p 2

4 b 2w7

4 5w6 c 8y

53 3

32y 2d 5

2g4 2

g e xyz3 5

y f ab3 c

b3 b

3ag 54 3

5b h 4t9

4 3 i 5mn2d

3 4dn

3 115mnj 5p4 7

10pt k s34 5s

23 3s

7 l 7h3 1

42hm 5ty

k3

5kyt n 6

r3 5r

94 15

yh o 6cfq

4 5qf

4 10ca

See Example 14

See Example 15

Worked solutions

Multiplying and dividingalgebraic fractions

MAT09NAWS100010

Investigation: A lifetime of heartbeats

How many times does your heart beat in an average lifetime of 80 years?1 Work in pairs and copy this table.

Name Trial 1 Trial 2 Average beats per minute

2 Use two fingers to measure your pulse. Have your partner time you for a minute. Do thistwice, record your results in the table and find the average.

3 Repeat Step 2 for your partner.4 Calculate how many times your heart (and your partner’s heart) beats in the following

periods. Write your answers in scientific notation correct to two significant figures.h b d k

Just for the record Hairy numbers

Straight hair round follicle

Wavy hair oval follicle

Curly hairflat follicle

There are about 110 000 hairs on your head. Each hair grows at the rate of about 1.33 10�3 cmper hour. A single hair lasts about six years. Every day you lose between 30 and 60 hairs.Each hair grows from a small depression in the skin called a follicle (a gland). After thehair falls out, the follicle rests for about three to four months before the next hair startsgrowing. Hair follicles are either oval, flat or round in shape. How straight, wavy or curlyyour hair is depends on the shape of your hair follicles.

Shutterstock.com

/with

God

Shutterstock.com

/StockLite

Shutterstock.com

/Jason

Stitt

Investigations explore the syllabus in more detail, through group work, discovery and modelling activities.

Important facts and formulas are highlighted in a Summary box.

NEW CENTURY MATHS

Just for the record contains interesting facts and applications of the mathematics in the chapter.

xiii9780170193047

Technology promotes ICT in the classroom, using spreadsheets, GeoGebra and the Internet.

Technology Similar right-angled trianglesIn this activity you will use GeoGebra to measure and calculate trigonometric ratios.1 a Before you start, set angles to measure in degrees, then click Options, Rounding and1 Decimal Place.

Mental skills 4 Maths without calculators

Estimating answersA quick way of estimating an answer is to round each number in the calculation.

1 Study each example.

a 631þ 280þ 51þ 43þ 96 � 600þ 300þ 50þ 40þ 100

¼ ð600þ 300þ 100Þ þ ð50þ 40Þ¼ 1000þ 90

Mental skills reinforce mental calculation strategies (‘maths

NelsonNet resources

ia resources found on the NelsonNet website, www.nelsonnet.com.au. These include:

MAT09MGVT10001, which stands for Mathematics, Year 9, Measurement and Geometry strand, Video Tutorial 10001.

New Century Maths User s guide

WorksheetsVideo tutorials of worked examples

Puzzle sheets of matching activities, crosswords and find-a-word puzzles

Worked solutions of selected exercise questions

Skillsheets of examples and exercises of prerequisite skills and knowledge

Technology worksheets: additional technology activities

Homework sheets for weekly practice and revision, including mental calculation, numeracy and literacy questions

ExamView quizzes: interactive and self-marking

Puzzle sheet

Geometry crossword

Worksheet

Venn diagrams

Skillsheet

Indices

Technology worksheet

Angle sum of a polygon

Worked solutions

Overtime pay

Video tutorial

Negative indices

Homework sheet

Pythagoras’ theorem 1

Quiz

Algebra

xiv 9780170193047

9Austral ian C urri culumfor the

At the end of each chapter

At the end of the book

Power plus Language of maths

Topic overview

Chapter revision

Mixed revision

General Revision exercise Instructional and Mathematical glossaries

Answers index

NelsonNetBook

NelsonNetBook

Zoom Search

n Language of maths

ascending base descending estimate

expanded form exponent index index laws

index notation indices negative power placeholder

product power quotient reciprocal

significant figures scientific notation term zero power

1 What does a power of zero mean?

2 Which two words from the list mean ‘power’?

3 What is the or key on a calculator used for?

4 What is the index law for dividing terms with the same base?

5 Which digits in 0.006 701 are significant figures?

6 What power is associated with the reciprocal of a term or number?

7 What type of numbers when written in scientific notation have negative powers of 10?

Puzzle sheet

Indices crossword

MAT09NAPS10062

Quiz

Numbers and indices

MAT09NAQZ00002

NEW CENTURY MATHS

xv9780170193047

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