new century maths - tutors.alchemytuition.com.au · new century maths australian curriculum for the...
TRANSCRIPT
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
Any URLs contained in this publication were checked for currencyduring the production process. Note, however, that the publishercannot vouch for the ongoing currency of URLs.
© 2013 Cengage Learning Australia Pty Limited
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
For product information and technology assistance, in Australia call 1300 790 853 ;in New Zealand call 0800 449 725
For permission to use material from this text or product, please [email protected]
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
Printed in China by China Translation & Printing Services.1 2 3 4 5 6 7 17 16 15 14 13
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.
ACARA Copyright Notice
All material identified by is material subject to copyright
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
Power plus 125Chapter 3 review 126
Mixed revision 1 129
Chapter 4: Trigonometry 132SkillCheck 134
9MG223 4-01 The sides of a right-angled triangle 135
iv 9780170193047
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
Power plus 168Chapter 4 review 169
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
Power plus 243Chapter 6 review 244
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
Mixed revision 2 277
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
Power plus 406Chapter 10 review 408
Mixed revision 3 412
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
Mixed revision 4 556
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)
7 Equations11 Coordinate geometry and
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
MEASUREMENT AND GEOMETRY
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
STATISTICS AND PROBABILITY
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
11 Coordinate geometry and graphs
ACMNA215: Sketch linear graphs using the coordinates of two points and solve linear equations
7 Equations11 Coordinate geometry and
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
11 Coordinate geometry and graphs
NSW STAGE 5.2: Interpret and graph linear relationships using the gradient-intercept form of the equation of a straight line
11 Coordinate geometry and graphs
ACMNA296: Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations
11 Coordinate geometry and graphs
This is an extract from the Australian Curriculum.
x 9780170193047
Content descriptionNew Century Maths 9 Stages 5.1/5.2chapter
MEASUREMENT AND GEOMETRY
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
10 Surface area and volume
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
10 Surface area and volume
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
STATISTICS AND PROBABILITY
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
9 Investigating data
ACMSP282: Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed , ‘symmetric and ‘bi-modal
9 Investigating data
ACMSP283: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
9 Investigating data
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