CambridgeMATHS Year 9 C&S Annotated Sample Pages

UNCORRECTEDSAMPLEPAGES Annotated

1 Integers,decimals,fractions,ratiosandrates

Warm-upquiz

1A Adding and subtracting positive and negative integers CONSOLIDATING

1B Multiplying and dividing positive and negative integers CONSOLIDATING

1C Decimal places and significant figures (Core)

1D Rational numbers and irrational numbers CONSOLIDATING

1E Adding and subtracting fractions CONSOLIDATING Progress quiz

1F Multiplying and dividing fractions CONSOLIDATING

1G Ratios CONSOLIDATING

1H Rates CONSOLIDATING Maths@Work: Cooks and chefs

Working mathematically

Puzzles and challenges

Chapter summary

Chapter checklist

Chapter review

2 Financialmathematics

Warm-upquiz

2A Percentages, fractions and decimals CONSOLIDATING

2B Applying percentages CONSOLIDATING

2C Percentage increase and decrease CONSOLIDATING

2D Profits and discounts CONSOLIDATING

2E Income (Core)

Progress quiz

2F Taxation (Core)

2G Simple interest (Core)

2H Applications of simple interest (Core)

Maths@Work: Facebook cake-decorating business

Working mathematically

Contents are subject to change prior to publication.

Contents are subject to change prior to publication.

Puzzlesandchallenges

Chaptersummary

Chapterchecklist

Chapterreview

3 Expressionsandequations

Warm-upquiz

3A Algebraic expressions CONSOLIDATING

3B Adding and subtracting algebraic expressions

CONSOLIDATING

3C Multiplyinganddividingalgebraicexpressions

CONSOLIDATING

3D Expanding algebraic expressions (Core)

3E Linear equations with a pronumeral on one side

CONSOLIDATING

3F Linear equations involving fractions (Core)

Progress quiz

3G Linear equations involving brackets (Core)

3H Equations with pronumerals on both sides (Core)

3I Using linear equations to solve problems (Core)

3J Using formulas (Core)

Maths@Work: Plumber

Working mathematically

Puzzles and challenges

Chapter summary Chapter

checklist Chapter review

4 Right-angledtriangles

Warm-upquiz

4A Exploring Pythagoras’ theorem CONSOLIDATING

4B Finding the length of the hypotenuse CONSOLIDATING

4C Finding the lengths of the shorter sides CONSOLIDATING

4D Using Pythagoras’ theorem to solve two-dimensional problems CONSOLIDATING

4E Introducing the trigonometric ratio (Core)

4F Finding unknown sides (Core)

Progress quiz

4G Solving for the denominator (Core)

4H Finding unknown angles (Core)

4I Using trigonometry to solve problems (Core)

Maths@Work: Carpenter

Working mathematically

Puzzles and challenges

Chaptersummary

Chapterchecklist

Chapterreview

5 Linearrelationships

Warm-upquiz

5A Points and lines on the Cartesian plane (Core)

5B The x -intercept and y -intercept (Core)

5C Graphing straight lines using intercepts (Path) EXTENDING

5D Lines with only one intercept (Core)

5E Gradient from rise and run (Core)

5F Gradient and direct variation (Core and Path)

5G Gradient–intercept form (Core)

Progress quiz

5H Finding the equation of a line using y = mx + c (Core)

5I Midpoint and length of a line segment from diagrams (Core)

5J Linear relationships in real-life contexts (Core)

Maths@Work: Trading in foreign currencies Working mathematically

Puzzles and challenges

Chapter summary

Chapter checklist

Chapter review

Semesterreview1

6 Length,area,surfaceareaandvolume

Warm-upquiz

6A Length and perimeter CONSOLIDATING

6B Circumferenceofcirclesandperimeterofsectors

CONSOLIDATING

6C Area of quadrilaterals and triangles CONSOLIDATING

6D Area of circles CONSOLIDATING

6E Perimeter and area of composite shapes (Core)

6F Surface area of prisms (Core)

Progress quiz

6G Surface area of cylinders (Core)

6H Volume of prisms (Core)

6I Volume of cylinders (Core)

Maths@Work: Vegetable and fruit growers Working mathematically

Puzzles and challenges

Contents are subject to change prior to publication.

Contents are subject to change prior to publication.

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All non-core topics are marked as CONSOLIDATING or EXTENDING to assist with differentiation and course planning.

All non-core topics are marked as CONSOLIDATING or EXTENDING to assist with differentiation and course planning.

Chaptersummary

Chapterchecklist

Chapterreview

7 Indices

Warm-upquiz

7A Index notation (Core)

7B Index laws for multiplying and dividing (Core)

7C The zero index and power of a power (Core)

7D Index laws extended (Core)

7E Negative indices (Core)

Progress quiz

7F Scientific notation (Core)

7G Scientific notation using significant figures (Core)

Maths@Work: Lab technician

Working mathematically

Puzzles and challenges

Chapter summary

Chapter checklist

Chapter review

8 Propertiesofgeometricalfigures

Warm-upquiz

8A Angles and triangles CONSOLIDATING

8B Parallel lines CONSOLIDATING

8C Quadrilaterals CONSOLIDATING

8D Polygons (Path) EXTENDING

8E Enlargement and similar figures (Core)

Progress quiz

8F Applying scale factor to similar triangles (Core)

Maths@Work: Animator

Working mathematically

Puzzles and challenges

Chapter summary

Chapter checklist

Chapter review

9 Quadraticexpressionsandalgebraicfractions

Warm-up quiz

9A Reviewing algebra CONSOLIDATING

9B Expanding binomial products (Core)

9C Expanding perfect squares (Core)

Contents are subject to change prior to publication.

Contents are subject to change prior to publication.

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9D Difference of two squares (Core)

9E Using HCF to factorise algebraic expressions CONSOLIDATING

Progress quiz

9F Simplifying algebraic fractions: multiplication and division (Core)

9G Simplifying algebraic fractions: addition and subtraction (Core)

Maths@Work: Automotive technology

Working mathematically

Puzzles and challenges

Chapter summary

Chapter checklist

Chapter review

10

Probabilityanddataanalysis

Warm-up quiz

10A Review of probability CONSOLIDATING

10B Venn diagrams and two-way tables (Path) EXTENDING

10C Using arrays for two-step experiments (Core)

10D Using tree diagrams (Core)

10E Using relative frequencies to estimate probabilities (Core)

10F Mean, median, mode and range CONSOLIDATING

Progress quiz

10G Interpreting data from tables and graphs (Core)

10H Stem-and-leaf plots (Core)

10I Grouping data into classes (Core)

Maths@Work:Personaltrainer

Workingmathematically

PuzzlesandChallenges

Chaptersummary

Chapterchecklist

Chapterreview

Semesterreview2

Glossary Answer

2

Financial mathematics

Chapter introductions set context for students about how the topic connects with the real world and the history of mathematics.

Whyskillsinfinancialmathematicsareimportant

Skillsinfinancialmathematicsareessentialfor successfulbusinessmanagementandforachieving personalfinancialindependence.Percentageskillsare neededforthefinancialcalculationsperformedby individuals,accountants,bookkeepers,smallbusiness managersandemployers.

Percentagesareusedtocalculatemark-upand discountamounts,costpricesandsellingprices, profits,losses,insurancepayments,GST,businesstax, wagetax,wageincreasesandtheinterestonloans.

Personalincomecanbeearnedinvariousways:

•afixedsalaryp.a(‘perannum’.i.e.peryear),e.g. accountants,businessowners,teachers,engineers, pharmacistsandsurveyors.

•awagecalculatedfromanhourlyrate,e.g.chefs, cleaners,florists,dentalassistants,nurses, receptionists,retailsalespeople,construction workers,panelbeatersandautomechanics.

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•bythejob,e.g.personaltrainers,fruitpickers, bricklayers,fishers,tailors,hairdressers,piano tunersandcarpetlayers.

•commission,e.g.carsalespeople,realestate agents.

•royalties,e.g.songwritersandbookauthors.

Chaptercontents

2A Percentages,fractionsanddecimals (CONSOLIDATING)

2B Applyingpercentages (CONSOLIDATING)

2C Percentageincreaseanddecrease (CONSOLIDATING)

2D Profitsanddiscounts (CONSOLIDATING)

2E Income

All non-core topics are marked as CONSOLIDATING or EXTENDING to assist with differentiation and course planning.

2F Taxation

2G Simpleinterest

2H Applicationsofsimpleinterest

NSWSyllabus

Inthischapter,astudent: developsunderstandingandfluencyin mathematicsthroughexploringandconnecting mathematicalconcepts,choosingandapplying mathematicaltechniquestosolveproblems,and communicatingtheirthinkingandreasoning coherentlyandclearly(MAO-WM-01) solvesfinancialproblemsinvolvingsimpleinterest, earningmoneyandspendingmoney (MA5-FIN-C-01)

NSW Syllabus Outcomes are listed at the start of each chapter (see also the teaching program for more syllabus information).

Onlineresources

Ahostofadditionalonlineresourcesareincluded aspartofyourInteractiveTextbook,including HOTmathscontent,videodemonstrationsofall workedexamples,auto-markedquizzesand muchmore.

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Warm-up quizzes (Core & Standard Paths only) refresh prior learning and prepare students for the chapter ahead.

2A Percentages, fractionsanddecimals CONSOLIDATING

Learningintentionsforthissection:

• Toreviewtheconversionsbetweenpercentages,fractionsanddecimals

• Tomemorisethemostusefulfraction/decimal/percentageconversions

• Tobeabletoexpressonequantityasapercentageofanother

Past,presentandfuturelearning:

• ThissectionconsolidatesStage4conceptswhichareusedinStages5and6

• SomeofthesequestionsaremorechallengingthanthoseinourStage4books

• PercentagesareusedextensivelyinthischapterandalsoChapter1ofourYear10book

• ExpertisewithpercentagesisassumedknowledgeforStage6Standardandmayalsoberequiredinnon-calculator examinationssuchasNAPLANandindustryaptitudetests

Weusepercentagesformanydifferentthingsinourdailylives.Someexamplesincludehomeloans,credit cards,salesandpro ts.

Weknowfromourpreviousworkonpercentagesthattheyrepresentafractionwithadenominatorof100. ‘Percent’comesfromtheLatinword percentum,andmeans‘outof100’.

LessonStarter:Orderingwithpercentages

Tendifferentvaluesaregivenbelow.

Inpairs,decide:

whichofthenumbersisthesmallest a whichofthenumbersisthelargest b

Writethe10numbersinascendingorder.

KEYIDEAS

Past, present and future learning places the lesson in the context of the syllabus, highlighting topics that build on previous learning, and topics that will be extended at a later stage.

■ Thetablebelowcontainssomecommonlyusedfractions,decimalsandpercentages.These shouldbememorised.

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Learning intentions at the beginning of each lesson clearly state what the student can expect to achieve.

■ Therearesix conversions involvingfractions,decimalsandpercentages.

Usetenths,hundredths,etc. Simplifythefraction.

Convertfractiontotenthsor hundredthsor Dividenumeratorbydenominator.

Multiplyby100. Add%symbol. (Thedecimalpointappearstomove twoplacestotheright.)

Remove%symbol. Divideby100. (Thedecimalpointappearstomove twoplacestotheleft.)

Convertthefractiontohundredths. Add%symbol

orDividenumeratorbydenominator. Multiplyby100. Add%symbol.

Typethedecimal. Press=. Pressthebuttonthatconverts fractionstodecimals.

Typethefraction. Press=. Pressthebuttonthatconverts fractionstodecimals.

Multiplyby100. Add%symbol.

Remove%symbol. Divideby100.

Multiplyby100. Add%symbol.

percentagetofraction

Remove%symbol. Writeas‘hundredths’. Simplifyfraction.

Remove%symbol. Divideby100. Pressthebuttonthatconverts fractionstodecimals.

■ Expressingonequantityasapercentageofanother(percentagecomposition):

• Formafraction,thenconverttoapercentage.

Forexample:4goalsfrom10attempts = 4 10 = 40 100 = 40%

Keyterminology: percentage,fraction,decimal

Exercise2A

UNDERSTANDING

1 Completethefollowingusingthewordsmultiplyordivide.

a Toconvertadecimalintoapercentage by100.

b Toconvertapercentageintoafraction by100.

c Toconvertafractionintoapercentage by100.

d Toconvertapercentageintoadecimal by100.

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2 Copyandcompletethistableofcommonpercentages.

Percentage 10% 50%

3 Whatpercentageofeachofthefollowingdiagramshasbeenshaded?

Hint:Considercommon fractionsandpercentages fortheshadedareas.

4 Scottscored38outof50onamathsquizandSarahscored79% onthesametest.Whoscoredthehigher mark?

Videos for all worked examples support both in-class and independent learning.

Writethepercentageasafraction,usinga denominatorof100, 7 5 100

Multiplythisfractionby 2 2 sothatwedon’t haveadecimalinthefractionanditwillbe easiertosimplify. 7 5 100 × 2 2 = 15 200

Simplify: 15 200 = 3 40 bycancellingacommon factorof5.

Worked examples, placed within each exercise (Core & Standard Paths only), provide vital support to less advanced students. In other resources, the worked examples are placed before the exercises, with clear links from the questions to the relevant example.

Example3 Writingaquantityasapercentage

Write50coutof$2.50asapercentage.

SOLUTION EXPLANATION

50coutof$2 50 = 1 ✚✚ 50 5 ✟✟ 250 × 100 = 20%

Nowyoutry

Write90coutof$3.60asapercentage.

Converttothesameunits ($2 50 = 250c) andwriteasa fraction.

Reducethefractiontosimplestform. Multiplyby100.

9 Ineachof thefollowingcases,expressthe rstquantityasapercentageofthesecond.

Hint:Writeasafraction andthenmultiplyby 100.

Now you try questions follow every worked example. Students get immediate practice at the type of question they have just seen in the worked example before they start the exercises.

10 Copyandcompletethetableofthefavouritesummersportsof Year9students.

They are also ideal for teachers to use as class demonstration questions.

11 Tonipays31 5centsinthedollarintax.Expressthisas apercentage.

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12 Badweatherstoppedacricketgamefor35minutesofascheduled 3 1 2 hourmatch.Whatpercentageofthescheduledtimewaslost?

13 Joelost4kgandnowweighs60kg.Whatpercentageofhis originalweightdidhelose?

Hint:WhatwasJoe’s originalweight?

14 Acompanyclaimsthattheapplepiesitmakesare97% fatfree.Ifthenutritionalinformationonthe sideofthepackstatesthattotalfatis7gramsofthe250grampie,istheclaimcorrect?

15

15 Completethistableby llinginestimatedtimes.Inthe rsttwocolumns,insertthetimesthatyou dideachactivity.Usethatinformationtohelpyou llintheothercolumns.Roundpercentagestoone decimalplace.

a Timeyouwenttobedlast night: Timeyouwokeup thismorning:

b Timeyoustarted breakfasttoday: Timeyoufinished breakfasttoday:

Hoursandminutes spentinbed:

Minutesspenteating breakfast:

c Timeschoolstartedtoday: Timeschoolisdueto finishtoday: Hoursandminutes spentatschool:

d Timethismathslesson started: Timethismaths lessonwillfinish: Minutesspentinthe mathslesson:

e Timeschoolwillfinish today: Timeyouwillarrive home: Minutesspent travellinghome:

f Timeyoustartedyour homeworkyesterday:

g Timeyoustarted watchingTVorplaying gamesyesterday:

Timeyoufinished yourhomework yesterday:

Timeyoufinished watchingTVor playinggames:

h Timeyouwokeuptoday: Timeyouwillgoto bedtonight:

Minutesspenton homework:

Minutesspentatthis activity:

Hoursandminutes spentawaketoday:

Percentageofadayspent inbed:

Percentageofthedayyou spentatbreakfast:

Percentageoftheday spentatschool:

Percentageoftheday spentinthemathslesson:

Percentageoftheday spenttravellinghome:

Percentageofyourday spentonhomework:

Percentageoftheday spentatthisactivity:

Percentageoftheday spentawake:

2B Applying percentages CONSOLIDATING

Learningintentionsforthissection:

• Toknowhowtocalculateacertainpercentageofagivenquantity

• Tobeabletofindtheoriginalamountfromagivenpercentage

Past,presentandfuturelearning:

• ThissectionconsolidatesStage4conceptswhichareusedinStages5and6

• SomeofthesequestionsaremorechallengingthanthoseinourStage4books

• PercentagesareusedextensivelyinthischapterandalsoChapter1ofourYear10book

• ExpertisewithpercentagesisassumedknowledgeforStage6Standardandmayalsoberequiredinnon-calculator examinationssuchasNAPLANandindustryaptitudetests

Themediaoftenquotespercentagesin newsstoriesandadvertisements.For example:

• 90% ofdentistspreferthis toothbrush.

• Ashirtisreducedby45%.

• Interestratesincreasedby2%.

Theseexamplesinvolve ndinga percentageofaquantityoramountand thisisanimportantpartoftheworkwe dowithpercentages.

LessonStarter:Today’snewschallenge

Inpairs,gothroughtoday’snewspaperoronlinenewssiteand ndarticlesandadvertisementsthatuse percentages.Choosetwoandexplaintotheclasshowpercentagesareusedinthearticlesyouchoose.

KEYIDEAS

■ To ndapercentageofaquantity(withoutacalculator):

• Writethepercentageasafractionordecimal.

• Multiplybythequantity.

■ Calculatormethod:

3%of200 = 3 ÷ 100 × 200 = 6

■ Mentalstrategies:

Key ideas summarise the knowledge and skills for the lesson.

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■ To ndtheoriginalamountwhengivenapercentage,youcanusetheunitarymethodorsolve anequation.

Forexample:3% ofanamountis 15. Whatistheoriginalamount?

∴

Exercise2B

Three working programs (two for Core & Standard Paths) provide pathways through each book to support differentiation for students of different abilities.

Note:‘of’meansto‘multiply’.

Nowyoutry

Nowyoutry

11 About80% ofthemassofthehumanbodyiswater.IfCarlaweighs60kg,howmanykilogramsof watermakeupherbodyweight?

d Write325% asafraction.

e $2000inabankaccountincreasesto$5000overaperiodoftime.Byhowmuchhastheamount increasedasapercentage?

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Enrichment questions at the end of each exercise encourage students to generalise and to think creatively. These questions provide a taste of the mathematics they will see in future studies and deepen their understanding of mathematics within a lesson rather than accelerating them to different lessons.

2C Percentage increaseanddecrease CONSOLIDATING

Learningintentionsforthissection:

• Tobeabletoincreaseordecreaseanamountbyagivenpercentage

• Tobeabletocalculatethepercentagebywhichanamounthasincreasedordecreased Past,presentandfuturelearning:

• ThissectionconsolidatesStage4conceptswhichareusedinStages5and6

• SomeofthesequestionsaremorechallengingthanthoseinourStage4books

• PercentagesareusedextensivelyinthischapterandalsoChapter1ofourYear10book

• ExpertisewithpercentagesisassumedknowledgeforStage6Standardandmayalsoberequiredinnon-calculator examinationssuchasNAPLANandindustryaptitudetests

Percentagesareoftenusedtodescribebyhow muchaquantityhasincreasedordecreased. Thepriceofacarinthenewyearmightbe increasedby5%.Ona$70000car,thisisa $3500increase.The priceofashirtmightbe markeddownby30%.Iftheshirtoriginally cost$60,this providesan$18discount.Itis importanttonotethattheincreaseordecrease iscalculatedontheoriginalamount.

LessonStarter:Thequickermethod

Twostudents,NickyandMila,considerthequestion:$250isincreasedby15%.Whatisthe nalamount?

Nickyputs hissolutionontheboardwithtwosteps.

Step1:15% of$250 = 0 15 × $250 = $37.50

Step2:Finalamount = $250 + $37.50 = $287 50

Milasaysthatthesameproblemcanbesolvedwithonlyonestepusingthenumber1 15.

• CanyoudescribeMila’smethod?Writeitdown.

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• Whatifthequestionwasalteredsothat$250isdecreasedby15%.HowwouldNicky’sandMila’s methodswork inthiscase?

• Whichofthetwomethodsdoyoupreferandwhy?

Lesson starter: an activity to start the lesson that can often be completed in groups.

KEYIDEAS

■ Toincreaseanamountbyagivenpercentage:

• Addthepercentageincreaseto100%.

• Multiplytheamount bythisnewpercentage. Forexample,toincreaseby25%,multiplyby 100%+ 25%= 125%= 1.25

■ Todecreaseanamountbyagivenpercentage:

• Subtractthepercentagefrom100%

• Multiplytheamount bythisnewpercentage.

%,multiplyby 100%− 25%= 75%= 0.75.

■ To ndapercentagechange,use:

Percentagechange = changeinprice originalprice × 100%

Forexample,ifapricechangesfrom$40to$50:

Percentagechange = 10 40 × 100%= 25%

Keyterminology: percentage

Exercise2C

2 Writethemissingnumberforthesedecreases.

a Todecreaseanumberby20%,multiplyby .

b Todecreaseanumberby73%,multiplyby

c Todecreaseanumberby ,multiplyby0.94.

d Todecreaseanumberby ,multiplyby0 31.

3 Findthepercentagechangeif

a Originalamount = $120,change = $30

b Originalamount = $35,change = $70

40%, need 140% ofamount

Hint:Todecreaseby 20%, need 80% ofamount

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Hints within the exercises (Core & Standard Paths only) provide support to less advanced students.

VIDEO DEMO

Example6 Increasingbyapercentage

Increase$70by15%

SOLUTION

100%+ 15%= 115% = 1.15

$70 × 1 15 = $80 50

Nowyoutry

Increase$120by30%

EXPLANATION

Firstadd15% to100%

Notethat15%= 0 15and100%= 1

Multiplyby1 15togive$70plustheincrease inonestep.

VIDEO DEMO

4 Completethefollowing,usingacalculatorifnecessary.

Increase56by10% a

Increase100by12% c

Increase180by15% e

Increase8by50% g

Example7 Decreasingbyapercentage

Decrease$5.20by40%

Increase980by20% b

Increase890by5% d

Increase450by20% f

Increase98by100% h

Firstsubtractthe40% from100% to ndthe percentageremaining.

Multiplyby60%= 0 6togettheresult.

.

Nowyoutry

Decrease$64by15%

5 Completethefollowing.

Decrease80by5% a

Decrease45by50% c

Decrease8000by8% e

Decrease68by75% g

Decrease7000by100% i

Decrease600by10% b

Decrease700by12% d

Decrease450by25% f

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Decrease9000by1% h

Decrease10000by1 5% j

4–5(½),6,7 4–5(½),6,7(½),8

Example8 Findingapercentagechange

Thepriceofamobilephoneincreasedfrom$250to$280.Findthepercentageincrease. a Thepopulationofatowndecreasesfrom3220to2985.Findthepercentagedecreaseandround toonedecimalplace.

b

SOLUTION EXPLANATION

a Increase = $280 $250 = $30 First ndtheactualincrease.

Percentageincrease = 30 250 × 100 1 = 12%

Dividetheincreasebytheoriginalamountand multiplyby100.

b Decrease = 3220 2985 = 235 First ndtheactualdecrease.

Percentagedecrease = 235 3220 × 100 1 = 7 3%(to1d.p.)

Nowyoutry

Dividethedecreasebytheoriginalpopulation andmultiplyby100.Roundasindicated.

Theheightofaplantincreasedfrom20cmto28cm.Findthepercentageincrease. a Thepriceofawashingmachinedecreasedfrom$649to$545.Findthepercentagedecreaseand roundtoonedecimalplace. b

6 Thepriceofa ightincreasedfrom$125to$150overnight.Findthepercentageincrease.

7 Copyandcompletethetablesshowingpercentagechange.Roundtoonedecimalplacewherenecessary.

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8 WhentheGoodsandServicesTax(GST)wasintroduced,allpricesincreasedby10%.

Copyandcompletethetable. OldPrice NewPrice GST (excludingGST) (includingGST) amount

Example9 Findingtheoriginalamountfromanincreaseordecrease

Afterrain,thevolumeofwaterinatankincreasedby24% to2200L.Howmuchwaterwasinthe tankbeforeitrained?Roundtothenearestlitre.

Writethetotalpercentage.

Theoriginalvolumeisincreasedby24% to give2200litres

Divideby124to nd1%

Multiplyby100to ndtheoriginalamount. Alternatemethod:100

Writethetotalpercentage.

Writeanequationusingthepronumeral V torepresentthevolume.

Dividebothsidesby1 24tosolvefor V

Roundtothenearestlitre.

Nowyoutry

Atthestartofanewyear,dailypublictransportticketsincreaseby4% to$9.20.Whatwasthecost ofadailyticketbeforetheincrease?Roundtothenearestcent.

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9 Findtheoriginalcostforeachofthefollowingif:

a anincreaseof10% onthecostofacanof coladrinkincreaseditto$3 30

b anincreaseof10% onthecostofameal increasedthecostto$88

c afteranincreaseof5%,thecostofapairof runningshoescameto$210

d adecreaseof30% madethecostofcar insurance$350

e adecreaseof60% broughtthepriceofa usedcardownto$5000

10 Thepriceofacomputerwasdecreasedby15% inasale.Whatisthesaleprice,iftheoriginalpricewas $2100?

11 Plumbersonasalaryof$82570weregivena2 1 2 % payincrease.Findtheirnewannualsalary.

12 Acarmanufacturerintendstoincreasesalesby14.7% nextyear.Ifthecompanysold21390newcars this year,howmanydoesitexpecttosellnextyear?

13 Thelengthofabikesprintraceisincreasedfrom800mto 1200m.Findthepercentageincrease. Hint: % increase = increase originalamount × 100

14 Thenumberofpeopleonabusdecreasedfrom25to18after onestop.Findthepercentagedecreaseinthenumberofpeopleonthebus.

15 Afterapriceincreaseof20%,thecostofentrytoamuseumroseto$25 80.Findtheoriginalprice.

16 ThetotalpriceofanitemincludingGST(at10%) is$120.HowmuchGST ispaid,tothenearestcent?

17 Aninvestorstartswith$1000.

Hint: $120 represents 110% ofthepricebefore GSTisadded.

a Afterabaddaytheinitialinvestmentisreducedby10%.Findthebalanceattheendoftheday.

b Thenextdayisbetterandthebalanceisincreasedby10%.Findthebalanceattheendofthe secondday.

c Theinitialamountdecreasedby10% onthe rstdayandincreasedby10% onthesecondday. Explainwhythebalanceontheseconddaydidn’treturnto$1000.

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Gradients within exercises: the working programs make use of the gradients that have been seamlessly integrated into the exercises in both the overall structure of each exercise and within each Working Mathematically component.

ENRICHMENT:Repeatedincreaseanddecrease

18

19

17,18

Ifthecostofapairofshoeswasincreasedtwice,by10% fromanoriginalpriceof$80andthenanother 15% fromthisnewprice,the nalpricewouldbe

$80 × 1 10 × 1 15 = $101 20

Useasimilartechniqueto ndthe nalpriceoftheseitems.Roundtothenearestcent.

a Skisstartingat$450andincreasingby20% and10%

b Acomputerstartingat$2750andincreasingby6% and11%

c ADVDplayerstartingat$280anddecreasingby10% and25%

d Acircularsawstartingat$119anddecreasingby18% and37%

Ifanamountisincreasedbythesamepercentageeachtime,powerscanbeused. Forexample,50kgincreasedby12% threetimeswouldincreaseto

50kg × 1.12 × 1.12 × 1.12

= 50kg ×(1 12)3

= 70 25kg (to2d.p.)

Hint:Youhavea power/indexkeyon yourcalculator.

Useasimilartechniqueto ndthe nalvalueinthesesituations.Roundtotwodecimalplaces.

a Themassofaratinitiallyat60gramsgrowsatarateof10% everymonthfor3months.

b Thecostofanewcarinitiallyat$80000increasesby5% everyyearfor4years.

c Thevalueofanapartmentinitiallyat$380000decreasesby4% peryearfor3years.

d Thelengthofapencilinitiallyat16cmdecreasesthroughbeingsharpenedby15% everyweekfor 5weeks.

Using technology: Questions intended to be answered using a calculator are identified by a calculator icon.

2D Profits anddiscounts CONSOLIDATING

Learningintentionsforthissection:

• Toknowandunderstandtheterminologyassociatedwithprofits,lossesanddiscounts

• Tobeabletosolveproblemsinvolvingpercentageprofits,lossesanddiscounts

Past,presentandfuturelearning:

• ThissectionconsolidatesStage4conceptswhichareusedinStages5and6

• SomeofthesequestionsaremorechallengingthanthoseinourStage4books

• PercentagesareusedextensivelyinthischapterandalsoChapter1ofourYear10book

• ExpertisewithpercentagesisassumedknowledgeforStage6Standardandmayalsoberequiredinnon-calculator examinationssuchasNAPLANandindustryaptitudetests

Percentagesarewidelyusedintheworldof nance.Pro ts,losses,commissions,discountsandtaxation areoftenexpressedandcalculatedusingpercentages.

LessonStarter:Thebestdiscount

Twobookshopsaresellingthesamebookatadiscountedprice.Therecommendedretailpriceforthebook isthesameforbothshops.Eachshophasasignnearthebookwiththegivendetails:

• ShopA.Discountedby25%

• ShopB.Reducedby20% thentakeafurther10% offthat.

Whichshopoffersthebiggerdiscount?

Isthedifferenceequalto5% oftheretailprice?

Examplesofpercentagesusedinthemedia.

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KEYIDEAS

■ Pro t istheamountofmoneymadeonasale. Pro t = sellingprice costprice

■ A loss ismadewhenthesellingpriceislessthanthecostprice.

Loss = costprice sellingprice

■ Mark-up istheamountaddedtothecostpricetoproducethesellingprice.

Sellingprice = costprice + mark-up

■ Thepercentagepro torlosscanbefoundbydividingthepro t orlossbythecostpriceandmultiplyingby100.

% pro t/loss = (pro torloss costprice × 100) %

■ Discount istheamountbywhichanitemismarkeddown.

Discount =% discount × originalprice

Newprice = originalprice discountamount

Keyterminology: pro t,sellingprice,costprice,loss,mark-up,percentage,discount

Exercise2D

VIDEO DEMO

Example10 Calculatingsellingpricefrommark-up

Anelectricalstoremarksupallentertainmentsystemsby30% Ifthecostpriceofoneentertainmentsystemis$8000,whatwillbeitssellingprice?

SOLUTION EXPLANATION

Mark-up = 30% of$8000 = 0.3 × 8000 = $2400

Sellingprice = $8000 + $2400 = $10400

Alternatively,multiplycostpriceby 130% or1 3.

Nowyoutry

Changepercentagetoadecimalorfraction andmultiplybythecostprice.

Sellingprice = costprice + mark-up

130% isa30% increaseonthecostprice

Acomputerstoremarksupallnotebookcomputersby24% Ifthecostpriceofonenotebookis$1200,whatwillbeitssellingprice?

5 Copyandcompletethistablebycalculatingthesellingpriceofeachitem.

VIDEO DEMO

Example11 Findingthediscountamount

Anelectricalstoreadvertisesa15% discountonallequipmentasaholidayspecial.Findthesale priceonaprojectionsystemthathasamarkedpriceof$18000.

SOLUTION EXPLANATION

Discount = 15% of$18000 = 0 15 × 18000 = $2700

Thenewprice = $18000 $2700 = $15300

Alternatively,multiplytheoriginalpriceby 85% or0.85.

Changethepercentagetoadecimaland evaluate.

Newpriceisoriginalpriceminusdiscount.

A15% discountleaves85%

Nowyoutry

Adepartmentstoreoffersapost-Christmasdiscountof35% onalldecorations.Findthesaleprice onawreaththathasamarkedpriceof $80.

6 Copyandcompletethetablebywritinginthemissingvalues.

Example12

Determiningprofit

Amanufacturerproducesanitemfor$400andsellsitfor$540.

tmade.

Nowyoutry

Ajewellerproducesanecklacefor$36andsellsitfor$49 50.

t made. a

7 Findthemissingvaluesinthesetablesby ndingthepro torlossandexpressingthisasapercentage ofthecostprice.Roundtotwodecimalplaceswherenecessary.

Example13 Calculatingtheoriginalprice

Atoystorediscountsatoyby10% inasale.Ifthesalepricewas$10.80,whatwastheoriginal price?

%

= 10.80 ÷ 90

Thediscountfactor = 100%− 10%= 90%. Thus,$10.80is90% oftheoriginalprice.

Usetheunitarymethodto nd1% Multiplyby100to ndtheoriginalamount. Theoriginalpricewas$12. Writetheanswerinwords.

Writeanequationusingthepronumeral P to representtheoriginalprice.

Solvetheequationfor P bydividingboth sidesby0.9

Nowyoutry

Anoutdoorequipmentstorediscountsatentby20% inasale. Ifthesalepricewas$176,whatwastheoriginalprice?

8 Answerthefollowingquestionsrelatingto nding theoriginalprice(costprice).

a Findtheoriginalpriceifacoffeemugwas discountedby20% andsoldfor$4 40.

b Findthecostpriceofapairofshoesthatsold for$250afteramark-upof25%

c Findthecostpriceafteradiscountof10% was givenonasurfboardthatsoldfor$1350.

d Findtheoriginalpriceonaconcertticketfor amajorrecordingartistifitwasmarkedupby 100% andsoldfor$250.

9 Amanufacturerproducesandsellsitemsforthepricesshown. Determinethepro tmade. i Expressthispro tasapercentageofthecostprice. ii Costprice$10,sellingprice$12 a Costprice$20,sellingprice$25 b Costprice$120,sellingprice$136.80 c Costprice$1400,sellingprice$3850 d

10 Lennymarksupallcomputersinhisstoreby12.5%.Ifacomputercosthim$890,whatwillbethe selling priceofthecomputer?

11 Aused-cardealerpurchasesavehiclefor$13000andsellsitfor $18500.Determinethepercentagemark-uponthevehicletoone decimalplace.

12 Arefrigeratorisdiscountedby25%.IfPaulapays$460forit,whatwasthe originalprice?Roundtothenearestcent.

13 Anelectricalstorebuysacomputerfromthewholesalerfor$500.Thestore marksupthecomputerby80%.

a Whatistheamountofthemark-upindollars?

b Whatistheretailpriceofthecomputerafterthestore’smark-up?

c Thestoreoffersthecomputeronsaleforadiscountof15%.Whatisthe pricenow?

d If the15% discountwascalculatedontheoriginal$500costprice,and thenthecomputerwasmarkedup80% afterthat,woulditmakea differencetothesaleprice?

Hint:Whatistheincrease asapercentageofthe originalprice?

14 Thegraphshowsthechangesinthevalueofaparticularhouse.

a Howmuchwasthehouseworthin1998?

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b Findthepercentageincrease,toonedecimalplace,inthevalueofthehousefrom1998to: 2002 i 2004 ii 2006 iii

c In2018theownerswishedtosellfor1.25milliondollars.Whatpercentageincreasewasneededin thetwoyearsfrom2016to2018sotheycouldsellforthatprice?

2E Income

Learningintentionsforthissection:

• Toknowandunderstandthedifferentwaysthatworkerscanbepaidfortheirlabour

• Touseratesandpercentagestocalculatesalaries,wages,commissions,royaltiesetc

• Tobeabletomakeconversionsbetweenpayperhour,day,week,fortnight,monthandyear Past,presentandfuturelearning:

• ThissectionintroducestheStage5CoreTopiccalled FinancialMathematicsA

• Section1DofourYear10bookrevisesandfurtherextendstheseconcepts

• FinancialMathematics isamajortopicinStage6Standard

Therearemanydifferentwaysofearningaliving.Youcanbeself-employedorworkforsomeoneelse. Yourincomeisusuallyrelatedtotheskillsyouhave.Itcanbecalculatedandpaidindifferentways.You canearn,forexample,asalary,awage,acommissionorpossiblyaroyalty.

LessonStarter:Typesofincome

Asaclass,writedownoneexampleofajobthatearnseachofthefollowingtypesofincome.

• Salary

• Wage(i.e.hourlyrateofpay)

• Overtime

• Commission

Inthenewspaperclassi edsoronline, ndajobadvertisementforeachoftheincometypesabove.

KEYIDEAS

■ Workerswhoearna wage (forexample,acasualwaiter)arepaida xedrateperhour.Hours outsidethenormalworkinghours(publicholidaysetc.)arepaidatahigherratecalled overtime. Thiscanoccurinacoupleofcommonways:

• Timeandahalf: payis1 5timestheusualhourlyrate

• Doubletime: payistwicetheusualhourlyrate

■ Workerswhoearna salary (forexample,anengineer)arepaida xedamountperyear,say, $125000.Thisispaidmonthly,fortnightlyorweekly.

• 12monthsinayearandapproximately52weeksinayear = 26fortnights

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■ Somewageandsalaryearnsarepaid leaveloading.Whentheyareonholidays,theyearntheir normalpayplusabounscalledleaveloading.Thisisusually17.5%oftheirnormalpay.

■ Commission isapercentageoftheoverallsalesamount.Salespeoplemayreceiveacommission ontheirsalesaswellasasetweeklyormonthlyfeecalleda retainer.

• Commission =% commission × totalsales

■ Somepeoplewhowritebooksormusicarepaid royalties,whichcouldbe10%ofthesalesprice ofeverybookorsongwhichissold.

■ Somepeoplewhomakeordothingsarepaid piecework.Forexample,$4foreverysheepshorn.

Keyterminology: wage,overtime,timeandahalf,doubletime,salary,commission,retainer

Exercise2E

1 Matchthepaydescription(a–d)withtheincometype(A–D).

a Sallyearns$22 70perhourworkinginashop A Overtime

b MathsteacherStephanieearns$72000peryear B Commission

c Rossearns5% ofallsaleshemakes

d MattearnstimeandahalfpayonSaturdays

Wage

Salary

2 Tomearns$12 70anhour.Howmuchdoesheearnfor: 2hoursofwork? a 8hoursofwork? b 38hoursofwork? c

3 Sela’shourlyrateofpayis$24.Calculateherovertimerateat: timeandahalf a doubletime b

4 Williamearnsasalaryof$136875eachyear.

Approximatelyhowmuchisthis:

a eachmonth?

b eachweek(tothenearestcent)?

c eachday?

Hint:Tofindapproximatemonthly salary,divideannualsalaryby 12

Tofindapproximateweeklysalary, divideannualsalaryby 52.

Tofindapproximatedailysalary, divideannualsalaryby 365

VIDEO DEMO

Example14 Comparingwagesandsalaries

Kenearnsanannualsalaryof$90000andworksa38-hourweek.HiswifeBrookeworksparttime inretailandearns$61.80perhour.

CalculatehowmuchKenearnsperweek. a

Determinewhohasthehigherhourlyrateofpay. b

IfBrookeworksonaverage18hoursperweek,whatisheryearlyincome? c

SOLUTION EXPLANATION

a Weeklyrate = $90000 ÷ 52 = $1730.77

∴ Kenearns$1730.77perweek

b Brooke:$61 80/h

Ken:$1730 77 ÷ 38 = $45 55/h

∴ Brookeispaidmoreperhour.

c Inoneweek:$61 80 × 18 = $1112.40

Yearlyincome = $1112.40 × 52 = $57844.80

Nowyoutry

$90000payinayear. Thereareapproximately52weeksinayear. Divideby52to ndtheweeklywage.

Kenworks38hoursintheweek.

Hourlyrate = weeklyrate ÷ number ofhours Roundtothenearestcent.

Comparehourlyrates.

Weeklyincome = hourlyrate × numberofhours

Multiplyby52 weekstogetyearlyincome.

Maliearnsanannualsalaryof$77200andworksa38-hourweek.HerpartnerBenworksparttime asaphotographerandearns$75perhour. CalculatehowmuchMaliearnsperweek. a Determinewhohasthehigherhourlyrateofpay. b

IfBenworksonaverage15hoursperweek,whatishisyearlyincomefromphotography? c

5 Talibearns$58000peryearatafastfoodrestaurant.Hissisterworksparttimeasawaitressandearns $33.20perhour.

a HowmuchdoesTalibearneachweek?

b EachweekTalibworks38hours.Calculateifhishourlyrateofpayishigherthanhissister’s.

c Ifhissisteraverages10hoursofworkperweek,whatisheryearlyincome?

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6 Paulearns$790eachweek.Howmuchdoesheearneach: Hint:Thereare 12 months inayear. year? a month? b hour,ifheworked40hourseachweek?

c

Example15 Calculatingovertime

Georgioworkssomeweekendsandlatenights,andearnsovertimeforthatwork.Hishourlyrateof payis$32perhour.

CalculateGeorgio’stimeandahalfrateofpayperhour. a

CalculateGeorgio’sdoubletimerateofpayperhour. b

c

CalculateGeorgio’sweeklywageforaweekwhereheworks18hoursathisnormalrate, 2hoursattimeandahalf,and1houratdoubletime.

SOLUTION EXPLANATION

a Timeandahalf = $32 × 1 5 = $48

b Doubletime = $32 × 2 = $64

c $32 × 18 = $576 $48 × 2 = $96 $64 × 1 = $64

Totalwage = $736

Timeandahalfis1 5timesthehourlyrate.

Doubletimeis2timesthehourlyrate.

Findthesumof:

• thenormalhourlyrate ($32) multipliedbythe numberofhoursworkedatthenormalrate (18)

• thetimeandahalfhourlyrate ($48) multiplied bythenumberofhoursworkedatthatrate (2)

• thedoubletimehourlyrate ($64) multipliedbythe numberofhoursworkedatthatrate (1)

Alternatively, 18hours +(2hours × 1 5) +(1hour × 2) = 18 + 3 + 2 = 23

Wage = 23 × 32 = $736

Nowyoutry

Calculatethenumberof‘normal’hours.

Multiplybythehourlyrate.

Kaneworkssomeweekendsandsomepublicholidaysandearnsovertimeforthatwork.Hishourly rateofpayis$24perhour.

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a

CalculateKane’stimeandahalfrateofpayperhour.

b

CalculateKane’sdoubletimerateofpayperhour.

c

CalculateKane’sweeklywageforaweekwhereheworks15hoursathisnormalrate,6hours attimeandahalfand3hoursatdoubletime.

VIDEO

DEMO

8 Ajobhasanormalworkinghourspayrateof$29 20perhour.Calculate thepay,includingovertime,fromthefollowinghoursworked.

a 3hoursatthenormalrateand4hoursattimeandahalf

b 4hoursatthenormalrateand6hoursattimeandahalf

c 14hoursatthenormalrateand3hoursatdoubletime

d 20hoursatthenormalrateand5hoursatdoubletime

Hint:Fortimeandahalf: × 1.5

Fordoubletime: × 2

e 10hoursatthenormalrateand8hoursattimeandahalfand3hoursatdoubletime

f 34hoursatthenormalrateand4hoursattimeandahalfand2hoursatdoubletime

Example16 Calculatingcommission

Apart-timesaleswomanispaidaretainerof$1500permonth.Shealsoreceivesacommissionof 5% onthevalueofgoodsshesells.Ifshesellsgoodsworth$5600duringthemonth,calculateher earningsforthatmonth.

SOLUTION EXPLANATION

Commission = 5% of$5600 = 0.05 × $5600 = $280

Earnings = $1500 + $280 = $1780

Nowyoutry

Calculatethecommissiononsales.Change thepercentagetoadecimalandevaluate.

Earnings = retainer + commission

Arealestateagentispaidaretainerof$2200permonth.Shealsoreceivesacommissionof0.4% onthe valueofhousesshesells.Ifshesellshousesworth $1575000duringthemonth,calculate herearningsforthatmonth.

9 Copyandcompletethetable.

11 Jim,apart-timegardener,earned$522inaweek.Ifheworked12hours duringnormalworkinghoursand4hoursovertimeattimeandahalf, whatwashishourlyrateofpay?

12 Sallyearned$658 80inaweek.Sheworked10hoursduringtheweek, 6hoursonSaturdayattimeandahalfand4hoursonSundayatdoubletime. Whatwasherhourlyrateofpay?

Hint:Calculatethenumber ofhoursatthestandard hourlyrate.

13 AmyworksatBestBookshop.Duringoneweekshesellsbooksvaluedat$800.Ifsheearns $450perweekplus5% commission,howmuchdoessheearninthisweek?

14 Jasonworksforacampervancompany.Ifhesells$84000worthofcampervansinamonth,andhe earns$1650permonthplus4% commissiononsales,howmuchdoesheearnthatmonth?

15 Stephenearnsanhourlyrateof$34 60forthe rst38hours,timeandahalfforthenext3hoursand doubletimefor eachextrahourabovethat.Calculatehisearningsifheworks44hoursinaweek.

16

16 Workersatafastfoodrestaurantarepaid$21.63perhourforworkingMondaytoFridayupuntil 7p.m.andtimeandahalfafter7p.m.TheyearntimeandahalfonSaturdaysanddoubletimeon Sundays.Theyaregivenanunpaid30minutemealbreakforanyshiftover5hours.

Donna’sshiftsfortheweekaregivenbelow.

a HowmuchcanDonnaexpecttoearn,tothenearestcent,ifsheworksthehourssheisrosteredfor?

b Therestaurantdecidesonanewworkplacedeal,getsridofallovertimeandcreatesa athourly rateof$24perhour.HowmuchworseoffwillDonnabefortheweekabove?

c HowmanyextrahoursaweekdoesDonnaneedtoworkduringtheweektomakeuptheextra income?Answerinawholenumberofhours.

% to961ticket

20toproduce andshesells themfor$10, ndherpercentagepro tcorrecttoonedecimalplace.

adresswasdiscountedby15% andsoldfor$187

80

A Progress quiz appears two thirds of the way through a chapter to ensure students are on track for successful understanding of the topic. Each question is clearly linked to the relevant section.

a Sebearnsanannualsalaryof$74100.(Assume52weeksintheyear.)

b Jodieworks22hoursinaweekat$18.20perhour.

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c Nedworksinafastfoodrestaurantandhasanormalhourlyrateof$15.10perhour. Inaweek heworks4hoursatthenormalrate,3hoursattimeandahalfand2hoursat doubletime.

d Harperispaidaweeklyretainerof$200andshealsoearnsa5% commissiononhersales. Inaparticularweekshemakes$8400worthofsales.

2F Taxation

Learningintentionsforthissection:

• Toknowandunderstandtheterminologygrossincome,netincomeandtaxableincome

• Tobeabletocalculatenetincomefromgrossincomeanddeductions

• TobeabletousetheATOtabletocalculatetaxpayable

Past,presentandfuturelearning:

• ThissectioncontinuestheStage5CoreTopiccalled FinancialMathematicsA

• Section1CofourYear10bookrevisesandfurtherextendstheseconcepts

• FinancialMathematics isamajortopicinStage6Standard

Allwageandsalaryearnershavesomedeductionstakenoutoftheirpay.Deductionsusuallyincludeincome tax.Taxispaidtothegovernment.Thegovernmentusesittopayforcommunitywelfare,educationanda numberofotherservices.

PAY SLIP

Payment date: 14 November 2016

Pay period: 1 November – 14 November 2016 Employee’s name:

name:

Smith

LessonStarter:Deductionsfrompay

Whattypesofdeductionscanyouandyourclassthinkofthatmightbetakenoutofsomeone’spay?

Discuss,asaclass,whatsuperannuationandtheMedicarelevyis,andwhopaysit.

KEYIDEAS

■ Grossincome = thetotalofallincomefromallsources

■ Netincome = grossincomeminus deductions suchastax,unionfeesandsuperannuation

■ Taxableincome = grossincomeminuswork-relatedexpensesanddonationstocharity

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■ Incometax ispaidtothegovernment.Itisbasedonaperson’staxableincome.

■ Incometaxpayable canbecalculatedusingthetaxtablepublishedeveryyearbytheAustralian TaxationOf ce(ATO).Everyrowinthetableiscalleda taxbracket.Thetablebelowshows thetaxratesforthe2022/2023 nancialyear.

The MedicareLevy isanadditionaltaxwhichthegovernmentusestosupportfundingfor medicines,doctors,hospitalsandotheraspectsofthehealthcaresystem.Answerstothe questionsinthefollowingexercisearebaseduponthistable,buttheactualratesmayvaryfrom yeartoyear.

Taxableincome Taxonthisincome

$0 $18200 Nil

$18201 $45000 19 centsforeach $1 over $18200

$45001 $120000 $5092 plus 32 5 centsforeach $1 over $45000

$120001 $180000 $29467 plus 37 centsforeach $1 over $120000

$180001 andover $51667 plus 45 centsforeach $1 over $180000

Theaboverates donot includetheMedicarelevyof 2%

Keyterminology: grossincome,netincome,taxableincome,incometax,deductions

Exercise2F

1 Copyandcompletethetablebyinsertingthenetincomeamounts.

Hint:Recallthatnet income = grossincome minusdeductions.

2 FindHoang’sgrossweeklyincomeifheearns:

• $1200aweekasateacher

• $60anhourfortutoring,whenhetutorsfor3hoursaweek

• $25interestonhisbankaccountperweek

3 Johnhasagrossincomeof$45000andanetincomeof$20000.Howmuchdidhisdeductions cometo?

4 Pamelapays31.5%ofhergrossincomeintax.Howmuchtaxdoesshepayonagrossincomeof $85790?

FLUENCY 5–6(½),7,8 5–6(½),8(½)

Example17

Liamstartsanewjobwithanannualsalaryof$52800.Hispayslipeachmonthshowsdeductions fortaxationof$968.

a CalculateLiam’snetincomeeachmonth.

b WhatpercentageofLiam’smonthlypayisbeingpaidtothegovernmentbyhisemployer fortaxation?

c Liam’ssalaryisincreasedto$65000andthetaxationrateforLiam’ssalarychangesto24% withthe rst$18200taxfree.CalculateLiam’snetincomefortheyear.

SOLUTION EXPLANATION

a Monthlypay = $52800 ÷ 12 = $4400

∴ netmonthlyincome = $4400 $968 = $3432

b % tax = 968 4400 × 100 = 22%

c Salaryfortaxpurposes = $65000 $18200 = $46800

Taxamount = 24% of$46800 = 0.24 × $46800 = $11232

∴ netincome = $65000 $11232 = $53768

Nowyoutry

Calculategrossincomepermonth.

Netincome = grossincome taxation

Calculatewhatfraction$968isofthemonthly income$4400.Multiplyby100toconverttoa percentage.

First$18200isnottaxed.

Calculatetaxamounton$46800.Convert percentagetoadecimalandevaluate.

Netincome = grossincome taxamount.

Poppyhasajobwithanannualsalaryof$74400.Herpayslipeachmonthshowsdeductionsfor taxationof$1488.

a CalculatePoppy’snetincomeeachmonth.

b WhatpercentageofPoppy’smonthlypayisbeingpaidtothegovernmentbyheremployer fortaxation?

c Poppy’ssalaryisincreasedto$82800andthetaxationrateforPoppy’ssalarychangesto28% withthe rst$18200taxfree.CalculatePoppy’snetincomefortheyear.

5 Foreachofthefollowing nd: theannualnetincome i thepercentageofgrossincomepaidastax.Roundtoonedecimalplacewherenecessary. ii

a Grossannualincome = $48241,taxwithdrawn = $8206

b Grossannualincome = $67487,taxwithdrawn = $13581 20

c Grossmonthlyincome = $4041, taxwithdrawn = $606.15

d Grossmonthlyincome = $3219,taxwithdrawn = $714 62

6 Calculatetheamountoftaxtobepaidusingthefollowing annualsalariesandtaxratesifthe rst$18200istaxfree.

Hint:Netincome = grossincome deductions

Hint:Remembertosubtractthe $18200 tofindthesalaryto calculatetaxon.

salary = $30400,taxrate = 15%

b

a salary = $56500,taxrate = 21%

salary = $69700,taxrate = 24.5%

d

c salary = $96400,taxrate = 30.4%

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7 Edearns$1400perweekandpays27% ofhisannualincomeintax.

a CalculatetheamountofincometaxthatEdpaysinoneyear.

b FindEd’sannualnetincome.

Example18

Usingthetaxtabletocalculatetaxpayable

Usethetaxtablebelowto ndtheincometaxpayableforataxableincomeof$124000.

Taxableincome Taxonthisincome

$0 $18200 Nil

$18201 $45000 19centsforeach$1over$18200

$45001 $120000 $5092plus32.5centsforeach$1over$45000

$120001 $180000 $29467plus37centsforeach$1over$120000

$180001andover $51667plus45centsforeach$1over$180000

Theaboverates donot includetheMedicarelevy2%.

SOLUTION

Tax = $29467 + 0.37 ×(124000 120000) = $30947

EXPLANATION

Findthetaxbracketinwhichtheamount $124000lies.Thisis ($120000 $180000).

Writedown thevaluesinthisbracket, rememberingthat37cinthedollaris37%,or0 37. Subtract120000from124000to nd theamountofincomethatthe37% appliesto.

Useyourcalculatorto ndtheanswer, workingfromlefttoright.

Nowyoutry

Usethetaxtableaboveto ndtheincometaxforanincomeof$75000.

8 UsethetaxtableinExample18to ndtheincometaxpayable oneachoftheseincomes.

Hint:Lookcarefullyforthe correcttaxbracket

9 Melhasanetannualincomeof$53246after21% ofherincomeis withdrawnfortaxpurposes.Whatwashergrossincome?

10 Fredearns$50000eachyearasashopclerkandan extra$1200eachyearfordoinggardeningonsome weekends.

a Calculatehisannualgrosssalary.

b Usehisgrosssalaryto ndhisincometax,using thetaxtableinExample18.

c Whatishisannualnetincome,aftertax?

d Whatishisapproximatefortnightlynetincome, tothenearestcent,aftertax?

Hint:What % ofgrossincome does $53246 represent?

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11 Williamearns$1600perweek.UsingthetaxtableinExample18,howmuchtaxisdeductedfromhis payeachweek?Assume52weeksinayear.

12 Johnpays$10000intaxayear.

a WhichtaxbracketdoesJohnfallinto?

b WorkbackwardsfromthisamounttoworkouthowmuchJohnearnsperyear.Answertothenearest dollar.

ENRICHMENT:Othertypesofdeductionsandtaxableincome

13–15

Theloweraperson’sincome,thelesstaxtheymustpay.Peoplethereforetrytolowertheirtaxableincome byclaimingallowabletaxdeductions.

Work-relatedexpensessuchasuniforms,stationeryandjob-relatedtravelexpensesareallexamplesof allowabletaxdeductions.Theincometaxisthereforecalculatedonwhatwecallaperson’staxableincome.

Taxableincome = grossincome allowabletaxdeductions

UsethetaxtablefromExample18tocomparethefollowingjobs.

13 Anyoungaccountantearns$3120afortnight,withnoallowabletaxdeductions.

a Whatistheaccountant’staxableincome?

b Howmuchtaxdoestheaccountantoweinayear?

c Whatistheaccountant’sannualnetpay?

d Whatistheaccountant’sfortnightlynetpay?

14 Ayounglawyerearns$3120afortnightwithallowable taxdeductionstotalling$2560ayear.

a Whatisthelawyer’staxableincome?

b Howmuchtaxdoesthelawyeroweinayear?

c Whatisthelawyer’sannualnetpay?

d Whatisthelawyer’sfortnightlynetpay?

15 Howmuchlessmoneydoesthelawyerinquestion 14 haveeachweekcomparedtotheaccountantin question 13?

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2G Simple interest

Learningintentionsforthissection:

• Tounderstandtheconceptofsimpleinterestandhowitiscalculated

• Tobeabletousethesimpleinterestformulatoperformcalculations

Past,presentandfuturelearning:

• ThissectioncontinuestheStage5CoreTopiccalled FinancialMathematicsA

• Thefollowingsection,2H,furtherextendstheseconcepts

• FinancialMathematics isamajortopicinStage6Standard

• YoumaybeexpectedtorecalltheformulafrommemoryintheHSCExamination

Interestischargedwhenapersonorinstitutionborrowsmoney. Theinterestisanextraamountthatmustbepaidback,ontop oftheborrowedamount.

Interestisalsoearned,whenapersonorinstitutioninvests money.

Simpleor atrateinterestisusuallychargedorearnedeachyear. Itiscalculatedonthefullamountborrowedorinvested atthebeginningoftheloan.

LessonStarter:Developingtherule

$5000isinvestedinabankand5% simpleinterestispaidtotheinvestoreveryyear.Inthetablebelow,the amountofinterestpaidisshownforYear1,andtheamountoftotalinterestisshownforYears1and2.

• Completethetable.

• Howmuchinterestwouldtheinvestorearnin10years?

KEYIDEAS

■ Simpleinterest isinterestcalculatedeachtimeperiodontheinitialamount.

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■ Tocalculatesimpleinterest,weapplytheformula:

I istheamountofsimpleinterest(in$)

P isthe principal amount;themoneyborrowedorinvested(in$),alsoknownaspresentvalue r istheinterestrateperperiod,expressedasadecimal,notapercentage t isthenumberoftimeperiods,whichcouldbedays,months,yearsetc.

■ Thefuturevalue ($A) equalstheprincipalplusinterest

A = P + I

■ p.a.means‘perannum’or‘peryear’.

Keyterminology: simpleinterest,principal,perannum

Exercise2G

UNDERSTANDING

1 $12000isinvestedat6% p.a.for42months.

a

Whatistheprincipalamount?

b

Whatistheinterestrate?

VIDEO DEMO

c

Whatisthetimeperiodinyears?

2 Jannearns$560p.a.insimpleinterestonaninvestment.Howmuchwouldheearnonthe investmentin: 2years? a 5years? b 10years? c

3 Usetherule I = Prn to ndthesimpleinterest (I ) earnedinthese nancialsituations.

a $10000,10% p.a.,3years

b $6000,12% p.a.,5years

c $5200,4% p.a.,2years

Example19

Usingthesimpleinterestformula

Calculatethesimpleinterestearnediftheprincipalis$1000,therateis5% p.a.andthetime is3years.

SOLUTION EXPLANATION

P = 1000, r = 0.05, n = 3

I = Prn = 1000 × 0.05 × 3 = 150

Interest = $150

Listtheinformationgiven,notingthat 5%= 0.05.

Writetheformulaandsubstitutethegiven values.

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Answerthequestion.

Nowyoutry

Calculatethesimpleinterestearnediftheprincipalis$2000,therateis4% p.aandthetimeis 5years.

4 Findthesimpleinterestearnedon:

a

$5000at6% p.a.for1year

b

$5000at6% p.a.for3years

c

$8000at4% p.a.for5years

d

$15000at3% p.a.for7years

e

$7250at5 5% p.a.for3years

5 Wallyinvests$15000atarateof6% p.a.for3years.Calculate thesimpleinterestandtheamountavailableattheendof3years.

Example20 Usingothertimeperiods

Hint: Amount = principal + interest

Calculatethesimpleintereston$7000investedat6 1 4 % p.a.for18months.

P = 7000, r = 6 1 4 ÷ 100 = 0.0625Listtheinformation.

n = 18months = 18 12 or1 5yearsConvert18monthsintoyearsbydividingby12.

I = Prn

I = 7000 × 0.0625 × 1.5 = 656 25 Interest = $656 25

Nowyoutry

Writetheformula. Substituteinthevaluesandevaluate.

Calculatethesimpleintereston$4500investedat5 1 2 % for30months.

6 Calculatethesimpleinterestearnedon: Hint: 365 days = 1 year

a $500at7% p.a.for18months

b $1000at5% p.a.for24months

c $2000at4% p.a.for6months

d $4700at4 1 2 % p.a.for15months(Roundtothenearestcent.)

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e $50000at3.75% p.a.for200days(Roundtothenearestcent.)

Example21 Calculatingthefuturevalue

AllanandRachelplantoinvestsomemoneyfortheirchildKaylan.Theyinvest$4000for 30monthsinabankthatpays4.5% p.a.Calculatethesimpleinterestandthefuturevalueat the endofthe30months.

Writetheformula,substituteandevaluate.

Interest = $450

Totalamount = $4000 + $450 = $4450Totalamount = principal + interest

Nowyoutry

Joywinssomemoneywhichshedecidestoinvest.Sheinveststhe$5000for36monthsinabank accountthatpays3 8% p.a.Calculatethesimpleinterestandtheamountavailableattheendofthe 36 months.

7 Annieinvests$22000atarateof4% p.a.for27months.Calculatethesimpleinterestandtheamount availableattheendof27months.

8 Copyandcompletethetable.

9 A nancecompanycharges14% p.a.simpleinterest.IfLynborrows$2000toberepaidover2years, calculatehertotalrepayment.

10 Markusborrows$20000tobuyacar.Heischargedsimpleinterestat18% p.a.foraperiodof5years.

a HowmuchinterestisMarkuschargedeachyear?

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b CalculatethetotalinterestMarkuswillpayonthisloan.

c WhatisthetotalamountthatMarkuswillhavepaidattheendoftheloanperiod?

11 Wendywins$5000duringachesstournament.Shewishestoinvestherwinnings,andhasthetwo choicesgivenbelow.Whichonegivesherthegreatertotalattheendofthetime?

Choice1:8 5% p.a.simpleinterestfor4years

Choice2:8% p.a.simpleinterestfor54months

12 Thetableshowstheamountofsimpleinterestpayable(in$,tothenearest$)onloansatacertain interestrate.

Usethetableto ndtheinterestpayableonthefollowingloans.

$5000for1year a

$500for3years b

$100for10years c

$150for1year d

$85500for5years e $9550for10years f

$5000for4years g

$50000for9years h

$100000for10years i

13 Thegraphontherightshowstheannual interestearnedoninvestmentsforinterest ratesof4% p.a.and6% p.a.Usethegraph toanswerthefollowing.

a Findtheannualinterestearnedonan investmentof:

$300at4% p.a. i $520at6% p.a. ii

$250at4% p.a. iii

b Whatinvestmentswouldearnannual interestof(tothenearest$5): $20at6% p.a.? i $20at4% p.a.? ii $14at6% p.a.? iii

SAMPLEPAGES

2H Applications ofsimpleinterest

Learningintentionsforthissection:

• Tobeabletousethesimpleinterestformulatosolveproblemsaboutinvestmentsandloans

• Tobeabletocalculaterepaymentamountsgiventhetermsofaloan

Past,presentandfuturelearning:

• ThissectioncontinuestheStage5CoreTopiccalled FinancialMathematicsA

• Section1FofourYear10bookrevisesandfurtherextendstheseconcepts

• FinancialMathematics isamajortopicinStage6Standard

• YoumaybeexpectedtorecalltheformulafrommemoryintheHSCExamination

Financialcalculationsareacriticalcomponentof thethinkingbehindthedecisionspeoplemakeas towheretoborroworinvestmoney.

LessonStarter:WheredoIinvest?

BankA:$4000at5% p.a.for8years

BankB:$5000at8% p.a.for4years

BankC:$8000at4% p.a.for5years

Calculatethesimpleinterestearnedoneachinvestmentoption.Whatdoyounotice?

Whichbankwouldyouchooseandwhy?

KEYIDEAS

■ Thesimpleinterestformula, I = Prn,containsfourvariables:

I isamountofinterest

P isprincipal(i.e.amountinvested)

r isinterestrate,expressedasadecimal

n isnumberoftimeperiods.

Ifvaluesaregivenforthreeofthese,thentheycanbeusedto ndthefourth.

■ Torepayaloan,youmustrepaytheamountborrowed(theprincipal)andtheinterest.

■ Repayments aretheamountofmoney,usuallythesameamounteachtimeperiod,requiredto repayaloan.

Keyterminology: simpleinterest,principal,repayment

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Exercise2H

UNDERSTANDING

1 IfPhilearns$100insimpleinterestinoneyear,howlongwouldittakehimtoearn: $200 a $400 b $5000 c $250 d

2 Howmanyyearsdoesittakefor$100toearn$50 ininterestifthesimpleinterestrateis10% p.a.?

Hint:Howmuchinterestisearned on $100 at 10% p.a.for 1 year?

3 Jodierepays$200amonthfor12monthstopaybackherloanandinterest.Howmuchdoessherepay?

4 Aloanof$4000hasinterestof$500addedtoit.Calculatethesizeofeachofthe10repaymentsneeded torepaytheloan.

Example22

Determiningtheinvestmentperiod

Remyinvests$2500at8% p.a.simpleinterest,foraperiodoftime,toproduce$50interest. Forhowlongdidsheinvestthemoney?

Time = 0 25years = 0 25 × 12months = 3months

Nowyoutry

Solvetheremainingequationfor t bydividing bothsidesby200.

Convertdecimaltimetomonthswhere appropriate.

Jasinvests$3000at6% p.a.simpleinterest,foraperiodoftime,toproduce$450interest.Forhow longdidheinvestthemoney?

5 Alviinvests$5000at8% p.a.simpleinterestandwantstoearn$1200ininterest.Forhowmanyyears shouldAlviinvesthismoney?

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6 Samearns$288interestonhis$1600investment.Iftheinterestwascalculatedat4% p.a.,howmany yearsdidSaminvestthemoneyfor?

7 $8000earns$600interestat5% p.a.overhowmanymonths?

VIDEO DEMO

Example23 Determiningtheinterestrate

BankEastadvertises$450interestayearonaninvestmentof$7500.Calculatethesimpleinterest rateforthisinvestment.

SOLUTION

I = 450, P = 7500, n = 1, r =?

I = Prn

450 = 7500 × r × 1

450 = 7500r 7500r = 450

r = 450 7500

r = 0 06

EXPLANATION

Listtheinformation.

Writetheformulaandsubstitute I = 450, P = 7500and t = 1.

Simplifyandsolvefor r .

VIDEO DEMO

Interestrateis6% p.a. Write r asapercentage.

Nowyoutry

OzLoansoffers$610interestayearonaninvestmentof$12200.Calculatethesimpleinterestrate forthisinvestment.

8 Findtheannualsimpleinterestrateneededforeachofthe

Hint:Setuptheformula I = Prn where r istheunknown. followingsituations.

$4000earns$500in2years

a $500earns$120in12years b

c $950earns$470 25in9years d

e

$18000earns$3510in3years

$3000earns$945in18months

Example24 Calculatingrepayments

$2500earns$393 75in4 5years f

‘Deals4You’offersaloanof$24000at16% p.a.simpleinterestiftheloanisrepaidinequal monthlyrepaymentsover5years.

Howmuchinterestischargedontheloan? a

Whatisthetotalamountoftheloanandtheinterest? b Calculatethesizeofeachrepayment. c

SOLUTION EXPLANATION

a I = Prn

P = 24000, r = 0.16, n = 5

I = 24000 × 0 16 × 5

= $19200

b Total = $24000 + $19200

= $43200

Writedownthesimpleinterestformulaand listtheinformation.

Substituteinthevaluesandevaluate.

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Total = principal + interest

c Repayments = 43200 60 = 720 Repaymentscometo$720 permonth.

Nowyoutry

Dividethetotalamountbythenumberofmonthsin 5years (5 × 12 = 60).

Aloanof$35000isrepaidinequalmonthlyinstalmentsover6yearsat8% p.a.simpleinterest.

Howmuchinterestischargedontheloan?

a Whatisthetotalamountoftheloanandtheinterest? b Calculatethesizeofeachrepayment.

9 Copyandcompletethistableand ndthemonthlyrepaymentforeachloan.

10 Calculatetheprincipalamountwhichearns$500simpleinterest over3yearsatarateof8% p.a.Roundtothenearestcent. Hint:Substituteinto I = Prn

11 Charlotteborrows$9000tobuyasecond-handcar.Theloanmustberepaidover5yearsat12% p.a. simpleinterest.Calculate:

a thetotalamounttoberepaid

b themonthlyrepaymentamountiftherepaymentsarespreadequallyoverthe5years

12 If$5000growsto$11000in12years, ndthesimpleinterestrate.

13 Aninvestorinvests$P andwantstodoublethis amountofmoney.

a Howmuchinterestmustbeearnedtodouble thisinitialamount?

b Whatsimpleinterestrateisrequiredtodouble theinitialamountin8years?

c Ifthesimpleinterestrateis5% p.a.: howmanyyearswillittaketodoublethe investment? i

howmanyyearswillittaketotriplethe investmentamount? ii

howdotheinvestmentperiodsinparts i and ii compare? iii

ENRICHMENT:Introducingcompoundinterest

14,15

Withsimpleinterest,theprincipalandtheinterestearnedeachyearremainthesamefortheperiodof theinvestment.

However,withcompoundinterest,eachtimetheinterestiscalculateditisaddedtotheprincipaltogivea newvalue.Thismeansthatthenexttimetheinterestiscalculated,itisdonesousingalargeramount.

Inthefollowingquestionsyouwillbeaskedtodorepeatedapplicationsofsimpleinterestto ndthe nal compoundedamount.

14 $500isinvestedfor4yearsat10% p.a.interestcompoundedannually.

a Completethetableto ndthe nalvalueoftheinvestmentattheendofthistimeandthetotal.

b Howmuchinterestdidtheinvestmentearnoverthe4years?

15 a Completethefollowingtableto ndthe nalvalueofaninvestmentof$4500compoundedat5% p.a.annuallyfor5years.

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b Type4500 × 1.055 intoyourcalculator.Whatdoyounoticeaboutthisanswer?

c Canyouexplainhowtheanswerstopart a andpart b relate?

Maths@Work activities encourage students to identify and apply maths in a range of real-world scenarios they may encounter.

Facebookcake-decoratingbusiness

Moreandmoreindividualsaresettingup abusinessusingFacebook.Forexample,a successfulcake-decoratingbusinesscanberun fromhomewhilelookingafterthekidsorwhile workingnormalbusinesshoursatotherjobs.

Aswithanybusiness,anunderstandingof nancialmathematicsisimportanttothesuccess ofthebusiness.Skillssuchascalculating costsandpro ts,percentagesandtaxationare importantforanymanager.

1 Calculatethetotalcostofbuyingeachofthefollowingcaketinsets: Roundset:6,8,9and12inchesby3inchesdeepat$64. Roundset:6,8,10and12inchesby4inchesdeepat$99.

Squareset:6,8and10inchesby3inchesdeepat$45.

Squareset:6,8,10and12inchesby4inchesdeepat$86.

2 Convertthefollowingmeasurementsfrominches(USstandard)towholenumberofcentimetresby usingthefollowingconversionrate:1inch = 2.54cm. 3inches a 4inches b 9inches c 10inches d

3 Imaginethatyouspend2hoursoutof9 1 2 workhoursontheinternetpromotingyourbusiness.Write thisasapercentage,roundedtothenearestwholepercentage.

4 Fondanticingcomesindifferentcoloursandindifferent-sizedtubes.Managingyourbudgetmeans lookingforthebestbuy.

a Whichofthefollowingrepresentsthebestbuyforeachcolouroffondantlistedbelow?

b Whatistheaveragecostper100gramsforwhitefondanticing?

c Underwhatcircumstanceswouldsomeonebuyasizethatwasnotthebestbuy?

5 Acustomerhasthefollowingquotesforalarge21stbirthdaycakefromfourdifferentFacebookcake suppliers:$195,$290,$225and$215.

Foreachofthefollowing,stateanswerstothenearestwholenumber.

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a Whatisthemeanoraveragecostforthistypeofcake?

b Whatisthepercentagechangefromthelowestquotetothehighestquote?

c Ifitcostseachsupplier$50inproducttomakethecake,calculatethepercentagepro tforeach ofthefourquotesgivenabove.

d Ifittakeseachsupplieronaverage5 1 2 hourstomakeanddecoratethecake,whatiseachperson chargingperhour,excludingthe$50productcosts?

Usingtechnology

6 ImaginethatyouhavestartedaFacebookcake-making business.Toanalysepossiblepro ts,setupanExcel spreadsheetasshownbelowandenterformulasin theshadedcells.Notethatthisisasimpli edanalysis andexcludespower,gasandequipmentcosts.

Hint:Formatall $ cellsas‘currency’ withzerodecimalplaces. Formatprofit % cellsas‘percentage’ withzerodecimalplaces.

a Howmuchpro twouldbemadefromselling2Valentines’Daycakesand3chocJaffa birthdaycakes?

b List,inascendingorder,the3cakesthatbringthelowestpercentagepro t.

c List,indescendingorder,the3cakesthatpaythehighesthourlyrates.

d Suggestareasonwhythecakesin c costthecustomermoreinhourlyrates.

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Using technology: Questions asking students to use spreadsheets or online graphing or geometry software are found throughout exercises and review material.

Working Mathematically investigative tasks in every chapter provide opportunities for students to apply learning through open-ended and exploratory tasks.

1 Theanswerstothecluesarehiddenintheword nd.Canyou ndall16words?

2 Findoutthefourclassicalelementsoftheworldbyansweringthefollowingsimpleinterestproblems. Matchtheletterbesideeachquestiontoitscorrespondinganswerineachgrid.

Chapter summary: a key point summary for revision and quick reference.

Percentages and decimals

Percentage Decimal

Percentage composition

÷ 100 PercentageFraction × 100 ÷ 100 49% = 0.49

a

percentage 17%

= 5.1 =× 30 100 17

Percentage Means

Percentage increase and decrease Increase 20 by 6% 20 × 1.06 = 21.2

Decrease 20 by 5% 20 × 0.95 = 19

= 0.17

Financial mathematics

Applications of percentages

Percentage pro t/loss pro t or loss

= cost price × 100 Mark-up and discount

Commission/tax

Simple interest

r = interest rate (as a fraction or decimal)

n = number of time periods

If $2000 is invested at 5% p.a. for 4 years:

I = Prn = $2000 × 0.06 × 4 = $400

Income and tax

gross income deductions tax: money taken from pay and given to the government

Uncorrected 1st sample pages • Cambridge University Press and Assessment © Palmer, et al 2023 • 978-1-009-40926-1 • Ph 03 8671 1400

Chapterchecklistwithsuccesscriteria

AprintableversionofthischecklistcanbedownloadedfromtheInteractive Textbook. ✔

1Icanconvertbetweenpercentagesandfractions.

2A

e.g.Write

a 7 40 asapercentage b 17 5% asafraction

2Icanconvertbetweenpercentagesanddecimals.

2A

e.g.Write

a 0 3 asapercentage b 72% asadecimal

3Icanwriteaquantityasapercentage.

2A

e.g.Write 27 cmoutof 1 8 masapercentage.

2B 4Icanfindapercentageofaquantity.

e.g.Find 35% of $75

2B 5Icanfindtheoriginalamountfromapercentage.

e.g.Determinetheoriginalamountif 12% oftheamountis $72

2C 6Icanincreaseanddecreasebyapercentage.

e.g. a Increase $80 by 12% b Decrease $40 by 8%

2C 7Icanfindapercentagechange.

e.g.Thepriceofagymmembershipincreasedfrom $320 to $370.Findthepercentageincrease correcttoonedecimalplace.

2C 8Icanfindtheoriginalamountafteranincreaseordecrease.

e.g.Adecreaseof 22% reducedthepopulationofatownto 1014.Whatwastheoriginalpopulation ofthetown?

2D 9Icancalculatethesellingpricefromamark-upordiscount.

e.g.Astoremarksupallwhitegoodsby 20%.Ifthecostpriceofafridgeis $1100,whatwillbeits sellingprice?

2D 10Icandeterminepercentageprofit.

e.g.Astallholdermakescandlesfor $8 andsellsthemfor $13.Findtheprofitandexpressthis profitasapercentageofthecostprice.

2D 11Icancalculatetheoriginalpricebeforediscount.

e.g.AdepartmentstorediscountsallChristmastreesby 15%.Ifthesalepriceofatreewas $106.25,whatwastheoriginalprice?

2E 12Icancomparewagesandsalaries.

e.g.Tonyhasanannualsalaryof $88000 andJodieearns $72 perhour.Calculate

a Tony’shourlyrateofpayifheworksa 38-hourweek

b Jodie’syearlyincomeifsheworksonaverage 22 hoursperweek.

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Chapter checklist with Success Criteria – including example questions – at the end of each chapter allows students to tick off what they have learnt and provides a quick revision tool.

Chapterchecklistwithsuccesscriteria

AprintableversionofthischecklistcanbedownloadedfromtheInteractive Textbook.

2E 13Icancalculateovertime.

e.g.CalculateJulian’sweeklywageforaweekwhereheworks 12 hoursathisnormalhourlyrate of $28, 4 hoursattimeandahalfand 3 hoursatdoubletime.

2E 14Icancalculatecommission.

e.g.Asalespersonispaidaretainerof $2200 permonthandreceivesan 8% commissiononsales. Ifonemonthhemakessalesworth $10400,calculatehisearningsforthatmonth.

2F 15Icancalculatenetincome.

e.g.Daniellehasanannualsalaryof $64800.Shehasmonthlytaxdeductionsonherpayslipof $1296.Calculatehernetincomeeachmonth.

2F 16Icancalculatenetincomeusingincometaxrates.

e.g.Annahasanannualsalaryof $78000 andataxationrateof 26% withthefirst $18200 tax free.CalculateAnna’snetincomefortheyear.

2F 17Icanusethetaxtabletocalculateincometax.

e.g.UsethetaxtablefromExample 18 tofindtheincometaxforanincomeof $90000.

2G 18Icanusethesimpleinterestformulaandfindthefuturevalue.

e.g.Calculatethesimpleinterestearnediftheprincipalis $4000,therateis 3% p.a.andthetimeis 4 years.Hence,whatistheamountattheendofthe 4 years?

2G 19Icanworkwithsimpleinterestusingothertimeperiods.

e.g.Calculatethesimpleintereston $6000 investedat 4 1 2 % p.a.for42months.

2H 20Icandeterminetheinvestmentperiodorinterestrateforsimpleinterest. e.g.Joshuainvests $3500 at 6% p.a.simpleinterest,foraperiodoftime,toproduce $315 interest. Forhowlongdidheinvestthemoney?

2H 21Icancalculaterepayments.

e.g.Sydtakesoutaloantopurchaseayacht.Theloanisfor $32000 at 8% p.a.simpleinterestif theloanisrepaidinequalmonthlyinstalmentsover 4 years. Calculatetheinterestchargedontheloanandhencethetotalamountowingandthesizeofthe requiredmonthlyrepayments.

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Short-answerquestions

Chapter review: short-answer, multiplechoice and extended-response questions to revise and consolidate the topic.

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a apersonwithanannualsalaryof$76076workinga38-hourweek

10

2F

11 2G

Jo’smonthlyincomeis$5270however20% ofthisispaidstraighttothegovernmentintaxes. WhatisJo’snetyearlyincome?

Findthesimpleinterestearnedon$1500at7% p.a.for5years. 12

2H Billinvests$6000at4% simpleinterest,foraperiodoftime,toproduce$720.Forhowlong didheinvestthemoney? 13 2F

Usethetaxtablebelowto ndtheincometaxpayableonanincomeof$78000.

$0 $18200 Nil

$18201 $45000 19 centsforeach $1 over $18200

$45001 $120000 $5092 plus 32 5 centsforeach $1 over $45000

$120001 $180000 $29467 plus 37 centsforeach $1 over $120000

$180001 andover $51667 plus 45 centsforeach $1 over $180000

Theaboverates donot includetheMedicarelevyof2%.

Multiple-choicequestions

8 2E Janeispaidawageof$27 80perhour.Sheworks12hoursatthisrateduringaweek,plus 4hourson apublicholidaywhereshegetspaidattimeandhalf.Herearningsinthe weekare:

.80 B

9 2E Simonearnsaweeklyretainerof$370and12% commissionofanysaleshemakes.Ifhe makes$2700worthofsalesinaparticularweek,hewillearn:

10

$1200isinvestedwithasimpleinterestrateof10% fortwoyears.Thefuturevalueattheend ofthetwoyearsis:

Extended-responsequestions

1 Paulinebuysadebutantedressatcost pricefromherfriendTila.Paulinepaid $420forthedresswhichisnormally markedupby55%.

a Howmuch didshesave?

b Whatisthenormalsellingpriceof thedress?

c IfTilagetsacommissionof15%: howmuchcommissiondidshe get? i

howmuchcommissiondidTilalosebysellingthedressatcostpriceratherthanthe normalsellingprice?

2 Adamstartsanewjobandworksa38-hourweekforawageof$975 84.

a Calculatehishourly rateofpay.

b Ifovertimeiscalculatedattimeandahalf,whatisAdam’sovertimerate?

c HowmuchdoesAdamearnfor4hoursofovertimework?

d HowmanyhoursofovertimedidAdamworkinaweekifhiswageforthatweekwas $1226 22?

e IfAdamusuallyworkstheamountofovertimeinpart d inthe52weeksoftheyearhe works,andhepays27% ofhispayintax,whatishisnetannualincome?

f IfAdaminvests10% ofhisnetincomeinanaccountearning8% p.a.simpleinterestfor 18months,howmuchextraincomewillhehaveearned?

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