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1. Algebra,2UG2014HSC3MC
STANDARD2:HSCComprehensiveRevisionSeries -ALGEBRA A1FormulaeandEquations(Y11)
A2LinearRelationships(Y11)
A4TypesofRelationships(Y12)
Teacher:SmarterMaths
ExamEquivalentTime:75minutes(basedonHSCallocationof1.5minutesapprox.permark)
Questions
Thediagramshowsthegraphofanequation.
Whichofthefollowingequationsdoesthegraphbestrepresent?
(A)
(B)
(C)
(D)
2. Algebra,2UG2015HSC24MC
3. FSDriving,2UG2014HSC22MC
Considertheequation .
Whichofthefollowingwouldbeacorrectstepinsolvingthisequation?
(A)
(B)
(C)
(D)
Heather’scarusesfuelattherateof6.6Lper100kmforlong-distancedrivingand 8.9L per100kmforshort-distancedriving.
Sheusedthecartomakeajourneyof560km,whichincluded65kmofshort-distance driving.
ApproximatelyhowmuchfueldidHeather’scaruseonthejourney?
(A)
(B)
(C)
(D)
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4. FSDriving,2UG2016HSC10MC
5. Algebra,2UG2010HSC7MC
Carolinedrinkstwosmallbottlesofwineoverathree-hourperiod.Eachofthesebottlescontains2.3standarddrinks.Carolineweighs53kg.
Usingtheformulabelow,whatisCaroline'sapproximatebloodalcoholcontent(BAC)attheendofthisperiod?
where isthenumberofstandarddrinksconsumed
isthenumberofhoursdrinking
istheperson'smassinkilograms
(A)
(B)
(C)
(D)
If ,whatisthevalueof
(A)
(B)
(C)
(D)
6. FSDriving,2UG2011HSC21MC
7. Algebra,2UG2009HSC16MC
AtraindepartsfromTown at3.00pmtotraveltoTown .Itsaveragespeedforthejourneyis90km/h,anditarrivesat5.00pm.AsecondtraindepartsfromTown at3.10pmandarrivesatTown at4.30pm.
Whatistheaveragespeedofthesecondtrain?
(A)
(B)
(C)
(D)
Thetimeforacartotravelacertaindistancevariesinverselywithitsspeed.
Whichofthefollowinggraphsshowsthisrelationship?
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8. Algebra,2UG2010HSC13MC
Thenumberofhoursthatittakesforablockoficetomeltvariesinverselywiththetemperature.At30°Cittakes8hoursforablockoficetomelt.
Howlongwillittakethesamesizeblockoficetomeltat12°C?
(A)
(B)
(C)
(D)
9. Algebra,2UG2011HSC20MC
Afunctioncentrehostseventsforupto500people.Thecost ,indollars,forthecentretohostanevent,where peopleattend,isgivenby:
Thecentrecharges$100perperson.Itsincome ,indollars,isgivenby:
Howmuchgreateristheincomeofthefunctioncentrewhen500peopleattendanevent,thanitsincomeatthebreakevenpoint?
(A)
(B)
(C)
(D)
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10. Algebra,2UG2004HSC16MC
Georgedrewacorrectdiagramthatgavethesolutiontothesimultaneousequations and .
Whichdiagramdidhedraw?
11. Algebra,2UG2004HSC22MC
12. Algebra,2UG2005HSC17MC
13. Algebra,2UG2007HSC15MC
Johnknowsthat
•oneAustraliandollarisworth0.62euros•oneVistabelladollar isworth1.44euros.
Johnchanges25AustraliandollarstoVistabelladollars.
HowmanyVistabelladollarswillheget?
(A)
(B)
(C)
(D)
Thetotalcost, ,ofaschoolexcursionisgivenby ,where isthenumberofstudents.
Ifthreeextrastudentsgoontheexcursion,byhowmuchdoesthetotalcostincrease?
(A)
(B)
(C)
(D)
Ifpressure( )variesinverselywithvolume( ),whichformulacorrectlyexpresses intermsof and ,where isaconstant?
(A)
(B)
(C)
(D)
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14. Algebra,2UG2007HSC19MC
15. Algebra,2UG2015HSC13MC
Whichofthefollowingcorrectlyexpresses asthesubjectof ?
(A)
(B)
(C)
(D)
Whatistheequationoftheline ?
(A)
(B)
(C)
(D)
16. FSHealth,2UG2014HSC4MC
17. Algebra,2UG2013HSC22MC
Young’sformulabelowisusedtocalculatetherequireddosagesofmedicineforchildren aged1–12years.
Howmuchofthemedicineshouldbegiventoan18-month-oldchildina24-hourperiod ifeachadultdosageis45mL?Themedicineistobetakenevery6hoursbybothadults andchildren.
(A)
(B)
(C)
(D)
Leannewantstobuildarectangularvegetablegardeninherbackyard.Shehas20metresoffencingandwilluseawallasonesideofthegarden.Theplanforhergardenisshown,where metresisthewidthofhergarden.
Whichequationgivesthearea, , ofthevegetablegarden?
(A)
(B)
(C)
(D)
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18. Algebra,2UG2007HSC18MC
Chrisstartedtomakethispatternofshapesusingmatchsticks.
Ifthepatternofshapesiscontinued,whichshapewoulduseexactly matchsticks?
(A) Shape
(B) Shape
(C) Shape
(D) Shape
19. Algebra,STD22014HSC26d
Whatdoesthisindicateabouttheheightsofgirlsaged6to11? (1mark)
20. Algebra,STD2A2SM-Bank03
GiveONEreasonwhythisequationisnotsuitableforpredictingheightsofgirlsolderthan12. (1mark)
Draweachgraphonthegridbelowandhencesolvethesimultaneousequations. (3marks)
(3marks)
Theaverageheight, ,incentimetres,ofagirlbetweentheagesof6yearsand11yearscanberepresentedbyalinewithequation
where istheageinyears. Forthisline,thegradientis6.
(i)
(i)
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21. Algebra,2UG2009HSC28c
22. Algebra,2UG2013HSC29a
Theheightabovetheground,inmetres,ofaperson’seyesvariesdirectlywiththesquareofthedistance,inkilometres,thatthepersoncanseetothehorizon.
Apersonwhoseeyesare1.6mabovethegroundcansee4.5kmouttosea.
Howhighabovetheground,inmetres,wouldaperson’seyesneedtobetoseeanislandthatis15kmouttosea?Giveyouranswercorrecttoonedecimalplace. (3marks)
SarahtriedtosolvethisequationandmadeamistakeinLine2.
CopytheequationinLine1intoyourwritingbookletandcontinueyoursolutiontosolvethisequationfor .
Showalllinesofworking. (2marks)
Writeanequationtorepresentthetotalcost, ,ofrunningthecallcentreforaweekinwhichphonecallsaremade. (1mark)Bygraphingthisequationontheaxesabove,determinethenumberofphonecallsthecharityneedstomakeinordertobreakeven. (2marks)
23. Algebra,2UG2015HSC28f
24. Algebra,2UG2018HSC28b
Acharityseekstoraisemoneybytelephoningpeopleatrandomfromacallcentreandaskingthemtodonate.
Overtheyears,thischarityhasfoundthattheamountofmoneyraised isrelatedtothenumber
oftelephonecallsmade .Agraphofthisrelationshipisshown.
Itcoststhecharity$2100perweektorunthecallcentre.Italsocostsanaverageof50centspertelephonecall.
(i)
(ii)
Solvetheequation ,leavingyouranswerasafraction. (3marks)
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25. Algebra,STD2A2SM-Bank02
26. FSDriving,2UG2015HSC30d
Theweightofasteelbeam, ,variesdirectlywithitslength, .
A1200mmsteelbeamweighs144kg.
Calculatetheweightofa750mmsteelbeam. (2marks)
Claireisdrivingonamotorwayataspeedof110kilometresperhourandhastobrakesuddenly.Shehasareactiontimeof2secondsandabrakingdistanceof59.2metres.
Stoppingdistancecanbecalculatedusingthefollowingformula
WhatisClaire'sstoppingdistance. (2marks)
Completethetablebelowby�llingintheTHREEmissingvalues. (1mark)
Usingthevaluesfromthetable,drawthegraphshowingtherelationship between and . (2marks)
Whatequationrepresentstherelationshipbetween and ? (1mark)
GiveONElimitationofthisequationinrelationtothiscontext. (1mark)
Isitpossibleforthecostperpersontobe$94?Supportyouranswerwith appropriatecalculations. (1mark)
27. Algebra,2UG2014HSC29a
Thecostofhiringanopenspaceforamusicfestivalis $120000.Thecostwill besharedequallybythepeopleattendingthefestival,sothat (indollars)is thecostperpersonwhen peopleattendthefestival.
(i)
(ii)
(iii)
(iv)
(v)
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Findtheequationoftheline . (1mark)
Explainwhythislineisonlyrelevantbetween and forthisfactory. (1mark)
Thepro�tperweek, ,canbefoundbyusingtheequation . Comparethepro�tsat and . (2marks)
28. Algebra,2UG2009HSC24d
Afactorymakesbootsandsandals.Inanyweek
•thetotalnumberofpairsofbootsandsandalsthataremadeis200•themaximumnumberofpairsofbootsmadeis120•themaximumnumberofpairsofsandalsmadeis150.
Thefactorymanagerhasdrawnagraphtoshowthenumbersofpairsofboots( )andsandals( )thatcanbemade.
(i)
(ii)
(iii)
Whatisthevalueof ? (1mark)
29. Algebra,2UG2016HSC29b
Whatisthedailygrowthrateofthepig’smass?Writeyouranswerasapercentage. (1mark)
Themass kgofababypigatage daysisgivenby where isaconstant.Thegraphofthisequationisshown.
(i)
(ii)
Copyright©2004-18TheStateofNewSouthWales(BoardofStudies,TeachingandEducationalStandardsNSW)
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1. Algebra,2UG2014HSC3MC
2. Algebra,2UG2015HSC24MC
3. FSDriving,2UG2014HSC22MC
WorkedSolutions4. FSDriving,2UG2016HSC10MC
♦♦Only31%ofstudentsansweredcorrectly!
5. Algebra,2UG2010HSC7MC
www.smartermaths.com.au
♦Meanmark49%
6. FSDriving,2UG2011HSC21MC
♦ Meanmark38%
7. Algebra,2UG2009HSC16MC
♦ Meanmark50%
8. Algebra,2UG2010HSC13MC
♦Meanmark50%COMMENT: Studentscanreadthe
incomelevelsdirectlyoffthegraph
tosavetimeandthencheckwith
theequationsgiven.
9. Algebra,2UG2011HSC20MC
www.smartermaths.com.au
10. Algebra,2UG2004HSC16MC
11. Algebra,2UG2004HSC22MC
12. Algebra,2UG2005HSC17MC
13. Algebra,2UG2007HSC15MC
14. Algebra,2UG2007HSC19MC
www.smartermaths.com.au
♦Meanmark48%.
15. Algebra,2UG2015HSC13MC
♦Meanmark42%
16. FSHealth,2UG2014HSC4MC
♦♦♦Meanmark24%(lowestmeanofanyMCquestionin2013exam)
17. Algebra,2UG2013HSC22MC
18. Algebra,2UG2007HSC18MC
19. Algebra,STD22014HSC26d
www.smartermaths.com.au
20. Algebra,STD2A2SM-Bank03
♦♦Meanmark22%CRITICALSTEP:Readingthe�rst
lineofthequestioncarefullyand
establishingtherelationship
isthekeypartofsolving
thisquestion.
21. Algebra,2UG2009HSC28c
♦♦Meanmark27%STRATEGY: TheRHSofthe
equationincreasesfrom1to15
(fromLine1toLine2),indicating
bothsidesmusthavebeen
multipliedby15.
22. Algebra,2UG2013HSC29a
(i)
(ii)
♦Meanmarksof48%and32%forparts(i)and(ii)respectively.
23. Algebra,2UG2015HSC28f
♦Meanmark35%.
24. Algebra,2UG2018HSC28b
i.
ii.
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25. Algebra,STD2A2SM-Bank02
♦Meanmark34%.
26. FSDriving,2UG2015HSC30d
♦ Meanmark48%
♦♦♦Meanmark7%
COMMENT:Whenaskedfor
limitationsofanequation,look
carefullyatpotentialrestrictions
withrespectto boththedomainand
range.
27. Algebra,2UG2014HSC29a
(i)
(ii)
(iii)
(iv)
(v)
www.smartermaths.com.au
♦ Meanmark38%
♦♦♦Meanmarkpart(i)14%. Using isalessef�cient
butequallyvalidmethod,using
and ( -
intercept).
♦ Meanmark49%
♦ Meanmark40%.
28. Algebra,2UG2009HSC24d
(i)
(ii)
(iii)
♦Meanmark48%.
♦♦♦Meanmarkpart(ii)6%.MARKER'SCOMMENT:
Interpretationoftheexponential
wasverypoorlyunderstood.
29. Algebra,2UG2016HSC29b
(i)
(ii)
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