AMBRIDGEINTERNATIONALEXAMINATIONS

GCEAdvancedSubsidiaryLevelandGCEAdvancedLevel

MARKSCHEMEfortheOctober/November2012series

9709MATHEMATICS

9709/13

Paper1,

umrawmark75

Thismarkschemeispublishedasanaidtoteachersandcandidates,toindicatetherequirementsoftheexamination.ItshowsthebasisonwhichExaminerswereinstructedtoawardmarks.ItdoesnotindicatethedetailsofthediscussionsthattookceatanExaminers’meetingbeforemarkingbegan,whichwouldhaveconsideredtheacceptabilityofalternativeanswers.

MarkschemesshouldbereadinconjunctionwiththequestionpaperandthePrincipalExaminerReportforTeachers.

Cambridgewillnotenterintodiscussionsaboutthesemarkschemes.

CambridgeispublishingthemarkschemesfortheOctober/November2012seriesformostIGCSE,GCEAdvancedLevelandAdvancedSubsidiaryLevelcomponentsandsomeOrdinaryLevelcomponents.

Page2

MarkScheme

Syllabus

Paper

GCEAS/ALEVEL–October/November2012

9709

13

?CambridgeInternationalExaminations2012

MarkSchemeNotes

Marksareofthefollowingthreetypes:

MMethodmark,awardedforavalidmethodappliedtotheproblem.Methodmarksarenotlostfornumericalerrors,algebraicslipsorerrorsinunits.However,itisnotusuallysufficientforacandidatejusttoindicateanintentionofusingsomemethodorjusttoquoteaformula;theformulaorideamustbeappliedtothespecificprobleminhand,e.g.bysubstitutingtherelevanttiesintotheformula.CorrectapplicationofaformulawithouttheformulabeingquotedobviouslyearnstheMmarkandinsomecasesanMmarkcanbeimpliedfromacorrectanswer.

Accuracymark,awardedforacorrectanswerorintermediatestepcorrectlyobtained.Accuracymarkscannotbegivenunlesstheassociatedmethodmarkisearned(orimplied).

Markforacorrectresultorstatementindependentofmethodmarks.

Whenapartofaquestionhastwoormore“method”steps,theMmarksaregenerallyindependentunlesstheschemespecificallysaysotherwise;andsimilarlywhenthereareseveralBmarksallocated.ThenotationDMorDB(ordep*)isusedtoindicatethataparticularMorBmarkisdependentonanearlierMorB(asterisked)markinthescheme.Whentwoormorestepsareruntogetherbythecandidate,theearliermarksareimpliedandfullcreditisgiven.

ThesymbolimpliesthattheAorBmarkindicatedisallowedforworkcorrectlyfollowingonfrompreviouslyincorrectresults.Otherwise,AorBmarksaregivenforcorrectworkonly.AandBmarksarenotgivenforfortuitously“correct”answersorresultsobtainedfromincorrectworking.

Note: B2orA2meansthatthecandidatecanearn2or0.

B2/1/0meansthatthecandidatecanearnanythingfrom0to2.

Themarksindicatedintheschememaynotbesubdivided.Ifthereisgenuinedoubtwhetheracandidatehasearnedamark,allowthecandidatethebenefitofthedoubt.Unlessotherwiseindicated,marksoncegainedcannotsubsequentlybelost,e.g.wrongworkingfollowingacorrectformofanswerisignored.

Wrongormissingunitsinananswershouldnotleadtothelossofamarkunlesstheschemespecificallyindicatesotherwise.

Foranumericalanswer,allowtheAorBmarkifavalueisobtainedwhichiscorrectto3s.f.,orwhichwouldbecorrectto3s.f.ifrounded(1d.p.inthecaseofanangle).Asstatedabove,anAorBmarkisnotgivenifacorrectnumericalanswerarisesfortuitouslyfromincorrectworking.ForMechanicsquestions,allowAorBmarksforcorrectanswerswhicharisefromtakinggequalto9.8or9.81insteadof10.

Thefollowingabbreviationsmaybeusedinamarkschemeorusedonthescripts:AEF AnyEquivalentForm(ofanswerisequallyacceptable)

AG AnswerGivenonthequestionpaper(soextracheckingisneededtoensurethatthedetailedworkingleadingtotheresultisvalid)

BODBenefitofDoubt(allowedwhenthevalidityofasolutionmaynotbeabsoluyclear)

CAOCorrectAnswerOnly(emphasisingthatno“followthrough”fromapreviouserrorisallowed)

CWO CorrectWorkingOnly–oftenwrittenbya‘fortuitous’answerISW IgnoreSubsequentWorking

MR Misread

PA PrematureApproximation(resultinginbasicallycorrectworkthatisinsufficientlyaccurate)

SOS SeeOtherSolution(thecandidatemakesabetttemptatthesamequestion)

SR SpecialRuling(detailingthemarktobegivenforaspecificwrongsolution,oracasewheresomestandardmarkingpracticeistobevariedinthelightofaparticularcircumstance)

Penalties

MR–1ApenaltyofMR–1isdeductedfromAorBmarkswhenthedataofaquestionorpartquestionaregenuinelymisreadandtheobjectanddifficultyofthequestionremainunaltered.InthiscaseallAandBmarksthen e“followthrough”marks.MRisnotappliedwhenthecandidatemisreadshisownfigures–thisisregardedasanerrorinaccuracy.AnMR–2penaltymaybeappliedinparticularcasesifagreedatthecoordinationmeeting.

PA–1ThisisdeductedfromAorBmarksinthecaseofprematureapproximation.ThePA–1penaltyisusuallydiscussedatthemeeting.

1

powers4and335seenorimplied–70

M1

B1

A1

[3]

f′(x)=

decreasingfunction

B1B1

B1

Dependentuponminussigns&even

[3]

powers

2

3

M1

Useof

cos =–0.5

A1

A1A1

[4]

ftfor360–1stsolution

4

area?=2√3

B1

AreasectorShadedarea

B1

M1A1

Accept60°

Useof

cao

with

inradians

[4]

5

(i)

M1A1

or0.75

A1

[3]

M1A1

cao

(ii) (or21or21.3)

[2]

6

(i)

x

(ii)

B1B1

cao

fornegativeoffirstanswer

[2]

B1

B1

B1B1

[4]

B1

oe

B1B1

cao

7

(i)

[3]

B1B1B1

B1B1

[5]

(ii)

8

(i)

f′(– )=2+6–8=0hencestatvalueat

x=

f″(–1)=9–6=3 >0henceminimum

y +(c)

Sub(–1,5)→+c=5 →

B2,1,0

1eacherror

[2]

B1

AG

B1

[2]

B1B1B1

M1A1

allowunsimp