Specification FREE STANDING MATHEMATICS … · FREE STANDING MATHEMATICS QUALIFICATION: ADDITIONAL...

Regulated

www.ocr.org.uk/FSMQ

LEVEL 3 CERTIFICATE

6993For first teaching in 2018

FREE STANDING MATHEMATICS QUALIFICATION: ADDITIONAL MATHS

Specification

http://www.ocr.org.uk/qualifications/free-standing-maths-qualification-fsmq-additional-mathematics-6993/

Copyright © 2018 OCR. All rights reserved.

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We will inform centres about changes to specifications. We will also publish changes on our website. The latest version of our specifications will always be those on our website (ocr.org.uk) and these may differ from printed versions.

© OCR 2018FSMQ: Additional Maths 1

Contents

1 WhychooseOCRLevel3FSMQ:AdditionalMaths? 21a. WhychooseanOCRqualification? 21b. WhychooseOCRLevel3FSMQ:AdditionalMaths? 31c. Whatarethekeyfeaturesofthisspecification? 41d. HowdoIfindoutmoreinformation? 5

2 Thespecificationoverview 62a. OCR’sLevel3FSMQ:AdditionalMaths(6993) 62b. ContentofLevel3FSMQ:AdditionalMaths(6993) 72c. ContentofFSMQ:AdditionalMaths(01) 102d. Priorknowledge,learningandprogression 17

3 AssessmentofLevel3FSMQ:AdditionalMaths(6993) 183a. Formsofassessment 183b. AssessmentObjectives(AO) 183c. Teachingtime 193d. Assessmentavailability 193e. Retakingthequalification 193f. Assessmentofextendedresponse 203g. Synopticassessment 203h. Calculatingqualificationresults 20

4 Admin:whatyouneedtoknow 214a. Pre-assessment 214b. Specialconsideration 214c. Externalassessmentarrangements 224d. Resultsandcertificates 224e. Post-resultsservices 234f. Malpractice 23

5 Appendices 245a. Overlapwithotherqualifications 245b. Accessibility 245c. Mathematicalnotation 255d. Mathematicalformulaeandidentities 28

Summaryofupdates 30

© OCR 2018FSMQ: Additional Maths2

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1 WhychooseOCRLevel3FSMQ:AdditionalMaths?

1a. WhychooseanOCRqualification?

ChooseOCRandyouhavegotthereassurancethatyou’reworkingwithoneoftheUK’sleadingexamboards.Allourqualificationsaredevelopedinconsultationwithteachers,employersandHigherEducationinstitutionstoprovidelearnerswithaqualificationthatisrelevanttothemandmeetstheirneeds.

We’repartoftheCambridgeAssessmentGroup,Europe’slargestassessmentagencyandadepartmentoftheUniversityofCambridge.CambridgeAssessmentplaysaleadingroleindevelopinganddeliveringassessmentsthroughouttheworld,operatinginover150countries.

Weworkwitharangeofeducationproviders,includingschools,colleges,workplacesandotherinstitutionsinboththepublicandprivatesectors.CentrescanchoosefromourextensiverangeofALevels,GCSEsandvocationalqualifications,includingCambridgeNationalsandCambridgeTechnicals.

OurSpecifications

Webelieveindevelopingspecificationsthathelpyoubringthesubjecttolifeandinspireyourlearnerstoachievemore.

Wehavecreatedteacher-friendlyspecificationsthataredesignedtobestraightforwardandaccessiblesothatyoucantailorthedeliveryofthecoursetosuityourlearners’needs.Wewantlearnerstobecomeconfidentindiscussingideasandengagedintheirownlearning.

Weprovidearangeofsupportservicesdesignedtohelpyouateverystage,frompreparationthroughtothedeliveryofourspecifications.Thisincludes:

• accesstoSubjectAdvisorstosupportyouthroughthelifetimeofthespecification

• CPD/Trainingforteacherstointroducethequalificationandprepareyouforfirstteaching

• ActiveResults–ourfreeresultsanalysisservicetohelpyoureviewtheperformanceofindividuallearnersorwholeschools.

AllqualificationsofferedbyOCRareaccreditedorregulatedbyOfqual,theRegulatorforqualificationsofferedinEngland.TheaccreditationnumberforOCR’sLevel3FSMQ:AdditionalMathsisQN:100/2548/0.


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1b. WhychooseOCRLevel3FSMQ:AdditionalMaths?

OCR’sFSMQ:AdditionalMathstargetslearnerswhowilltakeGCSE(9–1)HighertierMathematics.ManylearnerswillgoontostudyASandALevelMathematicsand,fortheselearners,thisqualificationprovidesanintroductiontothesubjectatthatlevel,withthepossibilityofsubsequent,acceleratedprogressintoASandALevelFurtherMathematics.

ThereareotherswhowillnotcontinuewithmathematicsbeyondYear11.Fortheselearnersthisqualificationprovidesaworthwhileandenrichingcourseinitsownright.

Thisqualificationprovidesabroad,coherentandsatisfyingcourseofstudy.Itencourageslearnerstodevelopmoreconfidencein,andapositiveattitude

towards,mathematicsfollowingonfromGCSE(9–1)Mathematicsqualifications.ItconsolidatesanddevelopsGCSElevelmathematicalskillandencourageslearnerstorecognisetheimportanceofmathematicsintheirownlivesandtosociety.Italsoprovidesastrongmathematicalfoundationforlearnerswhogoontostudymathematicsatahigherlevel,thoselearnerswhogoontostudyothersubjectswhichmakeuseofmathematicsorthoselearnersprogressingtovocationalqualificationsordirectlyintoemployment.

ThisqualificationispartofawiderangeofOCRMathematicsqualificationswhichallowsprogressionfromEntryLevelCertificate,throughGCSE(9–1),toCoreMaths,ASandALevel.

Aimsandlearningoutcomes

OCR’sFSMQ:AdditionalMathswillencouragelearnersto:

• developfluentknowledge,skillsandunderstandingofmathematicalmethodsandconcepts

• acquire,selectandapplymathematicaltechniquestosolveproblems

• reasonmathematically,makedeductionsandinferencesanddrawconclusions

• comprehend,interpretandcommunicatemathematicalinformationinavarietyofformsappropriatetotheinformationandcontext

• developconfidenceinusingmathematicaltechniquesinavarietyofways.


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1c. Whatarethekeyfeaturesofthisspecification?

ThekeyfeaturesofOCR’sLevel3FSMQ:AdditionalMathsforyouandyourlearnersarethat:

• itisdesignedforlearnerswhoarelikelytobehighachievingatGCSE(9–1)

• itwillallowlearnerstoexperiencethedirectionsinwhichthesubjectisdevelopedpost-GCSE(9–1)

• itprovidesanexcellentpreparationforASandAlevelstudy

• itprovidesanenrichingandchallengingcourseofmathematicalstudyforthosefollowinganon-mathematicalAlevelcoursewithouthavingtofollowafullAScourse

• itwillprovideaspringboardforfutureprogressandachievementinavarietyofsubjectsandinfutureemployment

• itattractsupto10UCASpointsinthenewtariff

• itisasimpleassessmentmodel,whichconsistsofonetwo-hourexamination,withnonon-examinationassessment

• itiseasilyco-taughtwithOCR’sGCSE(9–1)Mathematicsqualifications.

Worthwhile

Research,internationalcomparisonsandengagementwithbothteachersandthewidereducationcommunityhavebeenusedtoenhancethereliability,validityandappealofourassessmenttasksinmathematics.

Itwillencouragetheteachingofinterestingmathematics,aimingformasteryleadingtopositiveexamresults.

Learner-focused

OCR’sspecificationandassessmentwillconsistofmathematicsfitforthemodernworldandpresentedinauthenticcontexts.

Itwillallowlearnerstodevelopmathematicalindependencebuiltonasoundbaseofconceptuallearningandunderstanding.

Teacher-centred

OCRwilltargetsupportandresourcestodevelopfluency,reasoningandproblemsolvingskills.

OCR’sassessmentwillbesolidanddependable,recognisingpositiveachievementincandidatelearningandability.

Dependable

OCR’shigh-qualityassessmentisbackedupbysoundeducationalprinciplesandabeliefthattheutility,richnessandpowerofmathematicsshouldbemadeevidentandaccessibletoalllearners.

Thereisanemphasisonlearningandunderstandingmathematicalconceptsunderpinnedbyasound,reliableandvalidassessment.


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1d. HowdoIfindoutmoreinformation?

IfyouarealreadyusingOCRspecificationsyoucancontactusat: www.ocr.org.uk

IfyouarenotalreadyaregisteredOCRcentrethenyoucanfindoutmoreinformationonthebenefitsofbecomingoneat:www.ocr.org.uk

Ifyouarenotyetanapprovedcentreandwouldliketobecomeonegoto:www.ocr.org.uk

Wanttofindoutmore?

GetintouchwithoneofOCR’sSubjectAdvisors:

Email:[email protected]

CustomerContactCentre:01223553998

Teachersupport:www.ocr.org.uk

http://www.ocr.org.uk



mailto:maths%40ocr.org.uk?subject=



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2 Thespecificationoverview

2a. OCR’sLevel3FSMQ:AdditionalMaths(6993)LearnerstakethemandatoryPaper1tobeawardedtheOCRLevel3FSMQ:AdditionalMaths

ContentOverview AssessmentOverview

Thesinglepaperwillassesscontent,detailedinsection2c,covering:

• Algebra

• Enumeration

• CoordinateGeometry

• PythagorasandTrigonometry

• Calculus

• NumericalMethods

• ExponentialsandLogarithms

Paper1

(01)*

100marks

2hours

Writtenpaper

Calculatorspermitted

100%

oftotal FSMQ

*Indicatesinclusionofsynopticassessment.


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2b. ContentofLevel3FSMQ:AdditionalMaths(6993)

ThisFSMQbuildsontheskills,knowledgeandunderstandingacquiredduringtheGCSE(9–1)course.Itconsistsoffourmain‘pure’mathematicstopics,eachofwhichcontainsan‘applied’dimension,andtwonumericaltopics,allunderpinnedbyanAlgebrasection.

Thecontentisarrangedbytopicareastatementsthateachhaveauniquereferencecode.Thecontentisseparatedinto7sections,however,linksshouldbemadeacrosssectionsandcentresarefreetoteachthecontentintheordermostappropriatetotheirlearners’needs.

Exemplificationofthecontentstatementsprovidesfurtherdetailoftherequirementsofthisspecification.Allexemplarscontainedinthespecificationundertheheading‘e.g.’areforillustrationonlyanddonotconstituteanexhaustivelist.Theheading‘i.e.’isusedtodenoteacompletelist.Fortheavoidanceofdoubtanitalicstatementinsquarebracketsindicatescontentwhichwillnotbetested.

Theexpectationisthatsomeassessmentitemswillrequirelearnerstousetwoormorecontentstatementswithoutfurtherguidance.Learnersareexpectedtohaveexploredtheconnectionsbetweendifferentareasofthespecification.

Learnersareexpectedtobeabletousetheirknowledgetoreasonmathematicallyandsolveproblemsbothwithinmathematicsandincontext.Contentthatiscoveredbyanystatementmayberequiredinreasoningorproblem-solvingtasksevenifthatisnotexplicitlystatedinthestatement.

UseofcalculatorsLearnersarepermittedtouseascientificorgraphicalcalculator.CalculatorsaresubjecttotherulesinthedocumentInstructions for Conducting Examinations,publishedannuallybyJCQ(www.jcq.org.uk).

Itisexpectedthatcalculatorsavailableintheassessmentwillincludeaniterativefunction,suchasanANSkey.

Allowablecalculatorscanbeusedforanyfunctiontheycanperform.

Whenusingcalculators,candidatesshouldbearinmindthefollowing.

1. Candidatesareadvisedtowritedownexplicitlyanyexpressions,includingintegrals,thattheyusethecalculatortoevaluate.

2. Candidatesareadvisedtowritedownthevaluesofanyparametersandvariablesthattheyinputintothecalculator.Candidatesarenotexpectedtowritedowndatatransferredfromquestionpapertocalculator.

3. Correctmathematicalnotation(ratherthan‘calculatornotation’)shouldbeused.Incorrectnotationmayresultinlossofmarks.

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Formulae Learnerswillbegivenformulaeineachassessmentonpage2oftheintegratedanswerbooklet.SeeSection5dforalistoftheseformulae.

Themeaningsofsomeinstructionsandwordsusedinthisspecification

ExactAnexactanswerisonewherenumbersarenotgiveninroundedform.Theanswerwilloftencontainanirrationalnumbersuchas 3 ,eorrandthesenumbersshouldbegiveninthatformwhenanexactanswerisrequired.Theuseoftheword‘exact’alsotellslearnersthatrigorous(exact)workingisexpectedintheanswertothequestion.e.g.Findtheexactsolutionof3x = 2 .Thecorrectanswerisx 3

2= or .x 0 6= o ,notx =0.67orsimilar.

ShowthatLearnersaregivenaresultandhavetoshowthatitistrue.Becausetheyaregiventheresult,theexplanationhastobesufficientlydetailedtocovereverystepoftheirworking.e.g.Showthatthecurvey x x2 12 132= - + has a stationarypoint(3,−5).Inthiscase,candidateswouldbeexpectedtoshowthattherewasaturningpointatx =3,bycalculusorcompletingthesquare,andthatwhen x =3theny =−5.Asketchofthecurvewouldnotbesufficient.

DetermineThiscommandwordindicatesthatjustificationshouldbegivenforanyresultsfound,includingworkingwhereappropriate.

Give,State,WritedownThesecommandwordsindicatethatneitherworkingnorjustificationisrequired.

InthisquestionyoumustshowdetailedreasoningWhenaquestionincludesthisinstruction,learnersmustgiveasolutionwhichleadstoaconclusionshowingadetailedandcompleteanalyticalmethod.Theirsolutionshouldcontainsufficientdetailtoallowthelineoftheirargumenttobefollowed.Thisisnotarestrictiononalearner’suseofacalculatorwhentacklingthequestion,e.g.forcheckingananswerorevaluatingafunctionatagivenpoint,butitisarestrictiononwhatwillbeacceptedasevidenceofacompletemethod.

Intheseexamplesvariationsinthestructureofthesolutionsarepossible(forexampleusingadifferentbaseforthelogarithmsinexample1),anddifferentintermediatestepsmaybegiven.

Example1:

Uselogarithmstosolvetheequation3 4x2 1 100=+ ,givingyouranswercorrectto3significantfigures.Theanswerisx =62.6,butthelearnermust include thestepslog log3 4x2 1 100=+ ,( ) log logx2 1 3 4100+ =andanintermediateevaluationstep,e.g.

.x2 1 126 18+ = ….Usingthesolvefunctiononacalculatortoskiponeofthesestepswouldnotresultinacompleteanalyticalmethod.

Example2:

Evaluate x x x4 1d3 20

1+ -y .

Theansweris 127 ,butthelearnermustincludeatleast

x x x41 4

34 3

0

1+ -8 B andthesubstitution 14

134+ - .

Justwritingdowntheanswerusingthedefiniteintegralfunctiononacalculatorwouldthereforenotbeawardedfullmarks.

Hence Whenaquestionusestheword‘hence’,itisanindicationthatthenextstepshouldbebasedonwhathasgonebefore.Theintentionisthatlearnersshouldstartfromtheindicatedstatement.e.g.Showthat( )x 1- isafactorof x x x2 7 63 2- - + . Hencesolvetheequation x x x2 7 6 03 2- - + = .

YoumayusetheresultWhenthisphraseisuseditindicatesagivenresultthatlearnerswouldnotnormallybeexpectedtoknowbutwhichmaybeusefulinansweringthequestion.Thephraseshouldbetakenaspermissive.Useofthegivenresultisnotrequired.


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PlotLearnersshouldmarkpointsaccuratelyonthegraphintheirintegratedanswerbooklet.Theywilleitherhavebeengiventhepointsorhavehadtocalculatethem.Theymayalsoneedtojointhemwithacurveorastraightline,ordrawalineofbestfitthroughthem.e.g.Plotthisadditionalpointonthescatterdiagram.

SketchLearnersshoulddrawadiagram,notnecessarilytoscale,showingthemainfeaturesofacurve.Thesearelikelytoincludeatleastsomeofthefollowing:

• turningpoints • asymptotes • intersectionwiththey-axis • intersectionwiththex-axis • behaviourforlargex(+or–).

Anyotherimportantfeaturesshouldalsobeshown.

e.g.Sketchthecurvewithequationy x x3 23= - + .

(–1,4)

(–2,0)

(0,2)

(1,0)

DrawLearnersshoulddrawtoanaccuracyappropriatetotheproblem.Theyarebeingaskedtomakeasensiblejudgementaboutthis.e.g.Drawalineofbestfittoestimatethegradient.

OthercommandwordsOthercommandwords,forexample‘explain’or‘calculate’,willhavetheirordinaryEnglishmeaning.

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2c. ContentofFSMQ:AdditionalMaths(01)

Content Learnersshouldbeableto Notes

Algebra(AL)

AlgebraicManipulation AL1 Knowandusealgebraicvocabularyandnotation. AL2 Simplifyexpressionsinvolvingalgebraicfractionsandsquareroots.

AL3 Performoperationswithpolynomials,includingaddition,subtraction,multiplicationanddivision.

AL4 Findlinearfactorsofapolynomial.AL5 Completethesquareofaquadraticpolynomial.

i.e.constant,coefficient,expression,equation,identity,index,variable,unknown,f(x). e.g.Simplify x x1

21

1--+

.

e.g.Simplify 125 , 12 27+ ,2 3

1+

.

e.g. xx x x

13 33 2

-- - - .

Includestheuseofthefactortheorem.( )ax bx c a x p q2 2/+ + + +

Applicationsofequations AL6 Setupandsolveproblemsleadingtolinear,quadraticandcubicequationsinoneunknown,andtosimultaneousequationsintwounknowns.

Problemscouldbesetinmathematicalornon-mathematicalcontexts.

Inequalities AL7 Manipulateinequalities.AL8 Setupandsolvelinearandquadraticinequalitiesalgebraicallyand

graphically.AL9 Illustratelinearinequalitiesintwovariables.

e.g. x y24 28 400G+ e.g.solve x3 2 1 51 1- -

i.e.theuseofappropriateshading.

Recurrencerelationships AL10 Understandandusenotationofrecurrencerelationshipstodescribeanddeterminesequences.

AL11 Userecurrencerelationshipsinmodelling.

e.g.x x an n1 = ++

e.g.x axn n1 =+

e.g.x x xn n n2 1= ++ +

e.g.modellingcompoundinterest.

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Enumeration(EN)

Binomialexpansion EN1 Understandandbeabletoapplythebinomialexpansionof( )a b n+ wherenisapositiveinteger.

e.g.Expand( )x2 3 5+ inascendingpowersofx .

Representation EN2 Constructandusetreediagrams,twowaytables,VennDiagramsorthebinomialdistributiontoenumerateoutcomes.

ProductRule EN3 Usetheproductruleforcountingnumbersofoutcomesofcombinedevents.

e.g.Numberofoutcomesrollingndiceis6n

e.g.Numberofarrangementsofndistinctobjectsisn! .

Permutations EN4 Enumeratethenumberofwaysofobtaininganorderedlinearsubset(permutation)ofrelementsfromasetofndistinctobjects.

e.g.Howmanywaysofawardingtwoprizesinagroupoftenpeople.IncludestheuseofthenotationnPr (

nPr).

Combinations EN5 Enumerateanunorderedsubset(combination)ofrelementsfromasetofndistinctobjects.

e.g.Howmanywaysarethereofchoosingtwopeopleoutofagroupoftentositonacommittee?IncludestheuseofthenotationnCr (

nCr).

Applications EN6 Solveproblemsaboutoutcomes,includingproblemsinthecontextofprobability.

e.g.Findtheprobabilityofobtainingatleasttwosixeswhenfivedicearerolled.

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CoordinateGeometry(twodimensionsonly)(CG)

Thestraightline CG1 Calculatethedistancebetweentwopoints.

CG2 Findthemid-pointofalinesegment.

e.g. ( ) ( )x x y y2 12

2 12- + - .

e.g. ,

x x y y2 2

1 2 1 2+ +c m .Thecoordinategeometryofcircles

CG3 Knowandusetheequationofacircle( ) ( )x y b ra 2 2 2- + - = ,where(a,b)isthecentreandristheradiusofthecircle.

e.g.A(1,1)andB(5,7)aretheendsofadiameterofthecircle.Showthattheequationofthecircleis( ) ( )x y3 4 132 2- + - = .

Graphs CG4 Sketchandplotlinear,polynomial,trigonometricandexponentialfunctions.

CG5 Know,understandandusegradient,intercept,tangentandnormalinproblemsinvolvingpointsthatcanbedefinedbyequationsandinequalities.

Applicationsinlinearprogramming

CG6 Expressrealsituationsintermsoflinearinequalities.CG7 Usegraphsoflinearinequalitiestosolve2-dimensional

maximisationandminimisationproblems.CG8 Knowthedefinitionofobjectivefunctionandbeabletofinditin

2-dimensionalcases.

e.g.Given x y4 7 561+ , x y6 3 541+ ,x 02 ,y 02findthemaximumvalueofx y+ .

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Pythagoras’TheoremandTrigonometry(PT)

Ratiosofanyangles PT1 Usethedefinitionsofsini ,cosiandtaniforanyangleandtheirgraphs.

PT2 Knowthesineandcosinerulesandbeabletoapplythem,includingtheambiguouscaseforsine.

Measuredindegreesonly.

e.g.InatriangleABC,AB=10 m,AC=8 mandangleB= 40°.FindthetwopossiblevaluesofangleC.

Trigonometricidentities PT3 Knowandusetheidentitytan cossin

/iii .

PT4 Knowandusetheidentitysin cos 12 2 /i i+ .

Trigonometricequations PT5 Solvesimpletrigonometricequationsingivenintervals. e.g.Solve .tan x2 0 5= for x0 360° °G G .

Applicationsinmodelling PT6 ApplyPythagoras’Theoremandtrigonometryto2-and3-dimensionalproblems.

e.g.Findtheangleofgreatestslope.

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Calculus(CA)

Differentiation CA1 Differentiatekxnwherenisapositiveintegeror0,andthesumofsuchfunctions.

CA2 Knowthatthegradientfunctiongivesthegradientofthecurveandmeasurestherateofchangeofywithx .

CA3 Knowthatthegradientofthefunctionisthegradientofthetangentatthatpoint.

CA4 Findtheequationofatangentandnormalatanypointonacurve.CA5 Usedifferentiationtofindstationarypointsonacurve.CA6 Determinethenatureofastationarypoint.CA7 Sketchacurvewithknownstationarypoints.

i.e.useofnotation xy

dd

, ( )xfl ,xo .

e.g.Findtheequationsofnormaltothecurvey x x2 33= - + atthepoint(1,2).

Integration CA8 Integratekxnwherenisapositiveintegeror0,andthesumofsuchfunctions.

CA9 Beawarethatintegrationisthereverseofdifferentiation.

CA10 Knowwhatismeantbyanindefiniteandadefiniteintegral.

CA11 Evaluatedefiniteintegrals.CA12 Findtheareabetweenacurve,twoordinatesandthex-axis.CA13 Findtheareabetweentwocurves.

y xdye.g.beabletofindtheequationofacurve,givenitsgradientfunctionandonepoint.Understandtheconstantofintegration.

y xda

by

( ) ( )x x x xf d g da

b

a

b-y y

Applicationtokinematics CA14 Usedifferentiationandintegrationwithrespecttotimetosolvesimpleproblemsinvolvingvariableacceleration.

CA15 Recognisethespecialcasewheretheuseofconstantaccelerationformulaeisappropriate.

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NumericalMethods(NM)

Solvingequations NM1 Solveequationsapproximatelybyconsideringthechangeofsign.NM2 Useasimpleiterativemethodtosolveequationsapproximately.NM3 Recognisewhenthesenumericalmethodsmayfail.

Gradientsoftangents NM4 Useachordtoestimategradientofatangenttoacurveatapoint.NM5 Recognisehowtoimproveanestimateforthegradientofacurve

atapoint.

Areaunderacurve NM6 Userectangularstripstoestimatetheareabetweenacurveandthex-axis.

NM7 Usetrapeziumruletoestimatetheareabetweenacurveandthex-axis.

NM8 Recognisewhetheranestimatewouldbeanoverorunderestimate,andunderstandhowtocalculateanimprovedestimate.

Formulawillbeprovided.

ApplicationsofNumericalmethods

NM9 Applynumericalmethodsincontextwhereappropriate. e.g.determinethevelocityfromdisplacement-timecurve.

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Exponentialsandlogarithms(EL)

Propertiesoftheexponentialfunction

EL1 Knowandusethefunctionkaxanditsgraph,whereaispositive.

Propertiesofthelogarithmicfunction

EL2 Knowandusethedefinitionoflogaxastheinverseofax .EL3 Understandandusethelawsoflogarithms. i.e.

• ( )log log logx y xy+ =

• log log logx y yx

- = b l • log logx n xn = .

Reductiontolinearform EL4 Convertequationsoftheformy kax= and y kxn= toalinearformusinglogarithms.

EL5 Estimatevaluesofk and aork and nfromgraphs.

Equationsinvolvingexponentials

EL6 Solveequationsoftheforma bx = fora 02 .EL7 Useexponentialsandlogarithmsinproblemsinvolvingexponential

growthanddecay.


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2d. Priorknowledge,learningandprogression

AlthoughtherearenopriorqualificationsrequiredinorderforlearnerstoenterfortheLevel3FSMQ:AdditionalMaths,learnersareexpectedtohaveathoroughknowledgeofthecontentoftheHighertierofGCSE(9–1)Mathematics.

TheLevel3FSMQ:AdditionalMathsprovidesthefoundationsonwhichalargenumberoflearnerscontinuethesubjectbeyondGCSE(9–1)level.ItsupportstheirmathematicalneedsacrossabroadrangeofothersubjectsatLevel3andprovidesabasisforsubsequentquantitativeworkinaverywiderangeofhighereducationcoursesandinemployment.ItalsosupportsthestudyofASandALevelMathematics,andFurtherMathematics.

TheLevel3FSMQ:AdditionalMathsprepareslearnersforfurtherstudyandemploymentinawiderangeofdisciplinesinvolvingtheuseofmathematics,includingSTEMdisciplines.

Somelearnersmaychoosetofollowthisqualificationinordertobroadentheircurriculumandtoconsolidatetheirinterestandunderstandingofmathematics.Alearnerwhohastakenthisqualificationis,bydesign,wellpreparedtocontinuemathematicsatASandALevel.

ThereareanumberofMathematicsspecificationsatOCR.Findoutmoreatwww.ocr.org.uk



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3 AssessmentofLevel3FSMQ:AdditionalMaths(6993)

3a. Formsofassessment

OCR’sLevel3FSMQ:AdditionalMathsconsistsofonecomponentthatisexternallyassessed.

Theexaminationconsistsofonetwo-hourpaper,whichassessesalloftheAssessmentObjectives.Thetotalnumberofmarksavailableintheexaminationpaperis100.Learnersanswerallthequestions.Theassessmenthasagradientofdifficultyandconsistsofamixofshortandlonganswerquestions.

Ineachquestion,learnersareexpectedtosupporttheiranswerswithappropriateworking.

Learnersarepermittedtouseascientificorgraphicalcalculatorinthisexamination.Calculatorsaresubjecttotherulesinthedocument:Instructions for conducting examinationspublishedannuallybyJCQ(www.jcq.org.uk).

Theassessmentwillcontainsomesynopticassessment,someextendedresponsequestionsandatleastoneunstructuredproblemsolvingquestion.Aformulaesheetwillbeincludedatthebeginningoftheexaminationpaper.

3b. AssessmentObjectives(AO)

TherearethreeAssessmentObjectivesinOCR’sLevel3FSMQ:AdditionalMaths.Thesearedetailedinthetablebelow.

AssessmentObjective

AO1

UseandapplystandardtechniquesLearnersshouldbeableto: • selectandcorrectlycarryoutroutineprocedures • usemathematicallanguageandnotationcorrectly.

AO2

Reason,interpretandcommunicatemathematicallyLearnersshouldbeableto: • constructrigorousmathematicalarguments • makedeductionsandinferences • explaintheirreasoning.

AO3

SolveproblemswithinmathematicsandinothercontextsLearnersshouldbeableto: • translateproblemsintomathematicalprocesses,includingmodelling • interpretsolutionstoproblemsintheiroriginalcontext • evaluatetheaccuracyandlimitationsofsolutions,includingtheoutcome(s)ofmodels.

http://www.jcq.org.uk


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3c. Teachingtime

GuidedLearningHours

TheFSMQ:AdditionalMathsisallocated30GuidedLearningHours(GLH)intotal.Guidedlearningindicatestheapproximateallocationofteachingtime.

However,thisisonlyaguide.Centreswithparticularlyablecandidatescoulddeliverthiscourseconsiderablyfaster.

TotalQualificationTime

TotalQualificationTime(TQT)isthetotalamountoftime,inhours,expectedtobespentbyalearnertoachieveaqualification.Itincludesbothguidedlearning

hours,listedabove,andhoursspentinpreparation,studyandassessment.TheTotalQualificationTimefortheFSMQ:AdditionalMathsis60hours.

TotalQualificationTime(%)

Guidedlearning 30hours(50%)

Independentlearning 30hours(50%)

AOweightingsinFSMQ:AdditionalMaths

Therelationshipbetweentheassessmentobjectivesandthecomponentsisshowninthefollowingtable:

Component %ofoverallFSMQ:AdditionalMaths(6993)

AO1 AO2 AO3

Paper1 54–58 20–24 20–24

3d. Assessmentavailability

TherewillbeoneexaminationseriesavailableeachyearinMay/Junetoalllearners.

Theexaminedcomponentmustbetakenattheendofthecourse.

ThisspecificationwillbecertificatedfromtheJune2019examinationseriesonwards.

3e. Retakingthequalification

Learnerscanretakethequalificationasmanytimesastheywish.


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3f. Assessmentofextendedresponse

Theassessmentmaterialsforthisqualificationprovidelearnerswiththeopportunitytodemonstratetheirabilitytoconstructanddevelopasustainedand

coherentlineofreasoning,andanymarksforextendedresponsesareintegratedintothemarkingcriteria.

3g. Synopticassessment

Mathematicsis,bynature,asynopticsubject.Theassessmentinthisspecificationallowslearnerstodemonstratetheunderstandingtheyhaveacquiredfromthecourseasawholeandtheirabilitytointegrateandapplythatunderstanding.Thislevelofunderstandingisneededforsuccessfuluseoftheknowledgeandskillsfromthiscourseinfuturelife,workandstudy.

TheLevel3FSMQ:AdditionalMathsallowslearnerstorevisitearlierlearningtaughtatHighertierGCSE(9–1)inamorechallengingcontext.

Intheexaminationpaper,learnerswillberequiredtointegrateandapplytheirunderstandinginordertoaddressproblemswhichrequirebothbreadthanddepthofunderstandinginordertoreachasatisfactorysolution.

Learnerswillbeexpectedtoreflectonandinterpretsolutions,drawingontheirunderstandingofdifferentaspectsofthecourse.

3h. Calculatingqualificationresults

Alearner’soverallqualificationgradefortheLevel3FSMQ:AdditionalMathswillbecalculatedfromthecomponenttaken.

Thismarkwillthenbecomparedtothequalificationlevelgradeboundariesfortherelevantexamseriestodeterminethelearner’soverallqualificationgrade.


4

4 Admin:whatyouneedtoknow

Theinformationinthissectionisdesignedtogiveanoverviewoftheprocessesinvolvedinadministeringthisqualification.AllofthefollowingprocessesrequireyoutosubmitsomethingtoOCRbyaspecificdeadline.

MoreinformationabouttheprocessesanddeadlinesinvolvedateachstageoftheassessmentcyclecanbefoundintheAdministrationareaoftheOCRwebsite.

OCR’s Admin overviewisavailableontheOCRwebsiteat:http://www.ocr.org.uk/administration

4a. Pre-assessment

Estimatedentries

Estimatedentriesareyourbestprojectionofthenumberoflearnerswhowillbeenteredforaqualificationinaparticularseries.

EstimatedentriesshouldbesubmittedtoOCRbythespecifieddeadline.Theyarefreeanddonotcommityourcentreinanyway.

Finalentries

FinalentriesprovideOCRwithdetaileddataforeachlearner,showingeachassessmenttobetaken.Itisessentialthatyouusethecorrectentrycode,consideringtherelevantentryrules.

FinalentriesmustbesubmittedtoOCRbythepublisheddeadlinesorlateentryfeeswillapply.

AlllearnerstakingLevel3FSMQ:AdditionalMathsmustbeenteredfor6993.

Entrycode

Title Component code

Componenttitle Assessment type

6993 AdditionalMaths 01 Paper1 ExternalAssessment

4b. Specialconsideration

Specialconsiderationisapost-assessmentadjustmenttomarksorgradestoreflecttemporaryinjury,illnessoranyotherindispositionatthetimetheassessmentwastaken.

DetailedinformationabouteligibilityforspecialconsiderationcanbefoundintheJCQpublicationA guide to the special consideration process (www.jcq.org.uk).



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4c. Externalassessmentarrangements

RegulationsgoverningexaminationarrangementsarecontainedintheJCQInstructions for conducting examinations(www.jcq.org.uk).

HeadofCentreAnnualDeclaration

TheHeadofCentreisrequiredtoprovideadeclarationtotheJCQaspartoftheannualNCNupdate,conductedintheautumnterm,toconfirmthatthecentreismeetingalloftherequirementsdetailedinthespecification.

AnyfailurebyacentretoprovidetheHeadofCentreAnnualDeclarationwillresultinyourcentrestatusbeingsuspendedandcouldleadtothewithdrawalofourapprovalforyoutooperateasacentre.

PrivateCandidates

PrivatecandidatesmayenterforOCRassessments.

Aprivatecandidateissomeonewhopursuesacourseofstudyindependentlybuttakesanexaminationorassessmentatanapprovedexaminationcentre.Aprivatecandidatemaybeapart-timestudent,someonetakingadistancelearningcourseorsomeonebeingtutoredprivately.TheymustbebasedintheUK.

PrivatecandidatesneedtocontactOCRapprovedcentrestoestablishwhethertheyarepreparedtohostthemasaprivatecandidate.ThecentremaychargeforthisfacilityandOCRrecommendsthatthearrangementismadeearlyinthecourse.FurtherguidanceforprivatecandidatesmaybefoundontheOCRwebsite: http://www.ocr.org.uk/students/private-candidates

4d. Resultsandcertificates

Gradescale

Level3FSMQ:AdditionalMathsisgradedonthescale:A,B,C,D,E,whereAisthehighest.LearnerswhofailtoreachtheminimumstandardforEwillbeUnclassified(U).

OnlysubjectsinwhichgradesAtoEareattainedwillberecordedoncertificates.

Results

Resultsarereleasedtocentresandlearnersforinformationandtoallowanyqueriestoberesolvedbeforecertificatesareissued.

Centreswillhaveaccesstothefollowingresultsinformationforeachlearner:

• thegradeforthequalification

• thetotalweightedmarkforthequalification(equaltotherawmarkforthecomponent).

Thefollowingsupportinginformationwillbeavailable:

• weightedmarkgradeboundariesforthequalification.

Untilcertificatesareissued,resultsaredeemedtobeprovisionalandmaybesubjecttoamendment.

Alearner’sfinalresultswillberecordedonanOCRcertificate.Thequalificationtitlewillbeshownonthecertificateas‘OCRLevel3FreeStandingMathematicsQualification:AdditionalMaths’.


http://www.ocr.org.uk/students/private-candidates


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4e. Post-resultsservices

Anumberofpost-resultsservicesareavailable:

• Enquiriesaboutresults–Intheeventofdissatisfactionwithalearner’sresultcentresmaysubmitanenquiryaboutresults.

• Missingandincompleteresults–Thisserviceshouldbeusedifanindividualsubjectresultforalearnerismissing,orifthelearnerhasbeenomittedentirelyfromtheresultssupplied.

• Accesstoscripts–Centrescanrequestaccesstomarkedscripts.

4f. Malpractice

Anybreachoftheregulationsfortheconductofexaminationsandnon-examassessmentworkmayconstitutemalpractice(whichincludesmaladministration)andmustbereportedtoOCRassoonasitisdetected.

DetailedinformationonmalpracticecanbefoundintheJCQpublicationSuspected Malpractice in Examinations and Assessments: Policies and Procedures(www.jcq.org.uk).



5

5 Appendices

5a. Overlapwithotherqualifications

ThefullGCSE(9–1)MathematicssubjectcriteriadefinedbyDfEisassumedknowledgeforthisqualification.ThecontentofthiscourseintroducesaspectsoftheASandALevelmathematicssubjectcriteriaofDfE.

Consequently,astudentwhohastakenthisqualificationis,bydesign,well-preparedtocontinuetomathematicsatASandALevel.TherearealsoaspectsofoptionalcontentfromASLevelFurtherMathematics.

5b. Accessibility

Reasonableadjustmentsandaccessarrangementsallowlearnerswithspecialeducationalneeds,disabilitiesortemporaryinjuriestoaccesstheassessmentandshowwhattheyknowandcando,withoutchangingthedemandsoftheassessment.Applicationsfortheseshouldbemadebeforetheexaminationseries.DetailedinformationabouteligibilityforaccessarrangementscanbefoundintheJCQAccess Arrangements and Reasonable Adjustment (www.jcq.org.uk).

TheLevel3FSMQ:AdditionalMathshasbeenreviewedinordertoidentifyanyfeaturewhichcoulddisadvantagelearnerswhoshareaprotectedCharacteristicasdefinedbytheEqualityAct2010.Allreasonablestepshavebeentakentominimiseanysuchdisadvantage.



5

5c. Mathematicalnotation

1 MiscellaneousSymbols

1.1 = isequalto

1.2 ! isnotequalto

1.3 / isidenticaltooriscongruentto

1.4 . isapproximatelyequalto

1.5 3 infinity

1.6 \ isproportionalto

1.7 ` therefore

1.8 a because

1.9 1 islessthan

1.10 G islessthanorequalto,isnotgreaterthan

1.11 2 isgreaterthan

1.12 H isgreaterthanorequalto,isnotlessthan

2 Operations

2.1 a+b aplusb

2.2 a–b aminusb

2.3 a × b, ab, a.b amultipliedbyb

2.4 ,a b ba

' a divided by b

2.5 a the(non-negative)squarerootofa

2.6 n! n factorial: ! ( )n n n 1 2 1…# # # #= - ,forpositiveintegersn;0!=1

2.7 nPr ,nPr !!

rn

2.8nrc m,nCr ,nCr thebinomialcoefficient ! ( ) !

!r n r

n-

fornon-negativeintegersn,r,andr nG


5

3 Functions

3.1 Dx anincrementofx

3.2 xy

dd thederivativeofywithrespecttox

3.3xy

dd

2

2 thesecondderivativeofywithrespecttox

3.4 xo thefirstderivativeofxwithrespecttot

3.5 xp thesecondderivativeofxwithrespecttot

3.6 y xdy theindefiniteintegralofywithrespecttox

3.7 y xda

by thedefiniteintegralofywithrespecttoxbetweenthelimitsx a= and x b=

4 ExponentialandLogarithmicFunctions

4.1 loga x logarithmtothebaseaofx

5 TrigonometricFunctions

5.1 sin,cos,tan thetrigonometricfunctions

5.2sin−1,cos−1,tan−1

arcsin,arccos,arctantheinversetrigonometricfunctions

5.3 ° degrees

6 ProbabilityandStatistics

6.1 A,B,C,etc. events

6.2 P(A) probabilityoftheeventA

6.3 Al complementoftheeventA

6.4 X,Y,R,etc. randomvariables

6.5 x,y,r,etc. valuesoftherandomvariablesX,Y,R,etc.

6.6 ,( ) ( )p xx XP = probabilityfunctionofthediscreterandomvariableX

6.7 + hasthedistribution

6.8 B(n,p) binomialdistributionwithparametersn and p,wherenisthenumberoftrialsandp istheprobabilityofsuccessinatrial

6.9 q q p1= - forbinomialdistribution

⎫⎬⎭


5

7 Mechanics

7.1 kg kilograms

7.2 m metres

7.3 km kilometres

7.4 m/s,m s−1 metrespersecond(velocity)

7.5 m/s2,m s−2 metrespersecondpersecond(acceleration)

7.6 t time

7.7 s displacement

7.8 u initialvelocity

7.9 v velocityorfinalvelocity

7.10 a acceleration


5

5d. MathematicalformulaeandidentitiesLearnersmustbeabletousethefollowingformulaeandidentitiesforFSMQ:AdditionalMathswithouttheseformulaeandidentitiesbeingprovided,eitherintheseformsorinequivalentforms.Theseformulaeandidentitiesmayonlybeprovidedwheretheyarethestartingpointforaprooforasaresulttobeproved.

QuadraticEquations

ax bx c 02 + + = hasrootsx ab b ac

242!

=- -

LawsofIndices

a a ax y x y/ +

a a ax y x y' / -

( )a ax y xy/

LawsofLogarithms

logx a n xna+= = fora 02 and x 02

( )log log logx y xya a a/+

log log logx y yx

a a a/- b l ( )log logk x xa a

k/

Trigonometry

InthetriangleABC

Sinerule: sin sin sinAa

Bb

Cc

= =

Cosinerule: cosa b c bc A22 2 2= + -

Area sinab C21

=

tan sincos/i

ii

sin cos 12 2 /i i+ +


5

Mensuration

CircumferenceandAreaofcircle,radiusranddiameterd:

C r d A r2 2r r r= = =

Pythagoras’Theorem:Inanyright-angledtrianglewherea,b and carethelengthsofthesidesandcisthehypotenuse:

c a b2 2 2= +

Areaofatrapezium ( )a b h21

= + ,wherea and barethelengthsoftheparallelsidesandhistheirperpendicularseparation.

Volumeofaprism=areaofcrosssection×length

Calculus

Differentiation

Function Derivative

xn nxn−1

( ) ( )x xf g+ ( ) ( )x xf g+l l

Integration

Function Integral

xn ,n x c n11 1n 1 !+

+ -+

( ) ( )x xf g+l l ( ) ( )x x cf g+ +

Areaunderacurve ( )y x y 0da

bH= y

Kinematics

Formotioninastraightlinewithvariableacceleration:

v ts

dd

= a tv

ts

dd

dd

2

2= =

s v td= y tv a d= y


5

Learnerswillbegiventhefollowingformulaesheetineachquestionpaper.

FormulaeFSMQ:AdditionalMaths(6993)

Binomialseries

( ) … …a b a a b a b a b bC C Cn n n n n n nr

n r r n1

12

2 2+ = + + + + + +- - - ,forpositiveintegers,n,

where ! ( ) !!n

r r n rnC Cn

r n r= = =-

c m ,r nG

Thebinomialdistribution

If ( , )X B n p+ then ( ) (1 )P X xnx p px n x= = - -c m

Numericalmethods

Trapeziumrule: {( ) ( … )}y x h y y y y y2da

bn n2

10 1 2 1. + + + + + -y ,whereh n

b a=-

Summaryofupdates

Date Section SummaryofupdatesJanuary2018 Throughout

specificationThequalificationhasbeenformattedandupdatedtoreflectthechangesinboththeGCSE(9–1)andA/ASLevelMathematicsqualifications,aswellasbringingtheAssessmentObjectivesinlinewiththoseatASLevel.Thespecificationhasnewmathematicalcontent(AL4,AL10,AL11,EN2–EN5,NM1–NM9,EL1–EL7)andamendedmathematicalcontent(PT2,PT6).ATQTvalue has been added.

Your checklist

Our aim is to provide you with all the information and support you need to deliver our specifications.

Bookmark ocr.org.uk/maths for all the latest resources, information and news on Free Standing Mathematics Qualification: Additional Maths

Be among the first to hear about support materials and resources as they become available – register for Free Standing Mathematics Qualification: Additional Maths updates at ocr.org.uk/updates

Find out about our professional development at cpdhub.ocr.org.uk

View our range of skills guides for use across subjects and qualifications at ocr.org.uk/skillsguides

Learn more about Active Results at ocr.org.uk/activeresults

Join our maths social network community for teachers at social.ocr.org.uk

http://www.ocr.org.uk/maths

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http://ocr.org.uk/i-want-to/download-past-papers/examcreator/

http://social.ocr.org.uk/groups/maths

Download high-quality, exciting and innovative Free Standing Mathematics Qualification: Additional Maths resources from ocr.org.uk/FSMQ

Free resources and support for our Free Standing Mathematics Qualification: Additional Maths, developed through collaboration between our Maths Subject Advisors, teachers and other subject experts, are available from our website. You can also contact our Maths Subject Advisors for specialist advice, guidance and support, giving you individual service and assistance whenever you need it.

Contact the team at: 01223 553998 [email protected] @OCR_maths

To stay up to date with all the relevant news about our qualifications, register for email updates at ocr.org.uk/updates

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Specification FREE STANDING MATHEMATICS … · FREE STANDING MATHEMATICS QUALIFICATION: ADDITIONAL...

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