CCEA GCSE Specification in Mathematics · 2019. 9. 26. · CCEA GCSE Mathematics from September...

GCSE

CCEA GCSE Specification in

Mathematics

For first teaching from September 2017For first assessment in Summer 2018For first award in Summer 2019Subject Code: 2210

Version 2: 8 June 2017

Version2:8June2017

Contents 1 Introduction 3 1.1 Aims 41.2 Keyfeatures 41.3 Priorattainment 41.4 Classificationcodesandsubjectcombinations

5

2 Specification at a Glance

6

3 Subject Content 8 3.1 UnitM1:FoundationTier 83.2 UnitM5:FoundationTierCompletionTest 143.3 UnitM2:FoundationTier 173.4 UnitM6:FoundationTierCompletionTest 203.5 UnitM3:HigherTier 223.6 UnitM7:HigherTierCompletionTest 243.7 UnitM4:HigherTier 263.8

UnitM8:HigherTierCompletionTest

27

4 Scheme of Assessment 29 4.1 Assessmentopportunities 294.2 Assessmentobjectives 294.3 Assessmentobjectiveweightings 304.4 Functionalmathematics 304.5 Reportingandgrading 314.6 Useofcalculators

32

5 Grade Descriptions

34

6 Curriculum Objectives 36 6.1 Cross-CurricularSkillsatKeyStage4 366.2 ThinkingSkillsandPersonalCapabilitiesatKeyStage4

38

7 Links and Support 40 7.1 Support 407.2 Examinationentries 407.3 Equalityandinclusion 407.4 Contactdetails 41 Summary of Changes Since First Issue 42

Version2:8June2017

Thisspecificationisavailableonlineatwww.ccea.org.uk

SubjectCodeQAN

2210603/1688/3

ACCEAPublication©2017

CCEAGCSEMathematicsfromSeptember2017

Version2:8June2017 3

1 Introduction ThisspecificationsetsoutthecontentandassessmentdetailsforourGCSEcourseinMathematics.Wehavedesignedthisspecificationtomeettherequirementsof:

NorthernIrelandGCSEDesignPrinciples; NorthernIrelandGCEandGCSEQualificationsCriteria;and NorthernIrelandSubjectCriteriaandRequirementsforMathematics.

FirstteachingisfromSeptember2017.WewillmakethefirstawardbasedonthisspecificationinSummer2019.Thisspecificationisaunitisedcourse.Theguidedlearninghours,asforallGCSEs,are120hours.ThespecificationsupportstheaimoftheNorthernIrelandCurriculumtoempoweryoungpeopletoachievetheirpotentialandtomakeinformedandresponsibledecisionsthroughouttheirlives,aswellasitsobjectives:

todeveloptheyoungpersonasanindividual; todeveloptheyoungpersonasacontributortosociety;and todeveloptheyoungpersonasacontributortotheeconomyandenvironment.Ifthereareanymajorchangestothisspecification,wewillnotifycentresinwriting.Theonlineversionofthespecificationwillalwaysbethemostuptodate;toviewanddownloadthispleasegotowww.ccea.org.uk



1.1 Aims Thisspecificationaimstoencouragestudentsto:

developfluentknowledge,skillsandunderstandingofmathematicalmethodsandconcepts;

acquire,selectandapplymathematicaltechniquestosolveproblems; reasonmathematically,makedeductionsandinferencesanddrawconclusions;and

comprehend,interpretandcommunicatemathematicalinformationinavarietyofformsappropriatetotheinformationandcontext.

1.2 Key features Thefollowingareimportantfeaturesofthisspecification.

ItoffersopportunitiestobuildontheskillsandcapabilitiesdevelopedthroughthedeliveryoftheNorthernIrelandCurriculumatKeyStage3.

ItprovidesastrongfoundationforprogressiontoGCSEFurtherMathematicsand/orASlevelMathematicsandforotherdisciplineswhereunderstandingandapplicationofmathematicsisessential.

Itgivesstudentstheappropriatemathematicalskills,knowledgeandunderstandingtohelpthemprogresstofurtheracademicandvocationalstudyandtoemployment.

Thisspecificationhastwotiers:FoundationandHigher. Eachtieroffersachoiceofunitsthataresuitedtoawiderangeofabilitiesandenablestudentstodemonstrateachievement.

AtFoundationTier,studentscanachieveaLevel1orLevel2inFunctionalMathematicsaswellasagradeinGCSEMathematics.

Theassessmentmodelenablesstudentstomonitortheirprogressandoffersopportunitiestoimprovetheirresults.

Eachassessmentunitgivesstudentsenoughtimetoconsidervariousproblem-solvingstrategiesandtodecideonthebestapproach.

1.3 Prior attainment Thisspecificationbuildsontheknowledge,understandingandskillsdevelopedthroughthestatutoryrequirementsforMathematics(includingFinancialCapability)intheNorthernIrelandCurriculumatKeyStage3.Studentsdonotneedtohavereachedaparticularlevelbeforebeginningtostudythisspecification.



1.4 Classification codes and subject combinations Everyspecificationhasanationalclassificationcodethatindicatesitssubjectarea.Theclassificationcodeforthisqualificationis2210. Pleasenotethatifastudenttakestwoqualificationswiththesameclassificationcode,schools,collegesanduniversitiesthattheyapplytomaytaketheviewthattheyhaveachievedonlyoneofthetwoGCSEs.ThesamemayoccurwithanytwoGCSEqualificationsthathaveasignificantoverlapincontent,eveniftheclassificationcodesaredifferent.Becauseofthis,studentswhohaveanydoubtsabouttheirsubjectcombinationsshouldcheckwiththeschools,collegesanduniversitiesthattheywouldliketoattendbeforebeginningtheirstudies.StudentswhoenterforthisGCSEmayalsoenterforGCSEFurtherMathematicsandGCSEStatisticsinthesameexaminationseries.



2 Specification at a Glance ThetablesbelowandonthenextpagesummarisethestructureofthisGCSEcourse.Allunitsaddressthethreeassessmentobjectivesand,whereappropriate,questionsmayrequirestudentstoknowanduseproblem-solvingstrategies.Eachwrittenpaperhasarangeofquestiontypes.Questionsaresetinbothmathematicalandnon-mathematicalcontexts.Studentstaketwounits,onefromM1,M2,M3orM4andonefromM5,M6,M7orM8.Toreceiveanaward,oneofthesemustbeacompletiontest.Recommendedpathwaysaresummarisedbelow. Foundation Tier Option 1

Content

Assessment

Weightings

Availability

UnitM1:FoundationTier

Externalwrittenexaminationwithcalculator1hour45mins

45% Summerfrom2018andJanuaryfrom2019

UnitM5:FoundationTierCompletionTest

Twoexternalwrittenexaminations:• Paper1withoutcalculator 1hour• Paper2withcalculator 1hour


Foundation Tier Option 2

Content

Assessment

Weightings

Availability

UnitM2:FoundationTier

Externalwrittenexaminationwithcalculator1hour45mins


UnitM6:FoundationTierCompletionTest

Twoexternalwrittenexaminations:• Paper1withoutcalculator1hour

• Paper2withcalculator 1hour




Higher Tier Option 1

Content

Assessment

Weightings

Availability

UnitM3:HigherTier

Externalwrittenexaminationwithcalculator2hours



Twoexternalwrittenexaminations:• Paper1withoutcalculator 1hour15mins• Paper2withcalculator 1hour15mins


Higher Tier Option 2

Content

Assessment

Weightings

Availability

UnitM4:HigherTier

Externalwrittenexaminationwithcalculator2hours

45% Summerfrom2018andJanuary2019


Twoexternalwrittenexaminations:• Paper1withoutcalculator 1hour15mins• Paper2withcalculator 1hour15mins


Studentsmusttakeatleast40percentoftheassessment(basedonunitweightings)attheendofthecourseasterminalassessment.



3 Subject Content Wehavedividedthiscourseintoeightunits.Thecontentofeachunitandtherespectivelearningoutcomesappearbelow.AnimportantelementoftherevisedGCSEMathematicsistheassessmentandreportingofFunctionalMathematicsintheFoundationTier.FunctionalMathematicsreferstotheskillsandabilitiesstudentsneedtodevelopasayoungpersonandasanindividual,asacontributortosocietyandasacontributortotheeconomyandenvironment.Theseskillsenablelearnerstooperateconfidently,effectivelyandindependentlyineducation,workandeverydaylife.3.1 Unit M1: Foundation Tier ThisunittargetsgradesD,E,FandGatGCSElevelandLevel1inFunctionalMathematics.

Content

LearningOutcomes

Numberandalgebra

Studentsshouldbeableto:

usethe4operationsappliedtopositiveandnegativeintegers,includingefficientwrittenmethods;

orderpositiveandnegativeintegers,decimalsandfractions;

usesymbols=,≠,<,>,and; usecalculatorseffectivelyandefficiently; understandanduseconventionalnotationforthepriorityofoperations,includingbrackets,powers,rootsandreciprocals;

recogniseanduserelationshipsbetweenoperations,includinginverseoperations;

useindexnotationforsquares,cubesandpowersof10; usetheconceptsandvocabularyoffactor,multiple,commonfactor,commonmultipleandprime;and

usethetermssquare,positiveandnegativesquareroot,cubeandcuberoot.



Content

LearningOutcomes

Numberandalgebra(cont.)


understandplacevalueanddecimalplaces;

read,writeandcomparedecimalsuptothreedecimalplaces;

add,subtract,multiplyanddividedecimalsupto3decimalplaces;

roundtoaspecifiedorappropriatedegreeofaccuracy,numberofdecimalplacesor1significantfigure,includingagivenpowerof10;

usecorrectdecimalnotationwhenworkingwithmoney; understandanduseequivalentfractions; writeasimplefractionasaterminatingdecimal; addandsubtractsimplefractionsandsimplemixednumbers;

calculateafractionofaquantity; expressonequantityasafractionofanother; understandthatpercentagemeansnumberofpartsper100;

calculateapercentageofaquantity; expressonequantityasapercentageofanother; calculatepercentageincrease/decrease;and useequivalencesbetweenfractions,decimalsandpercentagesinavarietyofcontexts.



Content

LearningOutcomes



calculatewithmoneyandsolvesimpleproblemsinthecontextoffinance,forexampleprofitandloss,discount,wagesandsalaries,bankaccounts,simpleinterest,budgeting,debt,annualpercentagerate(APR)andannualequivalentrate(AER);

distinguishthedifferentrolesthatlettersymbolsplayinalgebra,usingthecorrectnotation;

understandandusetheconceptsandvocabularyofexpressions,equations,formulae,inequalities,termsandfactors;

interpretsimpleexpressionsasfunctionswithinputsandoutputs;

simplifyandmanipulatealgebraicexpressionsbycollectingliketermsandmultiplyingaconstantoverabracket;

manipulatealgebraicexpressionsbytakingoutcommonfactorsthatareconstants;

writesimpleformulaeandexpressionsfromreal-lifecontexts;

substitutenumbersintoformulae(whichmaybeexpressedinwordsoralgebraically)andexpressions;

usestandardformulae; setupandsolvelinearequationsinoneunknown; workwithco-ordinatesinall4quadrants; recogniseandplotequationsthatcorrespondtostraightlinegraphsintheco-ordinateplane;and

constructandinterpretlineargraphsinrealworldcontexts.



Content

LearningOutcomes

Geometryandmeasures


useconventionaltermsandnotationssuchaspoints,lines,vertices,edges,parallellines,perpendicularlines,rightangles,polygons,regularpolygonsandpolygonswithreflectionand/orrotationsymmetries;

usethestandardconventionsforlabellingandreferringtothesidesandanglesofshapes;

drawdiagramsfromawrittendescription;

applythepropertiesofangles:- atapoint;- atapointonastraightline;and- verticallyopposite;

understandandusealternateandcorrespondinganglesonparallellines;

identifyandapplycircledefinitionsandproperties,includingcentre,radius,chord,diameterandcircumference;

applythepropertiesanddefinitionsoftrianglesandquadrilaterals,includingsquare,rectangle,parallelogram,trapezium,andkiteandrhombus;

identifypropertiesofthefaces,surfaces,edgesandverticesofcubes,cuboids,prisms,cylinders,pyramids,conesandspheres;

drawandinterpret2Drepresentationsof3Dshapes,forexamplenets,plansandelevations;

understandandusemetricunitsofmeasurement;

makesensibleestimatesofarangeofmeasures;

convertmetricmeasurementsfromoneunittoanother;and

solveproblemsinvolvinglength,area,volume/capacity,mass,time,andtemperature.



Content

LearningOutcomes

Geometryandmeasures(cont.)


measurelinesegmentsandanglesingeometricfigures; usecompoundmeasures/unitssuchasspeed,heartbeatsperminuteandmilespergallon;

calculateperimetersandareasoftrianglesandrectanglesandsimplecompoundshapesmadefromtrianglesandrectangles;

calculatecircumferencesandareasofcircles; calculatesurfaceareaandvolumesofcubesandcuboids;

Handlingdata understandandusethehandlingdatacycletosolveproblems;

understandwhatismeantbyasampleandapopulation; understandsimplerandomsamplingandtheeffectofsamplesizeonthereliabilityofconclusions;

designanexperimentorsurveytotesthypotheses; designdata-collectionsheets,distinguishingbetweendifferenttypesofdata;

identifypossiblesourcesofbias; sort,classifyandtabulatequalitative(categorical)dataanddiscreteorcontinuousquantitativedata,includingtheuseof2circleVenndiagramstosortdata;

extractdatafromprintedtablesandlists; designandusetwo-waytablesfordiscreteandgroupeddata; findmean,median,modeandrangefromalistofvaluesandunderstandtheiruses;and

calculatemeanfromanungroupedfrequencytableandidentifythemodeandmedian.



Content

LearningOutcomes

Handlingdata(cont.)


constructandinterpretawiderangeofgraphsanddiagramsincludingfrequencytablesanddiagrams,pictograms,barcharts,piecharts,linegraphs,frequencytreesandflowcharts,recognisingthatgraphsmaybemisleading;

examinedatatofindpatternsandexceptions; comparedistributionsandmakeinferences;and plotandinterpretscatterdiagramsandrecognisecorrelation.



3.2 Unit M5: Foundation Tier Completion Test ThisunittargetsgradesD,E,FandGatGCSElevel.StudentsshouldknowthecontentofUnitM1beforetakingthisunit.

Content

LearningOutcomes

Numberandalgebra


solveproblemsinvolvingwholenumbers,fractions,decimalsandpercentageswithoutacalculator;

estimateanswersandcheckcalculationsusingapproximationandestimation;

userationotation,includingreductiontoitssimplestformanditsvariouslinkstofractionnotation;

divideaquantityinagivenratio; applyratioandproportiontoreal-lifecontextsandproblemssuchasconversion,best-buy,comparison,scaling,mixing,concentrationsandexchangerates;

recogniseandusesequencesof,forexample,triangular,squareandcubenumbers;

generatetermsofasequenceusingterm-to-termoraposition-to-termrule;and

plotandinterpretgraphsmodellingrealsituations,forexampleconversiongraphs,distance/timegraphsandintersectingtravelgraphs.



Content

LearningOutcomes

Geometryandmeasures


interpretscalesonarangeofmeasuringinstrumentsandrecognisethecontinuousnatureofmeasureandapproximatenatureofmeasurement;

knowanduseimperialmeasuresstillincommonuseandtheirapproximatemetricequivalents;

useandinterpretmaps,scalefactorsandscaledrawings; usethesumofanglesinatriangle,forexampletodeducetheanglesuminanypolygon;

describeandtransform2Dshapesusingsingletransformations;

describeandtransform2Dshapesusingreflectionsaboutthexandy axes;

describeandtransform2Dshapesusingsinglerotationsabouttheorigin;

describeandtransform2Dshapesusingtranslations; describeandtransform2Dshapesusingenlargementsbyapositivewholenumberscalefactor;and

drawtrianglesandother2Dshapesusingarulerandprotractor.



Content

LearningOutcomes

Handlingdata Studentsshouldbeableto:

understandandusethevocabularyofprobability,includingnotionsofuncertaintyandrisk;

usethetermsfair,random,evens,certain,likely,unlikelyandimpossible;

understandandusetheprobabilityscalefrom0to1; listalloutcomesforsingleevents,andfortwosuccessiveevents;

applysystematiclistingstrategies; workoutprobabilitiesexpressedasfractionsordecimalsfromsimpleexperimentswithequallylikelyoutcomesandsimplecombinedevents;

identifydifferentmutuallyexclusiveoutcomesandknowthatthesumoftheprobabilitiesofalltheseoutcomesis1;

understandtheprobabilityofaneventnotoccurringisoneminustheprobabilitythatitoccurs;and

useprobabilitiestocalculateexpectation.



3.3 Unit M2: Foundation Tier ThisunittargetsgradesC*,C,D,E,FandGatGCSELevelandLevel2inFunctionalMathematics.StudentsshouldknowthecontentofUnitM1beforetakingthisunit.

Content

LearningOutcomes

Numberandalgebra


useindexnotationandindexlawsforpositive,wholenumberpowers;

usetheconceptsandvocabularyofdivisor,highestcommonfactor,least(lowest)commonmultipleandprimefactordecomposition;

add,subtract,multiplyanddividedecimalsofanysize; roundtoaspecifiedorappropriatenumberofsignificantfigures;

recognisethatrecurringdecimalsareexactfractionsandthatsomeexactfractionsarerecurringdecimals;

add,subtract,multiplyanddividefractions,includingmixednumbers;

usepercentageandrepeatedproportionalchange; calculatewithmoneyandsolveproblemsinafinancecontext,forexamplecompoundinterest,insurance,taxation,mortgagesandinvestments;

simplifyandmanipulatealgebraicexpressionsbymultiplyingasingletermoverabracket;and

manipulatealgebraicexpressionsbytakingoutcommonfactorsthatareterms.



Content

LearningOutcomes



setupandsolvelinearequationsinoneunknown,includingthosewiththeunknownonbothsidesoftheequationandequationsoftheform:

𝑥4+ 3 = 7

findthemidpointandlengthofalinegivenin2Dco-ordinates;

findandinterpretgradientsandinterceptsoflineargraphs,forexampleplotandinterpretthegraphofthecostofcarhireat£40perdayplusacostof20ppermile;

Geometryandmeasures

usecompoundmeasuresorunitssuchasdensity; calculateperimetersandareasofkite,parallelogram,rhombusandtrapezium;

calculateperimetersandareasofcompositeshapes; calculatevolumesofrightprisms;and usePythagoras’theoremin2Dproblems.



Content

LearningOutcomes

Handlingdata


use3circleVenndiagramstosortdata; estimatemeanfromagroupedfrequencydistribution; identifythemodalclassandthemedianclassfromagroupedfrequencydistribution;

drawand/oruselinesofbestfitbyeye,understandingwhattheselinesrepresent;

drawconclusionsfromscatterdiagrams; usetermssuchaspositivecorrelation,negativecorrelationandlittleornocorrelation;

interpolateandextrapolatefromdataandknowthedangersofdoingso;

identifyoutliers;and appreciatethatcorrelationdoesnotimplycausality.



3.4 Unit M6: Foundation Tier Completion Test ThisunittargetsgradesC*,C,D,E,FandGatGCSElevel.StudentsshouldknowthecontentofUnitsM1,M2andM5beforetakingthisunit.

Content

LearningOutcomes

Numberandalgebra


understandtheprinciplesofnumbersystems; convertnumbersfromdecimaltobinary(base2)andviceversa;

useindexlawsinalgebraforpositivepowers; usesystematictrialandimprovementtofindapproximatesolutionsofequationswherethereisnosimpleanalyticalmethodofsolvingthem;

solvelinearinequalitiesinonevariable,andrepresentthesolutionsetonanumberline;

changethesubjectofasimpleformula; findthenthtermofasequencewheretheruleislinear; solvetwolinearsimultaneousequationsgraphically;and generatepointsandplotgraphsofsimplequadraticfunctionsandusethesetofindapproximatesolutionsforpointsofintersectionwithlinesoftheform 𝑦 = ±𝑎only.



Content

LearningOutcomes

Geometryandmeasures


understandandusebearings; calculateandusethesumsoftheinteriorandexterioranglesofpolygons;

distinguishpropertiesthatarepreservedunderparticulartransformations;

describeandtransform2Dshapesusingreflectionsinlinesparalleltothexoryaxis;

describeandtransform2Dshapesusingrotationsaboutanypoint;

describeandtransform2Dshapesusingtranslations,toincludeusingvectornotation;

understandandusetheeffectofenlargementonperimeterandareaofshapes;

understandthetermcongruent; usethestandardrulerandcompassconstructions; identifythelociofpoints,includingreallifeproblems;

Handlingdata systematicallylistalloutcomesforsingleeventsandfortwosuccessiveevents;

understandanduseestimatesormeasuresofprobabilityfromrelativefrequency;

compareexperimentaldataandtheoreticalprobabilities;and

understandthatincreasingsamplesizegenerallyleadstobetterestimatesofprobability.



3.5 Unit M3: Higher Tier ThisunittargetsgradesB,C*,C,DandEatGCSElevel.StudentsshouldknowthecontentofUnitsM1andM2beforetakingthisunit.

Content

LearningOutcomes

Numberandalgebra


findtheleastcommonmultiples(LCM)andhighestcommonfactor(HCF)ofnumberswrittenastheproductoftheirprimefactors;

findtheoriginalquantity,giventheresultofaproportionalchange;

calculatetheupperandlowerboundsincalculationsinvolvingadditionandmultiplicationofnumbersexpressedtoagivendegreeofaccuracy;

knowthedifferencebetweenanequationandanidentity; multiplytwolinearexpressions; factorisequadraticexpressionsoftheform:

𝑥+ + 𝑏𝑥 + 𝑐

factoriseusingthedifferenceoftwosquares; addorsubtractalgebraicfractions,forexamplesimplify:

4𝑥 + 310

+6𝑥 − 55

simplify,multiplyanddividealgebraicfractionswithlinearorquadraticnumeratorsanddenominators;

setupandsolvelinearequationsoftheform:

4𝑥 + 310

+6𝑥 − 55

=132

• setupandsolvequadraticequationsusingfactors.



Content

LearningOutcomes



understandthattheform𝑦 = 𝑚𝑥 + 𝑐representsastraightlineandthat𝑚isthegradientofthelineand𝑐isthevalueofthe𝑦–intercept;

findtheequationofalinethroughtwogivenpointsorthroughonepointwithagivengradient;

understandandusethegradientsofparallellines;

Geometryandmeasures

identifyandapplycircledefinitionsandproperties,includingtangent,arc,sectorandsegment;

usecompoundmeasuresorunitssuchaspressure; solvemensurationproblemsthatinvolvearclengthandareaofsector,surfaceareaofacylinderandvolumeandsurfaceareaofaconeandsphere;

understandandusethetrigonometricratiosofsine,cosineandtangenttosolve2Dproblems,includingthoseinvolvinganglesofelevationanddepression;

Handlingdata calculatequartilesandinterquartilerangefromalistofvaluesandunderstandtheiruses;

constructandinterpretcumulativefrequencytablesandthecumulativefrequencycurve;

estimatethemedian,quartilesandinterquartilerangefromacumulativefrequencycurveanddisplayinformationusingboxplots;and

inferpropertiesofpopulationsordistributionsfromasampleandknowthelimitationsofdoingso.



3.6 Unit M7: Higher Tier Completion Test ThisunittargetsgradesB,C*,C,D,andEatGCSElevel.StudentsshouldknowthecontentofUnitsM1,M2,M3,M5andM6beforetakingthisunit.

Content

LearningOutcomes

Numberandalgebra


usesurdsandπinexactcalculations; useindexnotationandindexlawsforzero,positiveandnegativepowers;

interpret,orderandcalculatewithnumberswritteninstandardindexform;

useindexlawsinalgebraforintegerpowers; setupandsolvetwolinearsimultaneousequationsalgebraically;

solvelinearinequalitiesintwovariablesrepresentingthesolutionsetonagraph;

changethesubjectofaformula,includingcaseswhereapowerorrootofthesubjectappearsandcaseswherethesubjectappearsinmorethanoneterm;

findthenthtermofnon-linearsequences;

recognise,sketchandinterpretgraphsoflinearfunctions,quadraticfunctions,simplecubicfunctionsandthereciprocalfunction𝑦 = 𝑎𝑥with𝑥 ≠ 0;

generatepointsandplotgraphsofsimplequadraticfunctionsandusethesetofindapproximatesolutionsforpointsofintersectionwithlinesoftheform𝑦 = 𝑚𝑥 + 𝑐;and

setupequationsandsolveproblemsinvolvingdirectproportion,includinggraphicalandalgebraicrepresentations.



Content

LearningOutcomes

Geometryandmeasures


describeandtransform2Dshapesusingcombinedtransformations;

describeandtransform2Dshapesusingreflectionsinthelinesy=±x;

describeandtransform2Dshapesusingenlargementsbyafractionalscalefactor;

understandandusetheeffectofenlargementonthevolumeofsolids;

usetherelationshipbetweentheratiosoflengthsandareasofsimilar2Dshapes;

Handlingdata usetheproductruleforcounting:iftherearemwaysofdoingonetaskandforeachofthese,therearenwaysofdoinganothertask,thenthetotalnumberofwaysthetwotaskscanbedoneism × n;

knowwhentoaddormultiplytwoprobabilities:ifAandBaremutuallyexclusive,thentheprobabilityofAorBoccurringisP(A)+P(B),whereasifAandBareindependentevents,theprobabilityofAandBoccurringisP(A)×P(B);and

usetreediagramstorepresentsuccessiveeventsthatareindependent.



3.7 Unit M4: Higher Tier ThisunittargetsgradesA,B,C*andCwithanallowablegradeDatGCSElevel.TheA*gradeisawardedatsubjectlevelandisdependentonthetotalmarksgainedfromtheM4andM8assessmentunits.StudentsshouldknowthecontentofUnitsM1,M2,andM3beforetakingthisunit.

Content

LearningOutcomes

Numberandalgebra


calculatetheupperandlowerboundsincalculationsinvolvingsubtractionanddivisionofnumbersexpressedtoagivendegreeofaccuracy;

factorisequadraticexpressionsoftheform:

𝑎𝑥+ + 𝑏𝑥 + 𝑐

addorsubtractalgebraicfractionswithlineardenominators,forexamplesimplify:

2𝑥 + 2

+3

2𝑥 − 1

setupandsolveequationssuchas:2

𝑥 + 2+

32𝑥 − 1

= 1

setupandsolvequadraticequationsusingfactorsandtheformulawherethecoefficientof𝑥+ ≠ 1,andmorecomplexequations;

understandandusethegradientsofperpendicularlines;

Geometryandmeasures

solvemorecomplexmensurationproblems,forexamplefrustums;

understandandusecircletheorems;

Handlingdata understandandusestratifiedsamplingtechniques;and constructandinterprethistogramsforgroupedcontinuousdatawithunequalclassintervals.



3.8 Unit M8: Higher Tier Completion Test ThisunittargetsgradesA,B,C*andCwithanallowablegradeDatGCSElevel.TheA*gradeisawardedatsubjectlevelandisdependentonthetotalmarksgainedfromtheM4andM8assessmentunits.StudentsshouldknowthecontentofUnitsM1,M2,M3,M4,M5,M6andM7beforetakingthisunit.

Content

LearningOutcomes

Numberandalgebra


distinguishbetweenrationalandirrationalnumbers; changearecurringdecimaltoafraction; useindexnotationandindexlawsforinteger,fractionalandnegativepowers;

setup,solveandinterprettheanswersingrowthanddecayproblems,forexampleusetheformulaforcompoundinterest;

simplifynumericalexpressionsinvolvingsurds,includingtherationalisationofthedenominatorofafractionsuchas:

53 2

useindexlawsinalgebraforinteger,fractionalandnegativepowers;

setupandsolvetwosimultaneousequations,onelinearandonenon-linear;

recognise,sketchandinterpretgraphsofexponentialfunctions𝑦 = 𝑘:forpositivevaluesofk,forexamplegrowthanddecayrates;and

findtheintersectionpointsofthegraphsofalinearandquadraticfunction,knowingthatthesearetheapproximatesolutionsofthecorrespondingsimultaneousequationsrepresentingthelinearandquadraticfunctions,whichmayrequirealgebraicmanipulation.



Content

LearningOutcomes



interpretthegradientatapointonacurveastheinstantaneousrateofchange;

recogniseandusetheequationofacircle,centretheoriginandradiusr;

findtheequationofatangenttoacircleatagivenpointonthecircle;

setupequationsandsolveproblemsinvolvingindirectproportion,includinggraphicalandalgebraicrepresentations;

Geometryandmeasures

understandandusethesineandcosinerules;

calculatetheareaofatriangleusing𝐴 = 12 𝑎𝑏 sin 𝐶 ;

usePythagoras’theoremandtrigonometrytosolve2Dand3Dproblems;

enlarge2Dshapesusingnegativescalefactors; usetherelationshipbetweentheratiosoflengths,areasandvolumesofsimilar3Dshapes;

Handlingdata usethemostappropriatemethodwhensolvingcomplexprobabilityproblems;and

usetreediagramstorepresentsuccessiveeventsthatarenotindependent.



4 Scheme of Assessment 4.1 Assessment opportunities Fortheavailabilityofexaminationandassessment,seeSection2.Thisisaunitisedspecification;candidatesmustcompleteatleast40percentoftheoverallassessmentrequirementsattheendofthecourse,intheexaminationseriesinwhichtheyrequestafinalsubjectgrade.Thisistheterminalrule.Candidatesmayresitindividualassessmentunitsoncebeforecash-in.ThebetterofthetworesultswillcounttowardstheirfinalGCSEgradeunlessaunitisrequiredtomeetthe40percentterminalrule.Ifitis,themorerecentmarkwillcount(whetherornotitisthebetterresult).ResultsforindividualassessmentunitsremainavailabletocounttowardsaGCSEqualificationuntilwewithdrawthespecification.4.2 Assessment objectives Therearethreeassessmentobjectivesforthisspecification.AO1 Use and apply standard techniques Candidatesmust:

accuratelyrecallfacts,terminologyanddefinitions; useandinterpretnotationcorrectly;and accuratelycarryoutroutineproceduresorsettasksrequiringmulti-stepsolutions.AO2 Reason, interpret and communicate mathematically Candidatesmust:

makedeductions,inferencesanddrawconclusionsfrommathematicalinformation;

constructchainsofreasoningtoachieveagivenresult; interpretandcommunicateinformationaccurately; presentargumentsandproofs;and assessthevalidityofanargumentandcriticallyevaluateagivenwayofpresentinginformation.

AO3 Solve problems in mathematics and other contexts Candidatesmust:

translateproblemsinmathematicalornon-mathematicalcontextsintoaprocessoraseriesofmathematicalprocesses;

makeanduseconnectionsbetweendifferentpartsofmathematics; interpretresultsinthecontextofagivenproblem; evaluatemethodsusedandresultsobtained;and evaluatesolutionstoidentifyhowtheymayhavebeenaffectedbyassumptionsmade.



4.3 Assessment objective weightings ThetablebelowsetsouttheassessmentobjectiveweightingsforeachassessmentcomponentandtheoverallGCSEqualification.

AssessmentObjective

UnitWeighting(%)

FoundationTierM1andM5

orM2andM6

HigherTierM3andM7

orM4andM8

AO1 47–53 37–43

AO2 22–28 27–33

AO3 22–28 27–33

4.4 Functional mathematics Inthisspecification,thetermFunctionalMathematicsreferstotheskillsandabilitiesstudentsneedtodevelopasayoungpersonandasanindividual,asacontributortosocietyandasacontributortotheeconomyandenvironment.FunctionalMathematicsrequiresstudentstousemathematicseffectivelyinawiderangeofcontexts.Theintroductionoffunctionalmathematicsisaresponsetoemployers’perceptionsthatmanystudentsarenotachievingasufficientlyfirmgroundinginthebasics.UnitsM1andM2aredesignedtoassessthefunctionalelementsinMathematics.ThefollowingtabledetailsthespecificunitsthatweusetodeterminetheawardinFunctionalMathematics:

GCSEUnits FunctionalAwardAvailable

M1 Level1

M2 Level1orLevel2



4.5 Reporting and grading Wereporttheresultsofindividualassessmentunitsonauniformmarkscalethatreflectstheassessmentweightingofeachunit.EachunitinGCSEMathematicsistargetedataspecificgraderangeasshownbelow:

Assessmentunit Targetedunitgrades Comment

M1 D,E,FandG Level1FunctionalMathematicsawarded

M2 C*,C,D,E,FandG Level1orLevel2FunctionalMathematicsawarded

M3 B,C*,C,DandE

M4 A,B,C*,CandallowableD

A*awardedatqualificationlevelandisdependentontotalmarksgainedfromM4andM8assessmentunits

M5 D,E,FandG

M6 C*,C,D,E,FandG

M7 B,C*,C,DandE

M8 A,B,C*,CandallowableD

A*awardedatqualificationlevelandisdependentontotalmarksgainedfromM4andM8assessmentunits

CandidatesmayenteranyoneofUnitsM1,M2,M3orM4togetherwithanyoneofUnitsM5,M6orM8toreceiveaGCSEgrade.Seethetableonthenextpageforthemostcommoncombinations.Wedeterminethegradesawardedbyaggregatingtheuniformmarksthatcandidatesobtaininindividualassessmentunits.WeawardGCSEqualificationsonagradescalefromA*toG,withA*beingthehighest.Theninegradesavailableareasfollows:

Grade A* A B C* C D E F GIfcandidatesfailtoattainagradeGorabove,wereporttheirresultasunclassified(U).



Thefollowingtabledetailstheoverallqualificationgradesavailablewhenunitsarecombinedasspecifiedbelow:

AssessmentUnitCombinations

AvailableFinalGCSEGrades

Comment

M1andM5 D–G Allgradesinthisrangeareavailable.

M2andM6 C*–G Allgradesinthisrangeareavailable.

M3andM7 B–E Allgradesinthisrangeareavailable.

M4andM8 A*–D Allgradesinthisrangeareavailable.

ExaminationsforUnitsM1,M2,M3andM4takeplaceatthesametime,socandidatescantakeonlyoneexamination.Therefore,candidatesmayenteronlyoneoftheseexaminationsineachsession.CompletionassessmentUnitsM5,M6,M7andM8aretimetabledconcurrently,onadifferentdaytoM1,M2,M3andM4.ForbothFoundationandHigherTiercompletionassessmentunits,Paper2(withcalculator)takesplaceimmediatelyafterPaper1(withoutcalculator).FunctionalMathematicsTheachievementinFunctionalMathematicsisbasedonthecandidate’sperformanceinUnitsM1andM2.InUnitM1,recognitionisatLevel1andinM2atLevel1orLevel2.InUnitM2,whereacandidatedoesnotachieveaLevel2,Level1maybeawardediftherequiredstandardisreached.Thestandardrequiredtoachievealevelwillbebasedonaminimumrawmarkthresholdthatwesetforeachseries.FunctionalMathematicsisawardedwithinthecontextofGCSEstudyandisreportedwiththeresultsforGCSEMathematicsasa‘pass’ateitherLevel1orLevel2.ForcandidatesachievingFunctionalMathematicsatLevel2,thisachievementwillbereportedasanendorsementontheGCSEMathematicscertificate.Ifacandidatedoesnotachievealevel,thiswillnotbereported.4.6 Use of calculators CandidatesmustusecalculatorsinassessmentUnitsM1,M2,M3andM4andinPaper2ofeachCompletionTest(M5,M6,M7andM8).CandidatesmustnotusecalculatorsinPaper1ofeachCompletionTest.Calculatorsshouldhavethefollowingfunctions: +, −, x, ÷ , √, xy andsinglememory.Thesearetheminimumfunctionsrequired.



FortheHigherTierpapers,candidatesmustuseelectroniccalculatorswithtrigonometricandrelevantstatisticalfunctions.FortheFoundationTierpapers,candidatesmustuseelectroniccalculatorswithrelevantstatisticalfunctions.Calculatorsmustbe:

• suitableforuseonthedesk;• eitherbatteryorsolarpowered;and• freeoflids,casesandcoversthathaveprintedinstructionsorformulae.Calculatorsmustnot:

• bedesignedoradaptedtooffer:- languagetranslators;- symbolicalgebramanipulation;- symbolicdifferentiationorintegration;or- communicationwithothermachinesortheinternet;

• beborrowedfromanothercandidateduringanassessmentbyexaminationforanyreason;or

• haveretrievableinformationstoredinthem,including(butnotlimitedto):- databanks;- dictionaries;- mathematicalformulae;or- text.



5 Grade Descriptions Gradedescriptionsareprovidedtogiveageneralindicationofthestandardsofachievementlikelytohavebeenshownbycandidatesawardedparticulargrades.Thedescriptionsmustbeinterpretedinrelationtothecontentinthespecification;theyarenotdesignedtodefinethatcontent.Thegradeawardeddependsinpracticeupontheextenttowhichthecandidatehasmettheassessmentobjectivesoverall.Shortcomingsinsomeaspectsofcandidates’performanceintheassessmentmaybebalancedbybetterperformancesinothers.

Grade

Description

A Candidatescharacteristically:

• performproceduresaccurately;• interpretandcommunicatecomplexinformationaccurately;• makedeductionsandinferencesanddrawconclusions;• constructsubstantialchainsofreasoning,includingconvincingargumentsandformalproofs;

• generateefficientstrategiestosolvecomplexmathematicalandnon-mathematicalproblemsbytranslatingthemintoaseriesofmathematicalprocesses;

• makeanduseconnections,whichmaynotbeimmediatelyobvious,betweendifferentpartsofmathematics;

• interpretresultsinthecontextofthegivenproblem;and• criticallyevaluatemethods,arguments,resultsandtheassumptionsmade.

C Candidatescharacteristically:

• performroutinesingle-andmulti-stepprocedureseffectivelybyrecalling,applyingandinterpretingnotation,terminology,facts,definitionsandformulae;

• interpretandcommunicateinformationeffectively;• makedeductionsandinferencesanddrawconclusions;• constructchainsofreasoning,includingarguments;• generatestrategiestosolvemathematicalandnon-mathematicalproblemsbytranslatingthemintomathematicalprocesses,realisingconnectionsbetweendifferentpartsof mathematics;

• interpretresultsinthecontextofthegivenproblem;and• evaluatemethodsandresults.



Grade

Description

F Candidatescharacteristically:

• recallandusenotation,terminology,factsanddefinitions;• performroutineprocedures,includingsomemulti-stepprocedures;

• interpretandcommunicatebasicinformation;• makedeductionsandusereasoningtoobtainresults;• solveproblemsbytranslatingsimplemathematicalandnon-mathematicalproblemsintomathematicalprocesses;

• providebasicevaluationofmethodsorresults;and• interpretresultsinthecontextofthegivenproblem.



6 Curriculum Objectives ThisspecificationbuildsonthelearningexperiencesfromKeyStage3asrequiredforthestatutoryNorthernIrelandCurriculum.ItalsooffersopportunitiesforstudentstocontributetotheaimandobjectivesoftheCurriculumatKeyStage4,andtocontinuetodeveloptheCross-CurricularSkillsandtheThinkingSkillsandPersonalCapabilities.Theextentofthedevelopmentoftheseskillsandcapabilitieswillbedependentontheteachingandlearningmethodologyused.6.1 Cross-Curricular Skills at Key Stage 4

Communication


• communicatemeaning,feelingsandviewpointsinalogicalandcoherentmanner,forexamplebyusingappropriatemathematicallanguageandnotationinresponsetoopen-endedtasks,problems,structuredquestionsorexaminationquestions;

• makeoralandwrittensummaries,reportsandpresentations,takingaccountofaudienceandpurpose,forexamplethroughtheuseofvariedlearningactivitiesappliedtoawiderangeofcontextsthatrequirestudentstoorganiseandrecorddata,justifychoiceofstrategytosolveproblems,articulateprocesses,proofsetc.andprovidefeedbackfromcollaborativelearningactivities;

• participateindiscussions,debatesandinterviews,forexamplebysharingideas,investigatingmisconceptions,exploringalternativestrategies,justifyingchoiceofstrategy,negotiatingdecisionsandlisteningtoothers;

• interpret,analyseandpresentinformationinoral,writtenandICTformats,forexamplebydevelopingamathematicalsolutiontoaproblemandcommunicatingideas,strategiesandsolutions;and

• exploreandrespond,bothimaginativelyandcritically,toavarietyoftexts,forexamplebyusingopen-endedtasksandactivities.

UsingMathematics


• usemathematicallanguageandnotationwithconfidence,forexamplebycommunicatingtheirideasandfindingsmathematicallyinaconsistentandaccuratewaythroughtheuseofvocabulary,symbols,algebraand/orgraphicalrepresentationstojustifytheirconclusions;

• usementalcomputationtocalculate,estimateandmakepredictionsinarangeofsimulatedandreal-lifecontexts,forexamplebyusingappropriateapproximationstoestimatetheanswertoaproblem;and

• selectandapplymathematicalconceptsandproblem-solvingstrategiesinarangeofsimulatedandreal-lifecontexts,forexamplebytranslatingproblemsinmathematicalornon-mathematicalcontextsintoaprocessoraseriesofmathematicalprocesses.



UsingMathematics(cont.)


• interpretandanalyseawiderangeofmathematicaldata,forexamplebychoosingthemostappropriatemeasuresofcentrallocationanddispersiontocomparetwosetsofdata;

• assessprobabilityandriskinarangeofsimulatedandreal-lifecontexts,forexamplebyexploringthelinkbetweenprobabilityandexpectedfrequencytoinvestigateriskanditsimpactonlife;and

• presentmathematicaldatainavarietyofformatswhichtakeaccountofaudienceandpurpose,forexamplebychoosingthebesttypeofgraph,chartordiagramtopresenttheirfindings.

UsingICT

Studentsshouldbeabletomakeeffectiveuseofinformationandcommunicationstechnologyinawiderangeofcontextstoaccess,manage,selectandpresentinformation,includingmathematicalinformation,forexamplebyresearchingdataonline,analysingdataandworkingwithformulaeinspreadsheets,andusingvarioussoftwareapplicationstoexploregeometryandalgebraicfunctions.



6.2 Thinking Skills and Personal Capabilities at Key Stage 4

Self-Management


• planworkforexamplebyidentifyingappropriatestrategies,workingsystematicallyandpersistingwithopen-endedtasksandproblems;

• setpersonallearninggoalsandtargetstomeetdeadlinesforexamplebyidentifying,prioritisingandmanagingactionstodevelopcompetenceandconfidenceinmorechallengingmathematics;

• monitor,reviewandevaluatetheirprogressandimprovetheirlearning,forexamplethroughself-evaluatingtheirperformance,identifyingstrengthsandareasforimprovementandseekingsupportwhererequired;and

• effectivelymanagetheirtime,forexamplethroughplanning,prioritisingandminimisingdistractionstomeetdeadlinesthatteachersset.

WorkingwithOthers


• learnwithandfromothers,forexamplebyco-operating,engagingindiscussions,explainingideas,challengingandsupportingoneanother,creatingandsolvingeachother’squestionsandworkingcollaborativelytosharemethodsandresultsduringsmallgrouptasks;

• participateineffectiveteamsandacceptresponsibilityforachievingcollectivegoals,forexamplebyworkingtogetheronchallengingsmallgrouptaskswithsharedgoalsbutindividualaccountability;and

• listenactivelytoothersandinfluencegroupthinkinganddecision-making,takingaccountofothers’opinions,forexamplebyparticipatingconstructivelyinsmallgroupactivities,proposingpossibleproblem-solvingstrategiesandpresentingawellthoughtoutrationaleforoneapproach.



ProblemSolving


• identifyandanalyserelationshipsandpatterns,forexamplemakelinksbetweencauseandeffectsbycomparingdistributionandmakinginferenceinstatistics;

• proposejustifiedexplanations,forexamplebyprovingamathematicalstatementistrue;

• reason,formopinionsandjustifytheirviews;• analysecriticallyandassessevidencetounderstandhowinformationorevidencecanbeusedtoservedifferentpurposesoragendas,forexampleusingdatatomakepredictionsaboutthelikelihoodoffutureeventsoccurring;

• analyseandevaluatemultipleperspectives,forexamplemodellingreal-lifescenariosasmathematicsproblems;

• exploreunfamiliarviewswithoutprejudice;• weighupoptionsandjustifydecisions,forexampleusingthemostappropriatemethodtosolvecomplexmathematicalproblems;and

• applyandevaluatearangeofapproachestosolveproblemsinfamiliarandnovelcontexts,forexamplebychoosingtheappropriatediagrammaticmethodinprobabilityortheuseofPythagoras’theoreminthesolutionofproblemsinvolvingrightangledtriangles.

Thisrevisedspecificationhasincreasedemphasisonproblemsolving,whichwillrequirestudentstofurtherdeveloptheseskills.



7 Links and Support 7.1 Support Thefollowingresourcesareavailabletosupportthisspecification:

ourMathematicsmicrositeatwww.ccea.org.ukand specimenassessmentmaterials.Wealsointendtoprovide:

pastpapers; markschemes; ChiefExaminer’sreports; PrincipalModerator’sreports; guidanceonprogressionfromKeyStage3; planningframeworks; centresupportvisits; supportdaysforteachers; aresourcelist;and exemplificationofexaminationperformance.

7.2 Examination entries EntrycodesforthissubjectanddetailsonhowtomakeentriesareavailableonourQualificationsAdministrationHandbookmicrosite,whichyoucanaccessatwww.ccea.org.ukAlternatively,youcantelephoneourExaminationEntries,ResultsandCertificationteamusingthecontactdetailsprovided.7.3 Equality and inclusion Wehaveconsideredtherequirementsofequalitylegislationindevelopingthisspecificationanddesignedittobeasfreeaspossiblefromethnic,gender,religious,politicalandotherformsofbias.GCSEqualificationsoftenrequiretheassessmentofabroadrangeofcompetences.Thisisbecausetheyaregeneralqualificationsthatpreparestudentsforawiderangeofoccupationsandhigherlevelcourses.Duringthedevelopmentprocess,anexternalequalitypanelreviewedthespecificationtoidentifyanypotentialbarrierstoequalityandinclusion.Whereappropriate,wehaveconsideredmeasurestosupportaccessandmitigatebarriers.Wecanmakereasonableadjustmentsforstudentswithdisabilitiestoreducebarrierstoaccessingassessments.Forthisreason,veryfewstudentswillhaveacompletebarriertoanypartoftheassessment.



Itisimportanttonotethatwhereaccessarrangementsarepermitted,theymustnotbeusedinanywaythatunderminestheintegrityoftheassessment.YoucanfindinformationonreasonableadjustmentsintheJointCouncilforQualificationsdocumentAccessArrangementsandReasonableAdjustmentsavailableatwww.jcq.org.uk7.4 Contact details Ifyouhaveanyqueriesaboutthisspecification,pleasecontacttherelevantCCEAstaffmemberordepartment:

SpecificationSupportOfficer:NualaTierney(telephone:(028)90261200,extension2292,email:[email protected])

SubjectOfficer:JoeMcGurk(telephone:(028)90261200,extension2106,email:[email protected])

ExaminationEntries,ResultsandCertification(telephone:(028)90261262,email:[email protected])

ExaminerRecruitment(telephone:(028)90261243,email:[email protected])

Distribution(telephone:(028)90261242,email:[email protected])

SupportEventsAdministration(telephone:(028)90261401,email:[email protected])

Moderation(telephone:(028)90261200,extension2236,email:[email protected])

BusinessAssurance(ComplaintsandAppeals)(telephone:(028)90261244,email:[email protected]@ccea.org.uk).



Summary of Changes since First Issue (Mostrecentchangesareindicatedinredonthelatestversion)

RevisionHistoryNumber

DateofChange PageNumber ChangeMade

Version1 N/A N/A FirstissueVersion2 8June2017 6 Wordingchanged

CCEA GCSE Specification in Mathematics · 2019. 9. 26. · CCEA GCSE Mathematics from September...

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