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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
55% Summerfrom2019andJanuaryfrom2020
Foundation Tier Option 2
Content
Assessment
Weightings
Availability
UnitM2:FoundationTier
Externalwrittenexaminationwithcalculator1hour45mins
45% Summerfrom2018andJanuaryfrom2019
UnitM6:FoundationTierCompletionTest
Twoexternalwrittenexaminations:• Paper1withoutcalculator1hour
• Paper2withcalculator 1hour
55% Summerfrom2019andJanuaryfrom2020
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Higher Tier Option 1
Content
Assessment
Weightings
Availability
UnitM3:HigherTier
Externalwrittenexaminationwithcalculator2hours
45% Summerfrom2018andJanuaryfrom2019
UnitM7:HigherTierCompletionTest
Twoexternalwrittenexaminations:• Paper1withoutcalculator 1hour15mins• Paper2withcalculator 1hour15mins
55% Summerfrom2019andJanuaryfrom2020
Higher Tier Option 2
Content
Assessment
Weightings
Availability
UnitM4:HigherTier
Externalwrittenexaminationwithcalculator2hours
45% Summerfrom2018andJanuary2019
UnitM8:HigherTierCompletionTest
Twoexternalwrittenexaminations:• Paper1withoutcalculator 1hour15mins• Paper2withcalculator 1hour15mins
55% Summerfrom2019andJanuaryfrom2020
Studentsmusttakeatleast40percentoftheassessment(basedonunitweightings)attheendofthecourseasterminalassessment.
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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.
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Content
LearningOutcomes
Numberandalgebra(cont.)
Studentsshouldbeableto:
understandplacevalueanddecimalplaces;
read,writeandcomparedecimalsuptothreedecimalplaces;
add,subtract,multiplyanddividedecimalsupto3decimalplaces;
roundtoaspecifiedorappropriatedegreeofaccuracy,numberofdecimalplacesor1significantfigure,includingagivenpowerof10;
usecorrectdecimalnotationwhenworkingwithmoney; understandanduseequivalentfractions; writeasimplefractionasaterminatingdecimal; addandsubtractsimplefractionsandsimplemixednumbers;
calculateafractionofaquantity; expressonequantityasafractionofanother; understandthatpercentagemeansnumberofpartsper100;
calculateapercentageofaquantity; expressonequantityasapercentageofanother; calculatepercentageincrease/decrease;and useequivalencesbetweenfractions,decimalsandpercentagesinavarietyofcontexts.
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Content
LearningOutcomes
Numberandalgebra(cont.)
Studentsshouldbeableto:
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.
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Content
LearningOutcomes
Geometryandmeasures
Studentsshouldbeableto:
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.
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Content
LearningOutcomes
Geometryandmeasures(cont.)
Studentsshouldbeableto:
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.
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Content
LearningOutcomes
Handlingdata(cont.)
Studentsshouldbeableto:
constructandinterpretawiderangeofgraphsanddiagramsincludingfrequencytablesanddiagrams,pictograms,barcharts,piecharts,linegraphs,frequencytreesandflowcharts,recognisingthatgraphsmaybemisleading;
examinedatatofindpatternsandexceptions; comparedistributionsandmakeinferences;and plotandinterpretscatterdiagramsandrecognisecorrelation.
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3.2 Unit M5: Foundation Tier Completion Test ThisunittargetsgradesD,E,FandGatGCSElevel.StudentsshouldknowthecontentofUnitM1beforetakingthisunit.
Content
LearningOutcomes
Numberandalgebra
Studentsshouldbeableto:
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.
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Content
LearningOutcomes
Geometryandmeasures
Studentsshouldbeableto:
interpretscalesonarangeofmeasuringinstrumentsandrecognisethecontinuousnatureofmeasureandapproximatenatureofmeasurement;
knowanduseimperialmeasuresstillincommonuseandtheirapproximatemetricequivalents;
useandinterpretmaps,scalefactorsandscaledrawings; usethesumofanglesinatriangle,forexampletodeducetheanglesuminanypolygon;
describeandtransform2Dshapesusingsingletransformations;
describeandtransform2Dshapesusingreflectionsaboutthexandy axes;
describeandtransform2Dshapesusingsinglerotationsabouttheorigin;
describeandtransform2Dshapesusingtranslations; describeandtransform2Dshapesusingenlargementsbyapositivewholenumberscalefactor;and
drawtrianglesandother2Dshapesusingarulerandprotractor.
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Content
LearningOutcomes
Handlingdata Studentsshouldbeableto:
understandandusethevocabularyofprobability,includingnotionsofuncertaintyandrisk;
usethetermsfair,random,evens,certain,likely,unlikelyandimpossible;
understandandusetheprobabilityscalefrom0to1; listalloutcomesforsingleevents,andfortwosuccessiveevents;
applysystematiclistingstrategies; workoutprobabilitiesexpressedasfractionsordecimalsfromsimpleexperimentswithequallylikelyoutcomesandsimplecombinedevents;
identifydifferentmutuallyexclusiveoutcomesandknowthatthesumoftheprobabilitiesofalltheseoutcomesis1;
understandtheprobabilityofaneventnotoccurringisoneminustheprobabilitythatitoccurs;and
useprobabilitiestocalculateexpectation.
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3.3 Unit M2: Foundation Tier ThisunittargetsgradesC*,C,D,E,FandGatGCSELevelandLevel2inFunctionalMathematics.StudentsshouldknowthecontentofUnitM1beforetakingthisunit.
Content
LearningOutcomes
Numberandalgebra
Studentsshouldbeableto:
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.
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Content
LearningOutcomes
Numberandalgebra(cont.)
Studentsshouldbeableto:
setupandsolvelinearequationsinoneunknown,includingthosewiththeunknownonbothsidesoftheequationandequationsoftheform:
!4 + 3 = 7
findthemidpointandlengthofalinegivenin2Dco-ordinates;
findandinterpretgradientsandinterceptsoflineargraphs,forexampleplotandinterpretthegraphofthecostofcarhireat£40perdayplusacostof20ppermile;
Geometryandmeasures
usecompoundmeasuresorunitssuchasdensity; calculateperimetersandareasofkite,parallelogram,rhombusandtrapezium;
calculateperimetersandareasofcompositeshapes; calculatevolumesofrightprisms;and usePythagoras’theoremin2Dproblems.
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Content
LearningOutcomes
Handlingdata
Studentsshouldbeableto:
use3circleVenndiagramstosortdata; estimatemeanfromagroupedfrequencydistribution; identifythemodalclassandthemedianclassfromagroupedfrequencydistribution;
drawand/oruselinesofbestfitbyeye,understandingwhattheselinesrepresent;
drawconclusionsfromscatterdiagrams; usetermssuchaspositivecorrelation,negativecorrelationandlittleornocorrelation;
interpolateandextrapolatefromdataandknowthedangersofdoingso;
identifyoutliers;and appreciatethatcorrelationdoesnotimplycausality.
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3.4 Unit M6: Foundation Tier Completion Test ThisunittargetsgradesC*,C,D,E,FandGatGCSElevel.StudentsshouldknowthecontentofUnitsM1,M2andM5beforetakingthisunit.
Content
LearningOutcomes
Numberandalgebra
Studentsshouldbeableto:
understandtheprinciplesofnumbersystems; convertnumbersfromdecimaltobinary(base2)andviceversa;
useindexlawsinalgebraforpositivepowers; usesystematictrialandimprovementtofindapproximatesolutionsofequationswherethereisnosimpleanalyticalmethodofsolvingthem;
solvelinearinequalitiesinonevariable,andrepresentthesolutionsetonanumberline;
changethesubjectofasimpleformula; findthenthtermofasequencewheretheruleislinear; solvetwolinearsimultaneousequationsgraphically;and generatepointsandplotgraphsofsimplequadraticfunctionsandusethesetofindapproximatesolutionsforpointsofintersectionwithlinesoftheform ' = ±*only.
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Content
LearningOutcomes
Geometryandmeasures
Studentsshouldbeableto:
understandandusebearings; calculateandusethesumsoftheinteriorandexterioranglesofpolygons;
distinguishpropertiesthatarepreservedunderparticulartransformations;
describeandtransform2Dshapesusingreflectionsinlinesparalleltothexoryaxis;
describeandtransform2Dshapesusingrotationsaboutanypoint;
describeandtransform2Dshapesusingtranslations,toincludeusingvectornotation;
understandandusetheeffectofenlargementonperimeterandareaofshapes;
understandthetermcongruent; usethestandardrulerandcompassconstructions; identifythelociofpoints,includingreallifeproblems;
Handlingdata systematicallylistalloutcomesforsingleeventsandfortwosuccessiveevents;
understandanduseestimatesormeasuresofprobabilityfromrelativefrequency;
compareexperimentaldataandtheoreticalprobabilities;and
understandthatincreasingsamplesizegenerallyleadstobetterestimatesofprobability.
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3.5 Unit M3: Higher Tier ThisunittargetsgradesB,C*,C,DandEatGCSElevel.StudentsshouldknowthecontentofUnitsM1andM2beforetakingthisunit.
Content
LearningOutcomes
Numberandalgebra
Studentsshouldbeableto:
findtheleastcommonmultiples(LCM)andhighestcommonfactor(HCF)ofnumberswrittenastheproductoftheirprimefactors;
findtheoriginalquantity,giventheresultofaproportionalchange;
calculatetheupperandlowerboundsincalculationsinvolvingadditionandmultiplicationofnumbersexpressedtoagivendegreeofaccuracy;
knowthedifferencebetweenanequationandanidentity; multiplytwolinearexpressions; factorisequadraticexpressionsoftheform:
!+ + ,! + - factoriseusingthedifferenceoftwosquares; addorsubtractalgebraicfractions,forexamplesimplify:
4! + 310 + 6! − 55
simplify,multiplyanddividealgebraicfractionswithlinearorquadraticnumeratorsanddenominators;
setupandsolvelinearequationsoftheform:
4! + 310 + 6! − 55 = 13
2
• setupandsolvequadraticequationsusingfactors.
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Content
LearningOutcomes
Numberandalgebra(cont.)
Studentsshouldbeableto:
understandthattheform' = 4! + -representsastraightlineandthat4isthegradientofthelineand-isthevalueofthe'–intercept;
findtheequationofalinethroughtwogivenpointsorthroughonepointwithagivengradient;
understandandusethegradientsofparallellines;
Geometryandmeasures
identifyandapplycircledefinitionsandproperties,includingtangent,arc,sectorandsegment;
usecompoundmeasuresorunitssuchaspressure; solvemensurationproblemsthatinvolvearclengthandareaofsector,surfaceareaofacylinderandvolumeandsurfaceareaofaconeandsphere;
understandandusethetrigonometricratiosofsine,cosineandtangenttosolve2Dproblems,includingthoseinvolvinganglesofelevationanddepression;
Handlingdata calculatequartilesandinterquartilerangefromalistofvaluesandunderstandtheiruses;
constructandinterpretcumulativefrequencytablesandthecumulativefrequencycurve;
estimatethemedian,quartilesandinterquartilerangefromacumulativefrequencycurveanddisplayinformationusingboxplots;and
inferpropertiesofpopulationsordistributionsfromasampleandknowthelimitationsofdoingso.
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3.6 Unit M7: Higher Tier Completion Test ThisunittargetsgradesB,C*,C,D,andEatGCSElevel.StudentsshouldknowthecontentofUnitsM1,M2,M3,M5andM6beforetakingthisunit.
Content
LearningOutcomes
Numberandalgebra
Studentsshouldbeableto:
usesurdsandπinexactcalculations; useindexnotationandindexlawsforzero,positiveandnegativepowers;
interpret,orderandcalculatewithnumberswritteninstandardindexform;
useindexlawsinalgebraforintegerpowers; setupandsolvetwolinearsimultaneousequationsalgebraically;
solvelinearinequalitiesintwovariablesrepresentingthesolutionsetonagraph;
changethesubjectofaformula,includingcaseswhereapowerorrootofthesubjectappearsandcaseswherethesubjectappearsinmorethanoneterm;
findthenthtermofnon-linearsequences;
recognise,sketchandinterpretgraphsoflinearfunctions,quadraticfunctions,simplecubicfunctionsandthereciprocalfunction' = *!with! ≠ 0;
generatepointsandplotgraphsofsimplequadraticfunctionsandusethesetofindapproximatesolutionsforpointsofintersectionwithlinesoftheform' = 4! + -;and
setupequationsandsolveproblemsinvolvingdirectproportion,includinggraphicalandalgebraicrepresentations.
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Content
LearningOutcomes
Geometryandmeasures
Studentsshouldbeableto:
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.
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3.7 Unit M4: Higher Tier ThisunittargetsgradesA,B,C*andCwithanallowablegradeDatGCSElevel.TheA*gradeisawardedatsubjectlevelandisdependentonthetotalmarksgainedfromtheM4andM8assessmentunits.StudentsshouldknowthecontentofUnitsM1,M2,andM3beforetakingthisunit.
Content
LearningOutcomes
Numberandalgebra
Studentsshouldbeableto:
calculatetheupperandlowerboundsincalculationsinvolvingsubtractionanddivisionofnumbersexpressedtoagivendegreeofaccuracy;
factorisequadraticexpressionsoftheform:
*!+ + ,! + - addorsubtractalgebraicfractionswithlineardenominators,forexamplesimplify:
2! + 2 +
32! − 1
setupandsolveequationssuchas:2
! + 2 +3
2! − 1 = 1
setupandsolvequadraticequationsusingfactorsandtheformulawherethecoefficientof!+ ≠ 1,andmorecomplexequations;
understandandusethegradientsofperpendicularlines;
Geometryandmeasures
solvemorecomplexmensurationproblems,forexamplefrustums;
understandandusecircletheorems;
Handlingdata understandandusestratifiedsamplingtechniques;and constructandinterprethistogramsforgroupedcontinuousdatawithunequalclassintervals.
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3.8 Unit M8: Higher Tier Completion Test ThisunittargetsgradesA,B,C*andCwithanallowablegradeDatGCSElevel.TheA*gradeisawardedatsubjectlevelandisdependentonthetotalmarksgainedfromtheM4andM8assessmentunits.StudentsshouldknowthecontentofUnitsM1,M2,M3,M4,M5,M6andM7beforetakingthisunit.
Content
LearningOutcomes
Numberandalgebra
Studentsshouldbeableto:
distinguishbetweenrationalandirrationalnumbers; changearecurringdecimaltoafraction; useindexnotationandindexlawsforinteger,fractionalandnegativepowers;
setup,solveandinterprettheanswersingrowthanddecayproblems,forexampleusetheformulaforcompoundinterest;
simplifynumericalexpressionsinvolvingsurds,includingtherationalisationofthedenominatorofafractionsuchas:
53 2
useindexlawsinalgebraforinteger,fractionalandnegativepowers;
setupandsolvetwosimultaneousequations,onelinearandonenon-linear;
recognise,sketchandinterpretgraphsofexponentialfunctions' = 9:forpositivevaluesofk,forexamplegrowthanddecayrates;and
findtheintersectionpointsofthegraphsofalinearandquadraticfunction,knowingthatthesearetheapproximatesolutionsofthecorrespondingsimultaneousequationsrepresentingthelinearandquadraticfunctions,whichmayrequirealgebraicmanipulation.
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Content
LearningOutcomes
Numberandalgebra(cont.)
Studentsshouldbeableto:
interpretthegradientatapointonacurveastheinstantaneousrateofchange;
recogniseandusetheequationofacircle,centretheoriginandradiusr;
findtheequationofatangenttoacircleatagivenpointonthecircle;
setupequationsandsolveproblemsinvolvingindirectproportion,includinggraphicalandalgebraicrepresentations;
Geometryandmeasures
understandandusethesineandcosinerules;
calculatetheareaofatriangleusing; = 12 *, sin ? ;
usePythagoras’theoremandtrigonometrytosolve2Dand3Dproblems;
enlarge2Dshapesusingnegativescalefactors; usetherelationshipbetweentheratiosoflengths,areasandvolumesofsimilar3Dshapes;
Handlingdata usethemostappropriatemethodwhensolvingcomplexprobabilityproblems;and
usetreediagramstorepresentsuccessiveeventsthatarenotindependent.