gcse maths designversion - amazing brains · ccea gcse mathematics from september 2017 version 2: 8...

Syllabus Snapshot

by Amazing Brains

Exam Body: CCEA

Level: GCSE Subject: Maths

CCEAGCSEMathematicsfromSeptember2017

Version2:8June2017 6

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


UnitM7:HigherTierCompletionTest

Twoexternalwrittenexaminations:• Paper1withoutcalculator 1hour15mins• Paper2withcalculator 1hour15mins


Higher Tier Option 2

Content

Assessment

Weightings

Availability

UnitM4:HigherTier

Externalwrittenexaminationwithcalculator2hours

45% Summerfrom2018andJanuary2019

UnitM8:HigherTierCompletionTest

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:

!4 + 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 ' = ±*only.



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:

!+ + ,! + - factoriseusingthedifferenceoftwosquares; addorsubtractalgebraicfractions,forexamplesimplify:

4! + 310 + 6! − 55

simplify,multiplyanddividealgebraicfractionswithlinearorquadraticnumeratorsanddenominators;

setupandsolvelinearequationsoftheform:

4! + 310 + 6! − 55 = 13

2

• setupandsolvequadraticequationsusingfactors.



Content

LearningOutcomes



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.



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,simplecubicfunctionsandthereciprocalfunction' = *!with! ≠ 0;

generatepointsandplotgraphsofsimplequadraticfunctionsandusethesetofindapproximatesolutionsforpointsofintersectionwithlinesoftheform' = 4! + -;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:

*!+ + ,! + - 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.



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,sketchandinterpretgraphsofexponentialfunctions' = 9:forpositivevaluesofk,forexamplegrowthanddecayrates;and

findtheintersectionpointsofthegraphsofalinearandquadraticfunction,knowingthatthesearetheapproximatesolutionsofthecorrespondingsimultaneousequationsrepresentingthelinearandquadraticfunctions,whichmayrequirealgebraicmanipulation.



Content

LearningOutcomes



interpretthegradientatapointonacurveastheinstantaneousrateofchange;

recogniseandusetheequationofacircle,centretheoriginandradiusr;

findtheequationofatangenttoacircleatagivenpointonthecircle;

setupequationsandsolveproblemsinvolvingindirectproportion,includinggraphicalandalgebraicrepresentations;

Geometryandmeasures

understandandusethesineandcosinerules;

calculatetheareaofatriangleusing; = 12 *, sin ? ;

usePythagoras’theoremandtrigonometrytosolve2Dand3Dproblems;

enlarge2Dshapesusingnegativescalefactors; usetherelationshipbetweentheratiosoflengths,areasandvolumesofsimilar3Dshapes;

Handlingdata usethemostappropriatemethodwhensolvingcomplexprobabilityproblems;and

usetreediagramstorepresentsuccessiveeventsthatarenotindependent.

gcse maths designversion - amazing brains · ccea gcse mathematics from september 2017 version 2: 8...

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