PEARSON EDEXCEL LEVEL 3 GCE MATHEMATICS
D D D D D D
PAPER 1/ 2 ADVANCED LEVEL PURE MATHS 2022/2
D D D D D D D
023
Pearson Edexcel Level 3 D D D
GCE Mathematics D
Advanced Level D
Paper 1 or 2: Pure Mathematics
D D D D D
Practice Paper A D D D Paper Reference(s)
D
Time: 2 hours
D D
9MA0/01 or 9MA0/02
D D
You must have:
D D
Mathematical Formulae and Statistical Tables, calculator
D D D D D
CandidatesDmayDuseDanyDcalculatorDpermittedDbyDPearsonDregulations.DCalculatorsDmustDnotDha
veDtheDfacilityDforDalgebraicDmanipulation,DdifferentiationDandDintegration,DorDhaveDretrievable
DmathematicalDformulaeDstoredDinDthem.
Instructions
• UseDblackDinkDorDball-pointDpen.
• IfDpencilDisDusedDforDdiagrams/sketches/graphsDitDmustDbeDdarkD(HBDorDB).
• AnswerDallDquestionsDandDensureDthatDyourDanswersDtoDpartsDofDquestionsDareDclearl
yDlabelled.
• AnswerDtheDquestionsDinDtheDspacesDprovidedD–DthereDmayDbeDmoreDspaceDthanDyouDneed.
• YouDshouldDshowDsufficientDworkingDtoDmakeDyourDmethodsDclear.DAnswersDwithoutDworkin
gDmayDnotDgainDfullDcredit.
• InexactDanswersDshouldDbeDgivenDtoDthreeDsignificantDfiguresDunlessDotherwiseDstated.
Information
• ADbookletD‘MathematicalDFormulaeDandDStatisticalDTables’DisDprovided.
• ThereDareD15DquestionsDinDthisDpaper.DTheDtotalDmarkDisD100.
• TheDmarksDforDeachDquestionDareDshownDinDbracketsD–
DuseDthisDasDaDguideDasDtoDhowDmuchDtimeDtoDspendDonDeachDquestion.
Advice
• ReadDeachDquestionDcarefullyDbeforeDyouDstartDtoDanswerDit.
• TryDtoDanswerDeveryDquestion.
• CheckDyourDanswersDifDyouDhaveDtimeDatDtheDend.
• IfDyouDchangeDyourDmindDaboutDanDanswer,DcrossDitDoutDandDputDyourDnewDanswerDandDan
yDworkingDunderneath.
, AnswerDALLDquestions.
k
1. ItDisDsuggestedDthatDtheDsequenc aDk =2D +1,DkD … producesDonlyDprimeDnumbers.
e 1
(a) ShowDthat a1, a2D and a4DproduceDprimeDnumbers.
(2Dmarks)
(b) ProveDbyDcounterDexampleDthatDtheDsequenceDdoesDnotDalwaysDproduceDaDprimeDnumber.
(2Dmarks)
2. FindD theD angleD thatD theD vectorDaD =4iD-D jD+D3kD makesD withD theD positiveD y-
axis. (3Dmarks)
æD xöD3 1
g(x)D=3sinD
∣ ∣ - 10 x-D1
3. èD 6D ,D–40D<DxD<D20,DxDisDinDradians.
æ ö
æD 1 1 ö ∣
xD= 6∣ 3DDarcsinD∣ +D
∣
è èD3D 30D ∣
(a) ShowDthatDtheDequationDg(x)D=D0DcanDbeDwrittenDas
x∣ (3Dmarks)
æ æD 1 1 ö ö
xn+1D=6∣D3D arcsin∣D + xDn∣D∣
è èD3 30 D∣D x0D =4
(b) UsingDtheDformula ,D ,D find,D toD 3D decimalD places,D theD valuesD ofD x1D ,
x2DandDx3.
(2Dmarks)
4.
TheD firstD 3D termsDofD aD geometricD sequenceD areD kD +D2,D4k,D2kD ,DkD >D0D.D FindD theD valueD o
2D
(4Dmarks)
fD k.
fD(x)D=Dx D +D2x D -D 29x D -D 47xD+D77
4 3 2
5. x2D -D 2xD-D 15
DDVD D WD
Px2D +DQx+DRD+ +
ShowDthatDfD(x)DcanDbeDwrittenDas x+D3 x-D5D andDfindDtheDvaluesDofDP,DQ,DR,DVDandDW.
(7Dmarks)
D D D D D D
PAPER 1/ 2 ADVANCED LEVEL PURE MATHS 2022/2
D D D D D D D
023
Pearson Edexcel Level 3 D D D
GCE Mathematics D
Advanced Level D
Paper 1 or 2: Pure Mathematics
D D D D D
Practice Paper A D D D Paper Reference(s)
D
Time: 2 hours
D D
9MA0/01 or 9MA0/02
D D
You must have:
D D
Mathematical Formulae and Statistical Tables, calculator
D D D D D
CandidatesDmayDuseDanyDcalculatorDpermittedDbyDPearsonDregulations.DCalculatorsDmustDnotDha
veDtheDfacilityDforDalgebraicDmanipulation,DdifferentiationDandDintegration,DorDhaveDretrievable
DmathematicalDformulaeDstoredDinDthem.
Instructions
• UseDblackDinkDorDball-pointDpen.
• IfDpencilDisDusedDforDdiagrams/sketches/graphsDitDmustDbeDdarkD(HBDorDB).
• AnswerDallDquestionsDandDensureDthatDyourDanswersDtoDpartsDofDquestionsDareDclearl
yDlabelled.
• AnswerDtheDquestionsDinDtheDspacesDprovidedD–DthereDmayDbeDmoreDspaceDthanDyouDneed.
• YouDshouldDshowDsufficientDworkingDtoDmakeDyourDmethodsDclear.DAnswersDwithoutDworkin
gDmayDnotDgainDfullDcredit.
• InexactDanswersDshouldDbeDgivenDtoDthreeDsignificantDfiguresDunlessDotherwiseDstated.
Information
• ADbookletD‘MathematicalDFormulaeDandDStatisticalDTables’DisDprovided.
• ThereDareD15DquestionsDinDthisDpaper.DTheDtotalDmarkDisD100.
• TheDmarksDforDeachDquestionDareDshownDinDbracketsD–
DuseDthisDasDaDguideDasDtoDhowDmuchDtimeDtoDspendDonDeachDquestion.
Advice
• ReadDeachDquestionDcarefullyDbeforeDyouDstartDtoDanswerDit.
• TryDtoDanswerDeveryDquestion.
• CheckDyourDanswersDifDyouDhaveDtimeDatDtheDend.
• IfDyouDchangeDyourDmindDaboutDanDanswer,DcrossDitDoutDandDputDyourDnewDanswerDandDan
yDworkingDunderneath.
, AnswerDALLDquestions.
k
1. ItDisDsuggestedDthatDtheDsequenc aDk =2D +1,DkD … producesDonlyDprimeDnumbers.
e 1
(a) ShowDthat a1, a2D and a4DproduceDprimeDnumbers.
(2Dmarks)
(b) ProveDbyDcounterDexampleDthatDtheDsequenceDdoesDnotDalwaysDproduceDaDprimeDnumber.
(2Dmarks)
2. FindD theD angleD thatD theD vectorDaD =4iD-D jD+D3kD makesD withD theD positiveD y-
axis. (3Dmarks)
æD xöD3 1
g(x)D=3sinD
∣ ∣ - 10 x-D1
3. èD 6D ,D–40D<DxD<D20,DxDisDinDradians.
æ ö
æD 1 1 ö ∣
xD= 6∣ 3DDarcsinD∣ +D
∣
è èD3D 30D ∣
(a) ShowDthatDtheDequationDg(x)D=D0DcanDbeDwrittenDas
x∣ (3Dmarks)
æ æD 1 1 ö ö
xn+1D=6∣D3D arcsin∣D + xDn∣D∣
è èD3 30 D∣D x0D =4
(b) UsingDtheDformula ,D ,D find,D toD 3D decimalD places,D theD valuesD ofD x1D ,
x2DandDx3.
(2Dmarks)
4.
TheD firstD 3D termsDofD aD geometricD sequenceD areD kD +D2,D4k,D2kD ,DkD >D0D.D FindD theD valueD o
2D
(4Dmarks)
fD k.
fD(x)D=Dx D +D2x D -D 29x D -D 47xD+D77
4 3 2
5. x2D -D 2xD-D 15
DDVD D WD
Px2D +DQx+DRD+ +
ShowDthatDfD(x)DcanDbeDwrittenDas x+D3 x-D5D andDfindDtheDvaluesDofDP,DQ,DR,DVDandDW.
(7Dmarks)
