OCR A-Level Math’s Questions and Answers Latest Update

OCR A-Level Math’s Questions and Answers
2025-2026 Latest Update
-ASnA=An/2A(2aA+A(n-1)d)
-ASnA=An/2A(aA+Al)AwhereAaAisAtheAfirstAtermAandAlAisAtheAlastAtermA-ACORRECTAANSWERS-
formulaAofAanAarithmeticAseries
theAsumAofAtheAtermsAofAanAarithmeticAsequenceA-ACORRECTAANSWERS-
whatAisAanAarithmeticAseries
-AUnA=AaA+A(n-1)d
-AaA=AtheAfirstAterm
-AdA=AtheAcommonAdifferenceA-ACORRECTAANSWERS-
nthAtermAofAanAarithmeticAsequence
-AUnA=Aar^(n-1)
-AaA=AfirstAterm
-ArA=AcommonAratioA-ACORRECTAANSWERS-nthAtermAofAaAgeometricAsequence
-ASnA=Aa(1-r^n)A/A1-r
-ASnA=Aa(r^nA-A1)A/Ar-1
whereArAdoesAnotAequalA1A-ACORRECTAANSWERS-
formulaAofAfirstAnAtermsAofAaAgeometricAsequence
theAsumAofAtheAvaluesAtendAtowardsAinfinityA-ACORRECTAANSWERS-divergentAsequence
-AtheAsumAofAtheAvaluesAtendAtowardsAaAspecificAnumber
-AitAisAonlyAconvergentAifA|r|<1A-ACORRECTAANSWERS-convergentAsequence
aA/A1-rA-ACORRECTAANSWERS-sumAtoAinfinityAofAaAgeometricAseries
A-ACORRECTAANSWERS-seriesAcanAbeAshownAusingAsigmaAnotation

-AdefinesAeachAtermAofAaAsequenceAasAaAfunctionAofAtheApreviousAterm
-
AtoAfindAtheAmembersAofAtheAsequenceAsubstituteAinAn=1,An=2A...AusingAtheApreviousAtermsA

givenA-ACORRECTAANSWERS-recurrenceArelationAofAformAUn+1A=Af(Un)
itAisAdecreasingA-ACORRECTAANSWERS-
ifAUn+1A<AUnAforAallAnA∈Aℕ,AwhatAisAtrueAofAtheAsequence
-AitAisAperiodic
-AmeansAthatAtheAtermsArepeatAinAaAcycle
-AkA=AtheAorderAofAtheAsequenceA(howAoftenAtheAtermsArepeat)A-ACORRECTAANSWERS-
ifAUn+kA=AUnAforAallAnA∈Aℕ,AwhatAisAtrueAofAtheAsequence
(x+y)(x-y)A-ACORRECTAANSWERS-x^2-y^2
*A(a-sqrt(b)A/Aa-sqrt(b))A-ACORRECTAANSWERS-
rationalisingAtheAdenominatorAofAe.g.A1/sqrt(b)+a
b^2A-A4acA>A0AhasA2AdistantArealAroots
B^2A-4acA=A0AhasAonArealArepeatedAroot
b^2A-A4acA<A0AhasAnoArealArootsA-ACORRECTAANSWERS-
usingAtheAdiscriminantAtoAfindAnumberAofAroots
ifAf(x)A=Aa(x+p)^2A+Aq,AthenAtheAturningApointAisA(-p,q)A-ACORRECTAANSWERS-
completingAtheAsquareAtoAfindAtheAturningApoint

, <AisAdottedAline
≤AisAsolidAlineA-ACORRECTAANSWERS-usingAlinesAtoArepresentA<AandA≤
x=0AandAy=0A-ACORRECTAANSWERS-whereAareAtheAasymptotesAofAyA=Ak/x
translationAupAbyAaAunitsA-ACORRECTAANSWERS-yA=Af(x)A+Aa
translationAleftAbyAaAunitsA-ACORRECTAANSWERS-yA=Af(x+a)
stretchAverticallyAbyAscaleAfactorAaA-ACORRECTAANSWERS-yA=Aaf(x)
stretchAbyAscaleAfactorA1/aAhorizontallyA-ACORRECTAANSWERS-yA=Af(ax)
reflectionAinAx-axisA-ACORRECTAANSWERS-yA=A-f(x)
reflectionAinAy-axisA-ACORRECTAANSWERS-yA=Af(-x)
mA=A(y2A-Ay1)/(x2A-Ax1)A-ACORRECTAANSWERS-calculatingAtheAgradientAwithA2Apoints
y-y1=m(x-x1)A-ACORRECTAANSWERS-anotherAwayAtoAcalculateAequationAofAaAline
y=A-(1/m)xA-ACORRECTAANSWERS-equationAofAlineAperpendicularAtoAyA=Amx
SqrtA((x2A-Ax1)^2A+A(y2A-Ay1)^2A)A-ACORRECTAANSWERS-
distanceAbetweenA(x1,y1)AandA(x2,y2)
x^2A+Ay^2A=Ar^2A-ACORRECTAANSWERS-equationAofAcircleAcentreA(0,0)
(x-a)^2A+A(y-b)^2A=Ar^2A-ACORRECTAANSWERS-equationAofAcircleAcentreA(a,b)
centre:A(-f,-g)
radius:AsqrtA(f^2A+Ag^2A-c)A-ACORRECTAANSWERS-
centreAandAradiusAofAx^2A+Ay^2A+A2fxA+A2gyA+AcA=A0
perpendicularA-ACORRECTAANSWERS-
aAtangentAtoAaAcircleAisA......AtoAtheAradiusAofAtheAcircleAatAtheApointAofAintersection
theAcentreAofAaAcircleA-ACORRECTAANSWERS-
theAperpendicularAbisectorAofAaAchordAwillAgoAthrough.....
aArightAangleA-ACORRECTAANSWERS-theAangleAinAaAsemicircleAisAalways
A-ACORRECTAANSWERS-ifA∠PRQA=A90°AthenARAliesAonAtheAcircleAwithAdiameterAPQ

-findAtheAequationsAofAtheAperpendicularAbisectorsAofA2AdifferentAchords
-findAtheAcoordinatesAofAtheAintersectionAofAtheAperpendicularAbisectorsA-
ACORRECTAANSWERS-findAtheAcentreAofAaAcircleAgivenAanyA3Apoints

ifAf(p)A=A0AthenA(x-p)AisAaAfactorAofAf(x)A-ACORRECTAANSWERS-factorAtheorem
startingAfromAknownAfactsAorAdefinitionsAthenAusingAlogicalAstepsAtoAreachAtheAdesiredAcon
clusionA-ACORRECTAANSWERS-proofAbyAdeduction
breakingAtheAstatementAintoAsmallerAcasesAandAprovingAeachAcaseAseparatelyA-
ACORRECTAANSWERS-proof AbyAexhaustion

anAexampleAthatAdoesAnotAworkAforAtheAstatementA-ACORRECTAANSWERS-
proofAbyAcounter-example
(n+1)thArowA-ACORRECTAANSWERS-
whichArowAofApascal'sAtriangleAgivesAtheAcoefficientsAofAtheAexpansionAofA(a+b)^n
nA*A(n-1)A*A(n-2)A*A...A*3A*A2A*A1A-ACORRECTAANSWERS-n!
n!/r!(n-r)!A-ACORRECTAANSWERS-nCr
a^nA+AnC1*a^n-1*bA+AnC2*a^n-2*b^2A+A...A+AnCr*a^n-r*b^rA+A...A+Ab^nA-
ACORRECTAANSWERS-binomialAexpansionAofA(a+b)^nAwithAnCr

A-ACORRECTAANSWERS-

ifAxAisAsmallAtheAfirstAfewAtermsAinAaAbinomialAexpansionAcanAbeAusedAtoAfindAanAapproxima
teAvalueAforAaAcomplicatedAexpression
a^2A=Ab^2A+Ac^2A-A2bcCosAA-ACORRECTAANSWERS-cosineArule
a/sinAA=Ab/sinBA=Ac/sinCA-ACORRECTAANSWERS-SineArule