Pearson Edexcel Level 3 GCE Further Mathematics Advanced PAPER 4D Decision Mathematics 2

Pearson Edexcel Level 3 GCE
R R R R




Paper
TimeR1RhourR30Rminutes
reference 9FM0/4D
Further Mathematics R



Advanced
PAPER 4D: Decision Mathematics 2
R R R R




YouRmustRhave:
MathematicalRFormulaeRandRStatisticalRTablesR(Green),Rcalculator,R
DecisionRMathematicsRAnswerRBookR(enclosed)

CandidatesRmayRuseRanyRcalculatorRpermittedRbyRPearsonRregulations.RCalculat
orsR mustR notR haveR theR facilityR forR symbolicR algebraR manipulation,RdifferentiationR
andR integration,R orR haveR retrievableR mathematicalR formulaeRstoredRinRthem.
Instructions
UseRblackRinkRorRball-pointRpen.

• IfRpencilRisRusedRforRdiagrams/sketches/graphsRitRmustRbeRdarkR(HBRorRB).RWrit
eRyourRanswersRforRthisRpaperRinRtheRDecisionRMathematicsRanswerRbookRprovi

• ded.
FillRinRtheRboxesRatRtheRtopRofRtheRanswerRbookRwithRyourRname,Rce
ntreRnumberRandRcandidateRnumber.

• DoR notR returnRtheR questionR paperR withR theRanswerR book.
AnswerRallRquestionsRandRensureRthatRyourRanswersRtoRpartsRofRquestionsRareRclearlyRlabell

• ed.
AnswerRtheRquestionsRinRtheRanswerRbookRprovided

• –RthereRmayRbeRmoreRspaceRthanRyouRneed.
YouR shouldR showR sufficientR workingR toR makeR yourR methodsR clear.R AnswersR withoutRworki

• ngRmayRnotRgainRfullRcredit.
InexactR answersR shouldRbeR givenR toR threeR significantRfiguresR unlessR otherwiseR stated.
Information
ARbookletR‘MathematicalRFormulaeRandRStatisticalRTables’RisRprovided.

• ThereRareR8RquestionsRinRthisRquestionRpaper.RTheRtotalRmarkRforRthisRpaperRisR75.RTh
eRmarksRforReachRquestionRareRshownRinRbrackets
–RuseRthisRasRaRguideRasRtoRhowRmuchRtimeRtoRspendRonReachRquestion.
Advice
ReadReachRquestionRcarefullyRbeforeRyouRstartRtoRanswerRit.R
TryRtoRanswerReveryRquestion.
• CheckRyourRanswersRifRyouRhaveRtimeRatRtheRend.
TurnRover


P72118A
©2022RPearsonREducationRLt
d.
1/1/1/

,1. FourRworkers,RA,RB,RCRandRD,RareRtoRbeRassignedRtoRfourRtasks,R1,R2,R3RandR4.REachRtas
kRmustRbeRassignedRtoRjustRoneRworkerRandReachRworkerRmustRdoRonlyRoneRtask.

TheRcostRofRassigningReachRworkerRtoReachRtaskRisRshownRinRtheRtableRbelow.RT

heRtotalRcostRisRtoRbeRminimised.

1 2 3 4
A 32 45 34 48
B 37 39 50 46
C 46 44 40 42
D 43 45 48 52


(a) ReducingRrowsRfirst,RuseRtheRHungarianRalgorithmRtoRobtainRanRallocationRthatRmini
misesRtheRtotalRcost.RYouRmustRmakeRyourRmethodRclearRandRshowRtheRtableRafterReac
hRstage.
(5)
(b) StateRtheRminimumRtotalRcost.
(1)
(TotalRforRQuestionR1RisR6Rmarks)

2. TheRgeneralRsolutionRofRtheRsecondRorderRrecurrenceRrelation

unR+R2R +R k1unR+R1R +R k2unR =R 0 nR 0
R




isRgivenRby

unR=R(AR+RBn)(–3)n

whereRARandRBRareRarbitraryRnon‑zeroRconstants.
(a) FindRtheRvalueRofRk1RandRtheRvalueRofR k2
(2)
GivenRthatR u0R=Ru1R=R1

(b) findRtheRvalueRofRAR andRtheRvalueRofRB.
(2)
(TotalRforRQuestionR2RisR4Rmarks)




2 P72118A

, 3. TheRtableRbelowRshowsRtheRtransportRoptions,RusualRtravelRtimes,RpossibleRdelayRtime
sRandRcorrespondingRprobabilitiesRofRdelayRforRaRjourney.RAllRtimesRareRinRminutes.


TransportRoption UsualRtravelRtime PossibleRdelayRtime ProbabilityRofRdelay

10 0.10
Car 52
25 0.02

15 0.05
Train 45
25 0.03

5 0.05
Coach 55
15 0.01


(a) DrawRaRdecisionRtreeRtoRmodelRtheRtransportRoptionsRandRtheRpossibleRoutcomes
. (5)


(b) StateRtheRminimumRexpectedRtravelRtimeRandRtheRcorrespondingRtransportRoptio
nRindicatedRbyRtheRdecisionRtree. (2)
(TotalRforRQuestionR3RisR7Rmarks)




P72118A 3
TurnRover