Pearson Edexcel Level 3 GCE Further Mathematics Advanced Subsidiary Further Mathematics options

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PearsonTEdexcelTLevelT3TGCE

ThursdayT14TMayT20
20
Afternoon PaperTReferenceT 8FM0/2
8
FurtherTMathematics
AdvancedTTSubsidiaryTFurt
herTMathematicsToptionsT2
8:TDecisionTMathematicsT2T
(PartTofToptionTKTonly)
YouTmustThave:
MathematicalTFormulaeTandTStatisticalTTablesT(Green),Tcalcul
ator,TD2TAnswerTBookT(enclosed)


CandidatesTmayTuseTanyTcalculatorTallowedTbyTPearsonTregulations.T
CalculatorsTmustTnotThaveTtheTfacilityTforTsymbolicTalgebraTmanipul
ation,TdifferentiationTandTintegration,TorThaveTretrievableTmathematic
alTformulaeTstoredTinTthem.
I nstructions
•UseTblackTinkTorTball-pointTpen.
• IfTpencilTisTusedTforTdiagrams/sketches/graphsTitTmustTbeTdarkT(HBT
• orTB).TFillTinTtheTboxesTatTtheTtopTofTtheTD2TAnswerTBookTwithTy
ourTname,TcentreTnumberTandTcandidateTnumber.
• AnswerTallTquestionsTandTensureTthatTyourTanswersTtoTpartsTofTquesti
• onsTareT clearlyTlabelled.
AnswerTtheTquestionsTinTtheTD2TAnswerTBookTprovided
–TthereTmayTbeTmoreTspaceTthanTyouTneed.
• YouTshouldTshowTsufficientTworkingTtoTmakeTyourTmethodsTclear.TA
• nswersTwithoutTworkingTmayTnotTgainTfullTcredit.
InexactTanswersTshouldTbeTgivenTtoTthreeTsignificantTfiguresTunlessT
otherwiseTstated.
• DoTnotTreturnTtheTquestionTpaperTwithTtheTD2TAnswerTBook.
I nformation

••ATbookletT‘MathematicalTFormulaeTandTStatisticalTTables’TisTprovided.
• TheTtotalTmarkTforTthisTpartTofTtheTexaminationTisT40.TThereTareT4Tq
uestions.TTheTmarksTforTeachTquestionTareTshownTinTbrackets
–TuseTthisTasTaTguideTasTtoThowTmuchTtimeTtoTspendTonTeachTquestion.
Advice
•• ReadTeachTquestionTcarefullyTbeforeTyouTstartTtoTanswerTit.
• TryTtoTanswerTeveryTquestion.
CheckTyourTanswersTifTyouThaveTtimeTatTth
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r
eTend.
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©2020TPearsonTEducationTLtd.
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1.
C1 C2
A 18T 1 D
5
7 8 5
15T 1
5 0 13 10
12 10
29T 2 E
S 6 B 37T 3 T
2
17 7 12
14
x 12
23 y 18T 1
8
C 26T 2 F
C1 3 C2

FigureT1

FigureT 1T showsT aT capacitated,T directedT networkT ofT pipes.TTheT numberT onT eachT arcT represe
ntsT theTcapacityTofTtheTcorrespondingTpipe.TTheTnumbersTinTcirclesTrepresentTaTfeasibleTflowTfr
omTSTtoTT.

(a) (i)T FindTtheTvalueTofTx.

(ii)T FindTtheTvalueTofTy.
(2)

(b) ListTtheTsaturatedTarcs.
(1)

TwoTcuts,TC1T andTC2,TareTshownTinTFigureT1.

(c) FindTtheTcapacityTof

(i) C1

(ii) C2
(2)

(d) WriteTdownTaTflow‑augmentingTroute,TusingTtheTarcTCF,TthatTincreasesTtheTflowTbyTtwoTunits.
(1)

GivenTthatTtheTflowTthroughTtheTnetworkTisTincreasedTbyTtwoTunitsTusingTtheTrouteTfoundTinT(d),

(e) proveTthatTthisTnewTflowTisTmax
imal. (3)

(TotalTforTQuestionT1TisT9Tmarks)




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2. FourTworkers,TA,TB,TCTandTD,TareTeachTtoTbeTassignedTtoToneTofTfourTtasks,TP,T

Q,TRTandTS.TEachTworkerTmustTbeTassignedTtoToneTtask,TandTeachTtaskTmustTbeT

doneTbyTexactlyToneTworker.TWorkerTCTcannotTbeTassignedTtoTtaskTQ.

TheTamount,TinTpounds,TthatTeachTworkerTwouldTearnTwhenTassignedTtoTeachTtas
kTisTshownTinTtheTtableTbelow.


P Q R S

A 72 98 59 84

B 67 87 68 86

C 70 – 62 79

D 78 93 64 81


TheTHungarianTalgorithmTisTtoTbeTusedTtoTfindTtheTmaximumTtotalTamountTthatTcanTb
eTearnedTbyTtheTfourTworkers.

(a) ExplainThowTtheTtableTshouldTbeTmodifiedTsoTthatTtheTHungarianTalgorithmTmayTbeTapplied.
(2)

(b) ModifyTtheTtableTsoTthatTtheTHungarianTalgorithmTmayTbeTapplied.
(1)

(c) ReducingTrowsTfirst,TuseTtheTHungarianTalgorithmTtoTobtainTanTallocationTthatTmaximise
sTtheTtotalTearnings.TYouTshouldTexplainThowTanyTinitialTrowTandTcolumnTreductionsTw
ereTmadeTandTalsoThowTyouTdeterminedTifTtheTtableTwasToptimalTatTeachTstage.
(6)

(TotalTforTQuestionT2TisT9Tmarks)




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