PMT
Pearson Edexcel Level 3 GCE M M M M
Thursday 14 May 2020 M M M
Afternoon PaperM ReferenceM 8FM0/2
8
Further Mathematics M
Advanced Subsidiary Furth MM M
er Mathematics options 28:
M M M M
Decision Mathematics 2 (Par M M M
t of option K only)
M M M M
YouMmustMhave:
MathematicalMFormulaeMandMStatisticalMTablesM(Green),Mcalculat
or,MD2MAnswerMBookM(enclosed)
CandidatesMmayMuseManyMcalculatorMallowedMbyMPearsonMregulations.MCal
culatorsM mustM notM haveM theM facilityM forM symbolicM algebraM manipulation,M
differentiationMandMintegration,MorMhaveMretrievableMmathematicalMformu
laeMstoredMinMthem.
I nstructions
• Use black ink or ball-point pen.
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or
M M M M M
• B). Fill in the boxes at the top of the D2 Answer Book with your na
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M M
M
M
M
M
M M
M M M M M M M
M M
M
M
M
M
M
M M
M
M
me, centre number and candidate number.
• Answer all questions and ensure that your answers to parts of questions
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M
M
M
M
M
M
M M
M
M M M M M M
are clearly labelled.
• Answer
M M M
the questions in the D2 Answer Book provided
M M M M M M M M
– there may be more space than you need.
• You should show sufficient working to make your methods clear. Ans
M
M
M M
M
M
M
M M
M
M M
M M M M M M
• wers without working may not gain full credit.
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M
M
Inexact answers should be given to three significant figures unless ot
M
M
M
M
M
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M M M M
herwise stated.
• Do not return the question paper with the D2 Answer Book.
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M
M M M M M M M M
I nformation
••AThebooklet
M ‘Mathematical Formulae and Statistical Tables’ is provided.
M M M M M M M
• ions.total mark for this part of the examination is 40. There are 4 quest
M M
The marks for each question are shown in brackets
M M
M
M
M
M
M
M
M M
M
M
M M
M
M
M M M M M
–MuseMthisMasMaMguideMasMtoMhowMmuchMtimeMtoMspendMonMeachMquestion.
Advice
•• Read each question carefully before you start to answer it.
M M M M M M M M M
• Try to answer every question.
M M
Check your answers if you have time at the e
M M
M M
M M M M M M M
TurnMove
r
nd.
P62675A
©2020MPearsonMEducationMLtd.
1/1/1/1/1/1/1/
, PMT
1.
C1 C2
A 18M 1 D
5
7 8 5
15M 1
5 0 13 10
12 10
29M 2 E
S 6 B 37M 3 T
2
17 7 12
14
x 12
23 y 18M 1
8
C 26M 2 F
C1 3 C2
FigureM1
FigureM 1M showsM aM capacitated,M directedM networkM ofM pipes.M TheM numberM onM eachM arcM representsM theMc
apacityMofMtheMcorrespondingMpipe.MTheMnumbersMinMcirclesMrepresentMaMfeasibleMflowMfromMSMtoMT.
(a) (i)M FindMtheMvalueMofMx.
(ii)M FindMtheMvalueMofMy.
(2)
(b) ListMtheMsaturatedMarcs.
(1)
TwoMcuts,MC1M andMC2,MareMshownMinMFigureM1.
(c) FindMtheMcapacityMof
(i) C1
(ii) C2
(2)
(d) WriteMdownMaMflow‑augmentingMroute,MusingMtheMarcMCF,MthatMincreasesMtheMflowMbyMtwoMunits.
(1)
GivenMthatMtheMflowMthroughMtheMnetworkMisMincreasedMbyMtwoMunitsMusingMtheMrouteMfoundMinM(d),
(e) proveMthatMthisMnewMflowMisMmaxim
al. (3)
(TotalMforMQuestionM1MisM9Mmarks)
2
P62675A
, PMT
2. FourMworkers,MA,M B,MCM andMD,MareMeachMtoMbeM assignedMtoMoneMofMfourMtasks,MP,MQ,MRMandM
S.MEachMworkerMmustMbeMassignedMtoMoneMtask,MandMeachMtaskMmustMbeMdoneMbyMexactlyMone
M worker.MWorkerMCMcannotMbeMassignedMtoMtaskMQ.
TheMamount,MinMpounds,MthatMeachMworkerMwouldMearnMwhenMassignedMtoMeachMtaskMisMsho
wnMinMtheMtableMbelow.
P Q R S
A 72 98 59 84
B 67 87 68 86
C 70 – 62 79
D 78 93 64 81
TheMHungarianMalgorithmMisMtoMbeMusedMtoMfindMtheMmaximumMtotalMamountMthatMcanMbeMearnedM
byMtheMfourMworkers.
(a) ExplainMhowMtheMtableMshouldMbeMmodifiedMsoMthatMtheMHungarianMalgorithmMmayMbeMapplied.
(2)
(b) ModifyMtheMtableMsoMthatMtheMHungarianMalgorithmMmayMbeMapplied.
(1)
(c) ReducingMrowsMfirst,MuseMtheMHungarianMalgorithmMtoMobtainManMallocationMthatMmaximisesMtheMto
talMearnings.MYouMshouldMexplainMhowManyMinitialMrowMandMcolumnMreductionsMwereMmadeMandMal
soMhowMyouMdeterminedMifMtheMtableMwasMoptimalMatMeachMstage.
(6)
(TotalMforMQuestionM2MisM9Mmarks)
3
P62675A
TurnMover
Pearson Edexcel Level 3 GCE M M M M
Thursday 14 May 2020 M M M
Afternoon PaperM ReferenceM 8FM0/2
8
Further Mathematics M
Advanced Subsidiary Furth MM M
er Mathematics options 28:
M M M M
Decision Mathematics 2 (Par M M M
t of option K only)
M M M M
YouMmustMhave:
MathematicalMFormulaeMandMStatisticalMTablesM(Green),Mcalculat
or,MD2MAnswerMBookM(enclosed)
CandidatesMmayMuseManyMcalculatorMallowedMbyMPearsonMregulations.MCal
culatorsM mustM notM haveM theM facilityM forM symbolicM algebraM manipulation,M
differentiationMandMintegration,MorMhaveMretrievableMmathematicalMformu
laeMstoredMinMthem.
I nstructions
• Use black ink or ball-point pen.
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or
M M M M M
• B). Fill in the boxes at the top of the D2 Answer Book with your na
M
M M
M
M
M
M
M M
M M M M M M M
M M
M
M
M
M
M
M M
M
M
me, centre number and candidate number.
• Answer all questions and ensure that your answers to parts of questions
M
M
M
M
M
M
M
M M
M
M M M M M M
are clearly labelled.
• Answer
M M M
the questions in the D2 Answer Book provided
M M M M M M M M
– there may be more space than you need.
• You should show sufficient working to make your methods clear. Ans
M
M
M M
M
M
M
M M
M
M M
M M M M M M
• wers without working may not gain full credit.
M
M
M
Inexact answers should be given to three significant figures unless ot
M
M
M
M
M
M
M
M
M
M
M M M M
herwise stated.
• Do not return the question paper with the D2 Answer Book.
M M
M
M M M M M M M M
I nformation
••AThebooklet
M ‘Mathematical Formulae and Statistical Tables’ is provided.
M M M M M M M
• ions.total mark for this part of the examination is 40. There are 4 quest
M M
The marks for each question are shown in brackets
M M
M
M
M
M
M
M
M M
M
M
M M
M
M
M M M M M
–MuseMthisMasMaMguideMasMtoMhowMmuchMtimeMtoMspendMonMeachMquestion.
Advice
•• Read each question carefully before you start to answer it.
M M M M M M M M M
• Try to answer every question.
M M
Check your answers if you have time at the e
M M
M M
M M M M M M M
TurnMove
r
nd.
P62675A
©2020MPearsonMEducationMLtd.
1/1/1/1/1/1/1/
, PMT
1.
C1 C2
A 18M 1 D
5
7 8 5
15M 1
5 0 13 10
12 10
29M 2 E
S 6 B 37M 3 T
2
17 7 12
14
x 12
23 y 18M 1
8
C 26M 2 F
C1 3 C2
FigureM1
FigureM 1M showsM aM capacitated,M directedM networkM ofM pipes.M TheM numberM onM eachM arcM representsM theMc
apacityMofMtheMcorrespondingMpipe.MTheMnumbersMinMcirclesMrepresentMaMfeasibleMflowMfromMSMtoMT.
(a) (i)M FindMtheMvalueMofMx.
(ii)M FindMtheMvalueMofMy.
(2)
(b) ListMtheMsaturatedMarcs.
(1)
TwoMcuts,MC1M andMC2,MareMshownMinMFigureM1.
(c) FindMtheMcapacityMof
(i) C1
(ii) C2
(2)
(d) WriteMdownMaMflow‑augmentingMroute,MusingMtheMarcMCF,MthatMincreasesMtheMflowMbyMtwoMunits.
(1)
GivenMthatMtheMflowMthroughMtheMnetworkMisMincreasedMbyMtwoMunitsMusingMtheMrouteMfoundMinM(d),
(e) proveMthatMthisMnewMflowMisMmaxim
al. (3)
(TotalMforMQuestionM1MisM9Mmarks)
2
P62675A
, PMT
2. FourMworkers,MA,M B,MCM andMD,MareMeachMtoMbeM assignedMtoMoneMofMfourMtasks,MP,MQ,MRMandM
S.MEachMworkerMmustMbeMassignedMtoMoneMtask,MandMeachMtaskMmustMbeMdoneMbyMexactlyMone
M worker.MWorkerMCMcannotMbeMassignedMtoMtaskMQ.
TheMamount,MinMpounds,MthatMeachMworkerMwouldMearnMwhenMassignedMtoMeachMtaskMisMsho
wnMinMtheMtableMbelow.
P Q R S
A 72 98 59 84
B 67 87 68 86
C 70 – 62 79
D 78 93 64 81
TheMHungarianMalgorithmMisMtoMbeMusedMtoMfindMtheMmaximumMtotalMamountMthatMcanMbeMearnedM
byMtheMfourMworkers.
(a) ExplainMhowMtheMtableMshouldMbeMmodifiedMsoMthatMtheMHungarianMalgorithmMmayMbeMapplied.
(2)
(b) ModifyMtheMtableMsoMthatMtheMHungarianMalgorithmMmayMbeMapplied.
(1)
(c) ReducingMrowsMfirst,MuseMtheMHungarianMalgorithmMtoMobtainManMallocationMthatMmaximisesMtheMto
talMearnings.MYouMshouldMexplainMhowManyMinitialMrowMandMcolumnMreductionsMwereMmadeMandMal
soMhowMyouMdeterminedMifMtheMtableMwasMoptimalMatMeachMstage.
(6)
(TotalMforMQuestionM2MisM9Mmarks)
3
P62675A
TurnMover
