Pearson Edexcel GCE
In AS Further Mathematics (8FM0) Paper 28 Decision Mathematics 2
Paper
Afternoon
■ ■
Further Mathematics
Advanced Subsidiary Further
Mathematics options 28: Decision
Mathematics 2 (Part of option K
only)
Mathematical Formulae and Statistical Tables (Green),
calculator, D2 Answer Book (enclosed)
Candidates may use any calculator permitted by Pearson regulations.
Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• Use black ink or ball‑point pen.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of the answer book with your name, centre
• Answer
number and candidate number.
all questions and ensure that your answers to parts of questions are
• Answer
clearly labelled.
the questions in the answer book provided
– there may be more space than you need.
• You should show sufficient working to make your methods clear. Answers without
•• Inexact
working may not gain full credit.
answers should be given to three significant figures unless otherwise stated.
Do not return the question paper with the D2 Answer Book.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The
total mark for this part of the examination is 40. There are 4 questions.
marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
Try to answer every question.
• Check your answers if you have time at the end. Turn over
,
,1.
C C
1 2
26 E
A
24 24
0 H
24
21 15
42 15 19
39 B 18 18
16 48
F 6
1 12 48
S 37 2 19
6
24 27 T
19 D 17 J
35 6
35 17
21 36
18 10 40
1
1
16 14
19 18 10
C
19
C1 G 26 26 K
C2
Figure 1
Figure 1 shows a capacitated, directed network of pipes. The number on
each arc represents the capacity of the corresponding pipe. The numbers in
circles represent a feasible flow from S to T.
(a) State the value of this flow.
(1)
(b) Explain why arcs CD and CG cannot both be saturated.
(1)
(c) Find the capacity of
(i) cut C1
(ii) cut C2
(2)
(d) Write down a flow augmenting route of weight 6 which saturates BF.
(1)
The flow augmenting route in part (d) is applied to give an increased flow.
(e) Prove that this increased flow is maximal.
(3)
(Total for Question 1 is 8 marks)
, 2. A team of 5 players, A, B, C, D and E, competes in a quiz. Each player must
answer one of 5 rounds, P, Q, R, S and T.
Each player must be assigned to exactly one round, and each round must be
answered by exactly one player.
Player B cannot answer round Q, player D cannot answer round T, and player
E cannot answer round R.
The number of points that each player is expected to earn in each round is
shown in the table.
P Q R S T
A 32 40 35 41 37
B 38 – 40 27 33
C 41 28 37 36 35
D 35 33 38 36 –
E 40 38 – 39 34
The team wants to maximise its total expected score.
The Hungarian algorithm is to be used to find the maximum total expected
score that can be earned by the 5 players.
(a) Explain how the table should be modified.
(2)
(b) (i) Reducing rows first, use the Hungarian algorithm to obtain an allocation
which maximises the total expected score.
(ii) Calculate the maximum total expected score.
(6)
(Total for Question 2 is 8 marks)
In AS Further Mathematics (8FM0) Paper 28 Decision Mathematics 2
Paper
Afternoon
■ ■
Further Mathematics
Advanced Subsidiary Further
Mathematics options 28: Decision
Mathematics 2 (Part of option K
only)
Mathematical Formulae and Statistical Tables (Green),
calculator, D2 Answer Book (enclosed)
Candidates may use any calculator permitted by Pearson regulations.
Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• Use black ink or ball‑point pen.
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of the answer book with your name, centre
• Answer
number and candidate number.
all questions and ensure that your answers to parts of questions are
• Answer
clearly labelled.
the questions in the answer book provided
– there may be more space than you need.
• You should show sufficient working to make your methods clear. Answers without
•• Inexact
working may not gain full credit.
answers should be given to three significant figures unless otherwise stated.
Do not return the question paper with the D2 Answer Book.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• The
total mark for this part of the examination is 40. There are 4 questions.
marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
Try to answer every question.
• Check your answers if you have time at the end. Turn over
,
,1.
C C
1 2
26 E
A
24 24
0 H
24
21 15
42 15 19
39 B 18 18
16 48
F 6
1 12 48
S 37 2 19
6
24 27 T
19 D 17 J
35 6
35 17
21 36
18 10 40
1
1
16 14
19 18 10
C
19
C1 G 26 26 K
C2
Figure 1
Figure 1 shows a capacitated, directed network of pipes. The number on
each arc represents the capacity of the corresponding pipe. The numbers in
circles represent a feasible flow from S to T.
(a) State the value of this flow.
(1)
(b) Explain why arcs CD and CG cannot both be saturated.
(1)
(c) Find the capacity of
(i) cut C1
(ii) cut C2
(2)
(d) Write down a flow augmenting route of weight 6 which saturates BF.
(1)
The flow augmenting route in part (d) is applied to give an increased flow.
(e) Prove that this increased flow is maximal.
(3)
(Total for Question 1 is 8 marks)
, 2. A team of 5 players, A, B, C, D and E, competes in a quiz. Each player must
answer one of 5 rounds, P, Q, R, S and T.
Each player must be assigned to exactly one round, and each round must be
answered by exactly one player.
Player B cannot answer round Q, player D cannot answer round T, and player
E cannot answer round R.
The number of points that each player is expected to earn in each round is
shown in the table.
P Q R S T
A 32 40 35 41 37
B 38 – 40 27 33
C 41 28 37 36 35
D 35 33 38 36 –
E 40 38 – 39 34
The team wants to maximise its total expected score.
The Hungarian algorithm is to be used to find the maximum total expected
score that can be earned by the 5 players.
(a) Explain how the table should be modified.
(2)
(b) (i) Reducing rows first, use the Hungarian algorithm to obtain an allocation
which maximises the total expected score.
(ii) Calculate the maximum total expected score.
(6)
(Total for Question 2 is 8 marks)
