Pearson Edexcel Level 3 GCE Further Mathematics Advanced Subsidiary Further Mathematics options 28: De
Mathematics 2 (Part of option K only QP MAY 2024
Pearson Edexcel Level 3 GCE
Friday 17 May 2024
Afternoon
Paper
reference 8FM0/28
Further Mathematics
🞍 🞍
Advanced Subsidiary
Further Mathematics options
28: Decision Mathematics 2
(Part of option K only)
You must have:
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.
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fill in the boxes at the top of the answer book with your name,
centre number and candidate number.
• Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
• Answer 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
working may not gain full credit.
• Inexact 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.
total mark for this part of the examination is 40. There are 4 questions.
• The 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
P75678A
©2024 Pearson Education Ltd.
F:1/1/1/
,1.
C C
1
2
E
A 26
24 24
0 H
24
21 15
42 15 19
39 B 18 18
16 48
F 6
12 12 48
S 37 19
24 6
19 27 T
D 17 J
35 6
35 17
21 36
18 11 10 40
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 P75678A
, 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)
P75678A 3
Mathematics 2 (Part of option K only QP MAY 2024
Pearson Edexcel Level 3 GCE
Friday 17 May 2024
Afternoon
Paper
reference 8FM0/28
Further Mathematics
🞍 🞍
Advanced Subsidiary
Further Mathematics options
28: Decision Mathematics 2
(Part of option K only)
You must have:
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.
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fill in the boxes at the top of the answer book with your name,
centre number and candidate number.
• Answer all questions and ensure that your answers to parts of questions are
clearly labelled.
• Answer 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
working may not gain full credit.
• Inexact 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.
total mark for this part of the examination is 40. There are 4 questions.
• The 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
P75678A
©2024 Pearson Education Ltd.
F:1/1/1/
,1.
C C
1
2
E
A 26
24 24
0 H
24
21 15
42 15 19
39 B 18 18
16 48
F 6
12 12 48
S 37 19
24 6
19 27 T
D 17 J
35 6
35 17
21 36
18 11 10 40
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 P75678A
, 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)
P75678A 3
