AS LEVEL FURTHER MATHEMATICS: Actual May 2025 PAST Decision Mathematics 2:
Decision Mathematics 2. All Assessment Questions & Mark Scheme [Edexcel 8FM0/28]
Exam Resource Summary
The May 2025 Pearson Edexcel AS Level Further Mathematics (8FM0/28) – Paper: Decision
Mathematics 2 (Part of Option K only) – Merged Question Paper & Mark Scheme document combines
the official examination paper with its full mark scheme. This paper assesses students’ knowledge and
application of advanced decision-mathematics techniques, including assignment and network-flow
algorithms, game theory, dynamic programming, and recurrence relation modelling. The merged
format presents each question alongside its marking criteria, providing full transparency of examiner
expectations, mark allocation, and solution structure. This resource supports targeted revision, self-
assessment of problem-solving strategies, and the development of analytical and modelling skills
necessary for success in the May 2025 Edexcel AS Level Further Mathematics Paper 8FM0/28
examination.
• Turn over
,1. Five workers, A, B, C, D and E, are each to be assigned to one of five tasks, J, K, L,
M and N. Each task must be assigned to exactly one worker and each worker must do
exactly one task.
Worker C cannot do task L and worker D cannot do task K.
The profit, in pounds, that each worker will make while assigned to each task is shown
in the table below.
J K L M N
A 38 33 40 35 32
B 26 24 27 25 23
C 33 29 – 30 27
D 36 – 41 37 33
E 32 27 31 29 25
The Hungarian algorithm is to be used to find the maximum total profit that can be
earned by the five workers.
(a) Explain how the contents of the table must be modified to allow the algorithm to be
used.
(2)
(b) Reducing rows first, use the Hungarian algorithm to obtain the maximum total
profit. You should explain how any initial row and column reductions are made and
also how you determine if the table is optimal at each stage.
(7)
(Total for Question 1 is 9 marks)
2 P74076A
■■■■
, 2. C1
C
31 C2
A 31 G
0 31 39
8
70 20
32 20 21
63 72
45 21 80
T
D
S F
32 36 14 14
20 25
20
21
44
48 6 3
6
6
B
H C
C2 30 1
24 24 18
E
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 two conditions satisfied by a feasible flow.
(2)
(b) List the seven saturated arcs in Figure 1.
(1)
(c) Find the capacity of
(i) cut C1
(ii) cut C2
(2)
(d) Write down a flow-augmenting route that increases the flow by four units.
(1)
(e) Use the answer to part (d) to draw the resulting flow pattern on Diagram 1 in the
answer book.
(2)
(f) Prove that the answer to part (e) is a maximum flow.
(3)
(Total for Question 2 is 11 marks)
P74076A 3
■■■■ Turn over
Decision Mathematics 2. All Assessment Questions & Mark Scheme [Edexcel 8FM0/28]
Exam Resource Summary
The May 2025 Pearson Edexcel AS Level Further Mathematics (8FM0/28) – Paper: Decision
Mathematics 2 (Part of Option K only) – Merged Question Paper & Mark Scheme document combines
the official examination paper with its full mark scheme. This paper assesses students’ knowledge and
application of advanced decision-mathematics techniques, including assignment and network-flow
algorithms, game theory, dynamic programming, and recurrence relation modelling. The merged
format presents each question alongside its marking criteria, providing full transparency of examiner
expectations, mark allocation, and solution structure. This resource supports targeted revision, self-
assessment of problem-solving strategies, and the development of analytical and modelling skills
necessary for success in the May 2025 Edexcel AS Level Further Mathematics Paper 8FM0/28
examination.
• Turn over
,1. Five workers, A, B, C, D and E, are each to be assigned to one of five tasks, J, K, L,
M and N. Each task must be assigned to exactly one worker and each worker must do
exactly one task.
Worker C cannot do task L and worker D cannot do task K.
The profit, in pounds, that each worker will make while assigned to each task is shown
in the table below.
J K L M N
A 38 33 40 35 32
B 26 24 27 25 23
C 33 29 – 30 27
D 36 – 41 37 33
E 32 27 31 29 25
The Hungarian algorithm is to be used to find the maximum total profit that can be
earned by the five workers.
(a) Explain how the contents of the table must be modified to allow the algorithm to be
used.
(2)
(b) Reducing rows first, use the Hungarian algorithm to obtain the maximum total
profit. You should explain how any initial row and column reductions are made and
also how you determine if the table is optimal at each stage.
(7)
(Total for Question 1 is 9 marks)
2 P74076A
■■■■
, 2. C1
C
31 C2
A 31 G
0 31 39
8
70 20
32 20 21
63 72
45 21 80
T
D
S F
32 36 14 14
20 25
20
21
44
48 6 3
6
6
B
H C
C2 30 1
24 24 18
E
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 two conditions satisfied by a feasible flow.
(2)
(b) List the seven saturated arcs in Figure 1.
(1)
(c) Find the capacity of
(i) cut C1
(ii) cut C2
(2)
(d) Write down a flow-augmenting route that increases the flow by four units.
(1)
(e) Use the answer to part (d) to draw the resulting flow pattern on Diagram 1 in the
answer book.
(2)
(f) Prove that the answer to part (e) is a maximum flow.
(3)
(Total for Question 2 is 11 marks)
P74076A 3
■■■■ Turn over
