Pearson Edexcel Level 3 GCE
Monday 22 June 2026
Afternoon (Time: 1 hour 30 minutes)
Paper
reference 9FM0/4D
Further Mathematics
Advanced
PAPER 4D: Decision Mathematics 2
You must have:
Mathematical Formulae and Statistical Tables (Green), calculator,
Decision Mathematics 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).
• Write your answers for this paper in the Decision Mathematics answer
book provided.
• Fill in the boxes at the top of the answer book with your name, centre number
and candidate number.
•• Do not return the question paper with the answer book.
Answer all questions and ensure 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
stated.
answers should be given to three significant figures unless otherwise
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 8 questions in this question paper. The total mark for this paper is 75.
• – use this asfora guide
The marks each question are shown in brackets
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
P79406A
©2026 Pearson Education Ltd.
P:1/1/1/1/1/1/
*P79406A*
,1. Five workers, A, B, C, D and E, are to be assigned to four tasks, P, Q, R and S. Each
task must be assigned to just one worker and each worker may do at most one task.
• Worker A cannot do task R
• Worker C cannot do task Q
• Worker E cannot do task S
The cost, in pounds, of assigning each worker to each task is shown in the table.
The total cost is to be minimised.
P Q R S
A 121 143 - 132
B 133 127 132 141
C 128 - 151 150
D 130 135 140 136
E 129 130 137 -
(a) Modify the table so that the Hungarian Algorithm can be used to obtain an allocation
with minimum total cost.
(2)
(b) Use the Hungarian Algorithm to obtain an allocation with minimum total cost.
(5)
(c) State the minimum total cost.
(1)
(Total for Question 1 is 8 marks)
2 P79406A
,2.
Player Y
P Q R
A 4 1 −3
B −3 −4 4
Player X
C 3 −1 2
D −1 −2 3
Two players, X and Y, are playing a zero-sum game which does not have a stable
solution. The table shows the pay-off matrix for Player X.
(a) Explain why Player Y should never play option P.
(2)
(b) Rewrite the pay-off matrix for the reduced game for Player Y.
(1)
(c) Use a graphical method to determine the optimum strategy for Player Y, defining
any variables that you use.
(6)
(d) State the value of the game to Player X.
(1)
(Total for Question 2 is 10 marks)
P79406A 3
Turn over
, 3.
C1 18 (5, 20)
A F
4 (3, 18) (4, 17) 6
34 (12, 34)
(8, 30) 26 4 (4, 14) 10 (6, 12)
D 10 (3, 10)
12 (5, 12)
B 15 (10, 22)
S G
6 (2, 7) T
(6, 24) 18 (5, 11) 11
4 (4, 13)
(10, 25) 25
4 (4, 16) E 3 (3, 10) 20 (8, 26)
2 (2, 14)
C H
(16, 27) 27
C1
The diagram shows a directed capacitated network.
The numbers in brackets on each arc show the lower and upper capacities of the
corresponding arc.
The numbers in circles represent a feasible flow from S to T.
(a) State the value of the feasible flow.
(1)
(b) Explain why the flow in HT can never be greater than 20
(2)
(c) Calculate the value of the cut C1
(1)
(d) By inspection, increase the flow by exactly 4 units. You must state the
flow-augmenting routes used and their values.
(1)
(e) Prove that the flow found in part (d) is maximal.
(3)
(Total for Question 3 is 8 marks)
4 P79406A
Monday 22 June 2026
Afternoon (Time: 1 hour 30 minutes)
Paper
reference 9FM0/4D
Further Mathematics
Advanced
PAPER 4D: Decision Mathematics 2
You must have:
Mathematical Formulae and Statistical Tables (Green), calculator,
Decision Mathematics 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).
• Write your answers for this paper in the Decision Mathematics answer
book provided.
• Fill in the boxes at the top of the answer book with your name, centre number
and candidate number.
•• Do not return the question paper with the answer book.
Answer all questions and ensure 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
stated.
answers should be given to three significant figures unless otherwise
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 8 questions in this question paper. The total mark for this paper is 75.
• – use this asfora guide
The marks each question are shown in brackets
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
P79406A
©2026 Pearson Education Ltd.
P:1/1/1/1/1/1/
*P79406A*
,1. Five workers, A, B, C, D and E, are to be assigned to four tasks, P, Q, R and S. Each
task must be assigned to just one worker and each worker may do at most one task.
• Worker A cannot do task R
• Worker C cannot do task Q
• Worker E cannot do task S
The cost, in pounds, of assigning each worker to each task is shown in the table.
The total cost is to be minimised.
P Q R S
A 121 143 - 132
B 133 127 132 141
C 128 - 151 150
D 130 135 140 136
E 129 130 137 -
(a) Modify the table so that the Hungarian Algorithm can be used to obtain an allocation
with minimum total cost.
(2)
(b) Use the Hungarian Algorithm to obtain an allocation with minimum total cost.
(5)
(c) State the minimum total cost.
(1)
(Total for Question 1 is 8 marks)
2 P79406A
,2.
Player Y
P Q R
A 4 1 −3
B −3 −4 4
Player X
C 3 −1 2
D −1 −2 3
Two players, X and Y, are playing a zero-sum game which does not have a stable
solution. The table shows the pay-off matrix for Player X.
(a) Explain why Player Y should never play option P.
(2)
(b) Rewrite the pay-off matrix for the reduced game for Player Y.
(1)
(c) Use a graphical method to determine the optimum strategy for Player Y, defining
any variables that you use.
(6)
(d) State the value of the game to Player X.
(1)
(Total for Question 2 is 10 marks)
P79406A 3
Turn over
, 3.
C1 18 (5, 20)
A F
4 (3, 18) (4, 17) 6
34 (12, 34)
(8, 30) 26 4 (4, 14) 10 (6, 12)
D 10 (3, 10)
12 (5, 12)
B 15 (10, 22)
S G
6 (2, 7) T
(6, 24) 18 (5, 11) 11
4 (4, 13)
(10, 25) 25
4 (4, 16) E 3 (3, 10) 20 (8, 26)
2 (2, 14)
C H
(16, 27) 27
C1
The diagram shows a directed capacitated network.
The numbers in brackets on each arc show the lower and upper capacities of the
corresponding arc.
The numbers in circles represent a feasible flow from S to T.
(a) State the value of the feasible flow.
(1)
(b) Explain why the flow in HT can never be greater than 20
(2)
(c) Calculate the value of the cut C1
(1)
(d) By inspection, increase the flow by exactly 4 units. You must state the
flow-augmenting routes used and their values.
(1)
(e) Prove that the flow found in part (d) is maximal.
(3)
(Total for Question 3 is 8 marks)
4 P79406A
