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Further Mathematics
Advanced
PAPER 4D: Decision Mathematics 2
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.
• IfWrite
pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
your answers for this paper in the Decision Mathematics answer book
• Fill
provided.
in the boxes at the top of the answer book with your name, centre number
and candidate number.
•• DoAnswer
not return the question paper with the answer book.
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.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 7 questions in this question paper. The total mark for this paper is 75.
•• 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
EDEXCEL A LEVEL FURTHER MATHEMATICS (9FM0/4D) QUESTION
PAPER 4D AND MARK SCHEME SUMMER 2025
, BLANK PAGE
2 P75692A
■■■■
,1. Ravi can choose one of three options, A, B or C, when playing a game. The profit, in
pounds, associated with each outcome, and the corresponding probabilities, are shown
in the decision tree in Figure 1.
370
0.55
0.25
250
A 0.2
–75
0.75 245
B
0.25 195
C 390
0.45
0.4 325
0.15
–280
Figure 1
Calculate the optimal EMV to determine Ravi’s best course of action. You must make
your working clear.
(Total for Question 1 is 3 marks)
P75692A 3
■■■■ Turn over
, 2. Five workers, A, B, C, D and E, are available to complete four tasks, P, Q, R and S.
Each worker can be assigned to at most one task, and each task must be done by at most
one worker.
Worker B cannot be assigned to task R.
The time, in minutes, that each worker takes to complete each task is shown in the
table below.
P Q R S
A 25 32 43 28
B 41 37 – 38
C 43 35 37 39
D 40 33 37 41
E 37 38 43 40
The Hungarian algorithm is to be used to find an allocation that minimises the total time
to complete all four tasks.
(a) Explain how the table should be modified so that the Hungarian algorithm can
be applied.
(2)
(b) Use the Hungarian algorithm to obtain an allocation that minimises the total time.
(6)
(c) Calculate the least total time to complete all four tasks.
(1)
(Total for Question 2 is 9 marks)
4 P75692A
■■■■
Further Mathematics
Advanced
PAPER 4D: Decision Mathematics 2
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.
• IfWrite
pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
your answers for this paper in the Decision Mathematics answer book
• Fill
provided.
in the boxes at the top of the answer book with your name, centre number
and candidate number.
•• DoAnswer
not return the question paper with the answer book.
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.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 7 questions in this question paper. The total mark for this paper is 75.
•• 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
EDEXCEL A LEVEL FURTHER MATHEMATICS (9FM0/4D) QUESTION
PAPER 4D AND MARK SCHEME SUMMER 2025
, BLANK PAGE
2 P75692A
■■■■
,1. Ravi can choose one of three options, A, B or C, when playing a game. The profit, in
pounds, associated with each outcome, and the corresponding probabilities, are shown
in the decision tree in Figure 1.
370
0.55
0.25
250
A 0.2
–75
0.75 245
B
0.25 195
C 390
0.45
0.4 325
0.15
–280
Figure 1
Calculate the optimal EMV to determine Ravi’s best course of action. You must make
your working clear.
(Total for Question 1 is 3 marks)
P75692A 3
■■■■ Turn over
, 2. Five workers, A, B, C, D and E, are available to complete four tasks, P, Q, R and S.
Each worker can be assigned to at most one task, and each task must be done by at most
one worker.
Worker B cannot be assigned to task R.
The time, in minutes, that each worker takes to complete each task is shown in the
table below.
P Q R S
A 25 32 43 28
B 41 37 – 38
C 43 35 37 39
D 40 33 37 41
E 37 38 43 40
The Hungarian algorithm is to be used to find an allocation that minimises the total time
to complete all four tasks.
(a) Explain how the table should be modified so that the Hungarian algorithm can
be applied.
(2)
(b) Use the Hungarian algorithm to obtain an allocation that minimises the total time.
(6)
(c) Calculate the least total time to complete all four tasks.
(1)
(Total for Question 2 is 9 marks)
4 P75692A
■■■■
