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, Pearson Edexcel Level 3 GCE
Monday 24 June 2024 tyrionpapers.com
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 allowed 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 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.
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.
• 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
P72803A
©2024 Pearson Education Ltd.
F:1/1/1/1/1/
*P72803A*
,1.
C1
A 2 2 E
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x 15 8 17
13 11
13 13
12 12 B 19 7 D 5 5
S T
4
7
10 4
15 5 y
10 12 4 16
16
C 11 8 F
C1
Figure 1
Figure 1 shows a capacitated, directed network of pipes. The numbers in circles
represent an initial flow from S to T. The other number on each arc represents the
capacity, in litres per second, of the corresponding pipe.
(a) (i) State the value of x
(ii) State the value of y
(2)
(b) State the value of the initial flow.
(1)
(c) State the capacity of cut C1
(1)
(d) Find, by inspection, a flow‑augmenting route to increase the flow by four units.
You must state your route.
(1)
The flow‑augmenting route from (d) is used to increase the flow from S to T.
(e) Prove that the flow is now maximal.
(3)
A vertex restriction is now applied so that no more than 12 litres per second can flow
through E.
(f) (i) Complete Diagram 1 in the answer book to show this restriction.
(ii) State the value of the maximum flow through the network with this restriction.
(2)
(Total for Question 1 is 10 marks)
2 P72803A
, 2. The general solution of the first order recurrence relation
un 1 aun
bn 2 cn d n 0
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is given by
un A(3) n
5n 2
1
where A is an arbitrary non‑zero constant.
By considering expressions for un+1 and un , find the values of the constants a, b, c and d.
(Total for Question 2 is 3 marks)
P72803A 3
Turn over
Scroll below to see the sample of the paper
O2ered to you by Tyrion Papers
https://tyrionpapers.com
If you have any issues or queries, do reach out to
I’ll help you out for sure
We have locked papers, Predicted Papers, Topic tests, Notes,
question banks and so much more
, Pearson Edexcel Level 3 GCE
Monday 24 June 2024 tyrionpapers.com
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 allowed 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 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.
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.
• 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
P72803A
©2024 Pearson Education Ltd.
F:1/1/1/1/1/
*P72803A*
,1.
C1
A 2 2 E
tyrionpapers.com
x 15 8 17
13 11
13 13
12 12 B 19 7 D 5 5
S T
4
7
10 4
15 5 y
10 12 4 16
16
C 11 8 F
C1
Figure 1
Figure 1 shows a capacitated, directed network of pipes. The numbers in circles
represent an initial flow from S to T. The other number on each arc represents the
capacity, in litres per second, of the corresponding pipe.
(a) (i) State the value of x
(ii) State the value of y
(2)
(b) State the value of the initial flow.
(1)
(c) State the capacity of cut C1
(1)
(d) Find, by inspection, a flow‑augmenting route to increase the flow by four units.
You must state your route.
(1)
The flow‑augmenting route from (d) is used to increase the flow from S to T.
(e) Prove that the flow is now maximal.
(3)
A vertex restriction is now applied so that no more than 12 litres per second can flow
through E.
(f) (i) Complete Diagram 1 in the answer book to show this restriction.
(ii) State the value of the maximum flow through the network with this restriction.
(2)
(Total for Question 1 is 10 marks)
2 P72803A
, 2. The general solution of the first order recurrence relation
un 1 aun
bn 2 cn d n 0
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is given by
un A(3) n
5n 2
1
where A is an arbitrary non‑zero constant.
By considering expressions for un+1 and un , find the values of the constants a, b, c and d.
(Total for Question 2 is 3 marks)
P72803A 3
Turn over
