n
Pearson Edexcel Level
3 GCE
Monday 26 June 2023
Afternoon (Time: 1 hour 30
minutes)
Pap
reference
er 9FM0/4
Further D
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-
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Write your answers for this paper in the Decision
point pen.
book
•Fill
your
in the boxes at the top of the answer book with
provided.
Mathematics answer
name, centre number and candidate number.
• Do not return the question paper with the
• Answer all questions and ensure your answers to parts of
clearly
• questions
answer are Answer the questions in the spaces
labelled.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.
Informat
• A booklet ‘Mathematical Formulae and Statistical
ion
• There are 8 questions in this question paper. The total mark for this paper
Tables’ is provided.
is 75.
• The marks for each question are shown
– use this as a guide as to how much time to spend on each question.
Advice
•Read
in brackets
each question carefully before you start to answer it.
• Check your answers if you have time at the end.
Try to answer every
•
Turn over
question.
pg. 1
, 1.
C1
C2
17 12
A F
8 2
20 8
6 10 10
26
5 5 D 4
17 15 B
S 4
29
17 22 T
10
21 11
1911 52 44
C 18 18 E
C2
C1
Figure 1
Figure 1 shows a capacitated, directed network of pipes. The number on each arc
represents the capacity of that pipe. The numbers in circles represent a feasible flow
from S to T.
(a) State the value of the feasible flow.
(1)
(b) Find the capacity of cut C1 and the capacity of cut C2
(2)
(c) By inspection, find a flow-augmenting route to increase the flow by two units. You
must state your route.
(1)
(d) Prove that, once the flow-augmenting route found in (c) has been applied, the flow
is now maximal.
(3)
(Total for Question 1 is 7 marks)
2 P74086
A
Pearson Edexcel Level
3 GCE
Monday 26 June 2023
Afternoon (Time: 1 hour 30
minutes)
Pap
reference
er 9FM0/4
Further D
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-
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Write your answers for this paper in the Decision
point pen.
book
•Fill
your
in the boxes at the top of the answer book with
provided.
Mathematics answer
name, centre number and candidate number.
• Do not return the question paper with the
• Answer all questions and ensure your answers to parts of
clearly
• questions
answer are Answer the questions in the spaces
labelled.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.
Informat
• A booklet ‘Mathematical Formulae and Statistical
ion
• There are 8 questions in this question paper. The total mark for this paper
Tables’ is provided.
is 75.
• The marks for each question are shown
– use this as a guide as to how much time to spend on each question.
Advice
•Read
in brackets
each question carefully before you start to answer it.
• Check your answers if you have time at the end.
Try to answer every
•
Turn over
question.
pg. 1
, 1.
C1
C2
17 12
A F
8 2
20 8
6 10 10
26
5 5 D 4
17 15 B
S 4
29
17 22 T
10
21 11
1911 52 44
C 18 18 E
C2
C1
Figure 1
Figure 1 shows a capacitated, directed network of pipes. The number on each arc
represents the capacity of that pipe. The numbers in circles represent a feasible flow
from S to T.
(a) State the value of the feasible flow.
(1)
(b) Find the capacity of cut C1 and the capacity of cut C2
(2)
(c) By inspection, find a flow-augmenting route to increase the flow by two units. You
must state your route.
(1)
(d) Prove that, once the flow-augmenting route found in (c) has been applied, the flow
is now maximal.
(3)
(Total for Question 1 is 7 marks)
2 P74086
A
