Pearson Edexcel Level
3 GCE
Friday 23 June 2023
Afternoon (Time: 1 hour 30
minutes)
Pap
reference
er 9FM0/3
Further D
Mathematics
Advanced
PAPER 3D: Decision
Mathematics 1
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 Mathematics answer
• Fill
pointinpen.
the boxes at the top of the answer book with your name,
centre number and candidate
number.
• book
Do not provided.
return the question paper with the
• clearly all questions and ensure that your answers to parts of
Answer
• questions are Answer the questions in the answer book
labelled.book.
answer
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
ion
• AThere
booklet
are ‘Mathematical
7 questions in Formulae andpaper.
this question Statistical
The total mark for
• this
The paper
marks is
spend
Tables’on
for75.
is each
– use
each this as a
question
question.
provided.
guide
are as to how much time to
shown
in brackets
Advice
• Read each question carefully before you start to answer it.
• Try to answer every
• Check your answers if you have time at the end.
question.
Turn over
1
,1.
E A
B
D
C
Figure 1
Figure 1 shows the graph G.
(a) State whether G is Eulerian, semi-Eulerian, or neither, giving a reason for
your answer.
(1)
(b) Write down an example of a Hamiltonian cycle on G.
(1)
(c) State whether or not G is planar, justifying your answer.
(1)
(d) State the number of arcs that would need to be added to G to make the graph K5
(1)
2 P72799
A
, E 5 A
7 10
4
8
B
D
15
2 3
C
Figure 2
Direct roads between five villages, A, B, C, D and E, are represented in Figure 2. The
weight on each arc is the time, in minutes, required to travel along the corresponding
road. Floyd’s algorithm is to be used to find the complete network of shortest times
between the five villages.
(e) For the network represented in Figure 2, complete the initial time matrix in the
answer book.
(1)
The time matrix after four iterations of Floyd’s algorithm is shown in Table 1.
A B C D E
A – 10 13 15 5
B 10 – 3 5 4
C 13 3 – 2 7
D 15 5 2 – 7
E 5 4 7 7 –
Table 1
(f) Perform the final iteration of Floyd’s algorithm that follows from Table 1, showing
the time matrix for this iteration.
(2)
(Total for Question 1 is 7 marks)
P72799 3
A Turn
3 GCE
Friday 23 June 2023
Afternoon (Time: 1 hour 30
minutes)
Pap
reference
er 9FM0/3
Further D
Mathematics
Advanced
PAPER 3D: Decision
Mathematics 1
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 Mathematics answer
• Fill
pointinpen.
the boxes at the top of the answer book with your name,
centre number and candidate
number.
• book
Do not provided.
return the question paper with the
• clearly all questions and ensure that your answers to parts of
Answer
• questions are Answer the questions in the answer book
labelled.book.
answer
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
ion
• AThere
booklet
are ‘Mathematical
7 questions in Formulae andpaper.
this question Statistical
The total mark for
• this
The paper
marks is
spend
Tables’on
for75.
is each
– use
each this as a
question
question.
provided.
guide
are as to how much time to
shown
in brackets
Advice
• Read each question carefully before you start to answer it.
• Try to answer every
• Check your answers if you have time at the end.
question.
Turn over
1
,1.
E A
B
D
C
Figure 1
Figure 1 shows the graph G.
(a) State whether G is Eulerian, semi-Eulerian, or neither, giving a reason for
your answer.
(1)
(b) Write down an example of a Hamiltonian cycle on G.
(1)
(c) State whether or not G is planar, justifying your answer.
(1)
(d) State the number of arcs that would need to be added to G to make the graph K5
(1)
2 P72799
A
, E 5 A
7 10
4
8
B
D
15
2 3
C
Figure 2
Direct roads between five villages, A, B, C, D and E, are represented in Figure 2. The
weight on each arc is the time, in minutes, required to travel along the corresponding
road. Floyd’s algorithm is to be used to find the complete network of shortest times
between the five villages.
(e) For the network represented in Figure 2, complete the initial time matrix in the
answer book.
(1)
The time matrix after four iterations of Floyd’s algorithm is shown in Table 1.
A B C D E
A – 10 13 15 5
B 10 – 3 5 4
C 13 3 – 2 7
D 15 5 2 – 7
E 5 4 7 7 –
Table 1
(f) Perform the final iteration of Floyd’s algorithm that follows from Table 1, showing
the time matrix for this iteration.
(2)
(Total for Question 1 is 7 marks)
P72799 3
A Turn
