Pearson Edexcel Level 3 GCE
Friday 15 May 2026
Afternoon
Paper
reference 8FM0/27
Further Mathematics
Advanced Subsidiary
Further Mathematics options
27: Decision Mathematics 1
(Part of options D, F, H and K)
You must have:
Mathematical Formulae and Statistical Tables (Green), calculator,
D1 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).
• Fill in the boxes at the top of the answer book with your name, centre number
and candidate number.
• clearly
Answer all questions and ensure that your answers to parts of questions are
labelled.
• – there may
Answer the questions in the answer book provided
be more space than you need.
• Answers without working
You should show sufficient working to make your methods clear.
may not gain full credit.
• otherwise stated.
Inexact answers should be given to three significant figures unless
• Do not return the question paper with the D1 Answer Book.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
total mark for this part of the examination is 40. There are 5 questions.
• 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
P81287A
©2026 Pearson Education Ltd.
P:1/1/1/1/
*P81287A*
,1.
B 52 G
E 10
34
32 28
28 22
34 C H 14
A J
6
18 32
28 3 18
F
26 24
D 56 I
Figure 1
(i) Figure 1 represents a network of cycle tracks. The number on each arc represents the
time taken, in minutes, to cycle along the corresponding track.
(a) Use Dijkstra’s algorithm to find the shortest time needed to cycle from A to J.
(b) State the quickest route from A to J.
(6)
2
(ii) One application of Dijkstra’s algorithm has order n where n is the number of nodes
in the network.
It takes a computer 0.32 seconds to find the shortest path from a given start node to
a given end node in a network of 20 nodes.
Calculate approximately how long it would take, in minutes, for the computer to
find the shortest path from a given start node to a given end node for a network of
4500 nodes.
(2)
(Total for Question 1 is 8 marks)
2 P81287A
, 2.
C 24 F
25 33
19 23
20
A E G
9 17
26 D 15
18 27
B 46 H
Figure 2
[The total weight of the network is 302]
Roads in a network connecting eight towns, A, B, C, D, E, F, G and H, are
represented in Figure 2. The number on each arc represents the length, in miles, of the
corresponding road.
(i) (a) Use Kruskal’s algorithm to find the minimum spanning tree for the network. You
should list the arcs in the order in which you consider them. In each case, state
whether or not you are adding the arc to your minimum spanning tree.
(3)
(b) State the weight of the minimum spanning tree.
(1)
(ii) A route is needed that travels along each road at least once. The route must start and
finish at A and the length of the route should be minimised.
(a) By considering the pairings of all relevant nodes, find the roads that need to be
traversed twice.
(4)
(b) State the total length of this route.
(1)
(Total for Question 2 is 9 marks)
P81287A 3
Turn over
Friday 15 May 2026
Afternoon
Paper
reference 8FM0/27
Further Mathematics
Advanced Subsidiary
Further Mathematics options
27: Decision Mathematics 1
(Part of options D, F, H and K)
You must have:
Mathematical Formulae and Statistical Tables (Green), calculator,
D1 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).
• Fill in the boxes at the top of the answer book with your name, centre number
and candidate number.
• clearly
Answer all questions and ensure that your answers to parts of questions are
labelled.
• – there may
Answer the questions in the answer book provided
be more space than you need.
• Answers without working
You should show sufficient working to make your methods clear.
may not gain full credit.
• otherwise stated.
Inexact answers should be given to three significant figures unless
• Do not return the question paper with the D1 Answer Book.
Information
•• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided.
total mark for this part of the examination is 40. There are 5 questions.
• 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
P81287A
©2026 Pearson Education Ltd.
P:1/1/1/1/
*P81287A*
,1.
B 52 G
E 10
34
32 28
28 22
34 C H 14
A J
6
18 32
28 3 18
F
26 24
D 56 I
Figure 1
(i) Figure 1 represents a network of cycle tracks. The number on each arc represents the
time taken, in minutes, to cycle along the corresponding track.
(a) Use Dijkstra’s algorithm to find the shortest time needed to cycle from A to J.
(b) State the quickest route from A to J.
(6)
2
(ii) One application of Dijkstra’s algorithm has order n where n is the number of nodes
in the network.
It takes a computer 0.32 seconds to find the shortest path from a given start node to
a given end node in a network of 20 nodes.
Calculate approximately how long it would take, in minutes, for the computer to
find the shortest path from a given start node to a given end node for a network of
4500 nodes.
(2)
(Total for Question 1 is 8 marks)
2 P81287A
, 2.
C 24 F
25 33
19 23
20
A E G
9 17
26 D 15
18 27
B 46 H
Figure 2
[The total weight of the network is 302]
Roads in a network connecting eight towns, A, B, C, D, E, F, G and H, are
represented in Figure 2. The number on each arc represents the length, in miles, of the
corresponding road.
(i) (a) Use Kruskal’s algorithm to find the minimum spanning tree for the network. You
should list the arcs in the order in which you consider them. In each case, state
whether or not you are adding the arc to your minimum spanning tree.
(3)
(b) State the weight of the minimum spanning tree.
(1)
(ii) A route is needed that travels along each road at least once. The route must start and
finish at A and the length of the route should be minimised.
(a) By considering the pairings of all relevant nodes, find the roads that need to be
traversed twice.
(4)
(b) State the total length of this route.
(1)
(Total for Question 2 is 9 marks)
P81287A 3
Turn over
