Edexcel Level 3 GCE
Friday 15 May 2026
Afternoon
Paper
reference 8FM0/27
Further Mathematics
Mark Scheme (Results)
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
Calculators must not have the facility for symb
regulations.
bra manipulation,
Summer 2026
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 labelled.
Answer all questions and ensure that your answers to parts of questions are
• Answer the questions in the answer book provided
– there may be more space than you need.
Edexcel GCE
• You should show sufficient working to make your methods clear.
Answers without working may not gain full credit. Advanced Sunsidiary Level
• Inexact answers should be given to three significant figures unless
otherwise stated. In Pure Mathematics (8FM0)
• Do not return the question paper with the D1 Answer Book.
Information Paper 27 Decision Mathematics 1
•• 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
P:1/1/1/1/
Education Ltd. *P81287A* for more:
for more:
,1. Edexcel and BTEC Qualifications
B G
E
28 Edexcel and BTEC qualifications are awarded by the UK’s
largest awarding body. We provide a wide range of qualifications
A
C H
J including academic, vocational, occupational and specific
programmes for employers. For further information visit our
qualifications websites at or .
Alternatively, you can get in touch with us using the details on our
contact us page at
F
D I
Figure 1
helping people progress, everywhere
(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. aspires to be the world’s leading learning company. Our aim is to help
(a) Use Dijkstra’s algorithm to find the shortest time needed to cycle from A to J. everyone progress in their lives through education. We believe in every kind of
learning, for all kinds of people, wherever they are in the world. We’ve been
(b) State the quickest route from A to J. involved in education for over 150 years, and by working across 70 countries, in
(6)
100 languages, we have built an international reputation for our commitment to
2
(ii) One application of Dijkstra’s algorithm has order n where n is the number of nodes high standards and raising achievement through innovation in education. Find
in the network.
out more about how we can help you and your students at:
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)
Summer 2027
Question Paper Log Number P81287A
Publication Code 8FM0_27_2706_MS
All the material in this publication is
Education Ltd
for more:
2
for more:
1287A
, 2. General Marking Guidance
C F
• All candidates must receive the same treatment. Examiners must mark the
first candidate in exactly the same way as they mark the last.
• Mark schemes should be applied positively. Candidates must be rewarded
for what they have shown they can do rather than penalised for omissions.
A E G • Examiners should mark according to the mark scheme not according to their
perception of where the grade boundaries may lie.
• There is no ceiling on achievement. All marks on the mark scheme should be
D used appropriately.
• All the marks on the mark scheme are designed to be awarded. Examiners
should always award full marks if deserved, i.e. if the answer matches the
B H
mark scheme. Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the mark scheme.
Figure 2
• Where some judgement is required, mark schemes will provide the principles
[The total weight of the network is 302] by which marks will be awarded and exemplification may be limited.
• When examiners are in doubt regarding the application of the mark scheme
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 to a candidate’s response, the team leader must be consulted.
corresponding road. • Crossed out work should be marked UNLESS the candidate has replaced it
(i) (a) Use Kruskal’s algorithm to find the minimum spanning tree for the network. You with an alternative response.
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)
for more:
P81287A for more:
3
Turn over
Friday 15 May 2026
Afternoon
Paper
reference 8FM0/27
Further Mathematics
Mark Scheme (Results)
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
Calculators must not have the facility for symb
regulations.
bra manipulation,
Summer 2026
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 labelled.
Answer all questions and ensure that your answers to parts of questions are
• Answer the questions in the answer book provided
– there may be more space than you need.
Edexcel GCE
• You should show sufficient working to make your methods clear.
Answers without working may not gain full credit. Advanced Sunsidiary Level
• Inexact answers should be given to three significant figures unless
otherwise stated. In Pure Mathematics (8FM0)
• Do not return the question paper with the D1 Answer Book.
Information Paper 27 Decision Mathematics 1
•• 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
P:1/1/1/1/
Education Ltd. *P81287A* for more:
for more:
,1. Edexcel and BTEC Qualifications
B G
E
28 Edexcel and BTEC qualifications are awarded by the UK’s
largest awarding body. We provide a wide range of qualifications
A
C H
J including academic, vocational, occupational and specific
programmes for employers. For further information visit our
qualifications websites at or .
Alternatively, you can get in touch with us using the details on our
contact us page at
F
D I
Figure 1
helping people progress, everywhere
(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. aspires to be the world’s leading learning company. Our aim is to help
(a) Use Dijkstra’s algorithm to find the shortest time needed to cycle from A to J. everyone progress in their lives through education. We believe in every kind of
learning, for all kinds of people, wherever they are in the world. We’ve been
(b) State the quickest route from A to J. involved in education for over 150 years, and by working across 70 countries, in
(6)
100 languages, we have built an international reputation for our commitment to
2
(ii) One application of Dijkstra’s algorithm has order n where n is the number of nodes high standards and raising achievement through innovation in education. Find
in the network.
out more about how we can help you and your students at:
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)
Summer 2027
Question Paper Log Number P81287A
Publication Code 8FM0_27_2706_MS
All the material in this publication is
Education Ltd
for more:
2
for more:
1287A
, 2. General Marking Guidance
C F
• All candidates must receive the same treatment. Examiners must mark the
first candidate in exactly the same way as they mark the last.
• Mark schemes should be applied positively. Candidates must be rewarded
for what they have shown they can do rather than penalised for omissions.
A E G • Examiners should mark according to the mark scheme not according to their
perception of where the grade boundaries may lie.
• There is no ceiling on achievement. All marks on the mark scheme should be
D used appropriately.
• All the marks on the mark scheme are designed to be awarded. Examiners
should always award full marks if deserved, i.e. if the answer matches the
B H
mark scheme. Examiners should also be prepared to award zero marks if the
candidate’s response is not worthy of credit according to the mark scheme.
Figure 2
• Where some judgement is required, mark schemes will provide the principles
[The total weight of the network is 302] by which marks will be awarded and exemplification may be limited.
• When examiners are in doubt regarding the application of the mark scheme
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 to a candidate’s response, the team leader must be consulted.
corresponding road. • Crossed out work should be marked UNLESS the candidate has replaced it
(i) (a) Use Kruskal’s algorithm to find the minimum spanning tree for the network. You with an alternative response.
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)
for more:
P81287A for more:
3
Turn over
