Edexcel Level 3 GCE
Friday 15 May 2026
Afternoon Paper
reference 8FM0/28
Further Mathematics
Advanced Subsidiary
Further Mathematics options
28: Decision Mathematics 2
(Part of option K only)
You must have:
Mathematical Formulae and Statistical Tables (Green),
calculator, D2 Answer Book (enclosed)
Mark Scheme (Results)
Candidates may use any calculator permitted by 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.
Summer 2026
• IfFillpencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• centre number
in the boxes at the top of the answer book with your name,
and candidate number.
• clearly
Answer all questions and ensure that your answers to parts of questions are
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. Edexcel GCE
• Do not return the question paper with the D2 Answer Book.
Advanced Subsidiary Level
Information
• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided. In Further Mathematics (8FM0)
• The total mark for this part of the examination is 40. There are 5 questions.
• – usemarks for each question are shown in brackets
this as a guide as to how much time to spend on each question.
Paper 28 Decision Mathematics 2
Advice
• Read each question carefully before you start to answer it.
• Checkanswer
Try to every question.
• your answers if you have time at the end. Turn over
P79775A
P:1/1/1/1/
Education Ltd. *P79775A* for more:
for more:
,1. Player A and Player B are playing a zero‑sum game. Edexcel and BTEC Qualifications
The game does not have a stable solution.
The pay‑off matrix for Player A is given below.
Player B Edexcel and BTEC qualifications are awarded by the UK’s
largest awarding body. We provide a wide rang ications
Option X Option Y Option Z including academic, vocational, occupational and specific
programmes for emplo fo
Player A Option R 3 –1 1 qualifications websites at or .
Alternatively, you c
Option S –3 3 –2 contact us page at
Use a graphical method to determine the best strategy for Player A. You must define any
variables that you use.
(Total for Question 1 is 7 marks)
helping people progress, everywhere
aspires to be the world’s leading learning company. Our aim is to
help 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 involved in education for over 150 years, and by working across
70 countries, in 100 languages, we have built an international reputation for
our commitment to high standards and raising achievement through
innovation in education. Find out more about how we can help you and your
students at:
Summer 2026
Question Paper Log Number P79775A
Publications Code 8FM0_28_MS_2606
All the material in this publication is
Education Ltd 2026
for more:
2
for more:
9775A
, 2. A relay team with four members is to be selected from five swimmers, A, B, C, D and E. General Marking Guidance
Each member of the team must swim one of four different strokes, Backstroke (1),
Breaststroke (2), Butterfly (3) or Freestyle (4). These notes offer general guidance, but the specific notes for examiners
appertaining to individual questions take precedence.
The table shows each swimmer’s best time, in seconds, for the different strokes.
1 All candidates must receive the same treatment. Examiners must
Backstroke (1) Breaststroke (2) Butterfly (3) Freestyle (4) mark the last candidate in exactly the same way as they mark the first.
A 78 87 74 63 Where some judgement is required, mark schemes will provide the
principles by which marks will be awarded; exemplification/indicative
B 80 85 72 71 content will not be exhaustive. When examiners are in doubt
regarding the application of the mark scheme to a candidate’s
C 85 84 71 68
response, the response should be sent to review.
D 83 90 78 65
2 All the marks on the mark scheme are designed to be awarded; mark
E 81 86 75 70 schemes should be applied positively. Examiners should also be
prepared to award zero marks if the candidate’s response is not
worthy of credit according to the mark scheme. If there is a wrong
(a) Modify the table so that the Hungarian Algorithm can be used to calculate the answer (or no answer) indicated on the answer line always check the
minimum potential total time for the relay team. working in the body of the script (and on any diagrams), and award
(1) any marks appropriate from the mark scheme.
(b) Use the Hungarian Algorithm to obtain an allocation of swimmers which minimises
the potential total time. Questions where working is not required: In general, the correct
(5) answer should be given full marks.
Questions that specifically require working: In general, candidates
State the minimum potential total time. who do not show working on this type of question will get no marks –
(1) full details will be given in the mark scheme for each individual
(Total for Question 2 is 7 marks) question.
3 Crossed out work
This should be marked unless the candidate has replaced it with an
alternative response.
4 Choice of method
If there is a choice of methods shown, mark the method that leads to
the answer given on the answer line.
If no answer appears on the answer line then mark both methods as
far as they are identical and award these marks.
5 Incorrect method
If it is clear from the working that the “correct” answer has been
obtained from incorrect working, award 0 marks.
for more:
P79775A for more:
3
Turn over
Friday 15 May 2026
Afternoon Paper
reference 8FM0/28
Further Mathematics
Advanced Subsidiary
Further Mathematics options
28: Decision Mathematics 2
(Part of option K only)
You must have:
Mathematical Formulae and Statistical Tables (Green),
calculator, D2 Answer Book (enclosed)
Mark Scheme (Results)
Candidates may use any calculator permitted by 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.
Summer 2026
• IfFillpencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• centre number
in the boxes at the top of the answer book with your name,
and candidate number.
• clearly
Answer all questions and ensure that your answers to parts of questions are
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. Edexcel GCE
• Do not return the question paper with the D2 Answer Book.
Advanced Subsidiary Level
Information
• AThebooklet ‘Mathematical Formulae and Statistical Tables’ is provided. In Further Mathematics (8FM0)
• The total mark for this part of the examination is 40. There are 5 questions.
• – usemarks for each question are shown in brackets
this as a guide as to how much time to spend on each question.
Paper 28 Decision Mathematics 2
Advice
• Read each question carefully before you start to answer it.
• Checkanswer
Try to every question.
• your answers if you have time at the end. Turn over
P79775A
P:1/1/1/1/
Education Ltd. *P79775A* for more:
for more:
,1. Player A and Player B are playing a zero‑sum game. Edexcel and BTEC Qualifications
The game does not have a stable solution.
The pay‑off matrix for Player A is given below.
Player B Edexcel and BTEC qualifications are awarded by the UK’s
largest awarding body. We provide a wide rang ications
Option X Option Y Option Z including academic, vocational, occupational and specific
programmes for emplo fo
Player A Option R 3 –1 1 qualifications websites at or .
Alternatively, you c
Option S –3 3 –2 contact us page at
Use a graphical method to determine the best strategy for Player A. You must define any
variables that you use.
(Total for Question 1 is 7 marks)
helping people progress, everywhere
aspires to be the world’s leading learning company. Our aim is to
help 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 involved in education for over 150 years, and by working across
70 countries, in 100 languages, we have built an international reputation for
our commitment to high standards and raising achievement through
innovation in education. Find out more about how we can help you and your
students at:
Summer 2026
Question Paper Log Number P79775A
Publications Code 8FM0_28_MS_2606
All the material in this publication is
Education Ltd 2026
for more:
2
for more:
9775A
, 2. A relay team with four members is to be selected from five swimmers, A, B, C, D and E. General Marking Guidance
Each member of the team must swim one of four different strokes, Backstroke (1),
Breaststroke (2), Butterfly (3) or Freestyle (4). These notes offer general guidance, but the specific notes for examiners
appertaining to individual questions take precedence.
The table shows each swimmer’s best time, in seconds, for the different strokes.
1 All candidates must receive the same treatment. Examiners must
Backstroke (1) Breaststroke (2) Butterfly (3) Freestyle (4) mark the last candidate in exactly the same way as they mark the first.
A 78 87 74 63 Where some judgement is required, mark schemes will provide the
principles by which marks will be awarded; exemplification/indicative
B 80 85 72 71 content will not be exhaustive. When examiners are in doubt
regarding the application of the mark scheme to a candidate’s
C 85 84 71 68
response, the response should be sent to review.
D 83 90 78 65
2 All the marks on the mark scheme are designed to be awarded; mark
E 81 86 75 70 schemes should be applied positively. Examiners should also be
prepared to award zero marks if the candidate’s response is not
worthy of credit according to the mark scheme. If there is a wrong
(a) Modify the table so that the Hungarian Algorithm can be used to calculate the answer (or no answer) indicated on the answer line always check the
minimum potential total time for the relay team. working in the body of the script (and on any diagrams), and award
(1) any marks appropriate from the mark scheme.
(b) Use the Hungarian Algorithm to obtain an allocation of swimmers which minimises
the potential total time. Questions where working is not required: In general, the correct
(5) answer should be given full marks.
Questions that specifically require working: In general, candidates
State the minimum potential total time. who do not show working on this type of question will get no marks –
(1) full details will be given in the mark scheme for each individual
(Total for Question 2 is 7 marks) question.
3 Crossed out work
This should be marked unless the candidate has replaced it with an
alternative response.
4 Choice of method
If there is a choice of methods shown, mark the method that leads to
the answer given on the answer line.
If no answer appears on the answer line then mark both methods as
far as they are identical and award these marks.
5 Incorrect method
If it is clear from the working that the “correct” answer has been
obtained from incorrect working, award 0 marks.
for more:
P79775A for more:
3
Turn over
