Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Edexcel Level 3 GCE
Friday 15 May 2026
Afternoon Paper
reference 8FM0/21
Further Mathematics Mark Scheme (Results)
Advanced Subsidiary
Further Mathematics options
21: Further Pure Mathematics 1
(Part of options A, B, C and D) Summer 2026
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator allowed by regulations.
Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae Edexcel GCE
stored in them.
Instructions Advanced Subsidiary Level
•• Use black ink or ball-point pen.
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). In Further Mathematics (8FM0)
• Fill in the boxes at the top of this page with your name,
centre number and candidate number. Paper 21 Further Pure Mathematics 1
• clearly labelled.
Answer all questions and ensure that your answers to parts of questions are
• Answer the questions in the spaces 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.
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
P79392A
P:1/1/1/
Education Ltd. *P79392A0120* for more:
for more:
, Edexcel and BTEC Qualifications
1. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
Use algebra to find the values of x for which Edexcel and BTEC qualifications are awarded by the UK’s
largest awarding body. We provide a wide rang ications
8x
x
3 including academic, vocational, occupational and specific
3 x programmes for emplo fo
qualifications websites at or .
giving your answer in set notation. Alternatively, you c
(7) contact us page at
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
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 P79392A
_____________________________________________________________________________________
Publications Code 8FM0_21_MS_2606
_____________________________________________________________________________________
All the material in this publication is
_____________________________________________________________________________________
Education Ltd 2026
_____________________________________________________________________________________
_____________________________________________________________________________________ for more:
2
for more:
*P79392A0220*
, General Marking Guidance
Question 1 continued
_____________________________________________________________________________________ These notes offer general guidance, but the specific notes for examiners
appertaining to individual questions take precedence.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________ 1 All candidates must receive the same treatment. Examiners must mark the last
_____________________________________________________________________________________ candidate in exactly the same way as they mark the first.
_____________________________________________________________________________________
Where some judgement is required, mark schemes will provide the principles
_____________________________________________________________________________________
by which marks will be awarded; exemplification/indicative content will not be
_____________________________________________________________________________________ exhaustive. When examiners are in doubt regarding the application of the
_____________________________________________________________________________________ mark scheme to a candidate’s response, the response should be sent to
review.
_____________________________________________________________________________________
_____________________________________________________________________________________ 2 All the marks on the mark scheme are designed to be awarded; mark 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 answer (or no answer) indicated on the answer
_____________________________________________________________________________________ line always check the working in the body of the script (and on any diagrams),
_____________________________________________________________________________________ and award any marks appropriate from the mark scheme.
_____________________________________________________________________________________
Questions where working is not required: In general, the correct answer
_____________________________________________________________________________________ should be given full marks.
_____________________________________________________________________________________ Questions that specifically require working: In general, candidates who do
_____________________________________________________________________________________ not show working on this type of question will get no marks – full details will be
given in the mark scheme for each individual 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.
_____________________________________________________________________________________
_____________________________________________________________________________________ 6 Follow through marks
_____________________________________________________________________________________ Follow through marks which involve a single stage calculation can be awarded
_____________________________________________________________________________________ without working as you can check the answer, but if ambiguous do not award.
_____________________________________________________________________________________
for more:
for more:
3
*P79392A0320* Turn over
Candidate surname Other names
Centre Number Candidate Number
Edexcel Level 3 GCE
Friday 15 May 2026
Afternoon Paper
reference 8FM0/21
Further Mathematics Mark Scheme (Results)
Advanced Subsidiary
Further Mathematics options
21: Further Pure Mathematics 1
(Part of options A, B, C and D) Summer 2026
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator allowed by regulations.
Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae Edexcel GCE
stored in them.
Instructions Advanced Subsidiary Level
•• Use black ink or ball-point pen.
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). In Further Mathematics (8FM0)
• Fill in the boxes at the top of this page with your name,
centre number and candidate number. Paper 21 Further Pure Mathematics 1
• clearly labelled.
Answer all questions and ensure that your answers to parts of questions are
• Answer the questions in the spaces 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.
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
P79392A
P:1/1/1/
Education Ltd. *P79392A0120* for more:
for more:
, Edexcel and BTEC Qualifications
1. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
Use algebra to find the values of x for which Edexcel and BTEC qualifications are awarded by the UK’s
largest awarding body. We provide a wide rang ications
8x
x
3 including academic, vocational, occupational and specific
3 x programmes for emplo fo
qualifications websites at or .
giving your answer in set notation. Alternatively, you c
(7) contact us page at
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
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 P79392A
_____________________________________________________________________________________
Publications Code 8FM0_21_MS_2606
_____________________________________________________________________________________
All the material in this publication is
_____________________________________________________________________________________
Education Ltd 2026
_____________________________________________________________________________________
_____________________________________________________________________________________ for more:
2
for more:
*P79392A0220*
, General Marking Guidance
Question 1 continued
_____________________________________________________________________________________ These notes offer general guidance, but the specific notes for examiners
appertaining to individual questions take precedence.
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
_____________________________________________________________________________________ 1 All candidates must receive the same treatment. Examiners must mark the last
_____________________________________________________________________________________ candidate in exactly the same way as they mark the first.
_____________________________________________________________________________________
Where some judgement is required, mark schemes will provide the principles
_____________________________________________________________________________________
by which marks will be awarded; exemplification/indicative content will not be
_____________________________________________________________________________________ exhaustive. When examiners are in doubt regarding the application of the
_____________________________________________________________________________________ mark scheme to a candidate’s response, the response should be sent to
review.
_____________________________________________________________________________________
_____________________________________________________________________________________ 2 All the marks on the mark scheme are designed to be awarded; mark 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 answer (or no answer) indicated on the answer
_____________________________________________________________________________________ line always check the working in the body of the script (and on any diagrams),
_____________________________________________________________________________________ and award any marks appropriate from the mark scheme.
_____________________________________________________________________________________
Questions where working is not required: In general, the correct answer
_____________________________________________________________________________________ should be given full marks.
_____________________________________________________________________________________ Questions that specifically require working: In general, candidates who do
_____________________________________________________________________________________ not show working on this type of question will get no marks – full details will be
given in the mark scheme for each individual 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.
_____________________________________________________________________________________
_____________________________________________________________________________________ 6 Follow through marks
_____________________________________________________________________________________ Follow through marks which involve a single stage calculation can be awarded
_____________________________________________________________________________________ without working as you can check the answer, but if ambiguous do not award.
_____________________________________________________________________________________
for more:
for more:
3
*P79392A0320* Turn over
