Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Edexcel Level 3 GCE
Monday 11 May 2026
Afternoon (Time: 1 hour 40 minutes) Paper
reference 8FM0/01
Further Mathematics Mark Scheme (Results)
Advanced Subsidiary
Summer 2026
PAPER 1: Core Pure Mathematics
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, Edexcel GCE
differentiation and integration, or have retrievable mathematical formulae
stored in them. Advanced Subsidiary Level
Instructions
•• Use black ink or ball-point pen. In Further Mathematics 8FM0)
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name, Paper 01
• clearly
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
• Answer
labelled.
the questions in the spaces provided
• working
– there may be more space than you need.
You should show sufficient working to make your methods clear. Answers without
may not gain full credit.
• Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• – use this asfora guide
are 9 questions in this question paper. The total mark for this paper is 80.
The marks each question are shown in brackets
as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end.
Try to answer every question.
Turn over
P79981A
P:1/1/1/1/1/
Education Ltd. *P79981A0132* for more:
for more:
,1. The cubic equation
Edexcel and BTEC Qualifications
2x3 – 3x2 + 5x + 7 = 0
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
Edexcel and BTEC qualifications are awarded by the UK’s
has roots α, β and γ.
largest awarding body. We provide a wide rang ications
Without solving the equation, determine the exact value of including academic, vocational, occupational and specific
programmes for emplo fo
(i) α 2 + β 2 + γ 2 qualifications websites at or .
(3)
Alternatively, you c
3 3 3
(ii) contact us page at
α β γ
(3)
(iii) (1 – α) (1 – β) (1 – γ)
(3)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
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 P79981A
_____________________________________________________________________________________
Publications Code 8FM0_01_MS_2606
_____________________________________________________________________________________
All the material in this publication is
_____________________________________________________________________________________ Education Ltd 2026
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
for more:
2
for more:
*P79981A0232*
, 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.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
for more:
for more:
3
*P79981A0332* Turn over
, 6 Follow through marks
Question 1 continued 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.
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
_____________________________________________________________________________________
Follow through marks which involve more than one stage of
_____________________________________________________________________________________ calculation can only be awarded on sight of the relevant working,
_____________________________________________________________________________________ even if it appears obvious that there is only one way you could get the
answer given.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________ 7 Ignoring subsequent work
It is appropriate to ignore subsequent work when the additional work
_____________________________________________________________________________________
does not change the answer in a way that is inappropriate for the
_____________________________________________________________________________________ question or its context. (eg an incorrectly cancelled fraction when the
_____________________________________________________________________________________ unsimplified fraction would gain full marks).
It is not appropriate to ignore subsequent work when the additional
_____________________________________________________________________________________
work essentially makes the answer incorrect (eg incorrect algebraic
_____________________________________________________________________________________ simplification).
_____________________________________________________________________________________
8 Probability
_____________________________________________________________________________________
Probability answers must be given as a fraction, percentage or
_____________________________________________________________________________________ decimal. If a candidate gives a decimal equivalent to a probability,
_____________________________________________________________________________________ this should be written to at least 2 decimal places (unless tenths).
Incorrect notation should lose the accuracy marks, but be awarded
_____________________________________________________________________________________
any implied method marks.
_____________________________________________________________________________________ If a probability fraction is given then cancelled incorrectly, ignore the
_____________________________________________________________________________________ incorrectly cancelled answer.
_____________________________________________________________________________________
9 Range of answers
_____________________________________________________________________________________ Unless otherwise stated, when an answer is given as a range (eg 3.5 –
_____________________________________________________________________________________ 4.2) then this is inclusive of the end points (eg 3.5, 4.2) and all
_____________________________________________________________________________________ numbers within the range.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
for more:
4
for more:
*P79981A0432*
Candidate surname Other names
Centre Number Candidate Number
Edexcel Level 3 GCE
Monday 11 May 2026
Afternoon (Time: 1 hour 40 minutes) Paper
reference 8FM0/01
Further Mathematics Mark Scheme (Results)
Advanced Subsidiary
Summer 2026
PAPER 1: Core Pure Mathematics
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, Edexcel GCE
differentiation and integration, or have retrievable mathematical formulae
stored in them. Advanced Subsidiary Level
Instructions
•• Use black ink or ball-point pen. In Further Mathematics 8FM0)
• Fill
If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
in the boxes at the top of this page with your name, Paper 01
• clearly
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are
• Answer
labelled.
the questions in the spaces provided
• working
– there may be more space than you need.
You should show sufficient working to make your methods clear. Answers without
may not gain full credit.
• Inexact answers should be given to three significant figures unless otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
• – use this asfora guide
are 9 questions in this question paper. The total mark for this paper is 80.
The marks each question are shown in brackets
as to how much time to spend on each question.
Advice
•• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end.
Try to answer every question.
Turn over
P79981A
P:1/1/1/1/1/
Education Ltd. *P79981A0132* for more:
for more:
,1. The cubic equation
Edexcel and BTEC Qualifications
2x3 – 3x2 + 5x + 7 = 0
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
Edexcel and BTEC qualifications are awarded by the UK’s
has roots α, β and γ.
largest awarding body. We provide a wide rang ications
Without solving the equation, determine the exact value of including academic, vocational, occupational and specific
programmes for emplo fo
(i) α 2 + β 2 + γ 2 qualifications websites at or .
(3)
Alternatively, you c
3 3 3
(ii) contact us page at
α β γ
(3)
(iii) (1 – α) (1 – β) (1 – γ)
(3)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
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 P79981A
_____________________________________________________________________________________
Publications Code 8FM0_01_MS_2606
_____________________________________________________________________________________
All the material in this publication is
_____________________________________________________________________________________ Education Ltd 2026
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
for more:
2
for more:
*P79981A0232*
, 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.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
for more:
for more:
3
*P79981A0332* Turn over
, 6 Follow through marks
Question 1 continued 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.
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
_____________________________________________________________________________________
Follow through marks which involve more than one stage of
_____________________________________________________________________________________ calculation can only be awarded on sight of the relevant working,
_____________________________________________________________________________________ even if it appears obvious that there is only one way you could get the
answer given.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________ 7 Ignoring subsequent work
It is appropriate to ignore subsequent work when the additional work
_____________________________________________________________________________________
does not change the answer in a way that is inappropriate for the
_____________________________________________________________________________________ question or its context. (eg an incorrectly cancelled fraction when the
_____________________________________________________________________________________ unsimplified fraction would gain full marks).
It is not appropriate to ignore subsequent work when the additional
_____________________________________________________________________________________
work essentially makes the answer incorrect (eg incorrect algebraic
_____________________________________________________________________________________ simplification).
_____________________________________________________________________________________
8 Probability
_____________________________________________________________________________________
Probability answers must be given as a fraction, percentage or
_____________________________________________________________________________________ decimal. If a candidate gives a decimal equivalent to a probability,
_____________________________________________________________________________________ this should be written to at least 2 decimal places (unless tenths).
Incorrect notation should lose the accuracy marks, but be awarded
_____________________________________________________________________________________
any implied method marks.
_____________________________________________________________________________________ If a probability fraction is given then cancelled incorrectly, ignore the
_____________________________________________________________________________________ incorrectly cancelled answer.
_____________________________________________________________________________________
9 Range of answers
_____________________________________________________________________________________ Unless otherwise stated, when an answer is given as a range (eg 3.5 –
_____________________________________________________________________________________ 4.2) then this is inclusive of the end points (eg 3.5, 4.2) and all
_____________________________________________________________________________________ numbers within the range.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
for more:
4
for more:
*P79981A0432*
