Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 19 June 2026
Mark Scheme (Results)
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/3A
Further Mathematics
Summer 2026
Advanced
PAPER 3A: Further Pure Mathematics 1
You must have: Total Marks
Mathematical Formulae and Statistics Tables (Green), calculator
Pearson Edexcel GCE
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
In Further Mathematics (9FM0)
Instructions Paper 3A Further Pure Mathematics 1
•• 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 this page with your name,
••
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are clearly labelled.
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
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
There are 9 questions in this question paper. The total mark for this paper is 75.
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
P74079APearson Education Ltd.
P:1/1/1/1/1/1/1/1/
*P74079A0132* for more:
for more:
, Edexcel and BTEC Qualifications
1.
y
H
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 Pearson, the UK’s
largest awarding body. We provide a wide range of qualifications
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
P
O x
Q
l
Pearson: helping people progress, everywhere
Pearson 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
Figure 1 languages, we have built an international reputation for our commitment to high
standards and raising achievement through innovation in education. Find out more
Figure 1 shows a rectangular hyperbola H with parametric equations
about how we can help you and your students at:
t 1
x y t
0
6 6t
The line l with equation 3 x 15 y 2
0 intersects H at the point P and at the point Q,
as shown in Figure 1.
(a) Show that the points of intersection of l and H satisfy the equation
t 2 4t 5
0
(2)
(b) Hence, or otherwise, determine the coordinates of P and Q.
(4)
_____________________________________________________________________________________
_____________________________________________________________________________________
Summer 2026
_____________________________________________________________________________________
Question Paper Log Number P74079A
_____________________________________________________________________________________ Publication Code 9FM0_3A_2606_MS
_____________________________________________________________________________________ All the material in this publication is
Pearson Education Ltd
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
for more:
2
for more:
*P74079A0232*
, General Marking Guidance
Question 1 continued • All candidates must receive the same treatment. Examiners must mark the
_____________________________________________________________________________________ first candidate in exactly the same way as they mark the last.
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
_____________________________________________________________________________________ • Mark schemes should be applied positively. Candidates must be rewarded for
_____________________________________________________________________________________ what they have shown they can do rather than penalised for omissions.
_____________________________________________________________________________________ • 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
_____________________________________________________________________________________ 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 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.
_____________________________________________________________________________________ • Where some judgement is required, mark schemes will provide the principles
_____________________________________________________________________________________ by which marks will be awarded and exemplification may be limited.
_____________________________________________________________________________________ • When examiners are in doubt regarding the application of the mark scheme to
_____________________________________________________________________________________ a candidate’s response, the team leader must be consulted.
_____________________________________________________________________________________ • Crossed out work should be marked UNLESS the candidate has replaced it
_____________________________________________________________________________________ with an alternative response.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(Total for Question 1 is 6 marks)
for more:
for more:
3
*P74079A0332* Turn over
, EDEXCEL GCE MATHEMATICS
General Instructions for Marking
2. The line l has vector equation
1. The total number of marks for the paper is 75.
2
4
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
r
1
3 0 2. The Edexcel Mathematics mark schemes use the following types of marks:
3
2
The plane Π contains the line l and the point A (3, 2, 1) • M marks: method marks are awarded for ‘knowing a method and attempting
to apply it’, unless otherwise indicated.
(a) Determine a vector equation for Π, giving your answer in the form r a λb μc
where λ and μ are scalar parameters. • A marks: Accuracy marks can only be awarded if the relevant method (M)
(3) marks have been earned.
• B marks are unconditional accuracy marks (independent of M marks)
(b) Determine a vector equation for the line of intersection of Π with the x-y plane.
• Marks should not be subdivided.
Give your answer in the form r = p + tq where t is a scalar parameter.
(3) 3. Abbreviations
_____________________________________________________________________________________
These are some of the traditional marking abbreviations that will appear in the mark
_____________________________________________________________________________________
schemes.
_____________________________________________________________________________________
• bod – benefit of doubt
_____________________________________________________________________________________ • ft – follow through
_____________________________________________________________________________________ • the symbol will be used for correct ft
_____________________________________________________________________________________ • cao – correct answer only
• cso - correct solution only. There must be no errors in this part of the
_____________________________________________________________________________________
question to obtain this mark
_____________________________________________________________________________________ • isw – ignore subsequent working
_____________________________________________________________________________________ • awrt – answers which round to
_____________________________________________________________________________________ • SC: special case
• oe – or equivalent (and appropriate)
_____________________________________________________________________________________
• dep – dependent
_____________________________________________________________________________________ • indep – independent
_____________________________________________________________________________________ • dp decimal places
_____________________________________________________________________________________ • sf significant figures
_____________________________________________________________________________________ • The answer is printed on the paper
• The second mark is dependent on gaining the first mark
_____________________________________________________________________________________
_____________________________________________________________________________________ 4. For misreading which does not alter the character of a question or materially
_____________________________________________________________________________________ simplify it, deduct two from any A or B marks gained, in that part of the question
_____________________________________________________________________________________ affected.
_____________________________________________________________________________________
5. Where a candidate has made multiple responses and indicates which response
_____________________________________________________________________________________ they wish to submit, examiners should mark this response.
_____________________________________________________________________________________ If there are several attempts at a question which have not been crossed out,
_____________________________________________________________________________________ examiners should mark the final answer which is the answer that is the most
_____________________________________________________________________________________ complete.
_____________________________________________________________________________________
for more:
4
for more:
*P74079A0432*
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Friday 19 June 2026
Mark Scheme (Results)
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/3A
Further Mathematics
Summer 2026
Advanced
PAPER 3A: Further Pure Mathematics 1
You must have: Total Marks
Mathematical Formulae and Statistics Tables (Green), calculator
Pearson Edexcel GCE
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebra manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
In Further Mathematics (9FM0)
Instructions Paper 3A Further Pure Mathematics 1
•• 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 this page with your name,
••
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are clearly labelled.
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
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
•
There are 9 questions in this question paper. The total mark for this paper is 75.
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
P74079APearson Education Ltd.
P:1/1/1/1/1/1/1/1/
*P74079A0132* for more:
for more:
, Edexcel and BTEC Qualifications
1.
y
H
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 Pearson, the UK’s
largest awarding body. We provide a wide range of qualifications
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
P
O x
Q
l
Pearson: helping people progress, everywhere
Pearson 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
Figure 1 languages, we have built an international reputation for our commitment to high
standards and raising achievement through innovation in education. Find out more
Figure 1 shows a rectangular hyperbola H with parametric equations
about how we can help you and your students at:
t 1
x y t
0
6 6t
The line l with equation 3 x 15 y 2
0 intersects H at the point P and at the point Q,
as shown in Figure 1.
(a) Show that the points of intersection of l and H satisfy the equation
t 2 4t 5
0
(2)
(b) Hence, or otherwise, determine the coordinates of P and Q.
(4)
_____________________________________________________________________________________
_____________________________________________________________________________________
Summer 2026
_____________________________________________________________________________________
Question Paper Log Number P74079A
_____________________________________________________________________________________ Publication Code 9FM0_3A_2606_MS
_____________________________________________________________________________________ All the material in this publication is
Pearson Education Ltd
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
for more:
2
for more:
*P74079A0232*
, General Marking Guidance
Question 1 continued • All candidates must receive the same treatment. Examiners must mark the
_____________________________________________________________________________________ first candidate in exactly the same way as they mark the last.
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
_____________________________________________________________________________________ • Mark schemes should be applied positively. Candidates must be rewarded for
_____________________________________________________________________________________ what they have shown they can do rather than penalised for omissions.
_____________________________________________________________________________________ • 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
_____________________________________________________________________________________ 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 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.
_____________________________________________________________________________________ • Where some judgement is required, mark schemes will provide the principles
_____________________________________________________________________________________ by which marks will be awarded and exemplification may be limited.
_____________________________________________________________________________________ • When examiners are in doubt regarding the application of the mark scheme to
_____________________________________________________________________________________ a candidate’s response, the team leader must be consulted.
_____________________________________________________________________________________ • Crossed out work should be marked UNLESS the candidate has replaced it
_____________________________________________________________________________________ with an alternative response.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
(Total for Question 1 is 6 marks)
for more:
for more:
3
*P74079A0332* Turn over
, EDEXCEL GCE MATHEMATICS
General Instructions for Marking
2. The line l has vector equation
1. The total number of marks for the paper is 75.
2
4
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
r
1
3 0 2. The Edexcel Mathematics mark schemes use the following types of marks:
3
2
The plane Π contains the line l and the point A (3, 2, 1) • M marks: method marks are awarded for ‘knowing a method and attempting
to apply it’, unless otherwise indicated.
(a) Determine a vector equation for Π, giving your answer in the form r a λb μc
where λ and μ are scalar parameters. • A marks: Accuracy marks can only be awarded if the relevant method (M)
(3) marks have been earned.
• B marks are unconditional accuracy marks (independent of M marks)
(b) Determine a vector equation for the line of intersection of Π with the x-y plane.
• Marks should not be subdivided.
Give your answer in the form r = p + tq where t is a scalar parameter.
(3) 3. Abbreviations
_____________________________________________________________________________________
These are some of the traditional marking abbreviations that will appear in the mark
_____________________________________________________________________________________
schemes.
_____________________________________________________________________________________
• bod – benefit of doubt
_____________________________________________________________________________________ • ft – follow through
_____________________________________________________________________________________ • the symbol will be used for correct ft
_____________________________________________________________________________________ • cao – correct answer only
• cso - correct solution only. There must be no errors in this part of the
_____________________________________________________________________________________
question to obtain this mark
_____________________________________________________________________________________ • isw – ignore subsequent working
_____________________________________________________________________________________ • awrt – answers which round to
_____________________________________________________________________________________ • SC: special case
• oe – or equivalent (and appropriate)
_____________________________________________________________________________________
• dep – dependent
_____________________________________________________________________________________ • indep – independent
_____________________________________________________________________________________ • dp decimal places
_____________________________________________________________________________________ • sf significant figures
_____________________________________________________________________________________ • The answer is printed on the paper
• The second mark is dependent on gaining the first mark
_____________________________________________________________________________________
_____________________________________________________________________________________ 4. For misreading which does not alter the character of a question or materially
_____________________________________________________________________________________ simplify it, deduct two from any A or B marks gained, in that part of the question
_____________________________________________________________________________________ affected.
_____________________________________________________________________________________
5. Where a candidate has made multiple responses and indicates which response
_____________________________________________________________________________________ they wish to submit, examiners should mark this response.
_____________________________________________________________________________________ If there are several attempts at a question which have not been crossed out,
_____________________________________________________________________________________ examiners should mark the final answer which is the answer that is the most
_____________________________________________________________________________________ complete.
_____________________________________________________________________________________
for more:
4
for more:
*P74079A0432*
