Pearson Edexcel International Advanced Level
Monday 12 January 2026
WFM01/01A
Paper
Morning (Time: 1 hour 30 minutes)
reference
Mathematics
International Advanced Subsidiary/ Advanced Level
Further Pure Mathematics F1
Question paper Mark Scheme (Final)
You must have:
Answer book (sent separately).
Do not return this question paper with the answer book.
January 2026
International Advanced Level in Further
Pure Mathematics F1
WFM01/01A
Turn over
P87589APearson Education Ltd.
C:1/1/1/
*P87589A*
, n n Edexcel and BTEC Qualifications
1. Use the standard results for
r and for
r 1
r
r 1
2
to show that, for all positive integers n,
n
n
r (r
3) a (n
1)(n
b)
r 1 Edexcel and BTEC qualifications are awarded by Pearson, the UK’s largest
awarding body. We provide a wide range of qualifications including academic,
where a and b are integers to be found. vocational, occupational and specific programmes for employers. For further
(4)
information visit our qualifications websites at or
(Total for Question 1 is 4 marks) .
Alternatively, you can get in touch with us using the details on our contact us
2. In this question you must show all stages of your working. page at
Solutions relying on calculator technology are not acceptable.
4 3 2
f (z) = z – 6z + 38z – 94z + 221
(a) Given that z = 2 + 3i is a root of the equation f (z) = 0, use algebra to find the three
other roots of f (z) = 0
(7)
Pearson: helping people progress, everywhere
(b) Show the four roots of f (z) = 0 on a single Argand diagram.
(2) Pearson aspires to be the world’s leading learning company. Our aim is to help everyone
(Total for Question 2 is 9 marks) 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
3. In this question you must show all stages of your working. years, and by working across 70 countries, in 100 languages, we have built an international
Solutions relying on calculator technology are not acceptable. 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:
The rectangular hyperbola H has parametric equations
4
=x 4=
t y
t
The straight line with equation 3y – 2x = 10 intersects H at the points A and B.
Given that the point A is above the x-axis,
(a) find the coordinates of the point A and the coordinates of the point B.
(5)
(b) Find the coordinates of the midpoint of AB.
(2)
(Total for Question 3 is 7 marks)
January 2026
Question Paper Log Number P87589A
Publication Code WFM01_01A_2601_MS
All the material in this publication is
Pearson Education Ltd
2 P87589A
,4. In this question you must show all stages of your working. General Marking Guidance
Solutions relying on calculator technology are not acceptable.
• All candidates must receive the same treatment. Examiners must mark the first
Given that z = x + iy, where x and y are real numbers, solve the equation
candidate in exactly the same way as they mark the last.
(z – 2i)(z* – 2i) = 21 – 12i • Mark schemes should be applied positively. Candidates must be rewarded for what they
where z* is the complex conjugate of z. have shown they can do rather than penalised for omissions.
(6) • Examiners should mark according to the mark scheme not according to their perception
(Total for Question 4 is 6 marks) of where the grade boundaries may lie.
• There is no ceiling on achievement. All marks on the mark scheme should be used
5. The quadratic equation appropriately.
2
x – 2x + 3 = 0 • All the marks on the mark scheme are designed to be awarded. Examiners should always
has roots α and β. 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
Without solving the equation,
of credit according to the mark scheme.
(a) (i) write down the value of (α + β) and the value of αβ • Where some judgement is required, mark schemes will provide the principles by which
2 2
(ii) show that α + β = –2 marks will be awarded and exemplification may be limited.
(iii) find the value of α + β
3 3 • When examiners are in doubt regarding the application of the mark scheme to a
(5) candidate’s response, the team leader must be consulted.
4 4 2
(b) (i) show that α + β = (α + β ) – 2(αβ)
2 2 2
• Crossed out work should be marked UNLESS the candidate has replaced it with an
alternative response.
(ii) find a quadratic equation which has roots
3 3
(α – β) and (β – α)
2
giving your answer in the form px + qx + r = 0 where p, q and r are integers.
(6)
(Total for Question 5 is 11 marks)
P87589A 3
Turn over
, EDEXCEL IAL MATHEMATICS
2 p 3q
6. A
General Instructions for Marking
3 p 5q
where p and q are non-zero real constants. 1. The total number of marks for the paper is 75.
–1
(a) Find A in terms of p and q. 2. The Edexcel Mathematics mark schemes use the following types of marks:
(3)
• M marks: Method marks are awarded for ‘knowing a method and attempting to
Given XA = B, where apply it’, unless otherwise indicated.
p q • A marks: Accuracy marks can only be awarded if the relevant method (M) marks
have been earned.
B
6 p 11q
5 p 8q • B marks are unconditional accuracy marks (independent of M marks)
Marks should not be subdivided.
(b) find the matrix X, giving your answer in its simplest form.
(4) 3. Abbreviations
(Total for Question 6 is 7 marks)
These are some of the traditional marking abbreviations that will appear in the mark
7 schemes and can be used if you are using the annotation facility on ePEN:
7. f ( x) 30
x5 x>0
x • bod – benefit of doubt
The only real root, α, of the equation f (x) = 0 lies in the interval [2, 2.1]. • ft – follow through
(a) Starting with the interval [2, 2.1], use interval bisection twice to find an interval of o the symbol will be used for correct ft
width 0.025 that contains α. • cao – correct answer only
(4)
• cso – correct solution only. There must be no errors in this part of the question to
(b) Find f ′(x). obtain this mark
(2)
• isw – ignore subsequent working
Taking 2 as a first approximation to α, apply the Newton–Raphson process once to • awrt – answers which round to
f (x) to find a second approximation to α, giving your answer to 2 decimal places.
(2) • SC – special case
(Total for Question 7 is 8 marks) • oe – or equivalent (and appropriate)
• d… or dep – dependent
• indep – independent
• dp – decimal places
• sf – significant figures
• – The answer is printed on the paper or ag- answer given
• or d… – The second mark is dependent on gaining the first mark
4. All A marks are ‘correct answer only’ (cao), unless shown, for example, as A1 ft to
indicate that previous wrong working is to be followed through. After a misread
however, the subsequent A marks affected are treated as A ft, but manifestly absurd
answers should never be awarded A marks.
4 P87589A
Monday 12 January 2026
WFM01/01A
Paper
Morning (Time: 1 hour 30 minutes)
reference
Mathematics
International Advanced Subsidiary/ Advanced Level
Further Pure Mathematics F1
Question paper Mark Scheme (Final)
You must have:
Answer book (sent separately).
Do not return this question paper with the answer book.
January 2026
International Advanced Level in Further
Pure Mathematics F1
WFM01/01A
Turn over
P87589APearson Education Ltd.
C:1/1/1/
*P87589A*
, n n Edexcel and BTEC Qualifications
1. Use the standard results for
r and for
r 1
r
r 1
2
to show that, for all positive integers n,
n
n
r (r
3) a (n
1)(n
b)
r 1 Edexcel and BTEC qualifications are awarded by Pearson, the UK’s largest
awarding body. We provide a wide range of qualifications including academic,
where a and b are integers to be found. vocational, occupational and specific programmes for employers. For further
(4)
information visit our qualifications websites at or
(Total for Question 1 is 4 marks) .
Alternatively, you can get in touch with us using the details on our contact us
2. In this question you must show all stages of your working. page at
Solutions relying on calculator technology are not acceptable.
4 3 2
f (z) = z – 6z + 38z – 94z + 221
(a) Given that z = 2 + 3i is a root of the equation f (z) = 0, use algebra to find the three
other roots of f (z) = 0
(7)
Pearson: helping people progress, everywhere
(b) Show the four roots of f (z) = 0 on a single Argand diagram.
(2) Pearson aspires to be the world’s leading learning company. Our aim is to help everyone
(Total for Question 2 is 9 marks) 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
3. In this question you must show all stages of your working. years, and by working across 70 countries, in 100 languages, we have built an international
Solutions relying on calculator technology are not acceptable. 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:
The rectangular hyperbola H has parametric equations
4
=x 4=
t y
t
The straight line with equation 3y – 2x = 10 intersects H at the points A and B.
Given that the point A is above the x-axis,
(a) find the coordinates of the point A and the coordinates of the point B.
(5)
(b) Find the coordinates of the midpoint of AB.
(2)
(Total for Question 3 is 7 marks)
January 2026
Question Paper Log Number P87589A
Publication Code WFM01_01A_2601_MS
All the material in this publication is
Pearson Education Ltd
2 P87589A
,4. In this question you must show all stages of your working. General Marking Guidance
Solutions relying on calculator technology are not acceptable.
• All candidates must receive the same treatment. Examiners must mark the first
Given that z = x + iy, where x and y are real numbers, solve the equation
candidate in exactly the same way as they mark the last.
(z – 2i)(z* – 2i) = 21 – 12i • Mark schemes should be applied positively. Candidates must be rewarded for what they
where z* is the complex conjugate of z. have shown they can do rather than penalised for omissions.
(6) • Examiners should mark according to the mark scheme not according to their perception
(Total for Question 4 is 6 marks) of where the grade boundaries may lie.
• There is no ceiling on achievement. All marks on the mark scheme should be used
5. The quadratic equation appropriately.
2
x – 2x + 3 = 0 • All the marks on the mark scheme are designed to be awarded. Examiners should always
has roots α and β. 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
Without solving the equation,
of credit according to the mark scheme.
(a) (i) write down the value of (α + β) and the value of αβ • Where some judgement is required, mark schemes will provide the principles by which
2 2
(ii) show that α + β = –2 marks will be awarded and exemplification may be limited.
(iii) find the value of α + β
3 3 • When examiners are in doubt regarding the application of the mark scheme to a
(5) candidate’s response, the team leader must be consulted.
4 4 2
(b) (i) show that α + β = (α + β ) – 2(αβ)
2 2 2
• Crossed out work should be marked UNLESS the candidate has replaced it with an
alternative response.
(ii) find a quadratic equation which has roots
3 3
(α – β) and (β – α)
2
giving your answer in the form px + qx + r = 0 where p, q and r are integers.
(6)
(Total for Question 5 is 11 marks)
P87589A 3
Turn over
, EDEXCEL IAL MATHEMATICS
2 p 3q
6. A
General Instructions for Marking
3 p 5q
where p and q are non-zero real constants. 1. The total number of marks for the paper is 75.
–1
(a) Find A in terms of p and q. 2. The Edexcel Mathematics mark schemes use the following types of marks:
(3)
• M marks: Method marks are awarded for ‘knowing a method and attempting to
Given XA = B, where apply it’, unless otherwise indicated.
p q • A marks: Accuracy marks can only be awarded if the relevant method (M) marks
have been earned.
B
6 p 11q
5 p 8q • B marks are unconditional accuracy marks (independent of M marks)
Marks should not be subdivided.
(b) find the matrix X, giving your answer in its simplest form.
(4) 3. Abbreviations
(Total for Question 6 is 7 marks)
These are some of the traditional marking abbreviations that will appear in the mark
7 schemes and can be used if you are using the annotation facility on ePEN:
7. f ( x) 30
x5 x>0
x • bod – benefit of doubt
The only real root, α, of the equation f (x) = 0 lies in the interval [2, 2.1]. • ft – follow through
(a) Starting with the interval [2, 2.1], use interval bisection twice to find an interval of o the symbol will be used for correct ft
width 0.025 that contains α. • cao – correct answer only
(4)
• cso – correct solution only. There must be no errors in this part of the question to
(b) Find f ′(x). obtain this mark
(2)
• isw – ignore subsequent working
Taking 2 as a first approximation to α, apply the Newton–Raphson process once to • awrt – answers which round to
f (x) to find a second approximation to α, giving your answer to 2 decimal places.
(2) • SC – special case
(Total for Question 7 is 8 marks) • oe – or equivalent (and appropriate)
• d… or dep – dependent
• indep – independent
• dp – decimal places
• sf – significant figures
• – The answer is printed on the paper or ag- answer given
• or d… – The second mark is dependent on gaining the first mark
4. All A marks are ‘correct answer only’ (cao), unless shown, for example, as A1 ft to
indicate that previous wrong working is to be followed through. After a misread
however, the subsequent A marks affected are treated as A ft, but manifestly absurd
answers should never be awarded A marks.
4 P87589A
