Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Thursday 14 May 2026
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/01 Mark Scheme (Results)
Further Mathematics
Advanced
Summer 2026
PAPER 1: Core Pure Mathematics 1
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator permitted by Pearson regulations. Pearson Edexcel GCE
Calculators must not have the facility for algebraic manipulation,
differentiation and integration, or have retrievable mathematical formulae In Further Mathematics (9FM0)
stored in them.
Instructions Paper 01 Core 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.
• 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.
•Information
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
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
P81303APearson Education Ltd.
P:1/1/1/1/1/
*P81303A0132* for more:
for more:
,1.
With respect to the right -hand rule , a rotation through θ° anticlockwise about the Edexcel and BTEC Qualifications
y -axis is represented by the matrix
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
cos 0 sin
M
0 1 0
sin 0 cos
Edexcel and BTEC qualifications are awarded by Pearson, the UK’s
largest awarding body. We provide a wide range of qualifications
The point P has coordinates (k, 2, k), where k is a constant. including academic, vocational, occupational and specific
(a) Determine the coordinates of the image of P under the transformation represented programmes for employers. For further information visit our
by M, giving the answer in terms of k and θ qualifications websites at or .
(2) Alternatively, you can get in touch with us using the details on our
Given that the image of P lies on the plane with equation contact us page at
x+z =4
(b) show that k = 2 sec θ
(2)
π Pearson: helping people progress, everywhere
Given also that k = 4 and 0 < θ <
2
describe the single geometric transformation represented by M Pearson aspires to be the world’s leading learning company. Our aim is to help everyone
(1) 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 P81303A
_____________________________________________________________________________________ Publication Code 9FM0_01_2606_MS
All the material in this publication is
_____________________________________________________________________________________ Pearson Education Ltd
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________ for more:
2
for more:
*P81303A0232*
, General Marking Guidance
Question 1 continued
_____________________________________________________________________________________ • All candidates must receive the same treatment. Examiners must mark the
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
_____________________________________________________________________________________ first candidate in exactly the same way as they mark the last.
_____________________________________________________________________________________ • 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 5 marks)
for more:
for more:
3
*P81303A0332* Turn over
, EDEXCEL GCE MATHEMATICS
2. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable. General Instructions for Marking
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
A complex number z is given by z = λ – 2i , where λ is a real constant and λ > 0
(a) Show that 1. The total number of marks for the paper is 75.
3z* + z2 = (λ2 + 3λ – 4) + i(6 – 4λ) 2. The Edexcel Mathematics mark schemes use the following types of marks:
(3)
Given that 3z* + z2 is imaginary, • M marks: method marks are awarded for ‘knowing a method and attempting to
apply it’, unless otherwise indicated.
(b) determine the value of λ.
• A marks: Accuracy marks can only be awarded if the relevant method (M) marks
(2)
have been earned.
Hence determine, • B marks are unconditional accuracy marks (independent of M marks)
• Marks should not be subdivided.
(i) the exact value of ½ z ½
(1)
3. Abbreviations
(ii) arg z, giving your answer in radians, to 3 significant figures.
(2)
These are some of the traditional marking abbreviations that will appear in the mark
(d) Show z, z* and 3z* + z2 on a single Argand diagram.
(2) 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.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________ for more:
4
for more:
*P81303A0432*
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Thursday 14 May 2026
Afternoon (Time: 1 hour 30 minutes) Paper
reference 9FM0/01 Mark Scheme (Results)
Further Mathematics
Advanced
Summer 2026
PAPER 1: Core Pure Mathematics 1
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), calculator
Candidates may use any calculator permitted by Pearson regulations. Pearson Edexcel GCE
Calculators must not have the facility for algebraic manipulation,
differentiation and integration, or have retrievable mathematical formulae In Further Mathematics (9FM0)
stored in them.
Instructions Paper 01 Core 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.
• 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.
•Information
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
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
P81303APearson Education Ltd.
P:1/1/1/1/1/
*P81303A0132* for more:
for more:
,1.
With respect to the right -hand rule , a rotation through θ° anticlockwise about the Edexcel and BTEC Qualifications
y -axis is represented by the matrix
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
cos 0 sin
M
0 1 0
sin 0 cos
Edexcel and BTEC qualifications are awarded by Pearson, the UK’s
largest awarding body. We provide a wide range of qualifications
The point P has coordinates (k, 2, k), where k is a constant. including academic, vocational, occupational and specific
(a) Determine the coordinates of the image of P under the transformation represented programmes for employers. For further information visit our
by M, giving the answer in terms of k and θ qualifications websites at or .
(2) Alternatively, you can get in touch with us using the details on our
Given that the image of P lies on the plane with equation contact us page at
x+z =4
(b) show that k = 2 sec θ
(2)
π Pearson: helping people progress, everywhere
Given also that k = 4 and 0 < θ <
2
describe the single geometric transformation represented by M Pearson aspires to be the world’s leading learning company. Our aim is to help everyone
(1) 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 P81303A
_____________________________________________________________________________________ Publication Code 9FM0_01_2606_MS
All the material in this publication is
_____________________________________________________________________________________ Pearson Education Ltd
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________ for more:
2
for more:
*P81303A0232*
, General Marking Guidance
Question 1 continued
_____________________________________________________________________________________ • All candidates must receive the same treatment. Examiners must mark the
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
_____________________________________________________________________________________ first candidate in exactly the same way as they mark the last.
_____________________________________________________________________________________ • 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 5 marks)
for more:
for more:
3
*P81303A0332* Turn over
, EDEXCEL GCE MATHEMATICS
2. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable. General Instructions for Marking
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
A complex number z is given by z = λ – 2i , where λ is a real constant and λ > 0
(a) Show that 1. The total number of marks for the paper is 75.
3z* + z2 = (λ2 + 3λ – 4) + i(6 – 4λ) 2. The Edexcel Mathematics mark schemes use the following types of marks:
(3)
Given that 3z* + z2 is imaginary, • M marks: method marks are awarded for ‘knowing a method and attempting to
apply it’, unless otherwise indicated.
(b) determine the value of λ.
• A marks: Accuracy marks can only be awarded if the relevant method (M) marks
(2)
have been earned.
Hence determine, • B marks are unconditional accuracy marks (independent of M marks)
• Marks should not be subdivided.
(i) the exact value of ½ z ½
(1)
3. Abbreviations
(ii) arg z, giving your answer in radians, to 3 significant figures.
(2)
These are some of the traditional marking abbreviations that will appear in the mark
(d) Show z, z* and 3z* + z2 on a single Argand diagram.
(2) 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.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________ for more:
4
for more:
*P81303A0432*
