Please write clearly in block capitals.
Centre number Candidate number
Surname __________________________________________________________________________
A-level
Forename(s) __________________________________________________________________________ FURTHER MATHEMATICS
Candidate signature __________________________________________________________________________
I declare this is my own work. 7367/1
Paper 1
A-level Mark scheme
FURTHER MATHEMATICS June 2026
Version: 1.0 Final
Paper 1
Thursday 21 May 2026 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the Formulae and statistical tables booklet for
Question Mark
A‑level Mathematic A‑level Further Mathematics.
l You should have a graphical or scientific calculator that meets the
requirements of the specification.
Instructions
l Use black ink or black ball‑point pen. Pencil should only be used for drawing.
l Fill in the boxes at the top of this page.
l Answer all questions.
l You must answer each question in the space provided for that question.
If you require extra space for your answer(s), use the lined pages at the end
of this book. Write the question number against your answer(s).
l Do not write outside the box around each page or on blank pages.
l Show all necessary working; otherwise marks for method may be lost.
l Do all rough work in this book. Cross through any work that you do not want
to be marked.
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100.
Advice
l Unless stated otherwise, you may quote formulae, without proof,
from the booklet.
l You do not necessarily need to use all the space provided. TOTAL
(JUN )
G/LM/Jun26/G4008/V6 7367/1
, 2
MARK SCHEME – A-LEVEL FURTHER MATHEMATICS – 7367/1 – JUNE 2026
Do not write
outside the
Answer all questions in the spaces provided. box
Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant
questions, by a panel of subject teachers. This mark scheme includes any amendments made at the
1 The vectors a and b are defined by standardisation events which all associates participate in and is the scheme which was used by them in
this examination. The standardisation process ensures that the mark scheme covers the students’
responses to questions and that every associate understands and applies it in the same correct way.
2 1–p
As preparation for standardisation each associate analyses a number of students’ scripts. Alternative
a = p b = 4
answers not already covered by the mark scheme are discussed and legislated for. If, after the
3 1 standardisation process, associates encounter unusual answers which have not been raised they are
It is given that a • b = 0 required to refer these to the Lead Examiner.
It must be stressed that a mark scheme is a working document, in many cases further developed and
Find the value of p expanded on the basis of students’ reactions to a particular paper. Assumptions about future mark
schemes on the basis of one year’s document should be avoided; whilst the guiding principles of
Circle your answer. assessment remain constant, details will change, depending on the content of a particular examination
[1 mark] paper.
No student should be disadvantaged on the basis of their gender identity and/or how they refer to the
– 5 – 5 5 5
2 3 3 2 gender identity of others in their exam responses.
A consistent use of ‘they/them’ as a singular and pronouns beyond ‘she/her’ or ‘he/him’ will be credited in
exam responses in line with existing mark scheme criteria.
2 The matrix A is defined by
Further copies of this mark scheme are available from
– √3 1
2 2
A=
– 1 – √3
2 2
The matrix A represents an anticlockwise rotation through an angle θ radians.
Find the value of θ
Circle your answer.
[1 mark]
π 5π 7π 11π
6 6 6 6
information
retains the on all its publications. However, registered schools/colleges for are permitted to copy material from this booklet for their own
internal use, with the following important exception: cannot give permission to schools/colleges to photocopy any material that is acknowledged to a third
party even for internal use within the centre.
and its licensors. All rights reserved.
(02)
2
G/Jun26/7367/1
, 3
MARK SCHEME – A-LEVEL FURTHER MATHEMATICS – 7367/1 – JUNE 2026
Do not write
outside the
3 Find the integrating factor which could be used to solve the differential equation box
dy 3y Mark scheme instructions to examiners
+ = x2 + 5
dx x
Circle your answer. General
[1 mark]
3 3
3In x x 3 x e x The mark scheme for each question shows:
• the marks available for each part of the question
• the total marks available for the question
• marking instructions that indicate when marks should be awarded or withheld including the principle
on which each mark is awarded. Information is included to help the examiner make his or her
judgement and to delineate what is creditworthy from that not worthy of credit
• a typical solution. This response is one we expect to see frequently. However credit must be given on
the basis of the marking instructions.
If a student uses a method which is not explicitly covered by the marking instructions the same
principles of marking should be applied. Credit should be given to any valid methods. Examiners should
seek advice from their senior examiner if in any doubt.
a + bi
4 Which one of the following expressions is equivalent to , where a and b are Key to mark types
2i
real numbers?
Circle your answer. M mark is for method
[1 mark] R mark is for reasoning
A mark is dependent on M marks and is for accuracy
– b – a i – b + a i b – a i b + a i B mark is independent of M marks and is for method and accuracy
2 2 2 2 2 2 2 2
E mark is for explanation
F follow through from previous incorrect result
Turn over for the next question
Key to mark scheme abbreviations
CAO correct answer only
CSO correct solution only
ft follow through from previous incorrect result
‘their’ indicates that credit can be given from previous incorrect result
AWFW anything which falls within
AWRT anything which rounds to
ACF any correct form
AG answer given
SC special case
OE or equivalent
NMS no method shown
PI possibly implied
sf significant figure(s)
dp decimal place(s)
ISW Ignore Subsequent Workings
Turn over U
(03)
3
G/Jun26/7367/1
, 4
MARK SCHEME – A-LEVEL FURTHER MATHEMATICS – 7367/1 – JUNE 2026
Do not write
outside the
5 The complex number z satisfies both box
Examiners should consistently apply the following general marking principles:
0 ≤ arg (z) ≤ tan–1 (2)
and No Method Shown
│ z│ ≤ 2 Where the question specifically requires a particular method to be used, we must usually see evidence
of use of this method for any marks to be awarded.
The region R is the locus of z
Where the answer can be reasonably obtained without showing working and it is very unlikely that the
Sketch and shade the region R on the Argand diagram in Figure 1 correct answer can be obtained by using an incorrect method, we must award full marks. However, the
[3 marks] obvious penalty to candidates showing no working is that incorrect answers, however close, earn no
marks.
Figure 1
Where a question asks the candidate to state or write down a result, no method need be shown for full
Im marks.
3
Where the permitted calculator has functions which reasonably allow the solution of the question directly,
the correct answer without working earns full marks, unless it is given to less than the degree of
2 accuracy accepted in the mark scheme, when it gains no marks.
Otherwise we require evidence of a correct method for any marks to be awarded.
1
Diagrams
Diagrams that have working on them should be treated like normal responses. If a diagram has been
–3 –2 –1 0 1 2 3 Re written on but the correct response is within the answer space, the work within the answer space should
be marked. Working on diagrams that contradicts work within the answer space is not to be considered
–1 as choice but as working, and is not, therefore, penalised.
Work erased or crossed out
–2 Erased or crossed out work that is still legible and has not been replaced should be marked. Erased or
crossed out work that has been replaced can be ignored.
–3 Choice
When a choice of answers and/or methods is given and the student has not clearly indicated which
answer they want to be marked, mark positively, awarding marks for all of the student’s best attempts.
Withhold marks for final accuracy and conclusions if there are conflicting complete answers or when an
incorrect solution (or part thereof) is referred to in the final answer.
(04)
4
G/Jun26/7367/1
Centre number Candidate number
Surname __________________________________________________________________________
A-level
Forename(s) __________________________________________________________________________ FURTHER MATHEMATICS
Candidate signature __________________________________________________________________________
I declare this is my own work. 7367/1
Paper 1
A-level Mark scheme
FURTHER MATHEMATICS June 2026
Version: 1.0 Final
Paper 1
Thursday 21 May 2026 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the Formulae and statistical tables booklet for
Question Mark
A‑level Mathematic A‑level Further Mathematics.
l You should have a graphical or scientific calculator that meets the
requirements of the specification.
Instructions
l Use black ink or black ball‑point pen. Pencil should only be used for drawing.
l Fill in the boxes at the top of this page.
l Answer all questions.
l You must answer each question in the space provided for that question.
If you require extra space for your answer(s), use the lined pages at the end
of this book. Write the question number against your answer(s).
l Do not write outside the box around each page or on blank pages.
l Show all necessary working; otherwise marks for method may be lost.
l Do all rough work in this book. Cross through any work that you do not want
to be marked.
Information
l The marks for questions are shown in brackets.
l The maximum mark for this paper is 100.
Advice
l Unless stated otherwise, you may quote formulae, without proof,
from the booklet.
l You do not necessarily need to use all the space provided. TOTAL
(JUN )
G/LM/Jun26/G4008/V6 7367/1
, 2
MARK SCHEME – A-LEVEL FURTHER MATHEMATICS – 7367/1 – JUNE 2026
Do not write
outside the
Answer all questions in the spaces provided. box
Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant
questions, by a panel of subject teachers. This mark scheme includes any amendments made at the
1 The vectors a and b are defined by standardisation events which all associates participate in and is the scheme which was used by them in
this examination. The standardisation process ensures that the mark scheme covers the students’
responses to questions and that every associate understands and applies it in the same correct way.
2 1–p
As preparation for standardisation each associate analyses a number of students’ scripts. Alternative
a = p b = 4
answers not already covered by the mark scheme are discussed and legislated for. If, after the
3 1 standardisation process, associates encounter unusual answers which have not been raised they are
It is given that a • b = 0 required to refer these to the Lead Examiner.
It must be stressed that a mark scheme is a working document, in many cases further developed and
Find the value of p expanded on the basis of students’ reactions to a particular paper. Assumptions about future mark
schemes on the basis of one year’s document should be avoided; whilst the guiding principles of
Circle your answer. assessment remain constant, details will change, depending on the content of a particular examination
[1 mark] paper.
No student should be disadvantaged on the basis of their gender identity and/or how they refer to the
– 5 – 5 5 5
2 3 3 2 gender identity of others in their exam responses.
A consistent use of ‘they/them’ as a singular and pronouns beyond ‘she/her’ or ‘he/him’ will be credited in
exam responses in line with existing mark scheme criteria.
2 The matrix A is defined by
Further copies of this mark scheme are available from
– √3 1
2 2
A=
– 1 – √3
2 2
The matrix A represents an anticlockwise rotation through an angle θ radians.
Find the value of θ
Circle your answer.
[1 mark]
π 5π 7π 11π
6 6 6 6
information
retains the on all its publications. However, registered schools/colleges for are permitted to copy material from this booklet for their own
internal use, with the following important exception: cannot give permission to schools/colleges to photocopy any material that is acknowledged to a third
party even for internal use within the centre.
and its licensors. All rights reserved.
(02)
2
G/Jun26/7367/1
, 3
MARK SCHEME – A-LEVEL FURTHER MATHEMATICS – 7367/1 – JUNE 2026
Do not write
outside the
3 Find the integrating factor which could be used to solve the differential equation box
dy 3y Mark scheme instructions to examiners
+ = x2 + 5
dx x
Circle your answer. General
[1 mark]
3 3
3In x x 3 x e x The mark scheme for each question shows:
• the marks available for each part of the question
• the total marks available for the question
• marking instructions that indicate when marks should be awarded or withheld including the principle
on which each mark is awarded. Information is included to help the examiner make his or her
judgement and to delineate what is creditworthy from that not worthy of credit
• a typical solution. This response is one we expect to see frequently. However credit must be given on
the basis of the marking instructions.
If a student uses a method which is not explicitly covered by the marking instructions the same
principles of marking should be applied. Credit should be given to any valid methods. Examiners should
seek advice from their senior examiner if in any doubt.
a + bi
4 Which one of the following expressions is equivalent to , where a and b are Key to mark types
2i
real numbers?
Circle your answer. M mark is for method
[1 mark] R mark is for reasoning
A mark is dependent on M marks and is for accuracy
– b – a i – b + a i b – a i b + a i B mark is independent of M marks and is for method and accuracy
2 2 2 2 2 2 2 2
E mark is for explanation
F follow through from previous incorrect result
Turn over for the next question
Key to mark scheme abbreviations
CAO correct answer only
CSO correct solution only
ft follow through from previous incorrect result
‘their’ indicates that credit can be given from previous incorrect result
AWFW anything which falls within
AWRT anything which rounds to
ACF any correct form
AG answer given
SC special case
OE or equivalent
NMS no method shown
PI possibly implied
sf significant figure(s)
dp decimal place(s)
ISW Ignore Subsequent Workings
Turn over U
(03)
3
G/Jun26/7367/1
, 4
MARK SCHEME – A-LEVEL FURTHER MATHEMATICS – 7367/1 – JUNE 2026
Do not write
outside the
5 The complex number z satisfies both box
Examiners should consistently apply the following general marking principles:
0 ≤ arg (z) ≤ tan–1 (2)
and No Method Shown
│ z│ ≤ 2 Where the question specifically requires a particular method to be used, we must usually see evidence
of use of this method for any marks to be awarded.
The region R is the locus of z
Where the answer can be reasonably obtained without showing working and it is very unlikely that the
Sketch and shade the region R on the Argand diagram in Figure 1 correct answer can be obtained by using an incorrect method, we must award full marks. However, the
[3 marks] obvious penalty to candidates showing no working is that incorrect answers, however close, earn no
marks.
Figure 1
Where a question asks the candidate to state or write down a result, no method need be shown for full
Im marks.
3
Where the permitted calculator has functions which reasonably allow the solution of the question directly,
the correct answer without working earns full marks, unless it is given to less than the degree of
2 accuracy accepted in the mark scheme, when it gains no marks.
Otherwise we require evidence of a correct method for any marks to be awarded.
1
Diagrams
Diagrams that have working on them should be treated like normal responses. If a diagram has been
–3 –2 –1 0 1 2 3 Re written on but the correct response is within the answer space, the work within the answer space should
be marked. Working on diagrams that contradicts work within the answer space is not to be considered
–1 as choice but as working, and is not, therefore, penalised.
Work erased or crossed out
–2 Erased or crossed out work that is still legible and has not been replaced should be marked. Erased or
crossed out work that has been replaced can be ignored.
–3 Choice
When a choice of answers and/or methods is given and the student has not clearly indicated which
answer they want to be marked, mark positively, awarding marks for all of the student’s best attempts.
Withhold marks for final accuracy and conclusions if there are conflicting complete answers or when an
incorrect solution (or part thereof) is referred to in the final answer.
(04)
4
G/Jun26/7367/1
