Please write clearly in block capitals.
Centre number Candidate number
Surname __________________________________________________________________________
A-level
Forename(s) __________________________________________________________________________ MATHEMATICS
Candidate signature __________________________________________________________________________
I declare this is my own work. 7357/3
Paper 3
A-level Mark scheme
MATHEMATICS June 2026
Version: 1.0 Final
Paper 3
Thursday 18 June 2026 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the Formulae for A‑level Mathematics booklet.
Question Mark
l You should have a ical 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.
l If you need 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/G4007/V7 7357/3
, 2
MARK SCHEME – A-LEVEL MATHEMATICS – 7357/3 – JUNE 2026
Do not write
outside the
Section A box
Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant
Answer all questions in the spaces provided. questions, by a panel of subject teachers. This mark scheme includes any amendments made at the
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’
1 A student claims that the product of two numbers is always at least as great as each of responses to questions and that every associate understands and applies it in the same correct way.
the two numbers. As preparation for standardisation each associate analyses a number of students’ scripts. Alternative
answers not already covered by the mark scheme are discussed and legislated for. If, after the
The student gives an example: standardisation process, associates encounter unusual answers which have not been raised they are
required to refer these to the Lead Examiner.
3× 4 =
12
It must be stressed that a mark scheme is a working document, in many cases further developed and
12 ≥ 3 and 12 ≥ 4 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
Determine which one of the options below shows that the student’s claim is not true. assessment remain constant, details will change, depending on the content of a particular examination
paper.
Circle your answer.
[1 mark] No student should be disadvantaged on the basis of their gender identity and/or how they refer to the
gender identity of others in their exam responses.
−1× −1 −1× 1 −1× 0 1× 1 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.
Further copies of this mark scheme are available from
2 Given that n is a positive integer, find nC1
Circle your answer.
[1 mark]
n! n–1 n n+1
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/Jun26/7357/3
, 3
MARK SCHEME – A-LEVEL MATHEMATICS – 7357/3 – JUNE 2026
Do not write
outside the
box
3 It is given that y = sin x
d2 y
Mark scheme instructions to examiners
Find an expression for
d x2
General
Circle your answer.
[1 mark] The mark scheme for each question shows:
• the marks available for each part of the question
• the total marks available for the question
− cos x − sin x cos x sin x • 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.
Turn over for the next question
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.
Key to mark types
M mark is for method
R mark is for reasoning
A mark is dependent on M marks and is for accuracy
B mark is independent of M marks and is for method and accuracy
E mark is for explanation
F follow through from previous incorrect result
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
ISW Ignore subsequent working
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)
Turn over U
(03)
3
G/Jun26/7357/3
, 4
MARK SCHEME – A-LEVEL MATHEMATICS – 7357/3 – JUNE 2026
Do not write
outside the
box
4 The graph with equation y = 2 x 2 − 3 x − 2 is shown on the diagram.
AS/A-level Maths/Further Maths assessment objectives
y
AO Description
3
AO1.1a Select routine procedures
AO1 AO1.1b Correctly carry out routine procedures
2
AO1.2 Accurately recall facts, terminology and definitions
AO2.1 Construct rigorous mathematical arguments (including proofs)
1
AO2.2a Make deductions
AO2.2b Make inferences
AO2
–1 0 1 2 3 x AO2.3 Assess the validity of mathematical arguments
AO2.4 Explain their reasoning
–1
AO2.5 Use mathematical language and notation correctly
AO3.1a Translate problems in mathematical contexts into mathematical processes
–2
AO3.1b Translate problems in non-mathematical contexts into mathematical processes
AO3.2a Interpret solutions to problems in their original context
–3
AO3.2b Where appropriate, evaluate the accuracy and limitations of solutions to problems
AO3 AO3.3 Translate situations in context into mathematical models
AO3.4 Use mathematical models
Shade the region defined by the inequalities
AO3.5a Evaluate the outcomes of modelling in context
y ≥ 2 x 2 − 3 x − 2 and y < x − 2 AO3.5b Recognise the limitations of models
[3 marks]
AO3.5c Where appropriate, explain how to refine models
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
(04)
4
G/Jun26/7357/3
Centre number Candidate number
Surname __________________________________________________________________________
A-level
Forename(s) __________________________________________________________________________ MATHEMATICS
Candidate signature __________________________________________________________________________
I declare this is my own work. 7357/3
Paper 3
A-level Mark scheme
MATHEMATICS June 2026
Version: 1.0 Final
Paper 3
Thursday 18 June 2026 Afternoon Time allowed: 2 hours
Materials For Examiner’s Use
l You must have the Formulae for A‑level Mathematics booklet.
Question Mark
l You should have a ical 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.
l If you need 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/G4007/V7 7357/3
, 2
MARK SCHEME – A-LEVEL MATHEMATICS – 7357/3 – JUNE 2026
Do not write
outside the
Section A box
Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant
Answer all questions in the spaces provided. questions, by a panel of subject teachers. This mark scheme includes any amendments made at the
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’
1 A student claims that the product of two numbers is always at least as great as each of responses to questions and that every associate understands and applies it in the same correct way.
the two numbers. As preparation for standardisation each associate analyses a number of students’ scripts. Alternative
answers not already covered by the mark scheme are discussed and legislated for. If, after the
The student gives an example: standardisation process, associates encounter unusual answers which have not been raised they are
required to refer these to the Lead Examiner.
3× 4 =
12
It must be stressed that a mark scheme is a working document, in many cases further developed and
12 ≥ 3 and 12 ≥ 4 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
Determine which one of the options below shows that the student’s claim is not true. assessment remain constant, details will change, depending on the content of a particular examination
paper.
Circle your answer.
[1 mark] No student should be disadvantaged on the basis of their gender identity and/or how they refer to the
gender identity of others in their exam responses.
−1× −1 −1× 1 −1× 0 1× 1 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.
Further copies of this mark scheme are available from
2 Given that n is a positive integer, find nC1
Circle your answer.
[1 mark]
n! n–1 n n+1
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/Jun26/7357/3
, 3
MARK SCHEME – A-LEVEL MATHEMATICS – 7357/3 – JUNE 2026
Do not write
outside the
box
3 It is given that y = sin x
d2 y
Mark scheme instructions to examiners
Find an expression for
d x2
General
Circle your answer.
[1 mark] The mark scheme for each question shows:
• the marks available for each part of the question
• the total marks available for the question
− cos x − sin x cos x sin x • 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.
Turn over for the next question
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.
Key to mark types
M mark is for method
R mark is for reasoning
A mark is dependent on M marks and is for accuracy
B mark is independent of M marks and is for method and accuracy
E mark is for explanation
F follow through from previous incorrect result
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
ISW Ignore subsequent working
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)
Turn over U
(03)
3
G/Jun26/7357/3
, 4
MARK SCHEME – A-LEVEL MATHEMATICS – 7357/3 – JUNE 2026
Do not write
outside the
box
4 The graph with equation y = 2 x 2 − 3 x − 2 is shown on the diagram.
AS/A-level Maths/Further Maths assessment objectives
y
AO Description
3
AO1.1a Select routine procedures
AO1 AO1.1b Correctly carry out routine procedures
2
AO1.2 Accurately recall facts, terminology and definitions
AO2.1 Construct rigorous mathematical arguments (including proofs)
1
AO2.2a Make deductions
AO2.2b Make inferences
AO2
–1 0 1 2 3 x AO2.3 Assess the validity of mathematical arguments
AO2.4 Explain their reasoning
–1
AO2.5 Use mathematical language and notation correctly
AO3.1a Translate problems in mathematical contexts into mathematical processes
–2
AO3.1b Translate problems in non-mathematical contexts into mathematical processes
AO3.2a Interpret solutions to problems in their original context
–3
AO3.2b Where appropriate, evaluate the accuracy and limitations of solutions to problems
AO3 AO3.3 Translate situations in context into mathematical models
AO3.4 Use mathematical models
Shade the region defined by the inequalities
AO3.5a Evaluate the outcomes of modelling in context
y ≥ 2 x 2 − 3 x − 2 and y < x − 2 AO3.5b Recognise the limitations of models
[3 marks]
AO3.5c Where appropriate, explain how to refine models
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
(04)
4
G/Jun26/7357/3
