A-level
MATHEMATICS
7357/1
Paper 1
Mark scheme
June 2022
Version: 1.1 Final Mark Scheme
, MARK SCHEME – A-LEVEL MATHEMATICS – 7357/1 – JUNE
2022
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 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.
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 standardisation process, associates encounter unusual answers which
have not been raised they are 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 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 assessment remain constant, details will change,
depending on the content of a particular examination paper.
Further copies of this mark scheme are available from aqa.org.uk
2
, MARK SCHEME – A-LEVEL MATHEMATICS – 7357/1 – JUNE
2022
Mark scheme instructions to examiners
General
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.
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
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)
3
, MARK SCHEME – A-LEVEL MATHEMATICS – 7357/1 – JUNE
2022
AS/A-level Maths/Further Maths assessment
objectives
AO Description
AO1.1a Select routine procedures
AO1 AO1.1b Correctly carry out routine procedures
AO1.2 Accurately recall facts, terminology and definitions
AO2.1 Construct rigorous mathematical arguments (including proofs)
AO2.2a Make deductions
AO2.2b Make inferences
AO2 AO2.3 Assess the validity of mathematical arguments
AO2.4 Explain their reasoning
AO2.5 Use mathematical language and notation correctly
AO3.1a Translate problems in mathematical contexts into mathematical
processes
AO3.1b Translate problems in non-mathematical contexts into mathematical
processes
AO3.2a Interpret solutions to problems in their original context
AO3 AO3.2b Where appropriate, evaluate the accuracy and limitations of solutions to
problems
AO3.3 Translate situations in context into mathematical models
AO3.4 Use mathematical models
AO3.5a Evaluate the outcomes of modelling in context
AO3.5b Recognise the limitations of models
AO3.5c Where appropriate, explain how to refine models
4
MATHEMATICS
7357/1
Paper 1
Mark scheme
June 2022
Version: 1.1 Final Mark Scheme
, MARK SCHEME – A-LEVEL MATHEMATICS – 7357/1 – JUNE
2022
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 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.
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 standardisation process, associates encounter unusual answers which
have not been raised they are 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 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 assessment remain constant, details will change,
depending on the content of a particular examination paper.
Further copies of this mark scheme are available from aqa.org.uk
2
, MARK SCHEME – A-LEVEL MATHEMATICS – 7357/1 – JUNE
2022
Mark scheme instructions to examiners
General
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.
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
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)
3
, MARK SCHEME – A-LEVEL MATHEMATICS – 7357/1 – JUNE
2022
AS/A-level Maths/Further Maths assessment
objectives
AO Description
AO1.1a Select routine procedures
AO1 AO1.1b Correctly carry out routine procedures
AO1.2 Accurately recall facts, terminology and definitions
AO2.1 Construct rigorous mathematical arguments (including proofs)
AO2.2a Make deductions
AO2.2b Make inferences
AO2 AO2.3 Assess the validity of mathematical arguments
AO2.4 Explain their reasoning
AO2.5 Use mathematical language and notation correctly
AO3.1a Translate problems in mathematical contexts into mathematical
processes
AO3.1b Translate problems in non-mathematical contexts into mathematical
processes
AO3.2a Interpret solutions to problems in their original context
AO3 AO3.2b Where appropriate, evaluate the accuracy and limitations of solutions to
problems
AO3.3 Translate situations in context into mathematical models
AO3.4 Use mathematical models
AO3.5a Evaluate the outcomes of modelling in context
AO3.5b Recognise the limitations of models
AO3.5c Where appropriate, explain how to refine models
4
