M21/5/MATHX/HP1/ENG/TZ1/XX/M
Markscheme
May 2021
Mathematics:
analysis and approaches
Higher level
Paper 1
26 pages
, –3– M21/5/MATHX/HP1/ENG/TZ1/XX/M
Instructions to Examiners
Abbreviations
M Marks awarded for attempting to use a correct Method.
A Marks awarded for an Answer or for Accuracy; often dependent on preceding M marks.
R Marks awarded for clear Reasoning.
AG Answer given in the question and so no marks are awarded.
FT Follow through. The practice of awarding marks, despite candidate errors in previous parts, for
their correct methods/answers using incorrect results.
Using the markscheme
1 General
Award marks using the annotations as noted in the markscheme eg M1, A2.
2 Method and Answer/Accuracy marks
• Do not automatically award full marks for a correct answer; all working must be checked,
and marks awarded according to the markscheme.
• It is generally not possible to award M0 followed by A1, as A mark(s) depend on the
preceding M mark(s), if any.
• Where M and A marks are noted on the same line, e.g. M1A1, this usually means M1 for
an attempt to use an appropriate method (e.g. substitution into a formula) and A1 for using
the correct values.
• Where there are two or more A marks on the same line, they may be awarded
independently; so if the first value is incorrect, but the next two are correct, award A0A1A1.
• Where the markscheme specifies A3, M2 etc., do not split the marks, unless there is a note.
• The response to a “show that” question does not need to restate the AG line, unless a Note
makes this explicit in the markscheme.
• Once a correct answer to a question or part question is seen, ignore further working even if
this working is incorrect and/or suggests a misunderstanding of the question. This will
encourage a uniform approach to marking, with less examiner discretion. Although some
candidates may be advantaged for that specific question item, it is likely that these candidates
will lose marks elsewhere too.
• An exception to the previous rule is when an incorrect answer from further working is used in
a subsequent part. For example, when a correct exact value is followed by an incorrect
decimal approximation in the first part and this approximation is then used in the second part.
In this situation, award FT marks as appropriate but do not award the final A1 in the first part.
Examples:
Correct Further Any FT issues?
Action
answer seen working seen
1. 5.65685... No. Award A1 for the final mark
8 2 (incorrect Last part in question. (condone the incorrect further
decimal value) working)
2. 0.468111… Yes. Award A0 for the final mark
35
(incorrect Value is used in (and full FT is available in
72 decimal value) subsequent parts. subsequent parts)
, –4– M21/5/MATHX/HP1/ENG/TZ1/XX/M
3 Implied marks
Implied marks appear in brackets e.g. (M1),and can only be awarded if correct work is seen
or implied by subsequent working/answer.
4 Follow through marks (only applied after an error is made)
Follow through (FT) marks are awarded where an incorrect answer from one part of a question
is used correctly in subsequent part(s) (e.g. incorrect value from part (a) used in part (d) or
incorrect value from part (c)(i) used in part (c)(ii)). Usually, to award FT marks, there must be
working present and not just a final answer based on an incorrect answer to a previous part.
However, if all the marks awarded in a subsequent part are for the answer or are implied, then
FT marks should be awarded for their correct answer, even when working is not present.
For example: following an incorrect answer to part (a) that is used in subsequent parts, where
the markscheme for the subsequent part is (M1)A1, it is possible to award full marks for their
correct answer, without working being seen. For longer questions where all but the answer
marks are implied this rule applies but may be overwritten by a Note in the Markscheme.
• Within a question part, once an error is made, no further A marks can be awarded for work
which uses the error, but M marks may be awarded if appropriate.
• If the question becomes much simpler because of an error then use discretion to award
fewer FT marks, by reflecting on what each mark is for and how that maps to the simplified
version.
• If the error leads to an inappropriate value (e.g. probability greater than 1, sin q = 1.5 , non-
integer value where integer required), do not award the mark(s) for the final answer(s).
• The markscheme may use the word “their” in a description, to indicate that candidates may
be using an incorrect value.
• If the candidate’s answer to the initial question clearly contradicts information given in the
question, it is not appropriate to award any FT marks in the subsequent parts. This includes
when candidates fail to complete a “show that” question correctly, and then in subsequent
parts use their incorrect answer rather than the given value.
• Exceptions to these FT rules will be explicitly noted on the markscheme.
• If a candidate makes an error in one part but gets the correct answer(s) to subsequent
part(s), award marks as appropriate, unless the command term was “Hence”.
Markscheme
May 2021
Mathematics:
analysis and approaches
Higher level
Paper 1
26 pages
, –3– M21/5/MATHX/HP1/ENG/TZ1/XX/M
Instructions to Examiners
Abbreviations
M Marks awarded for attempting to use a correct Method.
A Marks awarded for an Answer or for Accuracy; often dependent on preceding M marks.
R Marks awarded for clear Reasoning.
AG Answer given in the question and so no marks are awarded.
FT Follow through. The practice of awarding marks, despite candidate errors in previous parts, for
their correct methods/answers using incorrect results.
Using the markscheme
1 General
Award marks using the annotations as noted in the markscheme eg M1, A2.
2 Method and Answer/Accuracy marks
• Do not automatically award full marks for a correct answer; all working must be checked,
and marks awarded according to the markscheme.
• It is generally not possible to award M0 followed by A1, as A mark(s) depend on the
preceding M mark(s), if any.
• Where M and A marks are noted on the same line, e.g. M1A1, this usually means M1 for
an attempt to use an appropriate method (e.g. substitution into a formula) and A1 for using
the correct values.
• Where there are two or more A marks on the same line, they may be awarded
independently; so if the first value is incorrect, but the next two are correct, award A0A1A1.
• Where the markscheme specifies A3, M2 etc., do not split the marks, unless there is a note.
• The response to a “show that” question does not need to restate the AG line, unless a Note
makes this explicit in the markscheme.
• Once a correct answer to a question or part question is seen, ignore further working even if
this working is incorrect and/or suggests a misunderstanding of the question. This will
encourage a uniform approach to marking, with less examiner discretion. Although some
candidates may be advantaged for that specific question item, it is likely that these candidates
will lose marks elsewhere too.
• An exception to the previous rule is when an incorrect answer from further working is used in
a subsequent part. For example, when a correct exact value is followed by an incorrect
decimal approximation in the first part and this approximation is then used in the second part.
In this situation, award FT marks as appropriate but do not award the final A1 in the first part.
Examples:
Correct Further Any FT issues?
Action
answer seen working seen
1. 5.65685... No. Award A1 for the final mark
8 2 (incorrect Last part in question. (condone the incorrect further
decimal value) working)
2. 0.468111… Yes. Award A0 for the final mark
35
(incorrect Value is used in (and full FT is available in
72 decimal value) subsequent parts. subsequent parts)
, –4– M21/5/MATHX/HP1/ENG/TZ1/XX/M
3 Implied marks
Implied marks appear in brackets e.g. (M1),and can only be awarded if correct work is seen
or implied by subsequent working/answer.
4 Follow through marks (only applied after an error is made)
Follow through (FT) marks are awarded where an incorrect answer from one part of a question
is used correctly in subsequent part(s) (e.g. incorrect value from part (a) used in part (d) or
incorrect value from part (c)(i) used in part (c)(ii)). Usually, to award FT marks, there must be
working present and not just a final answer based on an incorrect answer to a previous part.
However, if all the marks awarded in a subsequent part are for the answer or are implied, then
FT marks should be awarded for their correct answer, even when working is not present.
For example: following an incorrect answer to part (a) that is used in subsequent parts, where
the markscheme for the subsequent part is (M1)A1, it is possible to award full marks for their
correct answer, without working being seen. For longer questions where all but the answer
marks are implied this rule applies but may be overwritten by a Note in the Markscheme.
• Within a question part, once an error is made, no further A marks can be awarded for work
which uses the error, but M marks may be awarded if appropriate.
• If the question becomes much simpler because of an error then use discretion to award
fewer FT marks, by reflecting on what each mark is for and how that maps to the simplified
version.
• If the error leads to an inappropriate value (e.g. probability greater than 1, sin q = 1.5 , non-
integer value where integer required), do not award the mark(s) for the final answer(s).
• The markscheme may use the word “their” in a description, to indicate that candidates may
be using an incorrect value.
• If the candidate’s answer to the initial question clearly contradicts information given in the
question, it is not appropriate to award any FT marks in the subsequent parts. This includes
when candidates fail to complete a “show that” question correctly, and then in subsequent
parts use their incorrect answer rather than the given value.
• Exceptions to these FT rules will be explicitly noted on the markscheme.
• If a candidate makes an error in one part but gets the correct answer(s) to subsequent
part(s), award marks as appropriate, unless the command term was “Hence”.
