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Cambridge International AS & A Level Cambridge International AS & A Level
FURTHER MATHEMATICS 9231/13
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Paper 1 Further Pure Mathematics 1 May/June 2026
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MARK SCHEME
Maximum Mark: 75
*
FURTHER MATHEMATICS 9231/13
Paper 1 Further Pure Mathematics 1 May/June 2026 Published
2 hours
You must answer on the question paper.
This mark scheme contains the instructions and marking guidance that our examiners used to mark
You will need: List of formulae (MF19) candidate responses for this component.
*
Before they start marking, examiners complete a standardisation process. They review a range of candidate
INSTRUCTIONS responses and discuss the mark scheme in detail to agree which answers can and cannot be accepted.
● Answer all questions. Examiners award marks where it is clear that candidate responses have met the requirements of the mark
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. scheme. These requirements may vary between different components or different versions of the same
● Write your name, centre number and candidate number in the boxes at the top of the page. component, depending on the exact requirements of the question and the candidate responses seen during
● Write your answer to each question in the space provided. the standardisation process.
● Do not use an erasable pen. Do not use correction fluid or tape.
Sometimes, our mark schemes may allow marks to be awarded to responses which contain elements that
● Do not write on any bar codes. are factually incorrect or for content not covered by the syllabus. We do this in response to the demands of a
● If additional space is needed, you should use the lined page at the end of this booklet; the question specific question to support candidates and make sure that our assessments are fair. However, these
number or numbers must be clearly shown. allowances should not be used as a guide for teaching and learning.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from We cannot discuss the mark scheme with schools, and we recommend that schools read the mark scheme
a calculator. together with the assessment material and the Principal Examiner Report for Teachers.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
INFORMATION
● The total mark for this paper is 75.
● The number of marks for each question or part question is shown in brackets [ ].
This document has 20 pages. Any blank pages are indicated.
DC (CJ) 355932/2 This document consists of 20 printed pages.
Cambridge University Press & Assessment 2026 [Turn over
Cambridge University Press & Assessment 2026 [Turn over
, * * DFD
9231/13 Cambridge International AS & A Level – Mark Scheme May/June 2026
DO NOT WRITE IN THIS MARGIN
2 PUBLISHED
, , General marking principles
3 2
1 The cubic equation x + bx + cx + d = 0 , where b, c and d are constants, has roots a, b and c . It is
given that All examiners must apply these marking principles when marking candidate responses.
a +b +c = , 1 Examiners must award marks for each response in line with:
a + b + c =- ,
• the specific content defined in the mark scheme
a- + b- + c- = .
• the specific skills defined in the mark scheme or in the level descriptions
• the standard of response required as exemplified by the standardisation scripts.
(a) Find the values of b, c and d. [5]
2 Examiners must award whole marks (not half marks, or other fractions).
............................................................................................................................................................
DO NOT WRITE IN THIS MARGIN
3 Examiners must award marks positively. This means that:
............................................................................................................................................................
• marks are not deducted for errors or omissions
............................................................................................................................................................ • marks are awarded for correct/valid answers as defined in the mark scheme and also for other valid answers which go beyond the scope of the
syllabus and mark scheme referring to your team leader as appropriate
............................................................................................................................................................ • the quality of spelling, punctuation and grammar are judged only when the mark scheme indicates that these features are specifically assessed in the
question. However, the meaning of all responses must be unambiguous.
............................................................................................................................................................
4 Examiners must consistently apply the requirements of the mark scheme and any rules for what to do when candidates have not followed instructions
............................................................................................................................................................ correctly.
............................................................................................................................................................ 5 Examiners must use the full range of marks defined in the mark scheme, unless limited by the quality of the candidate responses seen.
DO NOT WRITE IN THIS MARGIN
6 Examiners must award marks according to the mark scheme and must not award marks with grade thresholds or grade descriptions in mind.
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
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DO NOT WRITE IN THIS MARGIN
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Cambridge University Press & Assessment 2026 Page 2 of 20
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DO NOT WRITE IN THIS MARGIN
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Cambridge University Press & Assessment 2026 9231/13/M/J/26
ĬÕĊ®Ġ´íÈõÏĪÅĊÝû·þ×
ĬĄěñÕĥčíçċČõñÞÖÚĄĂ
ĥÕµÕõµąÕååąąÅõąµõÕ
, * * DFD
9231/13 Cambridge International AS & A Level – Mark Scheme May/June 2026
DO NOT WRITE IN THIS MARGIN
3 PUBLISHED
, ,
Mathematics-Specific Marking Principles
(b) Find the value of a 3 + b 3 + c 3 . [2]
1 Unless a particular method has been specified in the question, full marks may be awarded for any correct method. However, if a calculation is required
............................................................................................................................................................ then no marks will be awarded for a scale drawing.
............................................................................................................................................................ 2 Unless specified in the question, non-integer answers may be given as fractions, decimals or in standard form. Ignore superfluous zeros, provided that the
degree of accuracy is not affected.
............................................................................................................................................................
3 Allow alternative conventions for notation if used consistently throughout the paper, e.g. commas being used as decimal points.
............................................................................................................................................................
4 Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw).
............................................................................................................................................................
DO NOT WRITE IN THIS MARGIN
5 Where a candidate has misread a number or sign in the question and used that value consistently throughout, provided that number does not alter the
difficulty or the method required, award all marks earned and deduct just 1 A or B mark for the misread.
............................................................................................................................................................
6 Recovery within working is allowed, e.g. a notation error in the working where the following line of working makes the candidate’s intent clear.
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
DO NOT WRITE IN THIS MARGIN
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DO NOT WRITE IN THIS MARGIN
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Cambridge University Press & Assessment 2026 Page 3 of 20
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DO NOT WRITE IN THIS MARGIN
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Cambridge University Press & Assessment 2026 9231/13/M/J/26 [Turn over
Ĭ×Ċ®Ġ´íÈõÏĪÅĊÝù·þ×
ĬĄĜòÍģđýÒíõ´åÖĂÚôĂ
ĥÕÅĕµÕĥµµÕÕąÅĕĥõĥÕ
, ,
Cambridge International AS & A Level Cambridge International AS & A Level
FURTHER MATHEMATICS 9231/13
¬W. 4mHuOªE`y5W
¬rX¡PvnIX¦¢
Paper 1 Further Pure Mathematics 1 May/June 2026
¥ eU5UE5¥UEE5¥uUU
MARK SCHEME
Maximum Mark: 75
*
FURTHER MATHEMATICS 9231/13
Paper 1 Further Pure Mathematics 1 May/June 2026 Published
2 hours
You must answer on the question paper.
This mark scheme contains the instructions and marking guidance that our examiners used to mark
You will need: List of formulae (MF19) candidate responses for this component.
*
Before they start marking, examiners complete a standardisation process. They review a range of candidate
INSTRUCTIONS responses and discuss the mark scheme in detail to agree which answers can and cannot be accepted.
● Answer all questions. Examiners award marks where it is clear that candidate responses have met the requirements of the mark
● Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. scheme. These requirements may vary between different components or different versions of the same
● Write your name, centre number and candidate number in the boxes at the top of the page. component, depending on the exact requirements of the question and the candidate responses seen during
● Write your answer to each question in the space provided. the standardisation process.
● Do not use an erasable pen. Do not use correction fluid or tape.
Sometimes, our mark schemes may allow marks to be awarded to responses which contain elements that
● Do not write on any bar codes. are factually incorrect or for content not covered by the syllabus. We do this in response to the demands of a
● If additional space is needed, you should use the lined page at the end of this booklet; the question specific question to support candidates and make sure that our assessments are fair. However, these
number or numbers must be clearly shown. allowances should not be used as a guide for teaching and learning.
● You should use a calculator where appropriate.
● You must show all necessary working clearly; no marks will be given for unsupported answers from We cannot discuss the mark scheme with schools, and we recommend that schools read the mark scheme
a calculator. together with the assessment material and the Principal Examiner Report for Teachers.
● Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
INFORMATION
● The total mark for this paper is 75.
● The number of marks for each question or part question is shown in brackets [ ].
This document has 20 pages. Any blank pages are indicated.
DC (CJ) 355932/2 This document consists of 20 printed pages.
Cambridge University Press & Assessment 2026 [Turn over
Cambridge University Press & Assessment 2026 [Turn over
, * * DFD
9231/13 Cambridge International AS & A Level – Mark Scheme May/June 2026
DO NOT WRITE IN THIS MARGIN
2 PUBLISHED
, , General marking principles
3 2
1 The cubic equation x + bx + cx + d = 0 , where b, c and d are constants, has roots a, b and c . It is
given that All examiners must apply these marking principles when marking candidate responses.
a +b +c = , 1 Examiners must award marks for each response in line with:
a + b + c =- ,
• the specific content defined in the mark scheme
a- + b- + c- = .
• the specific skills defined in the mark scheme or in the level descriptions
• the standard of response required as exemplified by the standardisation scripts.
(a) Find the values of b, c and d. [5]
2 Examiners must award whole marks (not half marks, or other fractions).
............................................................................................................................................................
DO NOT WRITE IN THIS MARGIN
3 Examiners must award marks positively. This means that:
............................................................................................................................................................
• marks are not deducted for errors or omissions
............................................................................................................................................................ • marks are awarded for correct/valid answers as defined in the mark scheme and also for other valid answers which go beyond the scope of the
syllabus and mark scheme referring to your team leader as appropriate
............................................................................................................................................................ • the quality of spelling, punctuation and grammar are judged only when the mark scheme indicates that these features are specifically assessed in the
question. However, the meaning of all responses must be unambiguous.
............................................................................................................................................................
4 Examiners must consistently apply the requirements of the mark scheme and any rules for what to do when candidates have not followed instructions
............................................................................................................................................................ correctly.
............................................................................................................................................................ 5 Examiners must use the full range of marks defined in the mark scheme, unless limited by the quality of the candidate responses seen.
DO NOT WRITE IN THIS MARGIN
6 Examiners must award marks according to the mark scheme and must not award marks with grade thresholds or grade descriptions in mind.
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
DO NOT WRITE IN THIS MARGIN
............................................................................................................................................................
Cambridge University Press & Assessment 2026 Page 2 of 20
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
DO NOT WRITE IN THIS MARGIN
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
Cambridge University Press & Assessment 2026 9231/13/M/J/26
ĬÕĊ®Ġ´íÈõÏĪÅĊÝû·þ×
ĬĄěñÕĥčíçċČõñÞÖÚĄĂ
ĥÕµÕõµąÕååąąÅõąµõÕ
, * * DFD
9231/13 Cambridge International AS & A Level – Mark Scheme May/June 2026
DO NOT WRITE IN THIS MARGIN
3 PUBLISHED
, ,
Mathematics-Specific Marking Principles
(b) Find the value of a 3 + b 3 + c 3 . [2]
1 Unless a particular method has been specified in the question, full marks may be awarded for any correct method. However, if a calculation is required
............................................................................................................................................................ then no marks will be awarded for a scale drawing.
............................................................................................................................................................ 2 Unless specified in the question, non-integer answers may be given as fractions, decimals or in standard form. Ignore superfluous zeros, provided that the
degree of accuracy is not affected.
............................................................................................................................................................
3 Allow alternative conventions for notation if used consistently throughout the paper, e.g. commas being used as decimal points.
............................................................................................................................................................
4 Unless otherwise indicated, marks once gained cannot subsequently be lost, e.g. wrong working following a correct form of answer is ignored (isw).
............................................................................................................................................................
DO NOT WRITE IN THIS MARGIN
5 Where a candidate has misread a number or sign in the question and used that value consistently throughout, provided that number does not alter the
difficulty or the method required, award all marks earned and deduct just 1 A or B mark for the misread.
............................................................................................................................................................
6 Recovery within working is allowed, e.g. a notation error in the working where the following line of working makes the candidate’s intent clear.
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
DO NOT WRITE IN THIS MARGIN
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
............................................................................................................................................................
DO NOT WRITE IN THIS MARGIN
............................................................................................................................................................
Cambridge University Press & Assessment 2026 Page 3 of 20
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DO NOT WRITE IN THIS MARGIN
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Cambridge University Press & Assessment 2026 9231/13/M/J/26 [Turn over
Ĭ×Ċ®Ġ´íÈõÏĪÅĊÝù·þ×
ĬĄĜòÍģđýÒíõ´åÖĂÚôĂ
ĥÕÅĕµÕĥµµÕÕąÅĕĥõĥÕ
