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Prelims Mathematics and Philosophy Examination Conventions 2025-26

6.1 How USMs are determined in Mathematics

Analysis of Marks

In Mathematics the moderators may scale the raw marks when translating them into USMs.

  • The moderators may choose to scale marks where in their academic judgement:
    a paper was more difficult or easier than in previous years, and/or
  • a paper has generated a spread of marks which are not a fair reflection of student performance on the University's standard scale for the expression of agreed final marks, i.e.\ the marks do not reflect the qualitative marks descriptors.

Such scaling is used to ensure that all papers are fairly and equally rewarded.

When scaling the raw marks on a paper the moderators will consider the following:

  • the total sum of the marks for all questions on the paper, subject to the rules above on numbers of questions answered;
  • the relative difficulty of the paper compared to the other Prelims papers;
  • the report submitted by the moderator/assessor who set and marked the paper.

Moderators will use their academic judgement to ensure that appropriate USMs are awarded and may use further statistics to check that the marks assigned fairly reflect the students' performances on a paper.  Moderators will also review a sample of papers either side of the classification borderlines to ensure that the outcome of scaling is consistent with the qualitative marks descriptors.

Marking of Mathematics Examinations

All mathematics examinations are marked by a single assessor or moderator according to a pre-agreed mark scheme which is strictly adhered to.  The examination scripts are then checked by an independent checker to ensure that all work has been marked, and that the marks have been correctly totalled and recorded. Please see the qualitative descriptors of the bands of marks awarded to examination answers.  

Further information on the setting and marking of mathematics papers is given in the appendices to the Examination Conventions in Mathematics available online: https://www.maths.ox.ac.uk/members/students/undergraduate-courses/examinations-assessments/examination-conventions

Marking Schemes and Model Solutions

Those setting questions are asked to provide complete model solutions, annotated so as to indicate what is considered bookwork and standard material, what has been seen before on problem sheets and what is considered to be new and unseen, and with a draft marking scheme for the approval of the moderators; the solution, with additional comments, should also make clear how much of the question is accessible to less strong candidates.

Marking schemes for the questions should aim to ensure that the following qualitative criteria hold:

16--20 marks: A completely, or almost completely, correct answer, showing excellent understanding of the concepts and skill in carrying through the arguments and/or calculations; minor slips or omissions only.
11--15 marks: A good though not complete answer, showing understanding of the concepts and competence in handling the arguments and/or calculations, and some evidence of problem-solving ability. Such an answer might consist of an excellent answer to a substantial part of the question, or a good answer to the whole question which nevertheless shows some flaws in calculation or in understanding or in both.
6--10 marks: Standard material has been substantially and correctly answered with some possible minor progress on to other parts of the question.
0--5 marks: Some progress has been made with elementary, accessible material.

Qualitative description of examination performance in Mathematics

Whilst the Preliminary Examination is not classified, the average USM ranges  reflect the following general \textbf{Qualitative Class Descriptors} agreed by the Teaching Committee:

First Class: the candidate shows excellent skills in reasoning, deductive logic and problem-solving. They demonstrate an
excellent knowledge of the material, and can use that in unfamiliar contexts.

Upper Second Class: the candidate shows good or very good skills in reasoning, deductive logic and problem-solving. They demonstrate a good or
very good  knowledge of much of the material.

Lower Second Class: the candidate shows adequate basic skills in reasoning, deductive logic and problem-solving. They demonstrate a sound
knowledge of much of the material.

Third Class: the candidate shows reasonable understanding of at least part of the basic material and some skills in reasoning, deductive logic and problem-solving.

Fail: little evidence of competence in many of the topics examined; the work is likely to show major misunderstanding and confusion, coupled with inaccurate calculations; the answers to questions attempted are likely to be fragmentary only.