Part A Mathematics and Philosophy Examination Conventions 2025-26

After marks for each examination script and submitted piece of work have been determined (in accordance with Section 6 above), classifications in Finals are determined from each candidate's weighted overall average mark, average mark in Mathematics and average mark in Philosophy, according to conventions (see below) for each examination.

7.1 Decimal points and rounding of averaged marks in the determination of classification in Parts A + B

Averages of marks are calculated to two decimal points, which the examiners need in order to recognize candidates very close to a class borderline, in which case their marks profile needs to be given particular attention, and also for ranking candidates when awarding prizes.  However, at the stage of applying the classification rules to determine a candidate's classification from their average marks, the averages are then symmetrically rounded to a whole number, so that e.g. 69.50 is rounded to 70 (which, if this is as an overall average, gives that candidate a First), and 69.49 is rounded to 69 (in which case, unless Rule (2) for Part A + B classification applies, the candidate is classified II(i), but only in that case after the examiners have carefully gone over the candidate's marks, being so close to a borderline).

7.2 Classification in Parts A + B

The classification conventions for Parts A + B are in conformity with the stipulation that, ``The highest honours can be obtained by excellence either in Mathematics or in Philosophy provided that adequate knowledge is shown in the other subject of the examination.'' (in ``Regulations for the Honour School of Mathematics and Philosophy'', Examination Regulations 2019).

Weightings in the calculation of averages in Parts A + B

In calculating these averages, USMs for individual papers in Mathematics are first weighted to take account of the proportion of the course examined in each subject, and then scaled so that Parts A and B are weighted in the ratio 2 : 3. This gives the following weights:

 Paper A2: 16
 Each of Papers A0, A3, A4, A5, A8, A13, ASO: 8
 Part B Mathematics unit: 15

(Thus, in particular, the four Part A Mathematics papers jointly carry the same weight as half of Part A in the Honour School of Mathematics, and 2/3 of the weight, 60, of four Part B units in Mathematics.)

No weighting is applied to USMs for Philosophy papers.

Conventions for classification in Parts A + B

Let M denote the average USM for Mathematics papers in Parts A and B, calculated according to the weightings given above.  Let P denote the average of the USMs in Philosophy in Part B. The overall average A is calculated to be
A = [(8-k)M + kP]/8,
where k is the number of Philosophy papers taken (which may be either 3 or 4, depending on the papers chosen by the candidate).

In Mathematics & Philosophy a candidate may be given a class higher than the average of their marks, on the basis of particular strength in one of the two subjects.

The quantities M, P and A are calculated according to the above formulae. After these quantities have been symmetrically rounded to the nearest integer, as stipulated in Section 7.1, classifications are determined by the following inequalities:

1. No candidate will be given a classification lower than that implied by the place of the value of $A$ on the scale 70--100 First; 60--69 Upper Second; 50--59 Lower Second; 40--49 Third; 30--39 Pass; 0--29 Fail.
2. In the following circumstances a candidate will be given a higher classification than that implied by the value of A:
   • A candidate who achieves A ≥ 67 and either
     M ≥ 70 and P ≥ 60, or
     P ≥ 70 and M ≥ 60
     will be awarded a First.
   • A candidate who is not awarded a First but who achieves A ≥ 57 and either
     M ≥ 60 and P ≥ 50, or
     P ≥ 60 and M ≥ 50
     will be awarded an Upper Second.

The award of a Third, Pass or Fail will, in all cases, be by individual consideration.