The following is a guide for Higher Education admissions tutors to aid them when making offers to applicants for first degree courses.

The grading of GCE Mathematics qualifications is complex, particularly when candidates are requesting several mathematics qualifications. JCQ urges admissions tutors to make offers that comply with the grading rules which the awarding bodies use.

JCQ believes that an understanding of these rules will permit conditional offers to be made that will allow for discrimination between the performances of candidates.

When aggregating units for candidates cashing in both Mathematics and Further Mathematics, it is common that there will be various possible pairs of subject grades and various possible combinations of unit grades within each subject. The rules used by the awarding bodies determine which of the various alternatives will actually be awarded. There will be cases where a different alternative would meet a candidate’s HEI offer but where the aggregation under these rules has awarded a different set of grades. Offers which are conditional on unit grades in one particular Mathematics qualification can disadvantage candidates who are taking other Mathematics qualifications. Section 5 provides examples of the candidate outcomes and the evidence for discrimination in performance.

1. Background

2. The structure of the GCE Mathematics qualifications

All awarding bodies’ specifications in Mathematics and Further Mathematics have similar structures, although there are some differences in detail. In this paper, the following conventions and units are used:

Pure Mathematics units: C1, C2, C3, C4, FP1, FP2 and FP3 Applications units: M1, M2, M3, S1, S2, S3, D1 and D2

where C refers to core Pure Mathematics, FP to Further Pure Mathematics, M to Mechanics, S to Statistics and D to Decision Mathematics.

(Most awarding body specifications have other units in addition to these but they are not used in the following illustrations. Please check the actual specification for these additional units and how they may be used.)

(i) Unit combinations

For each of the qualifications, a candidate may certificate with one of the following
combinations of units:

    AS Mathematics

    • C1, C2, M1

    • C1, C2, S1

    • C1, C2, D1

     
    A Level Mathematics

    • C1, C2, C3, C4, M1, M2

    • C1, C2, C3, C4, S1, S2

    • C1, C2, C3, C4, D1, D2

    • C1, C2, C3, C4, M1, S1

    • C1, C2, C3, C4, S1, D1

    • C1, C2, C3, C4, M1, D1

     
    AS Further Mathematics Any combination of three units which does not include

    • C1–C4 but does include at least one Further Pure unit.

     
    A Level Further Mathematics

    • Any combination of six units which does not include C1–C4 but does include at least two Further Pure units.

(ii) Required number of units of study

Certification of:

  • A Level Mathematics and AS Further Mathematics requires nine different units of study (six units for A Level Mathematics and three different units for AS Further Mathematics).

  • A Level Mathematics and A Level Further Mathematics requires twelve different units of study.

  • A Level Mathematics, A Level Further Mathematics and AS Further Mathematics (Additional) requires fifteen different units of study.

  • A Level Mathematics, A Level Further Mathematics and A Level Further Mathematics (Additional) requires eighteen different units of study.

  •  

    Please note that ‘unit of study’ is defined as, for example, C1, C2 or M3; two results for C1 and one result for C2 is classed as two units of study.

    These requirements apply irrespective of whether the titles are certificated in the same examination series or in different examination series.

(iii) Certification rules

  • AS Further Mathematics cannot be certificated unless AS Mathematics or A Level
    Mathematics has been certificated, or is being concurrently certificated.

  • A Level Further Mathematics cannot be certificated unless A Level Mathematics has been
    certificated, or is being concurrently certificated.

  • AS Further Mathematics (Additional) cannot be certificated unless A Level Mathematics and

  • A Level Further Mathematics have been certificated, or are being concurrently certificated.

  • A Level Further Mathematics (Additional) cannot be certificated unless A Level
    Mathematics and A Level Further Mathematics have been certificated, or are being
    concurrently certificated.

3. Grade combinations

In this section:

Below is Rule 1 from the full version of the aggregation rules for centres. The other rules are not
expected to affect HEI conditional offers.

The full version of the aggregation rules for centres is available on the JCQ website at:

http://www.www.jcq.org.uk/Download/exams-office/entries/gce-maths-information/gce-maths-rules—guidance-for-centres

Rule 1

Grading of qualifications is determined as follows:

  • Step (i) maximisation of the qualification grades (including A*).
  • Step (ii) for the qualification grades determined under step (i), the maximisation of the uniform mark totals for each qualification.

The maximisation of grades and uniform mark totals for qualification titles is determined using
the sequence:

Mathematics; Further Mathematics; Additional Further Mathematics

The highest possible grade is awarded for the first qualification title requested in the above
sequence, followed by the highest possible grade for the second qualification title requested in
the above sequence (if the candidate has entered for two titles), followed by the highest
possible grade for the third qualification title requested in the above sequence (if the candidate
has entered for three titles). Only one qualification (A Level or AS) is maximised for each title.

For example, if a candidate has entered for AS and A Level Mathematics and AS and A Level
Further Mathematics (ie two titles), the highest possible grade is awarded for A Level
Mathematics followed by the highest possible grade for A Level Further Mathematics. The
uniform mark totals for A Level Mathematics and Further Mathematics (in that order) are
maximised before the AS qualification grades are considered.

Please note: the above maximisation process places, for example,

a grade combination of AU above a grade combination of, say, BE
and a grade combination of BU above a grade combination of, say, CE.

A request to change a grading combination that includes an unclassified award to an
arithmetically possible alternative will be granted. No other requests to change grading
combinations will normally be allowed.
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Please note:

For candidates with nine or twelve (or sometimes more) units, step (i) ensures that the units will
be distributed in the way which gives the best grades in the order stated. Given the appropriate
unit results, Mathematics at Grade A and Further Mathematics at Grade C would be awarded
rather than both qualifications at Grade B.

Step (ii) ensures that candidates receive the highest possible UMS total for Mathematics, without
lowering the subject grade for Further Mathematics.

The above two steps maximise qualification grades and the uniform mark totals, not the
individual unit grades.

4. Awarding A* in the GCE Mathematics Suite of Qualifications

The General Rule

To be awarded a grade A* at GCE A Level, a candidate must:

  • 1. Achieve grade A overall for the A Level. This can be also be described as having to achieve
    80% of the maximum uniform mark

    AND

  • 2. Achieve 90% of the combined maximum uniform mark for the A2 units.

    For example:

    For a 4 unit A Level, a candidate must achieve at least 320 of the 400 maximum uniform mark
    and 180 of the 200 combined maximum uniform mark for the A2 units.

    For a 6 unit A Level, a candidate must achieve at least 480 of the 600 maximum uniform mark
    and 270 of the 300 combined maximum uniform mark for the A2 units.

Please note:

  • i) The above rules are applied to the best available result for each AS and A2 unit; for each
    unit, this best available result may be achieved at the first or subsequent sitting

  • ii) Grade A* is not available for AS qualifications

The Application of the General Rule to the GCE Mathematics Suite of Qualifications

Since there is flexibility in the use of units in the grading of A Level Mathematics, A Level Further Mathematics and A Level Additional Further Mathematics, there are supplementary rules for the mathematics suite of qualifications. Please note that A Level Pure Mathematics conforms to the general rule for the award of an A* grade since it does not have this flexibility of unit use.

For A Level Mathematics, A* will be awarded to candidates who have achieved grade A overall (at least 480 of the 600 maximum uniform mark) and at least 180 of the 200 combined maximum uniform mark for the C3 and C4 units**.

For A Level Further Mathematics, A* will be awarded to candidates who have achieved a grade A overall (at least 480 of the 600 maximum uniform mark) and at least 270 of the 300 combined maximum uniform mark for their best three A2 units (whether pure or application units).

For A Level Additional Further Mathematics, A* will be awarded to candidates who have achieved a grade A overall (at least 480 of the 600 maximum uniform mark) and at least 270 of the 300 combined maximum uniform mark for their best three A2 units (whether pure or application units).

For reference: AS units are C1, C2, FP1, S1, M1, D1; all other units are designated as A2. For information: C denotes core pure mathematics, FP denotes further pure mathematics, S denotes statistics, M denotes mechanics and D denotes decision mathematics.
_____________________________________________________________________________________________

**The general rule has to be adapted for A level Mathematics since C3 and C4 are the only A2 units that must be
included in the A Level aggregation.

Illustrative Examples

A Level Mathematics

  • Example 1

    C1 = 90, C2 = 79, C3 = 95, C4 = 94, M1 = 87, M2 = 89

    Total: 534 uniform marks

    C3 + C4 total: 189 uniform marks

    Grade awarded: A*

  • Example 2

    C1 = 95, C2 = 98, C3 = 92, C4 = 87, D1 = 87, D2 = 89

    Total: 548 uniform marks

    C3 + C4 total: 179 uniform marks

    Grade awarded: A

  • Example 3

    C1 = 90, C2 = 92, C3 = 91, C4 = 92, M1 = 56, D1 = 58

    Total: 479 uniform marks

    C3 + C4 total: 183 uniform marks

    Grade awarded: B

 
A Level Further Mathematics

  • Example 4

    FP1 = 93, FP2 = 91, S1 = 95, S2 = 91, D1 = 89, D2 = 80

    Total: 539 uniform marks

    Best A2 total: 262 uniform marks

    Grade awarded: A

  • Example 5

    FP1 = 80, FP2 = 86, M2 = 94, M3 = 85, M4 = 88, M5 = 89

    Total: 522 uniform marks

    Best A2 total: 271 uniform marks

    Grade awarded: A*

5. Conditional offers

Overall conclusions on examples