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
In this section:
In 2008, changes were made to the administration and grading rules for all GCE qualifications. These changes included:

The introduction of the system whereby unit grades are provided to UCAS

The withdrawal of the facility to decline a GCE grade and the introduction of the facility to reuse unit results when claiming a second award in the same subject
Given that the GCE Mathematics qualifications are subject to the general GCE grading rules, the additional rules for GCE Mathematics qualifications had to be amended to ensure compliance with the changes above. This paper discusses the implications of these amendments to the grading of GCE Mathematics subjects for the offers made to students by Higher Education Institutions.
Under the new rules candidates will receive the best grade(s) possible for GCE Mathematics qualifications (as under the old rules) but with the best possible uniform mark total(s).
In many, but not all cases, this will ensure that a candidate’s grade(s) will be awarded using the best possible set of unit grade profiles. For example, where candidates have taken extra units, the best unit scores will be used.
Please note that candidates who have been entered for more than one Mathematics title (e.g. Mathematics and Further Mathematics) will have their grades maximised in combination. This is explored in more detail in later sections of this paper.
2. The structure of the GCE Mathematics qualifications
In this section:
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

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

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

Any combination of six units which does not include C1–C4 but does include at least two Further Pure units.
A Level Mathematics
AS Further Mathematics Any combination of three units which does not include
A Level Further Mathematics
(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:
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.
_____________________________________________________________________________________________
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
In this section:
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 markAND

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
In this section:
Please note:
All mathematics units have a maximum uniform mark of 100. 80 uniform marks are required for
Grade A at unit level.
Six units are required for an A Level award; three for an AS award. The uniform marks needed
to achieve each grade are shown in table 1.
Table 1
A Level  AS  

Maximum uniform mark  600  300  
Grade A threshold  480  240  
Grade B threshold  420  210  
Grade C threshold  360  180  
Grade D threshold  300  150  
Grade E threshold  240  120 
Example 1
Offer: Applicant has a conditional offer of BB for A Level Mathematics and A Level Further Mathematics.
Comments

In line with rule 1 (see section 3 above), a candidate will be awarded a grade combination
of AC (or even AD or A*E) in preference to BB, i.e. BB will be awarded only if Grade A for
Mathematics is not possible. 
Both grade combinations, BB and AC, confirm that the candidate has achieved a minimum
uniform mark total of 840. It would not be fair to reject a candidate who has been
awarded AC on the grounds that this does not meet the conditional offer, as the candidate
may in fact have a valid combination that delivers BB but which was not chosen by the
aggregation system. 
To discriminate between candidates with equivalent subject grades, unit grades can be
used. If, for example, performance in Pure Mathematics units were the most important
consideration for the chosen degree course then one would compare the performances of
the two candidates across the C and FP units.
Example 2
Offer: Applicant has a conditional offer which includes Grade A for A Level Mathematics with all six units at Grade A.
Comments

A candidate could successfully meet this offer with a UMS total of 480; each unit achieved
with 80 uniform marks. 
Another candidate could fail to meet this offer but have a UMS total as high as 579; five of
the units achieved with the maximum uniform mark of 100, the sixth unit achieved with 79
uniform marks. 
The second candidate has clearly outperformed the first candidate on five units. On the
sixth unit, the first candidate outperformed the second candidate by one uniform mark. 
The specification of unit grade performance has not identified the more able candidate.
Example 3
Offer: Two applicants have conditional offers which include Grade A for A Level Mathematics with all six
units at Grade A. The offers do not include any requirement for a qualification grade or unit grades for A Level Further Mathematics.
Comments

Candidate 1 (who just certificates A Level Mathematics) takes six units with results as follows:

C1 (80), C2 (80), C3(80), C4 (80), M1 (80), M2 (80).


Candidate 2 (who certificates A Level Mathematics and A Level Further Mathematics) takes
the same six units with results as follows:
C1, (100), C2 (100), C3 (100), C4 (100), M1 (100), M2 (100)
and a further six units with results as follows:
FP1 (80), FP2 (80), FP3 (80), S1 (79), S2 (80), S3 (80).


Candidate 2 out performs Candidate 1 on all of the six units taken by both candidates.
but 
Candidate 1 will be awarded Grade A for A Level Mathematics with all six units at Grade A. Candidate 2 will be awarded Grade A for both A Level Mathematics and A Level Further
Mathematics but the A Level Mathematics will include the S1 result, which has a unit
Grade B, to allow the M2 result to be included in the award of Grade A for A Level Further
Mathematics. 
In this case the awarding body cannot change the aggregation for Candidate 2. There is
no way of awarding Grade A for both A Level Mathematics and A Level Further
Mathematics without using unit S1 for A Level Mathematics.
Example 4
Offer: Applicant has a conditional offer which includes Grade A for A Level Mathematics and Grade C for A Level Further Mathematics.
Comments

The applicant reentered both A Levels, having obtained BC on the first occasion. (The
applicant may in fact have retaken only one unit in order to recertificate.) A slight
improvement on the results in the retaken unit(s) may give new grades AD – in line with
rule 1 (see section 3 above) a candidate will be awarded AD (or even AE or AU) in
preference to BC. 
All results (including grade U), from all examination series, are forwarded to Higher
Education Institutions. Admissions tutors should be aware that, in the (rare) example
quoted, the applicant should not be considered to have grade A in Mathematics and grade
C in Further Mathematics. He/she has therefore not met the offer.
Overall conclusions on examples
In this section:
Offers which are conditional on unit grades in one particular Mathematics qualification can
disadvantage candidates who are taking other Mathematics qualifications. In particular, offers
conditional on unit grades in A Level Mathematics are likely to disadvantage Further Mathematics
candidates.
The situation illustrated in example 3 could be avoided by making the offer conditional on the
grades in particular units of specific interest, e.g. the compulsory units C1C4.