AS-LEVEL
The Sixth year course is aimed at an AS-Level certificate in MEI Mathematics. Pupils will sit four unit exams in June, one of these being in Mechanics and one in Statistics; however, only one of these two is required
for certification at AS-Level and tuition in the Mechanics Unit will be available the following year, if desired.
The other two ‘Core’ Units cover Pure Mathematics topics as follows:
A. Coordinate geometry of the straight line & circle.
B. Elementary algebra. H. Elementary integral calculus
C. Quadratic functions and equations. I. Logarithms and exponentials.
D. Polynomials and their graphs. J. Trigonometry incl. relationships,
E. The remainder and binomial theorems. equations, graphs and the sine,
F. Sequences and series – arithmetic and geometric cosine and area formulae.
G. Elementary differential calculus.
H. Elementary integral calculus
I. Logarithms and exponentials.
J. Trigonometry incl. relationships, equations, graphs and the sine, cosine and area formulae.
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A-LEVEL
 If the subject is continued into the 7ths, a further two Units will be required to secure a full A-Level, one taken in January and one in June; these will also be in Pure Mathematics, but there will be an option to study a second Mechanics Unit in addition, this being particularly desirable for those contemplating Physics, Engineering or Architecture. Topics covered include:
A. Further differential calculus, incl. product, quotient and chain rules and implicit functions.
B. Further integral calculus incl. substitution and parts
C. Functions
D. Numerical methods for solution of equations
E. Vectors
F. Parametric curves
G. Partial fractions
H. General binomial expansion
I. Solution of elementary differential equations |
Asessment
Each unit examination consists of a single 1 hour 30 minute paper. In addition, one of the Pure Mathematics units involves a piece of coursework; this represents 20% of the marks for the unit, and the formal write-up is marked internally before submission to an external moderator.
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Resits
One resit is permitted in any case where a module result is considered unsatisfactory. Each module is marked out of a standard maximum of 100, marks are aggregated and there are standard published thresholds for each grade at both A and AS-Level. |
Further Mathematics
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6th |
7th |
| Higher |
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| AS Level |
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| A Level |
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Changes in content and style mean that Further Mathematics is no longer the preserve of the specialist that it once was and, instead, rounds out a general mathematical education, taking things beyond the level of the simple service subject and going some way towards creating the mind set needed by a working mathematician. Proof, abstraction and logical rigour all feature more prominently.
Entry Requirements
Entry to the Further Mathematics course should not be contemplated purely as a default option. An A* grade
at GCSE and/or a competent showing in the Additional Maths FSMQ should be regarded as the bench mark
for aspirants; Interest in, and aptitude for, the subject, beyond that of the ordinary A-Level candidate, is
assumed. Further Mathematics is an option only available to those in 6ths also taking Maths A-Level (not
Higher). It is not normally possible to begin a Further Mathematics course in the 7ths. |
Essential preparation for Oxbridge
.jpg) Further Mathematics may be taken as an AS-Level in the Sixths, possibly leading to an A-Level in the Sevenths, in addition to A-Level Mathematics. A further three or six modules are required, respectively. As the name implies, everything is taken a little further and topics are treated in a more sophisticated way, giving essential preparation for Oxbridge and other Maths courses and almost essential preparation for Oxbridge Engineering courses.
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Units
In the Sixth year, candidates for Further Maths will take one further module in each of Pure Mathematics and Statistics in addition to those required for AS-Level Maths. An extra four periods per week would be set aside for this purpose.
The compulsory Pure Mathematics Unit comprises:
A. Matrices.
B. Complex numbers.
C. Sketching rational functions.
D. Solution of rational inequalities.
E. Roots, coefficients and related polynomial equations.
F. Proof by induction.
G. Techniques for summation of series.
The Statistics Unit includes introductions to the Poisson, Normal and Chi-squared distributions and to bivariate
analysis and regression.
In the Seventh year (A2) one Pure Maths Unit in addition to those for A-Level Mathematics, two further Mechanics Units, and one on Differential Equations would then make up the necessary total. An allocation of eight teaching periods per week would provide for these four extra Units. |
Assessment
As for Mathematics, each Unit examination consists of a single 1 hour 30 minute paper. In addition, the
Differential Equations Unit includes a piece of coursework, involving practical experiment and mathematical
modelling; this represents 20% of the marks for the Unit, and the formal write-up is marked internally before
submission to an external moderator. The six Unit exams are taken as three pairs, in June of the 6th year
and in January and June of the 7th year respectively. One re-sit is permitted in any case where a Unit result
is considered unsatisfactory. Each Unit is marked out of a standard maximum of 100; marks are aggregated
and there are standard published thresholds for each grade at both A and AS-Level.
To avoid later difficulties over aggregation of Unit scores, AS-Level Further Mathematics is not normally
certificated at the end of the 6th year unless mathematics as a whole is being abandoned at that point.
However, care is taken to ensure that, when UCAS applications are being prepared, universities are aware
of the notional grade attained.
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