Further Maths

Further Mathematics is a separate A-level from Mathematics; it extends the core topics and introduces new material normally encountered during the first year of a degree course. It is therefore a particularly demanding A-level, although many find it even more exciting and rewarding than single Maths. Anyone considering applying to a top university to study a subject with substantial mathematical content would be well advised to give serious thought to taking this option; in recent years, a good number of the students taking Further Maths have gained Oxbridge places.

You will study Maths A-level in the Lower Sixth, with an exam sat in the Trinity Term of Upper Sixth. You will then study and sit Further Maths A-level (or AS-Level) in the Upper Sixth. In the Lower Sixth, you can either take A-level Maths over one or two blocks.

The two-block approach is open to all pupils and allows you to take Maths, Further Maths and two other subjects. The one-block approach is taught from the assumption that you have studied FSMQ (Additional Maths). It enables you to take Maths, Further Maths and three other subjects.

• If you have sat FSMQ then you can take the one block approach with no further work.
• If you have not studied FSMQ then you can still take the one block approach but will need to commit to an acceleration programme. This involves an extra two lessons per week throughout the year and some work in the summer before you start, which consists of: two half days of tuition in school before the start of the Michaelmas term and some self-study over the holidays, following a programme provided by the Maths Department. The Head of Maths is available by email to offer assistance throughout the summer.

• If you have studied Further Maths GCSE or another similar qualification then you may not have to complete the entire summer programme but would at least need to complete online tests confirming your mathematical knowledge in certain topics.
• Please note that Statistics GCSE or two separate Maths GCSEs (Methods and Applications) do not help with the content of A-Level, and are unlikely to count in this context.

Further Maths is a demanding course, and all those wishing to take it will have to demonstrate appropriate aptitude either in their Fifth Form at MCS or during their admissions interviews.

Is Further Maths right for me?

Further Maths is challenging, but extremely rewarding. If you have the potential and the interest, it is right for you. There can be some implications for choice of university course (especially for Medicine or Economics), and it is worth discussing this with one of the Sixth Form team or the Maths Department in advance. If you have any questions, please contact the Head of Maths, Mr Hearmon (ahearmon@mcsoxford.org) or the Deputy Head (Academic), Mr White (bwhite@mcsoxford.org).

In Lower Sixth, pupils study the Maths A-level course. This is examined at the end of U6.

All Further Mathematics is taught in the Upper Sixth; there is some compulsory content and some options (one major and one minor), which are outlined below.

Compulsory pure content

• Proof by induction is used in various contexts
• Complex numbers are introduced and lead to solutions of problems in algebra, geometry and trigonometry
• Matrices are used to solve systems of equations and to explore transformations
• Vector methods are applied to problems involving lines and planes
• Calculus techniques are extended, including the use of hyperbolic functions and polar coordinates, and culminate in the solution of differential equations

Options

We propose to offer:

• Mechanics Major with either Extra Pure Minor or Statistics Minor
• Statistics Major with either Extra Pure Minor or Mechanics Minor

although not all combinations may be possible in any particular year

Mechanics Major:

• Basic principles of forces and their moments
• Work and energy
• Impulse and momentum and centres of mass are used to model various situations, including: rigid bodies in equilibrium
• Particles moving under gravity, on a surface, in a circle, attached to springs
• Bodies colliding with direct or oblique impact

Statistics Major:

• Situations are modelled by discrete and continuous random variables; this allows inference about a population in the form of hypothesis testing and point and interval estimates of population parameters
• The suitability of models is tested; bivariate data are investigated and Bayes’ theorem used
• Simulation of random variables is introduced, a powerful way of tackling challenging problems

Mechanics Minor:

• Basic principles of forces and their moments
• Work and energy
• Impulse and momentum and centres of mass are used to model various situations, including:
• Rigid bodies in equilibrium
• Particles moving under gravity or on a surface
• Bodies colliding with direct impact

Statistics Minor:

• Situations are modelled by discrete random variables
• The suitability of models is tested using Chi-squared tests
• Bivariate data are investigated, with tests for correlation and association and modelling using regression

Extra Pure Minor:

• Sets and groups
• Recurrence relations
• Matrices and vectors
• Multivariable calculus

Examination arrangements

This is a linear course consisting of three written papers.

• Paper 1: 2hr40min on the compulsory core content. 50% of the overall grade
• Paper 2: 2hr15min on the major course. 1/3 of the overall grade
• Paper 3: 1hr15min on the minor course. 1/6 of the overall grade

Further Maths AS-level

Further Maths AS is also possible for those students who wish to study beyond A-Level but not complete the full A-level Further Maths course.

In U6 the course consists of Core Pure Maths, outlined below, and one of the Statistics or Mechanics major options outlined above.

Core content:

• The powerful technique of proof by induction is used in various contexts
• Complex numbers are introduced, including their geometrical representation
• Matrices are used to solve systems of equations and to explore transformations
• Scalar products of vectors are applied to problems involving planes.

Examination arrangements

This is a linear exam consisting of three papers, all of length 1 hour 15 minutes:

• Paper 1 on the compulsory core pure content,
• Paper 2 on the first part of the mechanics or statistics major option content,
• Paper 3 on the second part of the mechanics or statistics major option content.