### Why choose A Level Further Maths

#### Entry Requirements

Students will be expected to have met St Paul’s entry requirements of 2 Grade 5’s and 4 Grade 4’s. A minimum of grade 4 in English and Maths is essential for all courses.

Further Mathematics has an additional entry requirement of GCSE Maths at a minimum of grade 7 to study A level Maths AND A level Further Maths.

It is not possible to study A level Further Maths without studying A level Maths.

#### Course Content

We do not offer an AS level in Further Mathematics at St Paul’s for the new A-levels; however, the AS course is exactly identical to the year 12 scheme of study. Currently in Further Maths, we major in Statistics and minor in Mechanics at St. Paul’s.

1: CORE PURE

• AS and A level: Some pure topics from AS level Mathematics are studied in greater depth, while some new topics are introduced. Algebraic work with series is extended. 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.
• A level only: In addition to studying these topics in more depth, learners also applied vector methods to problems involving lines and planes and calculus techniques are extended, including the use of hyperbolic functions and polar coordinates, and culminate in the solution of differential equations.

2: MECHANICS

Mechanics minor In this option, basic principles of forces and their moments, work and energy, impulse and momentum and centres of mass are used to model various situations. These include rigid bodies in equilibrium; particles moving under gravity, on a surface, in a circle, attached to springs; bodies colliding with direct or oblique impact.

3: STATISTICS

Statistics minor In this option, 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.

4 MODELLING WITH ALGORITHMS

Modelling with algorithms minor In this option, what is an Algorithm and the effect of its complexity; Modelling with graphs and networks; Linear programming for finding optimised solutions; the simplex method is applied to a variety of problems.

#### Assessment

Assessment Board: OCR

#### Where can this A Level take you?

Further Maths has wide applications in industry, business, finance, science, technology and many others.

There are a number of degree courses where A-level Further Maths is favoured — including Chemistry, Maths, Medicine and some Engineering programmes.