# Further Mathematics

###### Subject Leader

##### Mr Black

__Aims of the course__

For those students with a true love of Mathematics we can offer Further Mathematics. We aim to stretch students in their use their mathematical knowledge to make logical and reasoned decisions in solving problems both within pure mathematics and in a variety of contexts, and communicate the mathematical rationale for these decisions clearly.

__Course content__

In order to take Further Mathematics at A level we recommend students should have achieved at least a grade 8 in Mathematics GCSE.

Both AS and A level Further Mathematics have a 50:50 split between compulsory and optional elements.

The A level Further Mathematics course has been split into four units, Further Pure 1, Further Pure 2 and two options from either Further Pure, Further Statistics, Further Mechanics or Decision Maths. Further Pure 1 is designed to be covered in the first year of A-level and also forms the content of the AS course, with one option to be taken at AS.

A brief outline of each unit is given below:

**Further Pure 1:** Proof, Complex numbers, Matrices, Further algebra and functions, Further calculus, Further vectors.

**Further Pure 2:** Complex numbers, Further algebra and functions, Further calculus, Polar coordinates, Hyperbolic functions, Differential equations.

**Optional units**

**Further Pure 3:** Further calculus, Further differential equations, Coordinate systems, Further vectors, Further numerical methods, Inequalities

**Further Statistics 1: **Linear regression, Statistical distributions (discrete), Statistical distributions (continuous), Correlation, Hypothesis testing, Chi squared tests.

**Further Mechanics 1:** Momentum and impulse, Collisions, Centres of mass, Work and energy, Elastic strings and springs.

**Decision Mathematics 1: **Algorithms and graph theory, Algorithms on graphs, Algorithms on graphs II, Critical path analysis, Linear programming.

__Assessment__

The structure of assessment differs depending on whether students take AS or A-level Further Mathematics. The timing of the assessment can also differ; a student can choose to study AS Further Mathematics during Year 13. An outline of the assessment structure for both AS and A-level is detailed below:

**AS Further Mathematics Assessment**

Assessment comprises of two written examinations.

**Paper 1: Further Pure Mathematics.** Content aligned to Paper 1 of A level Further Maths assessed at AS level standard. The paper lasts 1.5 hours and is worth 75 marks.

**Paper 2: Further Mathematics Option. **The paper lasts 1.5 hours and is worth 75 marks.

**A level Further Mathematics Assessment**

Assessment comprises of four written examinations.

**Paper 1: Further Pure Mathematics 1.** AS content assessed at A level standard. The paper lasts 1.5 hours and is worth 75 marks.

**Paper 2: Further Pure Mathematics 2. **Remaining pure content which builds on and incorporates AS content. The paper lasts 1.5 hours and is worth 75 marks.

**Paper 3: Further Mathematics Option 1. **The paper lasts 1.5 hours and is worth 75 marks.

**Paper 4: Further Mathematics Option 2. **The paper lasts 1.5 hours and is worth 75 marks.

__Career opportunities__

Studying Further Mathematics is a core requirement for top Universities and those students wishing to study Mathematics or Physics, in particular, are advised to take Further Mathematics at A-level. In addition, it stretches your skills in logical thinking, problem-solving and decision-making, which are valued by employers across many job sectors, such as;

- Actuarial analyst
- Actuary
- Chartered accountant
- Insurance underwriter
- Data analyst
- Investment analyst
- Research scientist
- Secondary school teacher
- Statistician
- Systems developer