# Further Mathematics

## Aims

The aims of the course are as follows:

• Give students a deep insight of Pure Maths (Algebra, Calculus, and Trigonometry) and its applications to Mechanics, Statistics, Further Pure Maths and/or Decision Maths.
• Challenge students to stretch their knowledge by enhancing their problem solving skills.
• Provide students with the confidence and skills needed to succeed in careers such as Engineering, Physics or Mathematics, since after completing the Further Maths course they will be familiar with most of the content they will have to face in the first year of these subjects at university.

## Entry Requirements

Further Mathematics A Level is aimed at talented students with excellent maths skills and abstract thinking abilities, who have a clear intention of studying Maths, Physics or Engineering at university.

Students should have Grade 8 or higher in GCSE English and Mathematics, or the equivalent grade/mark in their national system of secondary education.

## Course Structure

The course consists of a common Core Pure Maths component and students can then choose between Further Pure Maths, Mechanics, Statistics or Decision Maths.

During the course, students will have to deal with very challenging problems that will demand from them the ability to be creative, make deductions, link concepts from different topics and reason to a high level with a very reliable number manipulation.

### Core Pure 1

In this section, students will start studying the foundations of complex numbers, linear transformations and matrices and will stretch their algebra and geometry knowledge.

### Further Pure 1 (Optional)

Introduction to the study of conic sections, Taylor Series and further Numerical Methods, combined with the study of one of the most powerful mathematical tools: differential equations.

### Further Statistics 1 (Optional)

A more detailed approach to hypothesis testing, as well as new distributions, such as the Poisson and the geometric distributions.

### Decision Maths 1 (Optional)

In Decision Maths we study algorithms, linear programming or graph and networks and how these can be applied to real life cases.

### Further Mechanics 1 (Optional)

In Mechanics we study in depth some of the topics covered in GCSE which are key in Physics, such as the conservation of energy in different contexts, collisions in 2D and 3D and the study of Hooke’s Law.

### Core Pure 2

Here we move forward in the study of complex numbers, series and differential equations and start studying methods in calculus for integration and differentiation of special functions.

### Further Pure 2 (Optional)

Perhaps the most demanding area in terms of abstraction, this second year of Further Pure Maths ranges from number theory and groups to matrix algebra and advanced techniques of integration.

### Further Statistics 2 (Optional)

The statistics course is completed in the second year with the study of topics such as linear regression and correlation, continuous distributions or further hypothesis testing with which A level Maths students should already be familiar.

### Decision Maths 2 (Optional)

In the second year of Decision Maths, students learn how to solve efficiently transportation and allocation problems. In addition, there is an introduction to game theory and dynamic programming.

### Further Mechanics 2 (Optional)

Students learn to apply their Maths knowledge to deal with circular motion and centre of mass problems, as well as to gain skills to solve problems on dynamics (Simple Harmonic Motion and Gravitation)

## Assessment

• Paper 1 – Written exam of 1.5 hours (25 % of final grade) on Core Pure Maths.
• Paper 2 – Written exam of 1.5 hours (25 % of final grade) on Core Pure Maths (same as Paper 1).
• Paper 3 – Written exam of 1.5 hours (25 % of final grade) on either Further Pure, Further Statistics, Further Mechanics or Further Decision Maths.
• Paper 4 – Written exam of 1.5 hours (25 % of final grade) on either Further Pure, Further Statistics, Further Mechanics or Further Decision Maths (same as Paper 3).

## Core Text

For this course we use the Pearson Edexcel AS and A Level Further Mathematics set of textbooks (Series Editor: Harry Smith; various authors), consisting of the following:

• Core Pure Mathematics (1 and 2).
• Further Pure Mathematics (1 and 2).
• Further Statistics (1 and 2)
• Further Mechanics (1 and 2)
• Decision Mathematics (1 and 2)

## Careers and Opportunities

At the end of the course, students will be equipped with the skills, knowledge and confidence to succeed in the first year of any degree course in Maths, Physics or Engineering, since they will already be familiar with most of the traditionally hard topics such as complex numbers, number theory, advanced integration, proof, matrix algebra, etc.

Mathematical experts are in demand across all types of industries around the world. Students studying Maths have access to career opportunities that they may never have even considered, including specialised fields such as law and medicine. However, a large number of maths careers are still based within business or science and technology-related sectors, with maths graduates able to purse a range of career opportunities, including accountancy, computing, engineering, management, surveying, teaching and town planning.