A Level Further Maths

Overview of the course:

Awarding Body - Edexcel

In the first year, you will study one Further Pure Mathematics (FP1) unit and two applied units. In the second year, you will study two Further Pure Mathematics (FP2 and FP3) units and one applied unit. Applied units include Decision Mathematics, Mechanics and Statistics.

Each unit carries equal weight. There is a 1½ hour written examination for each unit. There is no coursework for any module. All exams are taken in May/June. Students will take AS level exams at the end of year one and A2 level exams at the end of year 2.

You will be expected to study A Level Mathematics when taking A Level Further Mathematics.

Topics:

When studying pure mathematics at AS and A2 level you will be extending your knowledge of such topics as algebra and trigonometry as well as learning some brand new ideas such as calculus.
While many of the ideas you will meet in pure mathematics are interesting in their own right, they also serve as an important foundation for other branches of mathematics, especially mechanics and statistics.
Mechanics deals with the action of forces on objects. It is therefore concerned with many everyday situations, e.g. the motion of cars, the flight of a cricket ball through the air, the stresses in bridges, and the motion of the earth around the sun. Such problems have to be simplified or modelled to make them capable of solution using relatively simple mathematics. The study of one or more of the Mechanics units will enable you to use the mathematical techniques which you learn in the Core units to help you to produce solutions to these problems. Many of the ideas you will meet in the course form an almost essential introduction to such important modern fields of study such as cybernetics, robotics, bio-mechanics and sports science, as well as the more traditional areas of engineering and physics.

When you study statistics you will learn how to analyse and summarise numerical data in order to arrive at conclusions about it. You will extend the range of probability problems that you looked at in GCSE using the new mathematical techniques learnt in the pure mathematics units. Many of the ideas in this part of the course have applications in a wide range of other fields, from assessing what your car insurance is going to cost to how likely it is that the Earth will be hit by a comet in the next few years. Many of the techniques are used in sciences and social sciences. Even if you are not going on to study or work in these fields, in today’s society we are bombarded with information (or data) and the statistics units will give you useful tools for looking at this information critically and efficiently.

In decision mathematics you will learn how to solve problems involving networks, systems, planning and resource allocation. You will study a range of methods, or algorithms, which enable such problems to be tackled. The ideas have many important applications in such different problems as the design of circuits on microchips to the scheduling of tasks required to build a new supermarket.

FP1: Series; complex numbers; numerical solution of equations; coordinate systems, matrix algebra, proof.
FP2: Inequalities; series, first order differential equations; second order differential equations; further complex numbers, Maclaurin and Taylor series.
FP3: Further matrix algebra; vectors, hyperbolic functions; differentiation; integration, further coordinate systems.