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Further Mathematics


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Course Description

Further mathematics is a challenging and fascinating course which allows students to study the subject in much greater depth and arrive at a more profound understanding of the connectedness of different areas of mathematics.


Course content

Further Core Pure Mathematics

The course introduces students to a new number system: the complex numbers, which contains not only the answer to “what number, , has the property that ?”, but also poses many new and interesting questions in which geometrical skills can be applied to shed light on algebraic problems. Students will learn to use matrices both to solve simultaneous equations and to explore transformations of points and shapes on the plane, and they will learn much more about using vectors to describe objects than that encountered at GCSE level. The calculus which they encounter in their A Level mathematics course is extended and developed so that they are able to solve a much greater number of problems, including finding solutions to equations which involve rates of change. Students will learn to describe points in space using not only (x, y) coordinates but using polar coordinates, through doing so encountering a much wider array of interesting graphs and functions.


Decision Mathematics

Students learn about the mathematics which underpins computer science: algorithms, critical path analysis, graph theory and linear programming. All of these will be brand new topics not encountered at GCSE level.



Depending on the group/teacher, students will study one of four possible courses which will either contain more pure mathematics, statistics, mechanics or decision mathematics.



Students sit four 90 minute papers at the end of year 13: two in pure mathematics, one in decision mathematics, and one in their other optional paper.


Career Possibilities

Most students who choose Further Mathematics choose it because they enjoy mathematics. Those who want to study mathematics, physics or computer science at university will benefit greatly from successfully completing the A Level in Further Mathematics. The course challenges students to reason carefully and critically in ways which are beneficial to many other possible study and career paths, and as such a highly regarded qualification it can add weight to applications for all sorts of jobs or university courses.


GCSE Grade profile

You need to enjoy mathematics! Due to the challenging nature of the course students should only consider it if they expect to achieve at least a grade 7, but ideally an 8 or 9.

We hope you have found the subject videos useful. If you would like to contact the subject leader directly please click on the link above.


Click here to access a bridging task for Further Maths. 

(The task worksheet can be found below)