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Sixth Form

Further Mathematics

Qualification Level 3 Advanced GCE in Further Mathematics

Exam Board AQA

Course Specific Entry Requirements 5 GCSEs at grade 9-5 including English Language or Literature.  Grade 8 or above in GCSE Mathematics, or Grade 7 in GCSE Mathematics and Grade 7 in Level 2 Further Mathematics. Students must be studying A Level Mathematics.



Particularly strong candidates can consider Further Mathematics A Level in addition to Mathematics A Level.  As the name suggests, Further Mathematics takes the elements, skills, and competencies developed in A Level Mathematics even further, with students studying elements of Pure Mathematics, Statistics, Mechanics, and Discrete Mathematics not seen on the A Level course. Two thirds of the course content is Pure Mathematics, with Statistics, Mechanics or Discrete Mathematics making up the rest of the course. This course is designed for students who enjoy exploring the world of mathematics and have a real passion for the subject.  It is particularly useful for anyone considering a career in Mathematics, engineering, electronics, economics or accountancy.  

What will I learn?

Within the Pure Mathematics elements of Further Mathematics, students will study new ‘stand alone’ topics such as matrices, complex numbers, graphs, further algebra and proof by induction. Students will study two of Statistics, Mechanics, and Discrete Mathematics; this choice will be made based on the interests of the class. In Statistics, students will further their understanding of distributions, expectations, and confidence intervals, and in Mechanics, students will learn about momentum and circular motion, whilst Discrete Mathematics will further students’ understanding of algorithms used in solving decision making problems.


How will I learn?

Through discussion, teacher-led exposition, individual study and group work, students will learn to analyse and solve problems.  Further Mathematics will differ to normal Mathematics in that there will be more emphasis on problem solving: this is what universities are looking for in good mathematicians.  Students studying Further Mathematics tend to benefit from smaller class sizes with a good teacher to pupil ratio.  Moreover, whilst many colleges offer Further Mathematics on a reduced timetable, at The Spires College the Further Mathematics course is given as much lesson time per week as any other A Level.  Students will be required to complete a substantial amount of independent study, however, Mathematics staff will also be available after school and during lunch to aid students in this.


Where could it lead?

Similar to the Mathematics A Level, Further Mathematics is regarded as a ‘facilitating’ subject for entry to higher education by the Russel Group of Universities. It is particularly useful for students aiming to move on to degree courses with large mathematical content, such as Engineering degrees, degrees in Science, and (obviously) degrees in Mathematics.  Moreover, having A Level Further Mathematics on a university application is a way to stand out, regardless of degree course.    Further Mathematics may also lead to careers in research, engineering, design and architecture, philosophy, geography, music and media.