Further Mathematics

This course develops the subject areas covered in A Level Mathematics to new concepts, such as imaginary numbers, differential equations and matrices. There are also options to further develop the Mechanics or Statistics studied in A Level Mathematics, take up Decision Mathematics, or further your studies in Pure Mathematics. The techniques learned can be used to solve complex problems in areas such as engineering, management and economics.

What skills will I develop?

You will develop your mathematical skills further, particularly with regards to algebra and calculus.

You will learn advanced mathematical concepts, such as complex numbers and matrices, which are applicable in a variety of contexts.

You will learn how to model situations mathematically, including the use of Decision Mathematics, Mechanics and Statistics, as well as developing your problem-solving and reasoning skills.

Ultimately, A Level Further Mathematics will teach you essential skills that allow you to apply mathematics to the real world, as well as more abstract concepts that are invaluable for supporting the transition to a degree in Mathematics or related disciplines.

What topics will I study?

This qualification awards you with an A Level in Mathematics after the first year, and an A level in Further Mathematics after the second year.Please see the Mathematics page for a list of first year units.

The following topics are assessed over four equally weighted 1 hour, 30 minute examinations

  • Further Pure Mathematics 1: Proof; Complex numbers; Matrices; further algebra and functions Further Calculus and Further Vectors
  • Further Pure Mathematics 2: Complex numbers; Further algebra and functions; Further calculus; Polar coordinates; Hyperbolic functions; Differential equations
  • Further Pure Mathematics 3: Further calculus; Further differential equations; Coordinate systems; Further vectors; Further numerical methods; Inequalities
  • Decision Mathematics 1: Algorithms and graph theory; Algorithms on graphs; Algorithms on graphs II; Critical path analysis; Linear programming


Component 1 - Examination: Further Pure 1 (1 hour, 30 minutes - 25%)

Component 2 - Examination: Further Pure 2 (1 hour, 30 minutes - 25%)

Component 3 - Examination: Further Pure 3 (1 hour, 30 minutes - 25%)

Component 4 - Examination: Decision (1 hour, 30 minutes - 25%)

Where does the course lead?

This course is especially useful if you intend to study higher education courses in Mathematics, Physics, Engineering, and Economics at renowned universities.


Exam Board


Head of Department

Jason Bagshaw

Entry Requirements

Five grades 4-9 (or equivalent) including at least a grade 7 in Mathematics.

Assessment Breakdown

Examination = 100%