Further Maths

Awarding Body: Oxford Cambridge & RSA Examinations [OCR]

Entry Requirements: Grade 8 in GCSE Mathematics

If you have a genuine passion for Mathematics and A Level Mathematics has already sparked your ambition, then Further Mathematics is the natural next step - often seen as the pinnacle, or even the Everest, of school-level mathematics. This course is designed for students with exceptional mathematical ability, curiosity and determination. It will challenge you to think more deeply, work more independently, and develop a sharper level of precision and reasoning. Many students find it both demanding and immensely rewarding, with a real sense of achievement as complex ideas begin to fall into place.

At its core is an advanced Pure Mathematics component, where you encounter the subject in its most elegant form. You will explore topics such as complex numbers, matrices and advanced calculus, while developing your ability to construct rigorous mathematical proofs. These ideas not only deepen your understanding but also form the foundation of many real-world applications, from computer graphics and cryptography to scientific modelling.

Alongside this, you will study Further Mechanics—closely linked to Physics—where you model motion, forces and dynamic systems with greater sophistication. You will also explore Discrete Mathematics, which connects directly to Computer Science, including the algorithms and decision-making processes that underpin technologies such as navigation systems like Google Maps. Highly valued by leading universities, Further Mathematics strengthens applications for degrees in mathematics, engineering, physics, computer science and beyond. If you are ready to push your limits and experience mathematics at its most challenging and rewarding, this course offers an inspiring and intellectually exhilarating journey.

Component 1: In Core Pure you will delve deeper into the vectors topic covered in A Level Maths. New topics include matrices and their applications, complex numbers, roots of polynomials, and polar coordinates. We also look at how mathematical induction can be used to prove mathematical statements as well as at what hyperbolic functions are and how they relate to trigonometric functions.

Component 2: You will study Discrete Mathematics which will include the study of algorithms, networks, Project management techniques such as Critical Path Analysis and how economists use Game Theory to produce optimal strategies. We will explore how Google maps selects the best route for a journey and explore historical Mathematical problems such as the Seven Bridges of Konigsberg. The course enables you to develop and extend your knowledge of how computer programmes have been developed to solve problems. This will be particularly beneficial for those studying Computer Science, or students with an interest in computer programming.

Component 3: You will study Further Mechanics which delves deeper into the Mechanics topics covered in A Level Maths. You will begin reinforcing the work covered in Physics about Work, Energy and Power, then move on to Newton’s experimental law for collisions before evaluating problems such as the limits of the banking in the Indy 500 circuit through circular motion. We round off the course exploring the centres of mass of objects and determining the angle of elevation required to topple objects on an inclined plane. This course serves to reinforce topics taught in Physics and prepares students wishing to pursue an engineering pathway.

There are four exams – two for Pure Core and one each for Discrete Mathematics and Further Mechanics. Each exam is 90 minutes long.