Physics Degrees

A level Mathematics and Further Mathematics

All Physics degree courses require A level Mathematics (or an equivalent qualification) for entry. Some courses prefer students to have studied more mechanics as part of their A level Mathematics.

Studying A level or AS level Further Mathematics is excellent preparation for a Physics degree as it not only provides more opportunity to study mechanics but also introduces new topics that you will find useful if you intend to study Physics, such as complex numbers, matrices, differential equations and vectors.

Some Physics degree courses specifically mention Further Mathematics in their entry requirements, encouraging students to take Further Mathematics if possible. Increasing numbers of students starting physics degrees have studied either AS or A level Further Mathematics in addition to A level Mathematics. In 2013/14 the proportion of students starting a Physics degrees who had studied A level Further Mathematics was 36%, up from 21% in 2010/11.

Overview of Mathematics covered in Physics Degrees

Whilst the first year mathematical content may vary from university to university, there are many topics that are common to all Physics courses:

  • Calculus and Differential Equations
  • Series expansions and limits
  • Complex numbers
  • Functions - Exponential, Logarithmic,Trigonometric and Hyperbolic
  • Matrices, eigenvalues and eigenvectors
  • Vectors
  • Mechanics Topics - circular motion, simple harmonic motion, rigid bodies
  • Probability distributions
  • Mathematical Modelling

The table below shows typical areas of A level Mathematics and Further Mathematics that you will encounter in a Physics degree course. The hyperlinked topics in red take you to examples of how this mathematics might be applied in a Physics degree.

Calculus Differential Equations Complex Numbers Functions
Differentiation – implicit and parametric

Integration methods - by parts, substitution, separation of variables

Volume of revolution, centroids

Numerical methods

Series expansions and limits

Partial differentiation

Calculating Energy of an Oscillating Body
Linear First Order ODEs

Linear Second Order ODEs

Particular solutions

Motion of a coupled spring system
Cartesian, Polar & Exponential Forms

Euler’s formula

De Moivre's theorem

Complex roots

Analysing AC current
Inverse Functions





Curve Sketching

Matrices Vectors Mechanics Probability
Inverse of a matrix


Solution of sets of linear equations

Eigenvalues and eigenvectors

Matrices as transformations

Calculating the current in a mesh
Vector Algebra

Scalar and vector products

Triple product

Differentiation and integration of vectors

Vector equations of lines and planes

Newton’s laws of motion

Conservation laws


Circular motion

Rigid body mechanics

Moments of inertia, rotation

Simple harmonic motion, damping, resonance

Random variables

Binomial distribution

Poisson distribution

Example Careers

Here are links to two profiles of physics graduates with very different careers.

Lucie - a research fellow in solar physics describes her work and the path to her career on the Futuremorph science careers website.

Harjinder - a solicitor who makes use of his physics degree to understand the technological aspects of contracts.

Useful links

The following websites and books have useful information about the mathematical topics you will study during your Physics degree together with other resources to support your preparation for Physics at university:

PhysNRICH - a section of the Nrich website with problems and articles specific to applications of Mathematics in Physics. It is for students aged 14 - 19 and is designed to complement and enhance the study of physics. Some of the examples in the table above are from this website.

Isaac Physics - a bank of challenging questions for improving your mathematical problem solving skills for physics problems. The site includes notes and explanations of techniques and is designed and maintained by the University of Cambridge. Careers - the careers sections of the Institute of Physics website has profiles of physics graduates follow a wide range of careers.

The Maths Centre - this site was developed by a group from the Universities of Loughborough, Leeds and Coventry and has been set up to deliver mathematics support to students looking for post-16 mathematics help.

References to Further Mathematics in Entry Requirements

Cambridge University

Essential A Level Mathematics, and either Physics or Further Mathematics (with three units of Mechanics)

Useful AS/A Level Further Mathematics

Oxford University

A-levels: A*AA
This should either be A*A in Physics and Mathematics (with the A* in either Physics or Mathematics) plus any other A, or A* in Further Mathematics with AA in Mathematics and Physics.
Candidates are expected to have Physics and Mathematics to A-level, Advanced Higher, or Higher Level in the IB or another equivalent. The inclusion of a Maths Mechanics module would also be highly recommended. Further Mathematics can be helpful to candidates in completing this course, although not required for admission.

Royal Holloway, University of London

Typical offers ask for three grade A’s at A2 level and must include Mathematics and Physics. Additionally, an A* is required in Mathematics for entry to the Mathematics & Physics degree programmes. Any subject may be chosen as the third A level, but preference in final decisions will be given to those studying Further Mathematics, science and other intellectually demanding subjects.

University of Leicester

We ask for three A-levels, including Physics and Mathematics. MPhys (AAB), BSc (ABB) with an A in either Physics or Mathematics.

Further Maths and Extended Project Qualifications
Further Maths and EPQ’s are not a formal requirement for entry onto our course. However, students with a Further Maths A-level or a relevant EPQ often find the transition to University study easier. If you have the opportunity we would certainly encourage you to take Further Maths or an EPQ.

If you narrowly miss your offer we will try to find you a place on the course and, every year, we are able to admit a few students in this position – typically those with the strongest grades in Physics and Mathematics, or those with additional relevant qualifications, for example, Further Maths or an EPQ