A-Level Mathematics + Further Mathematics + Physics: Subject Selection for UK STEM Applications and Requirements from Cambridge and Imperial College London

For A-Level students applying to STEM programs (Engineering, Physics, Natural Sciences, Computer Science) in the UK, the most common dilemma when choosing subjects is: Besides Math and Physics, should I take Further Mathematics? What should I pick for my third and fourth subjects? This decision shouldn't be based on gut feelings or just listening to what older students say, because universities have very specific subject requirements, which vary significantly across different majors. This article uses the official 2027 entry requirements from the University of Cambridge and Imperial College London as examples to clarify how to build the "Math + Further Math + Physics" combination and what each university requires. For details on how Further Mathematics is tested, see How to Take A-Level Further Mathematics; for Physics, see How to Take A-Level Physics.

1. Cambridge: Further Mathematics is "Must Take If Offered" for Most STEM Majors

The A-Level subject requirements for 2027 entry across Cambridge majors are as follows (minimum admission requirements are all A*A*A):

A few details worth noting:

• Engineering: Colleges typically require an A* in Math and/or Further Mathematics, and often an A* in Physics or another science. If your school doesn't offer Further Mathematics, you must contact your target college before applying to confirm if you can still apply; the website also recommends studying as much Pure Math and Mechanics as possible in this case, such as self-studying the AS Further Mathematics content;
• Mathematics and Physics track: To apply for Mathematics with Physics, you must have studied the Mechanics module in Further Mathematics, or be taking A-Level Physics, Math, and Further Mathematics concurrently;
• Natural Sciences (Physical Sciences track): The website recommends that students who have studied Physics and Math apply for Physical Sciences, as the interview will test subjects you have already learned. Among previously admitted A-Level students (entering in 2018, 2019, and 2023) published on the website, 97% of Physical Sciences students took Physics, and 92% took Further Mathematics;
• Admissions Tests: Both Engineering and Natural Sciences require the ESAT (Engineering and Science Admissions Test).

2. Imperial College London: Further Mathematics "Recommended but Not Essential", High Physics Requirements

A-Level requirements for 2027 entry across Imperial College London majors:

A few rules from Imperial College London:

• Different requirements for three and four subjects: Several engineering majors require an A* in Physics for three subjects, and at least an A for four subjects;
• Typical offers may be higher than minimum requirements: The website states that typical offers are the conditions met by at least half of the applicants for 2025 entry, and may be higher for competitive majors;
• General Studies and Critical Thinking are not accepted;
• Admissions Tests: All four majors above require three modules of the ESAT: Mathematics 1, Mathematics 2, and Physics. Each module has 27 multiple-choice questions and lasts 40 minutes. For candidates testing in Mainland China, Hong Kong, and Macau, the test dates for 2027 entry are October 12–13, 2026, or January 6, 2027; the registration deadline for the October session is 18:00 (UK time) on September 28, 2026, and registration for the January session opens on October 26, 2026.

In addition, the recommended subjects listed by Imperial College London for Electronic and Electrical Engineering, besides Further Mathematics, include Chemistry, Computer Science, Design and Technology, and Electronics.

3. How to Build Your Subject Combination

Below are empirical recommendations based on the above requirements. Please refer to the official website requirements for your target major in the specific year of application.

Three or Four Subjects?

• The minimum requirements for both Cambridge and Imperial are based on three subjects; Imperial's engineering majors also accept four subjects (A*AAA);
• The prerequisite for taking an extra subject is not lowering your core subject grades: these universities care most about A*s in Math and Physics (and Further Math);
• For Chinese students with a strong foundation in math and science, "Math + Further Math + Physics + Chemistry" is a common four-subject combination; if taking four subjects would cause any grade to drop below an A, it's better to focus on three (empirical recommendation).

4. How Math and Physics Complement Each Other

Taking the Cambridge system as an example (empirical recommendations):

• Mechanics overlap: Cambridge Math 9709 has a Mechanics paper, Further Math 9231 has a Further Mechanics paper, which overlap with the Mechanics, Circular Motion, and Simple Harmonic Motion sections in Physics 9702. For the same physical scenario, you can practice using the rigorous derivation from the Math paper and the experimental perspective from the Physics paper;
• Calculus and Differential Equations: Exponential decay in Physics (capacitor discharge, nuclear decay, decay formulas) is essentially a first-order differential equation. After studying differential equations in Further Math, the understanding becomes much deeper;
• Graphing and Logarithms: Physics Paper 5 requires converting relationships into straight lines and using logarithmic graphs to find constants, which is exactly what is covered in Math class. See How to Score an A* in A-Level Physics;
• ESAT: All three modules are Math and Physics. The combination of Math + Further Math + Physics is the best preparation in itself.

5. What If Your School Doesn't Offer Further Mathematics?

• First, confirm if it's mandatory for your target major: Cambridge Engineering and Computer Science state "must take if offered." If your school doesn't offer it, you must contact the target college before applying; Cambridge Mathematics lists Further Mathematics as a strict requirement;
• Follow the website's advice to make up for it: The Cambridge Engineering website recommends studying as much Pure Math and Mechanics as possible, such as self-studying the AS Further Mathematics content;
• Consider registering as a private candidate: You can consult exam board-authorized test centers (empirical recommendation; feasibility and fees depend on the test center).

Conclusion

For students applying to top STEM programs in the UK, "Math + Further Math + Physics" is almost the standard combination: Cambridge's Engineering and Computer Science require Further Mathematics if offered, Imperial's Physics, Electronic and Electrical Engineering, and Aeronautical Engineering recommend it, and the ESAT admissions test for both universities only tests Math and Physics. Before choosing your subjects, check the official website requirements for your target major for that year, build your combination accordingly, and then focus your energy on scoring A*s.

For the grading rules and scores needed for an A*, see How to Score an A* in A-Level; to expand your Physics problem-solving skills, check out the British Physics Olympiad (BPhO). If you need A-Level subject selection planning or academic tutoring, feel free to chat with our counselors.

Verification note: This article was verified against the official websites of the two universities in September 2026: the minimum admission requirements, required subjects, notes on Further Mathematics, college A* requirements, requirements for Mathematics with Physics, subject choice proportions for admitted Natural Sciences (Physical) students, and ESAT requirements for the Engineering, Computer Science, Mathematics, and Natural Sciences programs (for 2027 entry) at the University of Cambridge; the minimum requirements, typical offers, recommended subjects, unacceptable subjects, as well as ESAT modules, test dates in China, and registration deadlines for the Physics (MSci), Mechanical Engineering, Electrical and Electronic Engineering (MEng), and Aeronautical Engineering programs (for 2027 entry) at Imperial College London. The websites for the University of Oxford and University College London displayed verification pages during our visit and could not be verified, so they are not included. Our recommendations on subject combinations, whether to take three or four subjects, the connection between Mathematics and Physics, and the "private candidate" option when schools do not offer Further Mathematics are based on our practical experience.

References:

• University of Cambridge: Engineering
• University of Cambridge: Natural Sciences
• University of Cambridge: Computer Science
• University of Cambridge: Mathematics
• Imperial College London: Physics (MSci)
• Imperial College London: Mechanical Engineering
• Imperial College London: Electrical and Electronic Engineering (MEng)
• Imperial College London: Aeronautical Engineering