Start with your question
Why visitors arrive: You are applying to Oxford for physics, engineering or materials science and face the PAT.
Your question: What does the PAT test, and how much of it is actually mathematics?
You may also be asking
- How much of the PAT is maths rather than physics?
- What level of physics is assumed?
- How important is estimation?
- Are there free practice questions?
- How does it compare with the ESAT?
Where to go next
- PAT mock paper — Twenty questions with worked solutions
- ESAT library — Hand-checked physics and maths on overlapping content
- ESAT diagnostic — A quick read on where your physics stands
- Enquire about one-to-one — Direct PAT preparation
Oxford · Physics and mathematics
PAT Preparation
Physics and mathematics in one paper, weighted towards whether you can model a situation rather than whether you can recall a formula. Estimation, dimensional reasoning and knowing which effect to ignore matter more here than they do at A-level.
Taught by Lucas Rey · Oxford DPhil candidate, Rolls-Royce sponsored · Cambridge MRes
- What it is: the Physics Aptitude Test, used by Oxford for Physics, Engineering Science, Materials Science and their joint schools.
- Published here: 20 practice questions with worked solutions, free, no signup. AI-drafted, all 20 answer keys machine-checked. Read the notice on the paper before using them.
- Also here: the ESAT library, 1,053 questions written and checked by hand, which is the deeper resource on this site.
- Dates, deadlines and which course needs what: these change between cycles, so check the official specification rather than any tutor's summary of it.
- One-to-one preparation: by application, limited places.
What the PAT actually tests
[01]
Physics and maths together
Roughly half of each. The mathematics is a tool rather than the subject: it appears because the physics needs it.
[02]
Modelling over recall
Questions tend to describe a situation and ask what happens, rather than naming the topic. Deciding which physics applies is part of the question.
[03]
Estimation is a real skill here
Order-of-magnitude reasoning and sanity checks are rewarded. A candidate who can tell that an answer is a thousand times too large has a tool most do not.
How to prepare for it
- Check every answer against reality. Before writing a number down, ask whether it is the right size. A person cannot weigh 4 kg and a car cannot accelerate at 200 m s per second. This catches more marks than any formula.
- Work in symbols, substitute last. Carrying algebra to the end keeps the units checkable and often reveals that a quantity cancels, which is why it was never given to you in the first place.
- Do not neglect the mathematics half. Candidates preparing for a physics test often prepare only physics. The mathematics is half the paper and is the easier half to improve.
Practice material on this site
These papers were drafted with AI assistance and have not been through the review process the ESAT material goes through. The answer keys were checked by computer algebra where the notice on each paper says so; the difficulty and the explanations were not. They are extra practice, not a predictor, and not a substitute for real past papers.
Found an error in one of them? Tell me and it will be fixed or withdrawn.
What the practice material covers
Counted from the questions themselves, not transcribed from a specification. For what is actually examinable in your cycle, check the official specification: it is revised between cycles and no tutor's summary of it should be trusted over the source.
| Topic | Questions |
|---|---|
| Kinematics | 2 |
| Binomial expansion | 1 |
| Circular motion | 1 |
| Differentiation | 1 |
| Electric circuits | 1 |
| Energy and power | 1 |
| Exponentials and logarithms | 1 |
| Geometry | 1 |
| Graphs | 1 |
| Integration | 1 |
| Matter and pressure | 1 |
| Momentum and energy | 1 |
| Optics | 1 |
| Probability | 1 |
| Quadratics | 1 |
| Radioactivity | 1 |
| Series | 1 |
| Trigonometry | 1 |
| Waves | 1 |
20 questions across 19 topics. Thin coverage of a topic here does not mean it is unimportant in the real test; it means this practice set is small.
Common questions
- How much of the PAT is mathematics rather than physics? Roughly half. Candidates preparing for a physics test often prepare only physics, and the mathematics is both half the paper and the easier half to improve.
- How important is estimation? Very. Order-of-magnitude reasoning and sanity checks are rewarded, and a candidate who can tell that an answer is a thousand times too large has a tool most do not. Before writing any number down, ask whether it is the right size.
- Should I work in symbols or substitute numbers early? Symbols, substituting last. It keeps the units checkable and often reveals that a quantity cancels, which is usually why it was never given to you.
- How does the PAT compare with the ESAT? Both mix physics and mathematics. The PAT leans harder on modelling and estimation, while the ESAT is more tightly tied to a published specification and is separately timed by module. The physics content overlaps enough that ESAT practice is useful.
- Are the practice questions on this site official? No. They are AI-drafted mock questions with machine-checked answer keys, and every page says so at the top. They are also multiple choice, which is an adaptation: the real paper has used short numeric answers.
Sitting more than one of these?
Candidates often sit two admissions tests in the same cycle, and the overlap is larger than it looks: the pure mathematics is shared, and the habits that earn marks in one paper usually earn them in another. Each page below covers what its test rewards and what free practice exists for it.
- TMUA: Test of Mathematics for University Admission Two papers and Multiple choice and Pure mathematics
- MAT: Mathematics Admissions Test Oxford and Imperial and Multiple choice and long-form
- STEP: Sixth Term Examination Paper Cambridge and Warwick and Long-form proof
- ESAT: Engineering and Science Admissions Test The deepest library on this site, written and checked by hand
Part of
This page sits within the broader knowledge structure on lucasrey.com:
- Teaching - Engineering-informed teaching, mentoring, and quantitative reasoning.
Connected work
Related content from the same research and engineering work: