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Oxford University – changes to admissions tests for 2027 entry
On Physics and Maths Tutor, note the section on University Admissions where you can find papers and solutions for many of the tests. For the ESAT test, see the section below.
The following resources provide challenging questions for any students studying Mathematics beyond age 16.
From Nrich, Prepare for University.
MAT, STEP and AEA papers provide an excellent source of questions. Dr Jamie Frost has created such a useful resource with his STEP, MAT and AEA questions all aligned to new A Level chapters. This document is 156 pages of categorised questions (brief answers are given). See also on Dr Frost Maths, Oxbridge Prep.
For mark schemes see:
- MAT (Maths Admissions Test), scroll down the page for past papers, solutions and additionally video solutions. For superb resources for these questions, see these Underground Mathematics Review Questions, where you will find not only the questions but also suggestions and complete solutions. (Note September 2026 – Underground Maths no currently available)
- For details on STEP, see STEP Mathematics on OCR’s site. Note that STEP 1 no longer exists (from Summer 2021). STEP past paper worked solutions are available for many papers from MEI. See also the information below on the excellent STEP resources on Underground Maths. Recent STEP 2 and STEP 3 past question papers and examiner reports are available from OCR.
- The AEA questions ons,Legacy papers and mark schemes are available on Colmanweb (I found I could access the papers in pdf format, but not Word). The AEA qualification from Pearson is based on the A Level specification and designed for the top 10% of students to help differentiate between the most able candidates. On YouTube from Tayyub Majeed, worked solutions are available for AEA papers.
Also available on Dr Frost Maths, is Mr Bowler’s Problem Solving Booklet for University Preparation; the booklet contains 151 questions to help prepare students for undergraduate admissions interviews in mathematics. Answers are also available.
If Underground Maths is available, the Underground Mathematics Review Questions include Oxford Mathematics Admissions Test questions and full solutions.
From Warwick University, see their page for TMUA support and links which includes past papers and solutions. During Summer 2024, the university will develop and publish their own resources to support students in preparing to take the TMUA exam. The resources will include podcasts of TMUA exercises and ways to approach particular questions.
TUMA full papers and mark schemes can be found on Next Step Maths.
Talking to Julian Gilbey, he stresses that the more Maths you can do, the more you work on stretching problems and think hard about maths the better you will get at maths. Examples he mentions for resources are any questions on the Underground Maths website, (not just the review questions already mentioned here), UKMT and olympiad problems, STEP problems.
“And essentially your ability to ‘think mathematically’ and to solve mathematical problems is all that these tests are testing”
ESAT
The ESAT (Engineering and Science Admissions Test) is a computer-based university entrance examination delivered via Pearson VUE test centres by University Admissions Tests UK (UAT-UK).
The ESAT Admissions Test is required for 2027 entry by Cambridge, Imperial, Oxford and UCL It is used for undergraduate STEM applicants across:
Cambridge: Engineering, Natural Sciences, Chemical Engineering & Biotechnology, and Veterinary Medicine.
Imperial: Most Engineering disciplines (Aeronautical, Chemical, Civil, Electrical & Electronic, Mechanical, Design) and Physics.
Oxford: Engineering Science, Physics, Physics & Philosophy, and Biomedical Sciences.
UCL: Electronic & Electrical Engineering (with other engineering courses using alternative tests).
All applicants sit the compulsory Mathematics 1 module plus two course-specific modules chosen from Biology, Chemistry, Physics, or Mathematics 2.
A valuable resource for ESAT preparation comes from Lucas Rey. an Oxford DPhil aerothermal engineer.
Follow the plan suggested – Start here; the site has four sample papers and practice questions filed by topic published free, aditionally, full timed papers in ESAT practice, and the shortcut library, the essentials guide and the diagnostic.
Have a look at ESAT Mathematics 1 Practice Questions by Topic for example.
A comprehensive and clear worked solution is provided for each problem, including a section on why the incorrect options are wrong.
For further resources try UKMT Senior Maths Challenge Questions. See also Dr Frost Maths Riemann Zeta Club resources.
…and also see MadAsMaths with its many papers and solutions increasing in difficulty.
You can download a free pdf copy of Stephen Siklos’ Advanced Problems in Mathematics. Whilst written to support students taking STEP examination papers, Advanced Problems in Mathematics is excellent preparation for any undergraduate mathematics course.
Following each question, you will find a discussion and a full solution. The clear Contents page lists all 75 problems.
Note this searchable database for STEP.
Underground Mathematics has STEP questions within their Review Questions. Each question comes with a fully worked solution.
See also, from Cambridge University, their STEP Support Programme. From the home page, access the resources, you will see STEP Support Programme Foundation modules, STEP 2 modules and STEP 3 modules.
This webinar from Nrich which In this webinar Claire explains how STEP questions can be used to help students prepare for a University Maths degree and demonstrates the resources available on the STEP Support Programme. (maths.org/step).
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