Wednesday 18th October 2023

MAT Paper


Wednesday 5th June 2024

STEP Paper 1


Wednesday 24th January 2024

STEP Paper 2


Tuesday 17th October 2023

TMUA Paper


Uni & Uni Admissions


Every single University admissions past exam papers can be found below:

  • Cambridge STEP (Sixth Term Examination Paper)
  • Oxford MAT (Mathematics Admission Test)
  • Cambridge TMUA (Test of Mathematics for University Admission)

It is not unusual to do two entrance exams. For example, you may apply to both Cambridge and unis that accept the TMUA. You may want to sit both the TMUA and STEP, so that if STEP does not go wellyou will already have reduced offers by virtue of your TMUA score. You will obviously not be preparing for them at the same time (they're sat at the opposite ends of the year), so it's no big deal to sit STEP and either MAT or TMUA



STEP is used by universities including Cambridge, Warwick and Imperial College London. Other universities sometimes ask candidates to take STEP.

MAT is used by universities including Oxford, Imperial, Warwick, Durham and Bath.

TMUA is used by universities including Cambridge, Warwick, Bath, Durham, Cardiff, Lancaster, LSE, Sheffield, Nottingham and Southampton

STEP is generally thought to be harder than the MAT and significantly harder than the TMUA.  STEP is more similar to A-levels though than the MAT.   The STEP is considered harder because the MAT doesn't require as advanced mathematical knowledge. 

The MAT always has a more "logic puzzle" spin to it which is reminiscent of many maths challanges. There are two STEP papers (paper 2 and 3) and applicants for Maths are usually required to take both papers. STEP is administered by Cambridge Assessment Admissions Testing. In contrast, there is only one MAT paper. 

TMUA is based on AS Level and Higher Level GCSE Mathematics, whereas STEP is based on AS Level and A Level Mathematics.

The STEP III paper is not only the hardest of the STEP papers, but probably the most difficult entrance exam of any university course, ever.  The STEP papers are sat towards the end of the A Level examination period (in June).  The MAT paper is sat at the beginning of the A Level examination period (in November).



The STEP is a paper-based exam lasting 3 hours. The STEP consists of 2 papers and 12 questions in each paper. All questions are marked out of 20 and the final grade for the paper is based on the six best answers only. 

Since 2021, here are two STEP papers; each takes 3 hours and is based on different A Level knowledge:

  • STEP 2: A Level Maths + AS Level Further Maths
  • STEP 3: A Level Maths + A Level Further Maths

The STEP is taken towards the end of the A Levels eximinations in June and results come out in the in August.  Calculators are not allowed

The STEP paper has five possible grades:

  • S = Outstanding
  • 1 = Very Good
  • 2 = Good
  • 3 = Satisfactory
  • U = Unclassified

The grades required as part of an offer vary by College – see individual College websites for typical STEP requirements. All the questions that are attempted by a student will be marked. Candidates are rewarded for making good progress towards a solution, even if the final answer is incorrect. Correct answers always receive full marks, whatever the method used. Step is taken towards the end of your final year in June and results come out on A Level results day.  



The MAT is one paper-based exam lasting 2 hour 30 minutes and consists of 7 questions out of 100 marks, of which one should answer 5 depending on the subject one is applying to university for. 

The MAT is taken at the beginning of the final year in November and results come out in the following January.  Calculators are not allowed

The way that candidates access the questions is changing for October 2023. Candidates will see the questions on a computer screen. Candidates will write their responses in a paper answer booklet, which will be scanned by their test centre.

Question 1 is multiple choice and contains 10 parts each worth 4 marks. Marks are only given for the correct answers.

Questions 2-7 are longer questions, each worth 15 marks, and working must be shown. Partial marks are available for quesitons 2-7 only).

There is no pass mark of breakdown for the MAT exam.  Universities use the information from the test along with all other detail from a student’s UCAS application. 


MAT Loophole

One can avoid having to sit the MAT for Imperial by putting in your UCAS application with just 4 options, and then adding Imperial as a choice the day after Oxbridge applications close. At that point they won't be able to tell you've sent off your application to other universities already, as far as they're aware you'll have only just applied. (they will only be told about your other choices when you firm/insure) Adding choices is not very hard to do and is a clear option on the UCAS dashboard, you might want to tell your school you plan on doing this in case they thought you omitted a 5th choice by mistake.



The MAT is a paper-based exam lasting 75 minutesThere are two papers. It has 20 multiple-choice questions:

  • Paper 1: Questions assessing pure Maths in new unfamiliar situations
  • Paper 2: Questions assessing mathematical reasoning and logic


You are given a score based on your overall performance on both papers, which is given on a scale of 1.0 to 9.0.

The TMUA is designed to give you the opportunity to demonstrate that you have the essential mathematical thinking and reasoning skills needed for a demanding undergraduate Mathematics or Mathematics-related course, such as Computer Science or Economics.

For applications to most universities, you can decide whether or not you want to share your results with the university after you have received them. This means TMUA gives you a risk-free opportunity to prove your potential, and in some cases to receive a reduced offer.

For applications to the University of Cambridge (Economics and Computer Science) TMUA is compulsory, except for mature students applying to one of the mature Colleges for Economics. All results will be shared automatically with the University of Cambridge.


Click the folders below for more detail on each test


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