A Guide To The TMUA

What is the TMUA

The TMUA is the entrance exam, made by Cambridge University, that is used by Warwick and Imperial for Computer Science admissions (and Maths and Economics for Warwick and Imperial). It consists of 2 papers taken BACK TO BACK - that's 2.5 hours straight on the day - each consisting of 20 questions (so 40 questions total) and each paper is therefore 1 hour and 15 minutes. Your mark is then compared to other people to create grade boundaries and your grade is out of 9. If you are looking to get into Cambridge Computer Science then 7+ is good but 7.5+ is ideal. If it is lower then don't worry too much as there are definitely people who get in with low scores (for example someone got in in 2021 with a score of 2.2 but this was probably extenuating circumstances) but know that it lowers your chance of getting in. Having a higher TMUA score is probably the best thing you can do to improve your application if your personal statement is already at a good level.

How to answer the questions

1. Figure out what the question is asking you to do/be able to prove that you can do. For example, if the question mentions a maximum or minimum immediately think to complete the square. Having this planned ahead will make you a) faster but b) understand your route to the answer better at the start of the question
2. If you are tight on time, for example if you have maybe 5/10 minutes at the end of the test and you have 5 questions left to answer, do not spend those 5/10 minutes spending very little time on each question: skip through to the question you haven't done and guess random answers for each and use the time that you have to do the question that looks least difficult (I would normally just go for the next question as this is faster than figuring out the least difficult). It is better to guarantee yourself that extra mark than rush through 5 questions trying to cross out answers that you know are wrong just to get a higher expected score (probability of a higher score). If you do this you are leaving your mark to chance and on the day you may get unlucky. Take what you can and leave as little as possible to chance.
3. Get really good at graph sketching. So many questions are much quicker and simpler to understand when you sketch the graph. This is a super important skill, especially for the TMUA which is so time pressured.
4. Always look at the options. A lot of the time you can eliminate options down to 2. Also never follow the sunk cost fallacy in this case. Even though you may have spent a while on this question already you will get more marks if you keep going and just guess out of the options that are reasonable (if you are very close then spending an extra couple minutes out of the 3 minutes and 45 seconds per question is fine but if you have put 7-10+ minutes into a question and can't figure it out: MOVE ON!
5. Be super efficient at basic differentiation and integration. A lot of the time just evaluating and simplifying the function will lead to an easy/straightforward answer.
6. Know the arithmetic and geometric series formula. These often come up and are must-knows.

$$ \textbf{Arithmetic Series:} \quad S_n = \frac{n}{2} \left(2a + (n-1)d\right) $$

$$ \textbf{Geometric Series:} \quad S_n = \frac{a(1 - r^n)}{1 - r} \quad \text{for} \quad r \neq 1 $$

7. Be very careful. This is probably the most important (for me at least) because you can lose so many marks when you are rushing. This is one of the reasons that the second half of the paper is harder than the first - because you realise you don't have much time left so you start to make small mistakes. And these cost you.

How to prepare

1. Practice questions. You can find lots on TMUA Ninja
2. Mock exams. Tutors have made mock exams that you can try (I recommend in timed conditions). Be warned that the timing and/or the difficulty won't be exactly representative of the actual TMUA (a lot of the time these are more difficult than the actual TMUA).

3. Past TMUA papers. These can be found on Physics and Maths Tutor on the official TMUA website on Next Step Maths and on TMUA Ninja (on TMUA Ninja you can also sit them in the style that you would do in the actual exam so I do recommend this to get used to doing it through the Pearson platform)
4. R2Drew2 has some good video tutorials and TMUA paper walkthroughs which are reasonably useful to check out as well. His TMUA playlist is linked below:

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