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I’ve made this page as I’ve got a few requests for advice so far, and it’s just easier for everyone if I send them to a website that I can keep centrally updated.

If you are unsure about something not described on this page, either use your judgement, check on the provider’s site (if applicable), or email me using the link on the home screen.

TMUA

Test of Mathematics for University Admission

Format

Generally takes place around mid-October but all sorts of changes have taken place so check before you commit!

Used to be run by a company called Cambridge Assessment Admisions Testing which wound down after I sat TMUA, with some of its admissions tests passed onto other providers, for TMUA, that would be UAT-UK - a joint venture between Cambridge University and Imperial.

It is also now delivered using a computer (like the driving theory test), although my understanding is that paper will be given for workings out to be completed on. Furthermore, two sittings are available but the second (around January time) is not applicable to a couple of universities.

Doing the questions

The first thing to note is that questions are particularly time limited, 3 minutes and 45 seconds per question on average really is not much. But you can spread this out appropriately by the difficulty level of each question to redistribute time across the paper.

Also bear in mind that speed and ‘efficiency’ isn’t the only thing. If you’re well on the way to an answer but need a little bit longer than your internal stopclock, invest the time. Conversely, also you must know when to suspend effort on a question - too many people, especially mathematicians, can get drawn too closely to a question and then it all goes pear-shaped timewise.

Make sure your working out is neat in this regard, so that it is not intimidating to have to come back to a question - keep stuff clear in your working rather than clear in your head and messy on paper.

The one big thing I’d recommend for practice (also applies to STEP) is not to give in on a question. You should keep working to get a correct answer rather than giving in and checking a solutions video. TMUA mark schemes are useful as they only give the letter, so no immediate method spoilers if you’re wrong.

For TMUA questions you are stuck on, spend up to an hour working at it before giving in. Obviously suspend or modify this strategy the closer the exam gets, say less than a month or so away.

It goes without saying that total familiarity and comfort with A level maths questions (the bits pertaining to the TMUA spec) is needed before you can make really good progress on TMUA prep. Sheer algebraic speed and fluency is always good to have.

Bear in mind that paper 2 has all the logical reasoning arguments in it, so go through the specification with a fine toothcomb, making sure you know the difference between ‘if’, ‘only if’, if and only if’, or stuff like ‘necessary and sufficient’. This is all detailed in the specification. Don’t get lost in logic alone though - keep your typical mathematical toolbox handy!

Practice materials

Ensure you use the official practice papers in a well-planned way as they are limited in quantity. TMUA is much more limited than STEP this way. Other options for practice and learning include:

Outcomes

Do everything you need to and get as high a grade as possible!!! Aim for at least 7.5+ (scaled score) to stand out, and consistency of ability across both papers is pretty important. It’s no good getting a 9.0 in paper 1 then a 4.0 in paper 2.

If you’re interested, I got a 7.9 in paper 1, an 8.0 in paper 2, giving 8.0 overall. Getting a high TMUA score means all sorts of good things happen:

  • reassures yourself of your ability
  • leg up in admissions processes
  • post-matriculation prizes can be won, e.g. 7.0 or above gets you a £2000 cash prize if you go into the statistics department at Warwick University.

Cool (easy) maths

STEP

Sixth Term Examination Papers. Lots of these for all the different subjects used to exist, but only the mathematics ones have endured.

Format

Consists of two 3 hour examinations taken around the same time as your A levels (May/June of Y13): STEP 2 & STEP 3. These are both the same sort of difficulty in my opinion, but STEP 3 covers more Further Maths content and may well be trickier. This is a written exam, with questions in one booklet and answers to be submitted in another booklet.

The exam board switches around but this has no bearing on the papers - e.g. was with CAAT last year but switched to OCR for the year that I did it. You don’t need to worry about that stuff, just make sure you’re registered to sit the papers when you need to!

Doing the questions

So basically, the first thing is to think of STEP as totally different to other exams. It’s not something you have to revise for. It’s a challenge that you need to have the right toolbox for.

And the toolbox needs to have all the right skills, such as

  • Graph sketching
  • Trigonometrical reasoning
  • Manipulating equations
  • Algebra
  • Series
  • Etc.

And they all need to be appropriately honed, i.e. by practising them on older STEP questions to build them up. The key bit is for each one is knowing how/when they can work together, and how to use each one to get unstuck.

With practice, you should be able to look at a question and see one or more ‘ins’ (like an obvious way you can do some maths) but each way will lead to a ‘stuck’ position. This is when you use your toolbox to crack the question open. Getting to this stage of ability is tricky and takes hard work but is very much possible.

To build up each part of the toolbox and general familiarity, do STEP questions by topic either using the STEP database or the STEP Support Programme. Do STEP 1 questions at first and then progress to STEP 2&3 questions when you can (some questions are much harder/easier than others). After you have general familiarity with each topic, move onto past papers.

Also, solutions exist for each STEP question going way back (official and unofficial versions), but possibly the most important thing is to not immediately give in and look at the answer.

Not even after some time — getting to grips with the idea of ‘getting unstuck’ requires you to be stuck and practising the process yourself. In general, STEP questions should be 30 mins each at an examination standard, but at first, don’t spend any less than 2-3 hours on a question (if you’re stuck) before giving yourself a hint. You should relax this strategy eventually, obviously, but not too early!!

It’s much easier to verify an answer by reading it than coming up with one yourself. With time, you feel improvement and then you should start doing full length papers under timed conditions, finishing off questions in another colour before marking if you run out of time.

Pre-requisites

  • Total fluency with the A level maths/FM for the relevant bit of STEP.
  • Willingness to put in the time, depends on natural ability of course but for example, I averaged about 1-2 hours a day for just under a year.
  • (optional) Access to someone who can guide you at least a little and check if the solutions you write are of the required standard, teachers are probably your best bet.
  • Ability to write neatly and produce solutions that any competent person could read – Stephen Siklos himself (the former king of STEP) wrote on this topic in his book.

Practice materials

Use all the old STEP questions, at least as many as you can. Do the applied sections at your peril (I stuck to doing just the pure maths in mine). Some of the resources in the TMUA section above may also be handy, but here are some STEP-specific ones:

To help you keep track of all the questions you’ve done:

Loads and loads of resources out there, but these are some of the ones I leaned on most, excluding the past papers repository.

Outcomes

STEP is graded differently to other exams:

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

1,1 is typically needed for maths at Cambridge. A 2 in any one paper for other universities, though places like Imperial can be a bit bizarre with their offers sometimes.

You will need to work quite hard to get grades as high as a 1. Think along the lines of averaging about 1h 20m per day of STEP for (over) a year leading up to the exams, alongside 3 or 4 other A levels you ought to be getting A* in.

My experience was that I needed a 2 in STEP 2, and having done 557 past STEP questions going into the exams, I came out with an S,1. So hard work does pay off. Just make sure it’s the right sort of hard work.

To conclude

Whether you’re a TMUA-mo or a STEP-mo, make sure you put in the hours to get what you want. And even if you’re naturally bright at maths, especially for STEP, a great deal of practice is probably still necessary!

DO NOT GET COMPLACENT!

COMPLACENCY IS A FAST-TRACK TO DOOM!

Good luck.

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