How We Teach the TMUA: Our Method

Parents ask us three questions in almost every first email: what format will my child learn in, how will I know they are improving, and what does it cost.

Those are the right questions, and the honest answer to the third depends on the first two. So here is how we actually work — the same process we would walk you through on a call, written down.

What makes the TMUA different to teach

The TMUA is two papers, each 20 multiple-choice questions in 75 minutes, with no calculator and no dictionary. Oxford has retired the MAT in its favour, and Cambridge, Imperial, LSE, UCL, Warwick and Durham all use it for maths, computer science and economics courses.

The teaching problem is specific and unusual. Paper 1 applies AS-level pure mathematics to unfamiliar problems — students prepare for this instinctively and usually arrive competent. Paper 2 adds elementary logic and proof, and no school syllabus teaches it.

That creates the clearest asymmetry we see in any admissions test: the component most candidates neglect is also the smallest and most learnable. A focused few weeks on logic moves a TMUA score further than another month of calculus revision.

There is also no pass mark and no negative marking. Our TMUA Paper 2 guide sets out where the marks actually go.

Stage one: find the real starting point

We do not quote a plan before we know what we are planning for. The first step is a full timed paper from each of Paper 1 and Paper 2, marked by us rather than self-scored.

Both papers matter, and sitting only one tells us half the story. Students frequently score respectably on Paper 1 and then discover that Paper 2 asks something they have never been taught to do, which is information we need before planning anything.

What comes out of it is not a score. It is a profile: which topics are secure, which are shaky, and crucially why marks were lost — because that determines everything that follows.

Stage two: separate knowledge gaps from habit gaps

This is the distinction that most preparation misses, and it is the reason two students with identical scores can need opposite programmes.

On the TMUA the divide is almost always the same shape. Paper 1 losses are usually genuine technique gaps - a weak area in logarithms, integration or sequences. Paper 2 losses are almost never about mathematics: they are about precision over what a statement claims, and about not having the vocabulary of implication, converse and sufficiency available fast enough under time pressure.

A knowledge gap needs teaching. A habit gap needs a different kind of practice entirely, and more teaching will not touch it. Getting this wrong is how a student works hard for three months and does not move.

Stage three: build the pathway backwards from the date

There are normally two sittings, October and January, and which one applies to you is dictated by your universities rather than your readiness - Cambridge and Oxford applicants must sit in October. We plan backwards from your sitting: Paper 1 gaps first, then logic and proof taught explicitly as content, then mixed timed papers where the first task is identifying what a question is really testing.

We sequence it so the highest-yield work happens while there is still time to consolidate it, and we deliberately stop introducing new material in the final stretch so nothing goes in half-learned.

Stage four: monitor progress against something real

We track Paper 1 and Paper 2 separately, because they improve at different rates and averaging them hides progress. Logic questions get their own tally - specifically whether a student can now name the flaw in an argument rather than sense it, which is the switch that makes them fast.

You get a written summary you can actually read — what improved, what has not, and what next week targets. Not a percentage with no explanation attached.

Stage five: choose the format that fits the student

One-to-one suits a student with Paper 1 gaps to close on a timeline, or one who needs the logic content built from nothing at their own pace. Small group works well for logic and proof in particular, because hearing another student justify a step - correctly or incorrectly - is one of the fastest ways to learn what a rigorous argument sounds like.

Fees follow from that choice, which is why we do not publish a single number for every student. We tell you the fee once the format and duration are agreed, before you commit to anything, and it does not change afterwards.

The honest answer about scores

There is no pass mark for the TMUA, and universities do not generally publish thresholds — LSE states this directly. So nobody can tell you what score your child needs, and anyone quoting a guaranteed number is inventing it.

What we can tell you after a diagnostic is more useful: which of the two papers is costing you more, whether your Paper 2 losses are logic or mathematics, and how much of that is realistically closeable before your sitting.

Starting the conversation

Tell us which universities and courses are on the list, which sitting applies, and whether your child has met formal logic or proof before — most have not, and that is normal rather than a problem.

We will mark diagnostics for both papers, show you the split, and recommend a format and duration. The fee follows that, quoted before you commit.