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TMUA Flow

See why it is true. Then do it in three minutes forty-five.

Both TMUA papers, Applications of Mathematical Knowledge and Mathematical Reasoning, taught as exact figures you move yourself, then practised the way the exam sets them: without a calculator, against the clock.

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No sign-up. No card. Your progress stays in this browser until you choose to keep it.

a=3,a = 3, b=4,b = 4, a2+b2=25=52a^2 + b^2 = 25 = 5^2
a2+b2=c2a^2 + b^2 = c^2

A right-angled triangle with a hypotenuse of length 5 and a square standing outward on each side. The squares on the two shorter sides, 3 and 4, hold water drawn as horizontal hatching. The water drains into the square on the hypotenuse and fills it exactly to the brim: 9 plus 16 is 25. The right-angle corner then moves along the semicircle drawn on the hypotenuse, so the shorter sides change, and the water still fills the square on the hypotenuse exactly.

1 / 8Pythagoras, by water

The exam in five numbers

papers, both compulsory
2
questions in each paper
20
minutes for each paper
75
calculators and no formula booklet
0
one overall score
1.0–9.0

Paper 1 is Applications of Mathematical Knowledge. Paper 2 is Mathematical Reasoning: the same mathematics, plus logic, proof and spotting errors in proofs. Wrong answers cost nothing.

Where marks are lost

Five places the TMUA takes marks from strong students

None of them is a gap in A-level knowledge. Each one is a habit, and a habit can be practised.

  1. 1Paper 2 logic and proof

    A-level courses rarely teach formal logic, so “if”, “only if”, converse and contrapositive arrive for the first time in past papers, learnt as word rules that give way under time pressure.

  2. 2Necessary and sufficient

    Most students can recite the definitions and still point the arrow the wrong way. Drawn as sets, the sufficient condition is the smaller set inside and the necessary one is the larger set around it.

  3. 3Dense question stems

    Stems turn on single words: must, could, cannot, at least, for all. Marks go on answering a slightly different question from the one set.

  4. 4No-calculator arithmetic

    Surds, fractions, indices and exact values have to be quick and exact. After two years with a calculator the slips are slow, and they are silent.

  5. 5Timing

    75 minutes for 20 questions is 3 minutes 45 seconds each on average, not a target for every question. One hard question can take eight minutes and cost two easier marks.

How a lesson works

Move it first. Then predict, watch, and read why.

Every lesson runs in four beats. This is a real piece of the first Paper 2 lesson: try it.

  1. 1InteractMove something before anything is explained.
  2. 2PredictCommit to an answer while you are still unsure.
  3. 3RevealThe figure draws what is true over your answer.
  4. 4ExplainA short paragraph says why, with the numbers on screen.
n=6:n = 6: 2∣6,2 \mid 6, 4∤64 \nmid 6
{ n:4∣n }⊆{ n:2∣n }\{\, n : 4 \mid n \,\} \subseteq \{\, n : 2 \mid n \,\}

A frame of whole numbers. Inside it a large circle holds the even numbers, and inside that a smaller circle holds the multiples of 4. You place 4, 6 and 7 in the regions they belong to.

1. Interact

Put each number in the smallest region that holds it. Tap a number, then tap a region, or drag it across.

3 of 3 left to place.

Free tools

Three tools, free, no account

The course, drawn

Every idea as a figure you can take hold of

33 lessons across both papers, each built on figures like these.

See the whole course

The usual options

What each kind of preparation gives, and what it leaves out

Each has its place. This is where they fall short on the TMUA, and what we do about it.

KindGives youLeaves outHere instead
Official past papers and specimen materialGives youReal questions in the real format.Leaves outShort worked solutions, no teaching, no diagnosis, and a limited supply.Here insteadLessons end in questions in the same format. Lesson questions name the mistake behind a wrong answer; practice names it where we have checked it.
Question banksGives youVolume.Leaves outDrill without understanding; logic taught as rules, if at all.Here insteadPaper 2 is taught as a visual subject: implication as sets, and “if PP then QQ” as a grid with one failing cell.
Video coursesGives youExplanations.Leaves outPassive. You watch a proof rather than break it yourself.Here insteadEvery lesson screen asks you to move something before it explains anything.
BooksGives youDepth.Leaves outStatic figures, no feedback, no pacing.Here insteadFigures driven by the real mathematics, so every frame you scrub through is true; papers and exam mode are timed.
Private tutorsGives youAdaptation and feedback.Leaves outCost per hour, availability, and Paper 2 teaching that varies from tutor to tutor.Here insteadFeedback that names the mistake, and a mistake log that brings each one back on a spaced schedule.

Price

Free while TMUA Flow is in preview

Everything that is built is open to use: the diagnostic, the tools, the lessons, practice and timed papers.

No card details are asked for, and nothing is charged.

If a price is set, it will be shown here first.

What the full course includes

Questions

Before you start

What is the TMUA?

The Test of Mathematics for University Admission, set by UAT-UK. It has two compulsory papers: Paper 1, Applications of Mathematical Knowledge, and Paper 2, Mathematical Reasoning. Each has 20 multiple-choice questions in 75 minutes.

There is no calculator and no formula booklet. Wrong answers lose nothing, so answer every question. You get one overall score from 1.0 to 9.0.

What is free?

While TMUA Flow is in preview, everything that is built is free: the diagnostic, the three tools, the lessons, practice and timed papers. There is no checkout.

Why is there no predicted score?

The 1.0 to 9.0 scale is equated separately for each sitting, so the same raw mark can lead to different scores in different sittings. We have no validated way to turn practice results into that scale, and a short diagnostic could not produce one anyway.

So we show what we can measure: raw marks such as 13 out of 20, accuracy by topic, and time per question.

Do I need an account?

No. Your progress is kept in this browser as you go. Make an account only when you want to keep it across devices; whatever you have done so far moves into it.

What happens to my data?

Without an account, your progress is kept in your browser’s storage on this device.

With an account, your progress is saved to our server as small records tied to that account, so it follows you between devices. The account page lets you export or clear what is stored in this browser.

Which devices does it work on?

Phones, tablets and laptops in a current browser. Every figure works with touch, a mouse or the keyboard, and the switch at the foot of each page turns motion down to still frames.

Start with what you do not know yet.

The diagnostic is short, free, and needs no account. See where you stand, then pick a lesson.

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