The TMUA is won and lost on Paper 2

Most students prepare for the TMUA as if it's one exam. It's two, and they're not the same.

Paper 1 tests applications of mathematical knowledge, the kind of maths a strong A-level student already recognises. Paper 2 tests mathematical reasoning: building arguments, reading and writing proofs, and spotting where a proof goes wrong. That difference is where the marks are won and lost.

Paper 2 is where you're losing marks

In our practice data, students answer Paper 1 material at around 60% and Paper 2 at around 55%. A five-point gap across that many attempts isn't noise, and it matches what nearly every candidate says afterwards: Paper 2 is the hard one.

Here's the part that surprises people. Paper 2 questions are answered faster than average and still less accurately. If time were the problem, you'd see long, careful attempts. Instead you see quick, confident, wrong ones. That's not a lack of ability or time, it's unfamiliarity. The people sitting the TMUA are excellent by A-level standards; what catches them out is a style of question they've barely seen before.

Treat reasoning as its own subject

Paper 2 has three areas, and none of them is taught properly at school:

• The logic of arguments. Learn the vocabulary cold: necessary vs sufficient, converse, contrapositive, and how to negate an "all" or "some" statement. Our logic of arguments chapters cover it.
• Mathematical proof. Know the methods and pick one before you start writing: direct, contradiction, counterexample, induction. Start with methods of proof.
• Identifying errors in proofs. This is close reading. A broken proof usually fails at one step, like dividing by something that might be zero, or assuming what it's trying to prove. Name the step.

What to do this week

Stop practising both papers as one pile. Put at least half your reasoning time into Paper 2 specifically, and when you get one wrong, write down which area it was and what the intended step should have been. Practise reasoning questions here and let your mistakes tell you where to go back. The students who close the gap are the ones who stop treating reasoning as ordinary maths.