TMUA PAPER 1 VERSUS PAPER 2

Paper 1 is closest to a hard AS paper written in multiple choice form. Algebra and functions, quadratics, simultaneous equations and inequalities, polynomials and the factor theorem, coordinate geometry of lines and circles, sequences and series including the binomial expansion, logarithms and exponentials, trigonometric identities and equations, differentiation, integration, and elementary counting.

The distinctive feature is that the arithmetic is engineered to be doable without a calculator, and the intended route is almost always much shorter than the obvious one. A question that appears to want a full expansion usually wants one coefficient. A question that appears to want the solution of a cubic usually wants a sign change.

So the failure mode on Paper 1 is rarely ignorance. It is a correct method that takes four minutes on a question written to take ninety seconds, which then removes the last three questions of the paper from reach.

Paper 2 uses the same content and asks a different kind of question. The recurring subjects are logic and proof: implication and equivalence, necessary and sufficient conditions, converses and contrapositives, counterexamples, proof by contradiction, and the identification of the flaw in an argument that has been printed deliberately wrong.

A characteristic Paper 2 question gives a statement and four candidates, and asks which is equivalent to it, or which one would disprove it, or what the minimum additional assumption is. The mathematics involved is often modest. The precision of reading required is high.

Two habits carry most of the marks here. First, decide what kind of claim is being made before touching the algebra: for all, there exists, if then, if and only if. Second, when a statement is offered as always true, spend the first ten seconds looking for the single case that breaks it, usually zero, one, a negative, or an equal pair.

This is the paper that A-level teaching prepares candidates for least, which makes it the paper with the most available improvement.

The overall TMUA score is the average of the two papers. A candidate at 8.5 and 6.0 averages 7.25, below a candidate at a flat 7.5 who was weaker on their best paper.

Arithmetically, every 1.0 gained on the weaker paper is worth 0.5 overall, and it is almost always easier to find 1.0 on a paper you have neglected than 0.2 at the top of a paper you have already trained.

In practice this means that a candidate whose logic is shaky should be spending the majority of their remaining time on Paper 2, even though Paper 1 practice feels more productive because it produces recognisable mathematics.

For Paper 1, work in timed blocks and record the clock time next to each question. The output you want is not a score, it is a list of questions that cost more than three minutes, and for each of them a one line rule about the shorter route that was available.

For Paper 2, slow down first and speed up later. Take ten reasoning questions untimed and write out, in words, what the statement claims and what would falsify it, before choosing an option. Once that writing becomes automatic, put the clock back on.

For both, mark blind before reading any solution, and classify each error as knowledge, method, execution or time. The four errors have four unrelated fixes, and applying the wrong one is the most common way to work hard on a paper and gain nothing.

The free library carries live sittings for 2017, 2018 and 2020 papers, model answers for the specimen, 2017 and 2022 papers, and written analyses that classify the errors question by question. Those documents exist so that this process can be copied rather than described.

There is no negative marking, so an unanswered question is strictly worse than a guess. Reserve the last two minutes of each paper for filling in anything blank.

Take a first pass answering only what is quick, and leave a mark against anything you abandon. A paper with three unread questions is a scoring problem no amount of accuracy fixes.

Both papers are equally weighted. Treat the second one as half of your result rather than as an epilogue to the first.