TMUA Paper 1 vs Paper 2: What Each Paper Tests and How Indian Students Should Prepare

Every year, a few of my strongest maths students walk into the TMUA expecting it to feel like JEE or the SAT, and every year the same thing happens: Paper 1 feels fine, and Paper 2 feels like a completely different subject. With the October 2026 test window (12 to 16 October) only weeks away, understanding how the two papers differ is one of the most useful things you can do right now.

The two papers at a glance

Both papers are taken on the same day, so you also need stamina. That is 2 hours 30 minutes of continuous concentration on a computer screen at an approved test centre.

What Paper 1 tests

Paper 1 uses topics you already know from Class 11 and 12: algebra, functions and graphs, coordinate geometry, sequences and series, trigonometry, logs and exponentials, differentiation and integration, and basic probability. The catch is that the questions are disguised. You will often be given a problem in a form you have not seen, and the fastest solution is usually not the one you were taught in coaching class.

What separates a high score from an average one is not knowledge, it is choice of method. A student who expands a big expression will run out of time. A student who spots a substitution, a symmetry or a quick sketch will finish in under two minutes. Since you have roughly 3 minutes 45 seconds per question, and no calculator, mental arithmetic and clean algebra matter a lot.

What Paper 2 tests

Paper 2 uses the same mathematical content but adds elementary logic and proof. You will see questions that ask:

• Is this statement true, false, or is there not enough information?
• Which of these is the converse or contrapositive of the given statement?
• Which condition is necessary, sufficient, or both?
• Where is the first error in this proof?
• Which counterexample disproves this claim?

This is why the paper surprises good students. In school, we are taught to solve. In Paper 2, you are taught to judge. Words like “if and only if”, “for all” and “there exists” carry exact meanings, and one careless reading of a quantifier can flip your answer.

Who this affects

Anyone applying from India for a course that asks for the TMUA, which includes courses in Economics, Computer Science and Mathematics at UK universities such as Cambridge, Oxford, Imperial, LSE, Warwick and Durham. Requirements differ by course, so always check the specific course page for the current admissions cycle before you commit your preparation time.

My preparation plan

If you have about three to four weeks, this is the split I give my students.

1. Week 1: Diagnose. Sit one past paper under exam conditions, both papers, no calculator. Record your marks separately. Most Indian students I coach score noticeably better on Paper 1.
2. Week 1-2: Learn the logic language. Spend a few short sessions learning converse, contrapositive, negation of “for all” and “there exists”, necessary versus sufficient, and proof by contradiction and by counterexample. Write your own examples until they feel natural.
3. Week 2-3: Drill Paper 2 by type. Do 10 to 15 questions per day from one question type at a time, then mix them. Always write down why each wrong option is wrong. This habit alone raises accuracy.
4. Week 2-3: Train Paper 1 speed. Do timed sets of 10 questions in 35 minutes. After each set, redo the ones you got wrong using a faster method. Practise fractions, surds, logs and quadratics by hand every day.
5. Week 4: Full timed papers. Do at least three complete two-paper sessions, ideally at the same time of day as your booked slot. Review mistakes the same day.

Scoring and what it means

You do not receive a separate score for each paper. The two papers are equated and scaled together into one overall score between 1.0 and 9.0. Because the conversion is set after each sitting, do not trust any fixed “raw mark equals score” chart you find online. Use past-paper conversion tables only as a rough guide. Since Paper 1 and Paper 2 each have 20 questions, a weak Paper 2 can pull down your overall score about as much as a weak Paper 1. Improving your weaker paper is nearly always the quickest way to raise your total.

Recommended practice resources

• Official TMUA specification and specimen papers on the UAT-UK website (esat-tmua.ac.uk).
• Past papers from the admissions test provider, which are free and the closest match to the real test.
• Your own error log: a single notebook where you write down every mistake and the rule you should have applied.

If you also plan to apply for engineering or science courses that use the ESAT, plan both tests together, since some of your maths practice will overlap.

Not sure what to do next? Book a free consultation and I will create a personalised plan for you.