IB Maths AA HL to TMUA: What Extra Do You Need to Study?

You have already decided to sit the TMUA, so I will skip the part about whether you should. Two questions are worth your time now: what is actually different about this exam, and what do you have to learn that AA HL never taught you?

The reassuring bit first. The TMUA specification describes its own content as roughly AS-level pure maths plus Higher Level GCSE. AA HL sits above both. You are not walking into unfamiliar mathematics.

The catch is that “you already know it” and “you can do it in this exam” are different claims. So below: what carries over, what is genuinely missing, and what you can stop revising. I checked every line against the UAT-UK specification and the IB subject guide rather than going from memory.

Start with the format, not the syllabus

The content gap turns out to be small. The format gap is not, and it is what actually costs students marks.

Four things follow from that table, and they matter more than anything on the gap list.

You get under four minutes a question. Seventy-five minutes, twenty questions. An AA HL extended-response question can happily eat fifteen minutes. Here you have three minutes forty-five, and that is the whole game.

Nobody reads your working. Two years of IB trains you to write out every step, because a wrong answer with sound method still scores. In the TMUA only the letter you pick counts. Beautiful working on a question you got wrong is worth nothing.

No calculator and no formula booklet, in both papers. AA HL lets you reach for one or the other in two papers out of three. Every exact trig value, every log law, every derivative has to come out of your head.

Never leave a blank. There is no penalty for a wrong answer, so a blank and a wrong guess score the same. If you are running out of time, guess the rest.

What carries over from AA HL

Most of Paper 1 is content you have already met. Here it is mapped against your own syllabus codes, so you can see how little is genuinely new.

Every code above is listed in full on our AA HL syllabus page if you want to check what a particular one covers.

The five things AA HL never taught you

This is the part worth planning around. Four are quick. One is not.

1. Circle geometry

The biggest gap, and the one students are most often blindsided by. The TMUA wants the circle in Cartesian form — both (x − a)² + (y − b)² = r² and x² + y² + cx + dy + e = 0 — and then the full set of circle theorems: the perpendicular from the centre bisects a chord, the tangent meets the radius at a right angle, the angle at the centre is twice the angle at the circumference, the angle in a semicircle is 90°, angles in the same segment are equal, opposite angles of a cyclic quadrilateral sum to 180°, and the alternate segment theorem.

AA HL contains none of it. Your only circle content is SL 3.4, which is radians, arc length and sector area. If you did IGCSE you met the theorems at fifteen and have not touched them since. If you came through a different system you may never have seen them at all. Either way it is new work, and it can appear in both papers.

2. The trapezium rule

You need to approximate an area with the trapezium rule and say whether the result is an over- or under-estimate. AA HL has no numerical integration anywhere — the trapezoidal rule lives in the other IB maths course, Applications and Interpretation, at SL 5.8. It is an hour of work, but only if you know to do it.

3. Surds and rationalising denominators

Simplifying surds and rationalising denominators like 5/(3 + 2√5). AA HL assumes this rather than teaching it; SL 1.5 and SL 1.7 give you the laws of exponents, not surd technique. With no calculator in either paper you will be working exactly all day, and this is where the minutes quietly disappear.

4. Recurrence relations

Sequences defined by x_n+1 = f(x_n). AA HL teaches sequences through nth-term and sum formulae at SL 1.2 and SL 1.3, and never introduces a recurrence. Genuinely small, but unfamiliar notation under time pressure is its own problem.

5. The logic behind Paper 2

Paper 2 tests Section 1 and Section 2, and Section 2 is where AA HL leaves you most exposed. It is not harder mathematics. It is a way of arguing that the IB never explicitly teaches you. You need:

• The vocabulary: and, or, not; if A then B, A only if B, A if and only if B; the converse and the contrapositive, and how the truth of each relates to the original statement
• Necessary versus sufficient — a distinction most students think they understand until they are asked at speed
• The quantifiers for all, for some and there exists, and how to negate a statement containing them
• Proof by cases, such as splitting into odd and even
• Reordering a jumbled set of statements into a valid proof, and making a conjecture from small cases then justifying it
• Spotting errors in a proof that looks fine — that ab = ac does not give b = c, or that sin A = sin B does not give A = B

AA HL does hand you two pieces of this. AHL 1.15 covers proof by contradiction and disproof by counterexample, and SL 1.6 covers simple deductive proof and the difference between an equation and an identity. Useful, but it is a fraction of the list.

Worth noting: induction is not on the TMUA list. You will have spent a long time on it for AA HL, and it is the one proof technique the specification does not ask for.

What you can stop revising

Just as useful, and nobody tells you this bit. A large part of what makes AA HL hard sits outside the TMUA entirely. Here is what you can put down, with where it lives in your syllabus so you can check it off.

Three more are ruled out by the specification by name, which is worth seeing in its own words — all three are drilled hard in AA HL:

The order I would work through it

1. Section 2 first, and give it the most time. It is half of Paper 2, it is entirely new, and it is where being good at AA HL helps you least. You can learn the vocabulary in an evening. Using it quickly takes much longer.
2. Circle geometry next. A fixed list of theorems, so it is finite work, and it can come up in either paper.
3. Then the three small ones. Trapezium rule, surds, recurrence relations. About an hour each.
4. Then stop learning content and start timing yourself. Once the gap is closed everything left is speed and recall. No calculator, no formula booklet, under four minutes a question. That is what the remaining weeks are for.

Fitting this around the IB year is the genuinely awkward part. The October window lands in the middle of your Year 13 term, usually while the Internal Assessment is live and before your mocks. How that works depends on your school’s IA deadline, your mock dates, and how far your teacher has got through AA HL — which is a conversation to have with someone who can see your actual calendar.

Dates you cannot miss

For 2027 entry:

• Booking closes 28 September 2026, 6pm BST for the October sitting
• October test window: 12 to 16 October 2026, results on 16 November 2026
• January window: 4 to 8 January 2027 for January-round applicants, bookable 26 October to 21 December 2026
• Candidates in China, Hong Kong and Macau have restricted dates within those windows

The booking deadline is the one that catches people, because it falls a fortnight before the test itself and nothing reminds you. Confirm everything on esat-tmua.ac.uk — dates shift between cycles, and these were checked in August 2026.

Where we come in

Everything above is a content problem, and content problems are the easy kind. The hard part of running AA HL and the TMUA together is the calendar.

You are already carrying a demanding Diploma: six subjects, the Internal Assessment, the Extended Essay, CAS. Now add a test that lands mid-October, in term time, before your mocks. The usual response is to bolt TMUA prep on top of a full IB workload some time in September and push through it. That is where the hours go, and the stress with them.

Mathematics is our home ground, and AA HL in particular. That matters here for one specific reason: we can hold both syllabuses at once and plan them as a single piece of work instead of two competing ones. Your AA HL course is already covering most of TMUA Paper 1. Used on purpose, that overlap means fewer total hours, not more.

In practice that looks like:

• A diagnostic first, so you know which of the five gaps you actually have. Most students do not have all five
• One plan across both, built around your school’s IA deadline and mock dates rather than a generic countdown
• The Section 2 logic taught early and properly, because it is genuinely new and it is where the score moves
• Timed sets under real conditions: no calculator, nothing to look up, under four minutes a question
• The AA HL topics the TMUA never touches left alone until the test is behind you

There is a reason this is worth the planning. By the autumn of Year 13 most of your application is already fixed. Predicted grades are in, the personal statement is written. The TMUA is one of the few parts you can still move, and it is the part most students leave to three rushed weeks in September.

IBDP is demanding enough on its own. Better planning is what makes the extra thing fit, and it is most of what we do for students in this position. Sessions are 1-on-1 or in a batch capped at five, and everything is online.

The short version

AA HL leaves you over-prepared for the content and under-prepared for the conditions. Only five things are missing, and only one of them — the Paper 2 logic — is real work. After that it stops being a maths problem and becomes a speed problem: no calculator, nothing to look up, under four minutes a question, and no credit for the working you spent two years learning to show.

Every AA HL subtopic is listed under its official code on our AA HL syllabus page. Our TMUA coaching page covers how we drill both papers, and AA HL and TMUA together is built for exactly the position you are in. Still not certain the TMUA is the test your offer asks for? Start with TMUA vs ESAT vs TARA.

Checked against the UAT-UK TMUA Content Specification and the IB Mathematics: Analysis and Approaches guide (first exams 2021), August 2026. Check the current specification for your own cycle before relying on any detail here.