RENZO DIAZ — Reference library
TMUA for IB Students: The Two Papers, the Dates and What AA Covers
4 min readBy Renzo DiazLast reviewed October 7, 2026
The TMUA (Test of Mathematics for University Admission) is the computer-based mathematics test that Cambridge, Oxford, Imperial, LSE, Warwick and UCL use for mathematics, computer science and economics courses in 2027 entry. It is two 75-minute papers of 20 multiple-choice questions, with no calculator and no formula booklet, and one overall score from 1.0 to 9.0 on a scale whose median is 4.5. For a student taking IB Mathematics: analysis and approaches, most of Paper 1 is familiar; Paper 2's language of logic is new at both levels, and its proof methods beyond direct proof are HL content.
The TMUA is written around AS level pure mathematics and Higher Level GCSE, so most guides to it assume an A-level student. An IB student sits the same test from a different starting point, and the question worth answering is the narrow one: which lines of the specification has the Diploma not covered?
I read the official TMUA specification for 2026–27 against the IB guide for Mathematics: analysis and approaches, section by section. The tables below show where AA already prepares a student and where it does not, alongside the format, the score scale, the dates and the courses that require the test, all from the test's own pages.
Paper 1 rewards the mathematics an AA student already has. Paper 2 asks for a way of reasoning about statements that the IB course never names.
Key takeaways
- Who sits it: mathematics, computer science and economics applicants to Cambridge, Oxford, Imperial, LSE, Warwick and UCL in 2027 entry; Durham recommends it for mathematics.
- Two papers: Paper 1 applies mathematical knowledge, Paper 2 tests mathematical reasoning; 20 questions in 75 minutes each, no calculator, no formula booklet.
- One score: 1.0 to 9.0 overall, with no pass mark; the scale fixes the median at 4.5 and the 90th percentile at 7.0.
- The dates: 12–16 October 2026, results on 16 November; or 4–8 January 2027, results on 8 February, where the course accepts January. One sitting per admissions cycle.
- The IB gaps: for Paper 1, circle geometry and circle theorems, recurrence relations and the trapezium rule; for Paper 2, the language of logic, which AA teaches at neither level.
Which courses use the TMUA in 2027 entry
The TMUA is run by UAT-UK, the collaboration between Imperial College London and the University of Cambridge that also runs the ESAT, and it is delivered on computer by Pearson at test centres worldwide. For 2027 entry, six universities make it compulsory for some courses, and two of them, with Durham, recommend it for others. Oxford uses it for the first time this cycle.
| University | Courses | Status |
|---|---|---|
| Cambridge | Computer Science; Economics; Mathematics | Compulsory |
| Oxford | Computer Science; Computer Science and Philosophy; Mathematics; Mathematics and Statistics; Mathematics and Computer Science; Mathematics and Philosophy | Compulsory |
| Imperial | Computing (all streams); Mathematics (all streams); Mathematics and Computer Science; Economics, Finance and Data Science | Compulsory |
| LSE | Economics; Econometrics and Mathematical Economics | Compulsory |
| LSE | Actuarial Science; Data Science; Economics and Data Science; Financial Mathematics and Statistics; Mathematics, Statistics and Business; Mathematics with Data Science; Mathematics with Economics; Mathematics and Economics | Recommended |
| Warwick | Computer Science; Computer Science with Business Studies; Discrete Mathematics; Mathematics | Compulsory, except for applicants eligible for a contextual offer |
| Warwick | Data Science; Economics; Economics and Management; Economics, Politics and International Studies; Mathematics and Statistics; Mathematics, Operational Research, Statistics and Economics | Recommended |
| UCL | Economics | Compulsory |
| Durham | Mathematics; Mathematics and Statistics | Recommended |
Source: UAT-UK, Course List 2027 Entry (last updated April 2026), confirmed against the Cambridge and Oxford admissions-test pages. Checked 7 October 2026. The university's course page is the final word.
Check this first
Two tests, two bookings
An applicant to, say, engineering at one university and computer science at another may need both the ESAT and the TMUA. Each test is selected and booked separately, and both run in the same October and January windows.
The two papers and the score
The TMUA lasts two and a half hours: two 75-minute papers taken one after the other, each of 20 multiple-choice questions, about 3 minutes 45 seconds a question. Every question carries equal weight, wrong answers cost nothing, and there is no calculator and no formula booklet: candidates are expected to recall every formula they need.
Paper 1, Applications of Mathematical Knowledge, uses the content of Section 1 of the specification in unfamiliar settings. Paper 2, Mathematical Reasoning, draws on the same content but is about constructing and analysing arguments, using Section 2: logic, proof and spotting errors in proofs.
The two papers give one overall score from 1.0 to 9.0, with no pass mark. UAT-UK sets the scale on each year's cohort, with the median at 4.5 and the 90th percentile at 7.0, and warns that strong candidates should not expect to score as highly as they do in school exams: the test is built to separate very able applicants.
The TMUA at a glance
- Papers
- 2
- Applications of Mathematical Knowledge; Mathematical Reasoning.
- Per paper
- 20 in 75 min
- Multiple choice, no negative marking.
- Calculator and formula booklet
- Neither
Dates, booking and fees for 2027 entry
The TMUA runs in the same two windows as the ESAT, and a candidate can sit it once per admissions cycle. Cambridge and Oxford undergraduate applicants must take the October sitting; January is for the other universities, and at Cambridge and Oxford only for a mature college with a January deadline or Oxford's Astrophoria Foundation Year.
Booking means creating a UAT-UK account, with the name as on your ID and the same details as your UCAS application, then booking a slot in Pearson's system. The fee is £78 at a test centre in the UK or Ireland and £133 elsewhere, set by where the centre is.
| Step | October 2026 sitting | January 2027 sitting |
|---|---|---|
| Booking opens | 20 July 2026 | 26 October 2026 |
| Booking closes (6pm UK time) | 28 September 2026 | 21 December 2026 |
| Test window | 12–16 October 2026 | 4–8 January 2027 |
| Results | 16 November 2026 | 8 February 2027 |
| Open to | All 2027-entry candidates | Not Cambridge or Oxford undergraduate applicants, with the two exceptions above |
Sources: UAT-UK key dates and registration pages. Checked 7 October 2026. Candidates in China, Hong Kong and Macau sit the TMUA on 15–16 October or 8 January.
Paper 1 against IB Mathematics: analysis and approaches
Section 1 of the specification has two parts: the first is almost all AS level pure mathematics, the second almost all Higher Level GCSE. Against the AA guide, most of the first part is IB content at SL. What AA lacks is mostly classical geometry and a few algebraic techniques that the IB leaves to HL or leaves out.
| TMUA area | AA SL | AA HL |
|---|---|---|
| Indices, surds, quadratics and the discriminant, inequalities, simultaneous equations, functions | Yes; rationalising the denominator is HL prior learning | Yes |
| Polynomial division and the factor and remainder theorems | No | Yes |
| Arithmetic and geometric series, binomial expansion | Yes | Yes |
| Sequences defined by a recurrence relation | No | No |
| Straight lines | Yes | Yes |
| Equation of a circle; the circle theorems (chords, tangents, angles in segments, cyclic quadrilaterals) | No | No |
| Sine and cosine rules, radians, exact values, trigonometric identities, graphs and equations | Yes | Yes |
| Exponentials and logarithms | Yes | Yes |
| Differentiation and integration of polynomials and powers of x, the fundamental theorem | Yes | Yes |
| Trapezium rule | No, enrichment only | No, enrichment only |
| Graph transformations and curve sketching | Yes | Yes |
| GCSE geometry: congruence criteria for triangles | Not listed | Not listed |
| GCSE number, ratio, proportion, statistics and probability | Yes, largely as prior learning | Yes, largely as prior learning |
Sources: UAT-UK, TMUA Content Specification (for assessment in October 2026 and January 2027), Section 1; IB Mathematics: analysis and approaches guide (first assessment 2021), syllabus content and prior learning. Checked 7 October 2026.
The formula booklet
What the IB booklet gives you that the TMUA will not
In IB exams the AA formula booklet supplies the series sums, the binomial theorem, the sine and cosine rules, the area of a triangle, arc length and sector area, the laws of logarithms and the standard derivatives and integrals. In the TMUA there is no booklet: each of these has to be known.
Paper 2 against IB Mathematics: analysis and approaches
Paper 2 is where an IB student meets the most new material. The specification's logic section, the words if, only if, if and only if, converse, contrapositive, necessary and sufficient, for all and there exists, and how to negate statements that use them, has no counterpart in the AA syllabus. The proof section overlaps more: AA SL teaches simple deductive proof, and AA HL adds proof by contradiction and disproof by counterexample. Proof by induction, which AA HL also teaches, is not on the TMUA's list.
| TMUA area | AA SL | AA HL |
|---|---|---|
| True and false; and, or, not; if, only if, if and only if | No | No |
| Converse and contrapositive of a statement | No | No |
| Necessary and sufficient conditions | No | No |
| For all, for some, there exists; negating statements | No | No |
| Direct deductive proof | Yes | Yes |
| Proof by cases | Not listed | Not listed |
| Proof by contradiction; disproof by counterexample | No | Yes |
| Putting a proof's statements in order; finding the error in a flawed proof | Not listed | Not listed |
Sources: UAT-UK, TMUA Content Specification, Section 2; IB Mathematics: analysis and approaches guide (first assessment 2021), SL 1.6 and AHL 1.15. The TMUA does not use symbolic notation or formal truth tables. Checked 7 October 2026.
How an IB student can prepare
UAT-UK publishes all of its preparation material free, and states that it is not connected to, and does not endorse, any paid preparation service. For the TMUA that means the specification, the specimen and practice tests in the Pearson test player, two sets of notes, and every paper from 2016 to 2023 with worked answers. The archive still applies: UAT-UK says the specification and question style have not changed since the test moved to computer.
Preparing for the TMUA from the IB
Read the specification against your own course
Tick off Section 1 and Section 2 with the tables above, and list the lines your course has not covered.
Learn the formulas the booklet usually gives you
Series sums, the binomial theorem, the sine and cosine rules, arc and sector, the laws of logarithms: recalled, not looked up.
Learn the language of logic before Paper 2
UAT-UK's Notes on Logic and Proof cover the words and proof types Paper 2 uses. For an AA student this is the largest single gap, at SL and at HL.
Sit the past papers under time
2016 to 2023, Paper 1 then Paper 2, about 3 minutes 45 seconds a question, without a calculator. Read the worked answers for every question, including the ones you got right.
Practise in the test player
The specimen and practice tests open in the software used at the test centre. Use them on a desktop, as UAT-UK advises.
Terms used in this article
- TMUA
- Test of Mathematics for University Admission: a computer-based test of two 20-question papers, scored from 1.0 to 9.0 overall.
- UAT-UK
- University Admissions Tests UK, the collaboration between Imperial College London and the University of Cambridge that runs the TMUA, the ESAT and the TARA.
- Contrapositive
- For a statement "if A then B", the statement "if not B then not A". It is true exactly when the original is; the converse, "if B then A", need not be.
- Necessary and sufficient
- A is sufficient for B when A guarantees B; A is necessary for B when B cannot hold without A.
- Contextual offer
- An offer adjusted for an applicant's educational circumstances. At Warwick, applicants eligible for one are exempt from the compulsory TMUA.
Questions about the TMUA
What is a good TMUA score?
There is no pass mark, but the scale is fixed so that 4.5 is the median and 7.0 the 90th percentile. Universities read the score alongside the rest of the application, so check each course's own guidance.
Can you use a calculator or a formula booklet in the TMUA?
Neither. Candidates are expected to recall every formula, including the ones IB students normally find in their formula booklet.
Does IB Math AA HL cover the TMUA?
Most of Paper 1, and part of Paper 2. The gaps are circle geometry and the circle theorems, recurrence relations and the trapezium rule in Paper 1, and the language of logic in Paper 2. AA SL students also need polynomial division with the factor and remainder theorems, and proof by contradiction and counterexample.
Should an IB Math AI student take the TMUA?
If the course requires it, yes, but check the specification line by line first. The TMUA is written around AS level pure mathematics, and the tables here compare it with AA, not with Applications and interpretation.
When are TMUA results released?
16 November 2026 for the October sitting and 8 February 2027 for the January sitting, through the candidate's UAT-UK account.
Are old TMUA past papers still useful?
Yes. UAT-UK publishes every paper from 2016 to 2023 with worked answers, and says the content specification and question style are unchanged since the test became computer-based.
Written by
Teaching IB since 2016. Seven years of IB reviews you can check on Google — and named results with the documents behind them.
Last reviewed October 7, 2026
Sources
Format, scoring, the score scale, dates, fees, preparation materials and the course list come from UAT-UK's own pages and documents; the Cambridge and Oxford pages confirm the courses and dates. The comparison uses the IB Mathematics: analysis and approaches guide (first assessment 2021) and its formula booklet, which the IB makes available to schools. Everything was checked on 7 October 2026; course requirements change every cycle, so the university's course page is the final word.
- UAT-UK — TMUA: format and scoring
- UAT-UK — TMUA Content Specification (October 2026 and January 2027)
- UAT-UK — Course List 2027 Entry (April 2026)
- UAT-UK — Key dates and deadlines, 2027 entry
- UAT-UK — Prepare (score scale and statement on commercial preparation)
- UAT-UK — TMUA past papers, 2016–2023
- UAT-UK — Notes on Mathematics for TMUA Paper 1 and ESAT Mathematics 2 (June 2026)
- UAT-UK — Notes on Logic and Proof for TMUA Paper 2 (June 2025)
- UAT-UK — Registering for a test (fees)
- University of Oxford — Admissions tests (2027 entry)
- University of Cambridge — Admission tests and assessments