TMUA preparation guide
TMUA score statistics: where you actually sit
Most of the TMUA score benchmarks floating around online are second-hand paraphrase. UAT-UK's annual technical report actually prints the whole distribution in the body text: how many sat, the mean, where each percentile falls, and how it all breaks down by event and by group. This page works through the 2025/26 report table by table, using only figures printed as text, with nothing estimated off a chart and nothing converted across admissions cycles. By the end you will know where your score sits among 16,092 candidates, and which questions this data cannot answer.
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- 28
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- 827
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Quick answer: the official 2025/26 TMUA distribution
- Cohort size
- 16,092 in total: 9,685 in October (60%) and 6,407 in January (40%)
- Centre of the distribution
- Mean 4.28, standard deviation 1.74, median 4.1
- Upper end
- 75th percentile 5.3, 90th percentile 6.7; the scale is capped at 1.0 and 9.0
- What these are not
- Not a cut-off score: UAT-UK publishes no pass mark and no university publishes a fixed threshold
Every figure here comes from the body text and tables of UAT-UK Technical Report 3 2025-26: TMUA; nothing is read off a chart image. FrontierVue is an independent preparation platform, not affiliated with UAT-UK or with any admitting university.
In short
- 16,092 candidates sat the TMUA in the 2026 admissions cycle: mean 4.28, SD 1.74, median 4.1, 75th percentile 5.3, 90th percentile 6.7.
- October averaged 4.62 and January 3.78, yet both events ran on one set of scaling constants that UAT-UK says exists precisely to keep the two comparable. So the gap describes the two sets of candidates, not the two papers. Across cycles no such guarantee holds: the anchors are re-fixed on each cycle's own data.
- Gaps between subgroups run to a few tenths of a point, against a standard error of measurement of 0.62 to 0.64 on the same scale. These are cohort descriptions, and no individual score follows from them.
- Time genuinely binds: across the 15,481 candidates analysed the median test time was 02:29:37 against a 02:30:00 limit, and 2,517 candidates (16%) logged at least one answer inside 10 seconds, which the report reads as guessing.
- A percentile is not an admissions bar: UAT-UK publishes no pass mark and universities publish no fixed score threshold, so the report gives you position and nothing more.
01
The distribution itself: everyone, and each event
Start with the headline. In the 2026 admissions cycle 16,092 candidates sat the TMUA, with a mean scaled score of 4.28, a standard deviation of 1.74 and a median of 4.1. Put another way: half the field is at or below 4.1, 5.3 marks the 75th percentile and 6.7 the 90th. Every figure in the table below is printed in Table 4 of the report.
16,092
Candidates who sat the TMUA in the 2026 cycle
4.28
Overall mean, SD 1.74, on a 1.0 to 9.0 scale
4.1
Overall median: half the field is at or below this
6.7
Overall 90th percentile
| All candidates | October 2025 | January 2026 | |
|---|---|---|---|
| Candidates | 16,092 | 9,685 (60%) | 6,407 (40%) |
| Mean | 4.28 | 4.62 | 3.78 |
| Standard deviation | 1.74 | 1.77 | 1.57 |
| 25th percentile | 3.0 | 3.3 | 2.7 |
| 50th percentile (median) | 4.1 | 4.5 | 3.6 |
| 75th percentile | 5.3 | 5.8 | 4.6 |
| 90th percentile | 6.7 | 7.0 | 5.9 |
| Range | 1.0 to 9.0 | 1.0 to 9.0 | 1.0 to 9.0 |
Reproduced as printed: Table 4 is inconsistent about thousands separators, giving 16,092 for the total but 9685 and 6407 for the two events, while the same October figure appears as 9,685 in the prose. Nothing here is reformatted.
A percentile is not a cut-off score. UAT-UK publishes no pass mark for the TMUA, and universities publish no fixed score threshold. Table 4 answers exactly one question: where your score sits among these 16,092 candidates. Reading 6.7 as the 90th percentile is right; reading it as any university's bar is not.
02
How the scale was pinned down
Before reading the distribution, know that a TMUA score is not a raw mark count. Items are calibrated with a Rasch model, each candidate's responses become an ability estimate, and that estimate is mapped onto the 1.0 to 9.0 scale and capped at both ends. It also explains an apparent coincidence in Table 4: October's median lands on exactly 4.5 and its 90th percentile on exactly 7.0, because those are the two points the scale was nailed to.
01Rasch / Winsteps
Calibrate the items
Items are calibrated with a Rasch IRT model in Winsteps. For the 2025/2026 cycle, items were selected for the forms by the Chair on expert judgement.
02theta
Estimate ability
Each candidate's responses give a theta value, and the scaled score is derived from theta rather than straight from the number of correct answers.
034.5 and 7.0
Fix two anchors
Using the October 2025 data, the median candidate's theta was fixed at a scaled score of 4.5 and the 90th percentile ability at 7.0 (Table 2).
044.6046 / 1.6369
Derive constants, then cap
A regression line between the two anchors gives the scaling constants (Table 3: constant 4.6046, multiplier 1.6369). Results are capped at 1.0 and 9.0, and the same constants were applied to both events.
In UAT-UK's own words: 'The same scaling constants were used for both the October 2025 and January 2026 events to ensure the scaling was consistent and scaled scores were comparable across events.' The report even supplies a worked sentence: a candidate scoring 6.5 in either January or October has a higher ability than one scoring 4.2 in either event. That guarantee holds inside this cycle only, because the anchors were re-pinned on this cycle's October data, so comparing raw scaled scores across admissions cycles has no basis.
03
October sat higher than January, and what that is not
This is the most misread pair of numbers in the report. October averaged 4.62 with a median of 4.5; January averaged 3.78 with a median of 3.6, and its whole distribution sits lower. The instinct is to reach for a harder January paper. But UAT-UK ran both events through one set of scaling constants and says in as many words that this was done so the scores stay comparable across events, which closes that door.
October cohort
9,685
60% of the total
January cohort
6,407
40% of the total
October scores
Mean 4.62
Median 4.5, 90th percentile 7.0
January scores
Mean 3.78
Median 3.6, 90th percentile 5.9
If the two events are comparable under one set of constants, then the gap in their means belongs to the two groups of candidates, not to the two papers. On how those groups differ the report offers one fact and no more: candidates may sit only once per admissions cycle, and University of Cambridge applicants must sit in October, which is what drives October's much larger volume. Nothing further is claimed there, and nothing further is claimed here. The practical move: if you sat in January, read your position off the January column rather than October's percentiles, and the other way round if you sat in October.
04
Broken down by group: cohort numbers, not yours
The report breaks means and percentiles down by gender, area of residence, first language, ethnicity, school type, free school meals and parental education. Those figures are reproduced below, with one caveat up front: each is a description of a whole group of candidates, and none of them says anything about a particular candidate. Every row contains people who scored far above its mean and people who scored far below it.
Gender (all candidates)
Man: 11,253 candidates (70%), mean 4.41, median 4.2, 90th percentile 6.9. Woman: 4,642 (29%), mean 3.98, median 3.9, 90th percentile 6.0. Only these two rows are printed, and the percentages total 99%. UAT-UK's wording is that male candidates slightly outperformed female candidates. Separately, one item was flagged for significant DIF by gender, favouring male candidates after controlling for ability, and will be reviewed.
Area of residence (all candidates)
UK: 8,643 candidates (54%), mean 3.98, 90th percentile 6.0. EU: 716 (4%), mean 3.94, 90th percentile 6.4. Other: 6,733 (42%), mean 4.71, 90th percentile 7.5. The report notes that candidates outside the UK and the EU performed more strongly, and this group also carries the highest 90th percentile of the three at 7.5. Note that only these three rows are printed; the report does not break residence down to individual countries.
First language (all candidates)
English: 9,255 candidates (58%), mean 4.05, 90th percentile 6.2. Other: 6,837 (42%), mean 4.60, 90th percentile 7.3. Candidates whose first language is not English scored higher overall. The English share fell from 60% in the previous cycle to 58% here. No significant item DIF was found by first language.
Ethnicity (UK candidates only)
White: 3,591 (42%), mean 4.08. Asian: 3,534 (41%), mean 4.00. Mixed: 704 (8%), mean 4.08. Black: 499 (6%), mean 3.22. Other: 313 (4%), mean 3.68. The report says the gap is widest around the middle of the distribution, with medians running from 3.1 for UK-Black to 3.9 for UK-White. One item was flagged for significant DIF by ethnicity favouring Non-White candidates; it was relatively easy and will be reviewed to inform future item writing.
School type (UK candidates only)
Independent or private fee-paying schools: 1616 candidates (19%), mean 4.35, the strongest group. Grammar (selective) schools: 1887 (22%), mean 4.19. University: 86 (1%), mean 4.30. Academy or secondary school: 1506 (17%), mean 3.85. Further education or sixth form colleges: 3478 (40%), mean 3.75, simultaneously the largest group and, apart from Other, the lowest scoring. No significant item DIF was found by UK school type.
Free school meals (UK candidates only)
In receipt: 700 candidates (8% of UK candidates), mean 3.44. Not in receipt: 7,364 (85%), mean 4.04. 'I don't know': 368 (4%), mean 3.66. 'I prefer not to say': 209 (2%), mean 4.17. The previous cycle recorded 10% claiming free school meals; UAT-UK notes that the two new answer options added this cycle could account for the difference.
Parent or guardian in higher education
Yes: 12,604 candidates (78%), mean 4.37. No: 2,178 (14%), mean 3.73. Don't know: 612 (4%), mean 4.07. Prefer not to say: 698 (4%), mean 4.64. This table covers all candidates, not just UK ones.
Keep the scale in mind here. Most gaps between groups run to a few tenths of a point, while the report prints a standard error of measurement on the scaled score of 0.62 to 0.64 (Table 17). The uncertainty band around one person's own score is already the same size as the gaps being compared. Reading a group mean as a forecast for an individual is more than this data will carry.
05
What this data should change about your prep
The most actionable part of the report is not the distribution but the test design and the timing data. The TMUA runs as two papers, 20 items and 75 minutes each, 150 minutes and 40 items in total. Everything feeds one scaled score, and the report prints no separate scaled-score distribution per paper.
TMUA test design
40 multiple-choice items, 150 minutes in total
Paper 1Applications of Mathematical Knowledge
- 20 multiple-choice questions
- 75 minutes
- Applying mathematics in new situations
Paper 2Mathematical Reasoning
- 20 multiple-choice questions
- 75 minutes
- Mathematical reasoning and elementary logic
How it is reportedOne overall scaled score
- Scaled 1.0 to 9.0
- Reported to one decimal place
- The report gives no per-paper distribution
Tap a branch to unfold
Mean test time
02:27:01
Across the 15,481 candidates analysed (Table 18)
Median test time
02:29:37
Against a standard limit of 02:30:00
Took between 02:15:00 and 02:30:04
91%
Of all candidates, comparable with the previous cycle
Candidates with unreached items
322 and 135
Paper 1 and Paper 2; the report puts the base at 16,091 here against 16,092 in Table 4, reproduced as printed
On item quality and score precision: 100% of the items used across the forms met the criteria, well above the 80% typical target for new items (Table 19). Raw score reliabilities run 0.82 to 0.88, scaled score reliabilities 0.82 to 0.87, with a standard error of measurement of 0.62 to 0.64. Under classical measurement theory there is roughly a 68% probability that a candidate's true score lies within plus or minus 1 SEM of the observed score, and roughly 95% within 2 SEMs. Read your score as a band, not a point.
That makes pacing worth more than another paper on the pile: the median candidate finishes within a whisper of the limit, so running out of time is the norm, not the exception. A further 2,517 candidates (16%) recorded at least one answer in 10 seconds or less, which the report treats as guessing, down from 23% in the previous cycle. Drill by paper with the Paper 1 guide and the Paper 2 guide, check the mechanics in the scoring guide, and sit full timed sets in the online question bank or the past papers overview.
FAQ
Frequently asked questions
What TMUA score is good enough?
The report cannot answer it: UAT-UK publishes no pass mark and universities publish no fixed threshold. What it does give is position. Across all candidates the median is 4.1, the 75th percentile 5.3 and the 90th percentile 6.7. How any university uses a score is a matter for that university's own pages.
Are October and January scores directly comparable?
Within one admissions cycle, yes. UAT-UK applied the same scaling constants to both events specifically so scores stay comparable, and states that 6.5 in either event beats 4.2 in either event. Across cycles, no: the anchors are re-pinned on each cycle's own data, so absolute scores do not travel between cycles.
January's mean was lower, so was that paper harder?
The report does not put that gap on the papers. What it says is that both events went through one set of scaling constants, precisely so scores stay comparable across events. If the scores are comparable, then what is left describes two different groups of candidates. On how those groups differ the report offers a single fact: candidates may sit only once per cycle, and Cambridge applicants must sit October. So read your position against your own event rather than converting it to the other one.
Does the report give separate distributions for Paper 1 and Paper 2?
No. Only one overall scaled-score distribution is printed (Table 4), with no per-paper breakdown, so any claim about what your Paper 1 alone is worth has no support in this document. The two papers are held apart in only two places: the test design (20 items and 75 minutes each) and the unreached-item counts (322 candidates on Paper 1, 135 on Paper 2). The reliability tables are reported by event, not by paper.
Can more detail be read off the report's charts?
Not here. Figure 1's binned distribution, and the charts for gender, residence and the other groups, exist in the PDF only as images, with no corresponding numbers printed as text. Any figure that could only be estimated by eye is left out, which is why every number on this page can be pointed back to a specific table.
SOURCES
Official sources
- UAT-UK Technical Report 3 2025-26: TMUA (July 2026, the sole source for this page)
- Same report, Tables 2 to 4: scale anchors, scaling constants and the overall and by-event distributions
- Same report, Tables 6 to 14: statistics by gender, residence, ethnicity, first language and school type
- Same report, Tables 16 to 20: reliability, standard error of measurement, test time and item quality
- UAT-UK Annual Reports index (public entry point for all four 2025-26 reports)
MORE GUIDES
Other TMUA preparation guides
- TMUA Paper 1: Applications of Mathematical Knowledge
- TMUA Paper 2: Mathematical Reasoning, from Syllabus to Strategy
- TMUA Logic and Proof: The Complete Paper 2 Reasoning Guide
- The TMUA Syllabus in Full: Section 1, Section 2 and Every Topic Boundary
- The TMUA revision plan: from registration to results
- TMUA time management: pacing, guessing and stamina across both papers
- TMUA Common Mistakes: Where Strong Candidates Lose Marks
- How TMUA Scoring Works: From Rasch Scaling to University Data
- TMUA test day: from arriving at the centre to reading your score
- TMUA vs MAT: After the Switch
- TMUA vs ESAT: The Course Decides, Not You
- TMUA vs STEP: One Screens, One Seals the Offer
- TMUA Registration and Test Dates for 2027 Entry
- TMUA sittings compared: October 2025 against January 2026
- TMUA overseas candidates: the official numbers, and where they stop
- TMUA candidate numbers: how big the 2026 cohort really was
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