TMUA 2023: The Last CAAT Year, Papers, Scores and Practice

TMUA 2023 was the last year the test was delivered by Cambridge Assessment Admissions Testing (CAAT): the paper was sat on 18 October 2023 and results were released on 28 November 2023 at 9:00 GMT. The year kept the format in place since 2017: 2 hours 30 minutes in total, with Paper 1 and Paper 2 each carrying 20 multiple-choice questions over 75 minutes. This page covers the 2023 papers and dates, how the CAAT-era 1 to 9 scale is read, why the exam provider says 2023 scores cannot be set alongside scores from 2024 onwards, the topic emphasis and difficulty profile of the year as catalogued by FrontierVUE, and a concrete route for practising both papers.

TMUA 2023 at a Glance

Papers sat: Two papers sat back to back over 2 hours 30 minutes: Paper 1 (Applications of Mathematical Knowledge) and Paper 2 (Mathematical Reasoning), each 20 multiple-choice questions in 75 minutes
Test and results dates: Sat on 18 October 2023, results released 28 November 2023 at 9:00 GMT; the CAAT Dates and costs page lists one autumn sitting for the year
How results were reported: On a scale from 1 (low) to 9 (high) reported to one decimal place, with Paper 1 and Paper 2 each scored separately alongside the overall score
Universities on the list: The 2023 official list ran to 10 universities: Cardiff, Durham, Lancaster, LSE, Bath, Cambridge, Nottingham, Sheffield, Southampton and Warwick
Comparable with later years?: No. The official wording states that the scaling process was revised for 2024/25 and that scores should not be compared directly with TMUA scores from earlier years
Difficulty (FrontierVUE catalogue): 1 of the 20 Paper 1 questions and 7 of the 20 Paper 2 questions are rated hard

The 2023 facts on this page come from archived CAAT sources: the Dates and costs page as captured on 2023-09-25 and the 2023 Courses accepting TMUA list. The description of the score scale is quoted from the 2022 official Explanation of Results, the last CAAT-era EoR we retrieved from the archives; we did not retrieve a 2023 EoR, so this page gives no score distribution figures for the year. The difficulty line reflects FrontierVUE's own catalogue ratings, not an official assessment. Scores from 2023 and earlier and scores from 2024 onwards come from two different scaling processes, and the official guidance says they should not be compared directly.

What TMUA 2023 looked like and how results were reported

TMUA 2023 kept the two-paper format settled in 2017: 2 hours 30 minutes in total, Paper 1 and Paper 2 sat one after the other, each with 20 multiple-choice questions in 75 minutes. The first sitting in 2016 ran to 2 hours with 60 minutes per paper; from 2017 the test was lengthened to its present shape and has stayed there. What made 2023 distinctive was not the paper but the delivery body: it was the last year CAAT ran the test, the CAAT website closed in early 2024, and UAT-UK took over from 2024.

Format

Two papers sat back to back, 2 hours 30 minutes in total

The 2016 first sitting ran to 2 hours with 60 minutes per paper; from 2017 it became 2 hours 30 minutes and has stayed so

Paper 1

Applications of Mathematical Knowledge, 20 multiple-choice questions, 75 minutes

In the earlier CAAT years this paper was called Mathematical Thinking; the present name was in use by 2021 at the latest

Paper 2

Mathematical Reasoning, 20 multiple-choice questions, 75 minutes

Sittings

One autumn sitting in 2023, on 18 October

CAAT ran one sitting a year; UAT-UK introduced the October and January pair of sittings from 2024

Delivery body

CAAT, for the last time in 2023

The CAAT website closed in early 2024 and its closure notice listed TMUA among the tests for which other delivery arrangements were being made; UAT-UK has run it since 2024

Score scale

1 (low) to 9 (high), reported to one decimal place

In the CAAT era Paper 1 and Paper 2 were each scored separately alongside the overall score, and the official EoR carried three distribution charts each year

2023Timeline

Sep 23

Oct 23

Nov 23

Dec 23

Test day

18 October 2023

The last CAAT-era sitting of TMUA: both papers sat back to back over 2 hours 30 minutes.

Results released

28 November 2023, 9:00 GMT

Results were reported on the 1 to 9 scale to one decimal place, with an overall score and a score for each paper.

Hard deadline Event WindowBoth dates come from the CAAT Dates and costs page as archived on 2023-09-25, which lists one autumn sitting for the year.

Cambridge is worth reading separately. It joined the official TMUA list for the 2021 sitting with G400 Computer Science, added L100 Economics from the 2022 sitting, and the official wording stated: "For applications to the University of Cambridge TMUA is compulsory (except in cases of mature students applying to one of the mature Colleges for Economics)". Before that, Cambridge Computer Science applicants had been sitting the same test since October 2019 under the Cambridge-specific CTMUA label, in the same 2 paper format; 2021 was simply the point at which it folded into the general list.

One note on test conditions: the current official TMUA page states that no calculator or dictionary may be used and that final scores are based on the number of correct answers, with no marks lost for wrong ones. That wording is from the current UAT-UK page and is quoted here for reference; every statement of fact about 2023 itself on this page rests on archived CAAT sources from that year.

How to read a TMUA 2023 score

A TMUA score is not a raw mark but a scaled one. Through the CAAT era, from 2016 to 2023, results were reported on a scale from 1 (low) to 9 (high) to one decimal place, with Paper 1 and Paper 2 each scored separately alongside the overall score, and the official Explanation of Results carried three distribution charts each year. The board stated the anchor points of the scale in the EoR year by year. One caveat matters here: the last CAAT-era EoR we retrieved from the archives is the 2022 document, so this page quotes the scale from that document.

Range and precision of the scale

In the CAAT era TMUA results were reported on a scale running from 1 (low) to 9 (high), to one decimal place. The 2022 official Explanation of Results puts it thus: "Results for TMUA are reported on a scale that runs from 1 (low) to 9 (high), with scores being reported to one decimal place."

You received three scores, not one

Alongside the overall score, Paper 1 and Paper 2 each carried their own score. The 2022 official EoR reads: "The distribution of the 2022 TMUA scores, overall and for Papers 1 and 2 are shown below.", followed by three bar charts. This changed from 2024: under UAT-UK the two papers are equated together and a single overall score is reported.

How the scale was anchored

The anchors were stated by the board in each year's EoR. For 2016 the wording put roughly 50% of candidates above 5.0 and roughly 10% above 7.5; from 2017 to 2022 the wording settled on approximately one third of candidates above 6.5, with high scores capped at 9.0. The 2022 EoR reads: "The scale has been designed so that approximately one third of candidates will achieve overall scores higher than 6.5. High scores are capped at 9.0." That is the last CAAT-era anchor statement we retrieved from the archives.

Can percentiles be read off the official charts?

No. The 2022 Explanation of Results presents three bar charts, and what accompanies them is the charts themselves rather than a data table, so a figure for how many candidates sat above a given score, read off by eye, is a reader's own estimate rather than an official number. What this page quotes are the anchor statements the board wrote out in each year's EoR. It gives no score distribution figures for 2023.

Did the score have to go to universities?

In the CAAT era candidates decided for themselves whether to share their results, the official page stating: "As you can decide if you want to share you results with universities or not after you have received them, the test gives you a risk-free opportunity to prove your potential". From 2024 UAT-UK sends scores automatically to institutions matched through the UCAS application, and candidates cannot choose which institutions see them.

Do not compare across the two eras. The UAT-UK Explanation of Results states: "This scaling process has been revised for 2024/25, and scores should not be compared directly with TMUA scores from earlier years." Scores from 2023 and earlier (the CAAT era) and from 2024 onwards (the UAT-UK era) are produced by two different scaling processes. Both sit on a 1 to 9 range, but the same number means different things in each era: they cannot be plotted as one trend, and a score in one era cannot be used to infer a level in the other.

	2023 and earlier (CAAT era)	2024 onwards (UAT-UK era)
Delivery body	Cambridge Assessment Admissions Testing	UAT-UK, established in 2023 as a joint venture between Imperial College London and the University of Cambridge
What is reported	An overall score plus a separate score for Paper 1 and for Paper 2	The two papers are equated and scaled together into a single overall score
How the scale is set	Anchor statements written out by the board in each year's Explanation of Results	Rasch IRT equating across papers, anchored on the October cohort with the median fixed at 4.5 and the 90th percentile at 7.0
Sittings	One autumn sitting a year; in 2023 that was 18 October	Two sittings a year, in October and January
Where the score goes	Candidates decided for themselves whether to share results with universities	Sent automatically to institutions matched through UCAS; candidates cannot choose who sees the score

This table sets out how the two eras differ as systems; it is not a conversion of any kind. The official guidance is that scores from 2024 onwards should not be compared directly with TMUA scores from earlier years.

Topic emphasis and difficulty in 2023 (FrontierVUE catalogue)

Everything below reflects the FrontierVUE catalogue: the platform's own difficulty ratings and topic tags applied to the 2023 questions. It is not an official analysis of the papers, nor an official verdict on how hard the year was. We did not retrieve a 2023 Explanation of Results from the archives, so this section carries no official distribution data.

20 questions

Held from Paper 1: 5 rated easy, 14 medium, 1 hard

20 questions

Held from Paper 2: 4 rated easy, 9 medium, 7 hard

×6

The most frequent topic of the year: quadratic functions, the discriminant and completing the square

The two papers carry very different difficulty profiles. In the FrontierVUE catalogue only 1 of the 20 Paper 1 questions is rated hard, with the bulk sitting at medium, while 7 of the 20 Paper 2 questions are rated hard. That is where the year separates candidates, and it matches how the papers are defined: Paper 1 tests the application of mathematical knowledge, Paper 2 tests mathematical reasoning and demands steady judgement about proof, logic and counterexamples. Treating the two as equivalent in revision usually means underestimating what Paper 2 costs in time.

Quadratic functions, discriminant, completing the square

Solving quadratic equations algebraically

Necessary and sufficient conditions

Gradient and intercept of straight lines

Geometric series and convergent infinite sums

Trigonometric equations on a given interval

Exponential equations and substitution

Integration of powers

Mathematical logic: converse and contrapositive

Spotting the flaw in a false proof

The grid above counts topic-tag occurrences across both 2023 papers in the FrontierVUE catalogue; it is not an official analysis. Two practical points follow. First, quadratics carry the most weight this year, so the discriminant, completing the square and algebraic solution methods are worth a focused pass before sitting a full paper. Second, the logic tags (necessary and sufficient conditions, converse and contrapositive, spotting the flaw in a false proof) appear steadily, and that is Paper 2 territory: scattered practice rarely closes that gap, so it needs systematic work.

How to practise the 2023 papers on FrontierVUE

01Step 1

Open the TMUA past paper list

Go to /papers/tmua and find Paper 1 and Paper 2 listed under 2023.

02Step 2

Sit one paper against the clock

Each paper is 20 questions in 75 minutes, so time them one at a time. Work the papers separately first, and only run the full 2 hours 30 minutes back to back once both feel steady.

03Step 3

Review question by question

After submitting, work through the question-by-question breakdown; every question comes with a full worked solution and a Chinese translation. Start with what you got wrong, then look at what you got right but slowly, since that is where a timed test actually costs you marks.

04Step 4

Drill the weak topics

Use topic-based practice to drill the areas listed in the previous section, taking quadratics and logic and proof first.

16 papers

TMUA past papers held, 320 questions across the 16, plus 2 official specimen papers (FrontierVUE catalogue)

1102 questions

TMUA questions on the site in total, including mock papers and the topic bank, not the past-paper count (FrontierVUE catalogue)

20 questions / 75 minutes

The pacing target for a single timed paper, matching the 2023 format

For method alongside the papers, the guides under /exams/tmua/guides/ are built to pair with them.

TMUA guides

/exams/tmua/guides/

syllabusThe syllabus in detail, and what each paper actually asks for

paper-1What Paper 1 demands and how to work through it

paper-2The reasoning paper, where this year's hard-rated questions cluster

logic-and-proofLogic and proof, matching this year's frequent conditions and false-proof tags

scoringHow scoring and the scale work, including the difference between the two eras

time-managementPacing drills for 75 minutes on a single paper

common-mistakesCommon mistakes, to read alongside your question-by-question review

Tap a branch to unfold

FrontierVUE is an independent preparation platform with no affiliation to, authorisation from, or partnership with UAT-UK, Cambridge Assessment Admissions Testing or any university. Every official rule and date quoted here is sourced; for registration arrangements and current requirements, always go by the official announcements.

FAQ

Frequently asked questions

How hard was TMUA 2023?

We did not retrieve an official Explanation of Results for 2023 from the archives, so this answer draws on no official distribution data. What can be looked at is the paper itself: 20 multiple-choice questions in 75 minutes on each of the two papers. In the FrontierVUE catalogue, 5 of the 20 Paper 1 questions are rated easy, 14 medium and 1 hard, while Paper 2 has 4 easy, 9 medium and 7 hard, so the hard-rated questions cluster clearly in Paper 2. These are the platform's own ratings, not an official verdict.

When was TMUA 2023 sat and when did results come out?

The test was sat on 18 October 2023 and results were released on 28 November 2023 at 9:00 GMT, per the CAAT Dates and costs page as archived on 2023-09-25. Note that CAAT ran one autumn sitting a year, so candidates had that single attempt within the cycle; UAT-UK introduced the October and January pair of sittings after taking over in 2024.

Can a TMUA 2023 score be compared with scores from 2024 onwards?

No. The official wording is explicit: "This scaling process has been revised for 2024/25, and scores should not be compared directly with TMUA scores from earlier years." Both eras report on a 1 to 9 range, but the scaling differs. Through 2023 CAAT set the scale and reported Paper 1 and Paper 2 separately alongside the overall score; from 2024 UAT-UK equates the two papers with a Rasch IRT model into a single overall score anchored on the October cohort, with the median at 4.5 and the 90th percentile at 7.0. The same number therefore means different things in each era and cannot be converted.

Which universities were on the official TMUA list in 2023?

The 2023 official list ran to 10 universities: Cardiff, Durham, Lancaster, LSE, Bath, Cambridge, Nottingham, Sheffield, Southampton and Warwick, the last such list of the CAAT era. Cambridge had joined for the 2021 sitting with G400 Computer Science and added L100 Economics from the 2022 sitting. After UAT-UK took over in 2024 the list was redrawn: on the current 2027 entry basis, seven universities use the UAT-UK tests, namely Imperial, Cambridge, Durham, LSE, Oxford, Warwick and UCL. Cardiff, Lancaster, Sheffield, Southampton, Nottingham and Bath from the CAAT list are not among them.

Sources

Official sources

By year

Other TMUA years

TMUA 2025 TMUA 2024 TMUA 2022 TMUA 2021 TMUA 2020 TMUA 2019 TMUA 2018 TMUA 2017 TMUA 2016

FrontierVUE is an independent practice platform. It is not affiliated with or endorsed by UAT-UK, Pearson, OCR, the University of Cambridge, Imperial College London, or any official admissions-test owner.

FrontierVUE 是独立的备考练习平台，与 UAT-UK、Pearson、OCR、剑桥大学、帝国理工学院或任何官方入学考试主办方均无隶属或背书关系。

Practise TMUA 2023 online

Timed interface, worked solutions and per-question analytics. The two most recent past papers are free to try.

Practise TMUA papers All TMUA past papers