TMUA 2022: Papers, Scores and Topic Breakdown

TMUA 2022 was delivered by Cambridge Assessment Admissions Testing (CAAT) and ran for 2 hours 30 minutes in total, with Paper 1 (Applications of Mathematical Knowledge) and Paper 2 (Mathematical Reasoning) sat back to back, each carrying 20 multiple-choice questions over 75 minutes. Scores that year were still reported on the CAAT-era basis: a scale running from 1 (low) to 9 (high), reported to one decimal place, with separate results for each paper alongside the overall score. This page brings together the 2022 format and scoring basis, the official wording on what a score means, FrontierVUE's own difficulty and topic breakdown for that year, and a practical route for sitting both papers on the platform.
TMUA 2022 at a Glance
Papers sat
Paper 1 (Applications of Mathematical Knowledge) and Paper 2 (Mathematical Reasoning), 20 multiple-choice questions and 75 minutes each, 2 hours 30 minutes in total
Score scale
From 1 (low) to 9 (high), reported to one decimal place; Paper 1 and Paper 2 are each reported separately alongside the overall score
Official anchor
The scale is designed so that approximately one third of candidates score above 6.5 overall, with high scores capped at 9.0
Delivery body and sittings
Delivered by Cambridge Assessment Admissions Testing (CAAT), which ran one autumn sitting a year; UAT-UK introduced the October and January pair from 2024
What changed in 2022
The Cambridge entry on the official course list expanded to G400 Computer Science and L100 Economics, with the list stating that TMUA is compulsory for Cambridge applications, except for mature students applying to one of the mature Colleges for Economics
Difficulty (FrontierVUE catalogue)
4 of the 20 Paper 1 questions and 2 of the 20 Paper 2 questions in the catalogue are rated hard

The format, the scale and the anchor come from the official Explanation of Results for 2022 and from official documents tracing the test's history; the difficulty line reflects FrontierVUE's own catalogue ratings rather than any official assessment of the papers. From 2024 the TMUA has been delivered by UAT-UK on a revised scaling process, and the exam board states plainly that the two generations of scores cannot be compared directly. Even inside the CAAT era the anchor moved once: every year from 2017 to 2022 was anchored so that approximately one third of candidates scored above 6.5, with scores capped at 9.0, whereas the first sitting in 2016 was anchored at about 50% of candidates above 5.0 and about 10% above 7.5. A 2022 score therefore reads only against the years 2017 to 2022, and not directly against 2016.

01

What TMUA 2022 tested and how scores were reported

TMUA 2022 was delivered by Cambridge Assessment Admissions Testing (CAAT), and the paper structure was the one settled on in 2017: 2 hours 30 minutes in total, with two papers sat back to back. Paper 1, Applications of Mathematical Knowledge, is about putting mathematical knowledge to work; Paper 2, Mathematical Reasoning, is about mathematical argument itself. Each paper carries 20 multiple-choice questions and runs for 75 minutes. In the CAAT era the test ran once a year in the autumn; UAT-UK introduced the October and January pair of sittings from 2024.

Total length

2 hours 30 minutes

Two papers sat back to back

Papers

Paper 1 and Paper 2

Paper 1: Applications of Mathematical Knowledge. Paper 2: Mathematical Reasoning

Per paper

20 multiple-choice questions, 75 minutes

The two papers are identical in length and question count

Delivery body

Cambridge Assessment Admissions Testing (CAAT)

CAAT was the brand adopted in 2017; the CAAT website closed in early 2024 and the TMUA has been delivered by UAT-UK since 2024

Sittings

One autumn sitting a year

The October and January pair of sittings is a UAT-UK arrangement introduced from 2024

What changed for applicants in 2022

The Cambridge entry expanded to G400 Computer Science and L100 Economics

The 2022 official list reads: 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)

Paper 1Paper 2
Paper nameApplications of Mathematical KnowledgeMathematical Reasoning
Questions20 multiple-choice20 multiple-choice
Time75 minutes75 minutes
How results were reportedIts own distribution chartIts own distribution chart
FrontierVUE section labelMathematical ThinkingMathematical Reasoning

The two papers match exactly in length and question count. The official Explanation of Results for 2022 carries a distribution chart for Paper 1 and for Paper 2 as well as one for the overall score. The last row is FrontierVUE's own section label, where Paper 1 keeps the earlier CAAT-era title Mathematical Thinking; the official 2022 title was already Applications of Mathematical Knowledge.

On exam-room rules: the current official TMUA page states that calculators and dictionaries may not be used, and that final scores are based on the number of correct answers with no marks lost for wrong ones, so every question is worth attempting. That wording comes from the current official page rather than from a 2022 document, but it is a sound set of conditions to practise this year's papers under.
02

How to read a TMUA 2022 score

Scores in 2022 were reported on a scale running from 1 (low) to 9 (high), to one decimal place. The 2022 Explanation of Results sets out two things about it: that results are reported on that scale, and that the scale is designed so that approximately one third of candidates achieve overall scores higher than 6.5, with high scores capped at 9.0. Those two sentences are where reading a TMUA score starts. In that document 6.5 is the point the scale was anchored at, and the document presents it as a design target rather than as a pass mark or an admissions threshold. Individual universities did set their own conditions around it in the CAAT era, so check each one on its own admissions pages.
What the 1 to 9 scale means
The official wording: results for TMUA are reported on a scale that runs from 1 (low) to 9 (high), with scores being reported to one decimal place. What you receive is therefore not a raw count of correct answers but a converted figure on that scale. In 2022, Paper 1 and Paper 2 each carried a score of their own alongside the overall result.
Where the figure 6.5 comes from
The official wording: the scale has been designed so that approximately one third of candidates will achieve overall scores higher than 6.5, and high scores are capped at 9.0. Note that this describes how the scale was designed, not a measured statistic for the year, and certainly not an admissions threshold. For what a university actually asks for, go to that university's own admissions pages for the cycle.
Did the exam board publish a score distribution?
It did, in the form of charts. The 2022 Explanation of Results states that the distribution of the 2022 TMUA scores, overall and for Papers 1 and 2, are shown below, and what follows is three bar charts: one for the overall score, one for Paper 1 and one for Paper 2. That document presents the distributions graphically and carries no table of figures. Claims of the form "this score puts you in the top such-and-such per cent" therefore cannot be read out of that document, and it is worth asking where any such number came from.
Did anything change from 2021?
The scoring basis did not change. The 2021 Explanation of Results likewise reports scores on a scale from 1 (low) to 9 (high) to one decimal place, likewise states that the scale is designed so that approximately one third of candidates score above 6.5 with a cap at 9.0, and likewise gives distributions for the overall score and for both papers. The real difference between the two years is on the university side: the Cambridge entry on the 2021 official course list was G400 Computer Science, and on the 2022 list it expanded to G400 and L100 Economics.
Not comparable across generations: UAT-UK states plainly that this scaling process has been revised for 2024/25, and scores should not be compared directly with TMUA scores from earlier years. 2022 belongs to the CAAT era and everything from 2024 belongs to the UAT-UK era; the two differ both in how scores are reported and in where the scale is anchored, so a chart that runs a trend line across the two sits directly against that official statement.
CAAT era, including 2022UAT-UK era, from 2024
Scale1 (low) to 9 (high), to one decimal placeStill 1.0 to 9.0, to one decimal place
How scores are reportedPaper 1 and Paper 2 are reported separately alongside the overall scoreThe two papers are equated and scaled together into a single overall score
Where the scale is anchoredApproximately one third of candidates score above 6.5, with a cap at 9.0The median is fixed at 4.5 and roughly 10% of candidates sit above 7.0
SittingsOne autumn sitting a yearTwo sittings a year, in October and January
Who sees the scoreCandidates could decide whether to share their results with universitiesResults are sent automatically via the UCAS application, and candidates cannot choose which institutions see the score

Each column stands on its own and the two cannot be measured against each other. On the revised scaling from 2024/25 the exam board states that scores should not be compared directly with TMUA scores from earlier years, so any chart that draws a score trend across the 2023 and 2024 boundary has misread the official position.

03

Topic emphasis and difficulty in 2022 (FrontierVUE catalogue)

Everything below reflects the FrontierVUE catalogue: the platform's own difficulty ratings and syllabus tags for the 2022 questions, not official paper data. The official document reporting the 2022 results, the Explanation of Results, covers the score scale and the distribution charts; it stays clear of how hard the papers were and of how topics were distributed.

20 questions

Held from Paper 1: 3 rated easy, 13 medium, 4 hard

20 questions

Held from Paper 2: 6 rated easy, 12 medium, 2 hard

6 questions

The most frequent topic tag: quadratic functions and equations

Both papers are held in full at 20 questions each, matching the official structure of 20 multiple-choice questions per paper. On difficulty, medium-rated questions make up the bulk of both papers, Paper 1 carries more hard-rated questions than Paper 2, and Paper 2 carries more easy-rated ones than Paper 1. These are platform ratings only: the 2022 Explanation of Results, the exam board's own document for that year's results, sets out the scale and the distribution charts and does not rate the difficulty of the papers, so treat the split as a guide to allocating practice rather than as an official verdict.

Quadratic functions and equations

6

Graphs and the discriminant, completing the square, solving

Applications of differentiation

4

Gradients, tangents and normals, stationary points, strictly increasing and decreasing behaviour

Quantifiers

3

Reading and negating for all, for some and there exists

Trigonometric identities

3

tanθ = sinθ/cosθ and sin²θ + cos²θ = 1

Necessary and sufficient

2

Telling a necessary condition from a sufficient one

Spotting the flaw in a false proof

2

Locating the step where a plausible-looking argument breaks

Ratio and similarity

2

Ratios of length, area and volume, similarity and scale factors

Forming and solving equations

2

Simultaneous equations in two unknowns, linear with linear or linear with quadratic, and turning a situation into an equation

Properties of plane shapes

2

Definitions and properties of the special quadrilaterals and of the types of triangle

Pythagoras

2

Using a² + b² = c² in two and three dimensions

Laid out together, these tags make the emphasis of 2022 clear. One group is mathematical machinery: quadratics, applications of differentiation, trigonometric identities, ratio and similarity, simultaneous equations, properties of plane shapes and Pythagoras. The other is the language of argument: quantifiers, necessary and sufficient conditions, and spotting the flaw in a false proof. That is exactly what the two paper titles promise, one on putting knowledge to work and one on reasoning precisely. The practical takeaway: give quadratics and applications of differentiation a dedicated pass before sitting either paper in full, and drill the logical vocabulary until you parse it on sight, because the official exam rules bar dictionaries from the room.
04

How to practise the 2022 papers on FrontierVUE

01Step 1

Open the TMUA past paper list

Go to the past paper list at /papers/tmua.

02Step 2

Find the two 2022 papers by year

Locate Paper 1 and Paper 2 under 2022.

03Step 3

Sit them under time

Work in the timed interface at the official pace: 75 minutes for a single paper, or sit both back to back for the full 2 hours 30 minutes to reproduce test conditions, with no calculator throughout.

04Step 4

Review by error type

After submitting you get a question-by-question breakdown with a full worked solution for each. Reviewing by error type is far quicker than resitting the whole paper blind.

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)

2 papers

Held from 2022: Paper 1 and Paper 2

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

TMUA guides

/exams/tmua/guides/

scoringHow the scale works and how to read a score
paper-1What Applications of Mathematical Knowledge asks of you
paper-2What Mathematical Reasoning asks of you
logic-and-proofQuantifiers, necessary and sufficient, and false proofs
time-managementAllocating the time within a paper
common-mistakesThe recurring error types and a self-check list

Tap a branch to unfold

Two cautions when using the 2022 papers to gauge where you stand. The TMUA scale is designed around the distribution of a whole cohort, so a practice score is not the same object as a reported one. And 2022 sits in the CAAT era: its scores cannot be compared directly with UAT-UK scores from 2024 onwards, so looking across that boundary for a benchmark will only mislead you.
FAQ

Frequently asked questions

What was the TMUA 2022 grade boundary?
The official Explanation of Results for 2022 gives a scale and a design anchor rather than a boundary. Results are reported on a scale from 1 (low) to 9 (high) to one decimal place, and the scale is designed so that approximately one third of candidates achieve overall scores higher than 6.5, with high scores capped at 9.0. The document presents the results as three distribution bar charts and carries no table of figures, so any claim about what percentage of candidates a given score beats cannot be sourced to that document. On the university side, the 2022 official course list states that TMUA is compulsory for Cambridge applications, except for mature students applying to one of the mature Colleges for Economics; for anything more specific, use each university's own admissions pages for that cycle.
How many questions and how long was TMUA 2022?
Two papers sat back to back, 2 hours 30 minutes in total. Paper 1 (Applications of Mathematical Knowledge) and Paper 2 (Mathematical Reasoning) each carry 20 multiple-choice questions and run for 75 minutes. In the CAAT era there was a single autumn sitting each year; the October and January pair arrived with UAT-UK from 2024.
Was TMUA 2022 hard?
The official document reporting the 2022 results, the Explanation of Results, sets out the scale and the distribution charts and does not assess how hard the papers were. What can be offered instead is FrontierVUE's own catalogue: of the 20 Paper 1 questions, 3 are rated easy, 13 medium and 4 hard; of the 20 Paper 2 questions, 6 are easy, 12 medium and 2 hard. More to the point, the TMUA scale is designed around the distribution of the whole cohort, so whether a given year was hard shows up in where you sit relative to the people who sat it with you rather than in any absolute score, and comparing raw impressions across years is not a reliable guide.
Can a TMUA 2022 score be compared with scores from 2024 onwards?
No. UAT-UK states that this scaling process has been revised for 2024/25, and scores should not be compared directly with TMUA scores from earlier years. Three concrete differences: from 2024 the two papers are equated and scaled together into a single overall score, whereas 2022 reported each paper separately as well as the overall; the anchor moved from approximately one third of candidates above 6.5 with a cap at 9.0 to a median fixed at 4.5 with roughly 10% above 7.0; and the single autumn sitting became a pair of sittings in October and January. Comparisons only work across 2017 to 2022, the years that share one anchor; the first sitting in 2016 was anchored at about 50% of candidates above 5.0 and about 10% above 7.5, so it does not line up with 2022 directly either.
Sources

Official sources

By year

Other TMUA years

TMUA 2025TMUA 2024TMUA 2023TMUA 2021TMUA 2020TMUA 2019TMUA 2018TMUA 2017TMUA 2016

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