TMUA 2018: What Was Tested and How Scores Were Reported

The TMUA 2018 sitting was delivered by Cambridge Assessment Admissions Testing: 2 hours 30 minutes in total, Paper 1 and Paper 2 taken together, each paper 20 multiple-choice questions in 75 minutes, with results reported on a scale from 1 (low) to 9 (high) to one decimal place. The official Explanation of Results for that year states that the scale was designed so that approximately one third of candidates achieve overall scores higher than 6.5, with high scores capped at 9.0. This page pulls together the 2018 paper structure, the scoring rules, what that year's official distribution material says, and the topic emphasis and difficulty as catalogued by FrontierVUE, plus why a 2018 score cannot be lined up against scores from 2024 onwards.
TMUA 2018 at a Glance
Papers sat
Paper 1 and Paper 2 taken together, 2 hours 30 minutes in total, each paper 20 multiple-choice questions in 75 minutes
How it was scored
Marks for correct answers and no penalty for wrong ones; results on a 1 (low) to 9 (high) scale to one decimal place, with Paper 1 and Paper 2 each reported separately alongside the overall score
Official scale anchor
Official wording: the scale was designed so that approximately one third of candidates achieve overall scores higher than 6.5, and high scores are capped at 9.0
Delivery body
Cambridge Assessment Admissions Testing (CAAT), which published that year's Explanation of Results
Difficulty (FrontierVUE catalogue)
Of the 20 Paper 1 questions held, 10 are rated easy, 9 medium and 1 hard; of the 20 Paper 2 questions, 6 are easy, 8 medium and 6 hard
Cross-era caveat
From 2024 the TMUA has been delivered by UAT-UK under a revised scaling process, and the official guidance states that those scores should not be compared directly with TMUA scores from earlier years

The paper structure, scoring rules and scale anchor come from the official Explanation of Results for TMUA 2018 and the official test description pages; the difficulty line reflects FrontierVUE's own catalogue ratings, not an official judgement of the papers. FrontierVUE has no affiliation with, endorsement from, or partnership with UAT-UK, Cambridge Assessment or the University of Cambridge, and this page is an independent compilation.

01

What TMUA 2018 tested and how results were reported

TMUA 2018 ran on the two-paper format settled in 2017: 2 hours 30 minutes in total, Paper 1 and Paper 2 taken together, each paper 20 multiple-choice questions in 75 minutes. Scoring is based on the number of correct answers with no marks lost for wrong ones, so on the official guidance every question is worth attempting. In 2018 Paper 1 was officially titled Mathematical Thinking and Paper 2 Mathematical Reasoning; Paper 1 was renamed Applications of Mathematical Knowledge by 2021 at the latest, while the division of labour between the two papers stayed the same.

Format

Two papers taken together, 2 hours 30 minutes in total

The format established in 2017 and kept for 2018

Questions and timing per paper

20 multiple-choice questions in 75 minutes each

Marking

Marks for correct answers, none deducted for wrong ones

On the official guidance it is worth attempting every question

Score scale

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

Candidates who do not respond to any items receive a score of 0; this wording appears in the Explanation of Results from 2016 to 2019 and drops out from 2020

What was reported

An overall score plus separate scores for Paper 1 and Paper 2

That year's Explanation of Results carries distribution charts for the overall score and for each of the two papers

Delivery body and sittings

Cambridge Assessment Admissions Testing

In the CAAT era the exam board ran the TMUA once a year in the autumn; the October and January pair of sittings arrived with UAT-UK

Calculator and dictionary

Not permitted

From the official current description of this two-paper format

Paper 1Paper 2
Title in 2018Mathematical ThinkingMathematical Reasoning
Questions20 multiple-choice20 multiple-choice
Timing75 minutes75 minutes
Later renamingRenamed Applications of Mathematical Knowledge by 2021 at the latestName unchanged to this day

The two papers are sat together within 2 hours 30 minutes. Source: the official test description pages and the record of format changes.

The 2018 cycle saw the test's footprint widen. By February 2018 at the latest, the official list of universities encouraging the TMUA had grown from Durham, Lancaster and Warwick to include Sheffield and Southampton. Pages from the same cycle also record that Nottingham's School of Mathematical Sciences would take TMUA results into account, and that Cardiff welcomed applications with a TMUA score, noting that candidates at 6.5 and above may be eligible for an offer on an Undergraduate Mathematics programme without A Level Mathematics. One CAAT-era rule differs sharply from today's arrangements: candidates could decide for themselves whether to share their results with universities after receiving them.
02

How to read a TMUA 2018 score

Reading a 2018 TMUA score comes down to three statements in that year's Explanation of Results: results are reported on a scale running from 1 (low) to 9 (high) to one decimal place; candidates who do not respond to any items receive a score of 0; and the scale was designed so that approximately one third of candidates achieve overall scores higher than 6.5, with high scores capped at 9.0. Alongside the overall figure, the document also shows the score distributions for Paper 1 and Paper 2.
The scale: 1 to 9, to one decimal place
The official wording is that results are reported on a scale running from 1 (low) to 9 (high), with scores reported to one decimal place. What appears on the result slip is therefore a scaled score, not a raw count of correct answers and not a percentage.
What 6.5 meant that year
The quantitative statement the 2018 Explanation of Results makes about the scale is that it was designed so that approximately one third of candidates achieve overall scores higher than 6.5. In the same cycle, Cardiff used 6.5 as a concrete threshold, noting that candidates at that level and above may be eligible for an offer on an Undergraduate Mathematics programme without A Level Mathematics. That document presents its distributions as three bar charts and prints no band-by-band table alongside them.
The cap at 9.0
The 2018 Explanation of Results states that high scores are capped at 9.0, so a result slip tops out at 9.0. It also means the scale stops separating candidates at the very top.
When a 0 appears
The official wording is that candidates who do not respond to any items receive a score of 0. The sentence appears in the Explanation of Results from 2016 through 2019 and is absent from 2020 onwards.
How to read the official distribution charts
The 2018 Explanation of Results carries three bar charts, for the overall distribution and for Papers 1 and 2, introduced by a single line saying the distributions are shown below. That document prints no numeric table beside them, so this page makes no percentage estimates from the charts; to see their shape, go to the official PDF listed in the sources.
Compared with 2017: the same reporting wording
The scale anchor in the 2017 and 2018 Explanation of Results documents is word-for-word identical: approximately one third of candidates achieve overall scores higher than 6.5, with high scores capped at 9.0. The exam board repeated that wording in each Explanation of Results from 2017 to 2022, and the two-paper format had been fixed since 2017, so the 2018 document reports results on the same terms as the 2017 one.
A 2018 score cannot be set beside a score from 2024 onwards. From 2024 the TMUA has been delivered by UAT-UK: Papers 1 and 2 are equated and scaled together into a single overall score, and the scale is anchored on the October cohort with the median fixed at 4.5 and roughly 10% of candidates above 7.0. The board is explicit about the change: this scaling process has been revised for 2024/25, and scores should not be compared directly with TMUA scores from earlier years. A 6.5 in 2018 and a 6.5 from 2024 onwards are marks on two different rulers, so on that guidance the two eras belong on separate segments rather than a single trend line.
Even within the CAAT era the anchor sentence changed with the year: the 2016 Explanation of Results anchored on approximately 50% of candidates above 5.0 and approximately 10% above 7.5, while the one third above 6.5 and cap at 9.0 wording ran from 2017 to 2022. Before reading a score from an earlier year, check which anchor sentence that year's Explanation of Results used.
03

Topic emphasis and difficulty in 2018 (FrontierVUE catalogue)

Every figure below comes from the FrontierVUE catalogue: the platform's own difficulty ratings and topic tags for the 2018 papers. They are not an official analysis of the papers and do not represent any official view of their difficulty.

20 questions

Held from Paper 1: 10 rated easy, 9 medium, 1 hard (FrontierVUE catalogue)

20 questions

Held from Paper 2: 6 rated easy, 8 medium, 6 hard (FrontierVUE catalogue)

1 vs 6

Questions rated hard: Paper 1 against Paper 2 (FrontierVUE catalogue)

In catalogue terms the two papers pull apart sharply: 1 of the 20 Paper 1 questions is rated hard against 10 rated easy, while Paper 2 has 6 hard and 6 easy. That fits the division of labour between them. Paper 1 asks you to apply mathematics you already know, whereas Paper 2 tests reasoning and argument itself, and reasoning questions can be made harder without moving outside the same syllabus. Treating the two papers as one undifferentiated sitting is how candidates lose the timing battle on Paper 2.

Applications of differentiation: tangents, normals, stationary points, increasing and decreasing functions

6

Syllabus code MM6.3

Sine, cosine and tangent: graphs, symmetry and periodicity

4

Syllabus code MM4.4

Solving quadratics algebraically: factorising, completing the square, the formula

3

Syllabus code M4.16

Quadratic functions, the discriminant and completing the square

3

Syllabus code MM1.3

Recognising and sketching the standard function graphs

3

Syllabus code MM8.1

Spotting common errors in proof, that is, invalid steps

2

Tag Err2

Primes, factors, multiples and prime factorisation

2

Syllabus code M2.3

Ratio and proportion, and how they link to fractions and linear functions

2

Syllabus code M3.6

Setting up and solving equations, including simultaneous equations

2

Syllabus code M4.15

Mean, median, mode, range and related summary statistics

2

Syllabus code M6.3

The counts above are topic-tag occurrences across both 2018 papers in the FrontierVUE catalogue. The two areas worth revisiting first are applications of differentiation and the graphs of trigonometric functions, followed by the two quadratic-related tags; together they form the spine of this year's paper. Note too the questions tagged for common errors in proof: they ask you to identify an invalid step rather than to compute an answer, which is a different skill from calculation and deserves its own practice.
04

How to practise the 2018 papers on FrontierVUE

01Step 1

Open the TMUA past paper list

Go to /papers/tmua to see the TMUA past papers held on FrontierVUE.

02Step 2

Find the two 2018 papers

Locate Paper 1 and Paper 2 under 2018.

03Step 3

Sit each paper against the clock

Each paper is 20 questions in 75 minutes. Time yourself one paper at a time first to build the pacing, then try both back to back.

04Step 4

Review the solutions and close the gaps

After submitting you get a question-by-question breakdown with worked explanations; take the topic tags behind your mistakes back into topic practice for another pass.

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)

Paper 1 and Paper 2

The two 2018 papers available to sit, 20 questions in 75 minutes each

Once you have sat both papers, fill the method gaps with the TMUA guides on the site. The pieces under /exams/tmua/guides/ are designed to pair with the past papers, and the paper-by-paper and proof-focused ones speak directly to the density of reasoning questions on Paper 2 in 2018.

TMUA guides

/exams/tmua/guides/

paper-1What Paper 1 demands and how to train for it
paper-2The reasoning question types on Paper 2 and how to handle them
logic-and-proofLogic and proof, matching the questions on spotting invalid steps
syllabusThe syllabus, for mapping your weak tags onto the specification
time-managementHow to spend the 75 minutes on a single paper
scoringHow scores are produced and read, including the difference between eras

Tap a branch to unfold

After a full run at the papers, the practice centre also offers topic-based and random practice, which is a faster way to drill the specific tags behind your mistakes than sitting the whole paper again.
FAQ

Frequently asked questions

Can I still practise the TMUA 2018 papers?
Yes. FrontierVUE holds both Paper 1 and Paper 2 from 2018, so you can sit each as 20 questions in 75 minutes and review worked explanations afterwards. Bear in mind that 2018 sits in the CAAT era, with two papers of 20 multiple-choice questions and a different reporting model from the UAT-UK era that began in 2024: the questions themselves are good practice, but scores have to be read era by era.
What counted as a high TMUA score in 2018?
The quantitative anchor the 2018 Explanation of Results gives is that the scale was designed so that approximately one third of candidates achieve overall scores higher than 6.5, with high scores capped at 9.0. In the same cycle Cardiff used 6.5 as a concrete threshold: candidates at that level and above may be eligible for an offer on an Undergraduate Mathematics programme without A Level Mathematics. That document presents its distributions as bar charts and prints no numeric table beside them, so a claim pinned to a specific percentage does not come from it. This anchor also belongs to the CAAT era, and the exam provider states that scores from 2024 onwards should not be compared directly with earlier years.
How did Paper 1 and Paper 2 differ in 2018?
Both papers are 20 multiple-choice questions in 75 minutes, sat together within 2 hours 30 minutes. In 2018 Paper 1 was titled Mathematical Thinking and Paper 2 Mathematical Reasoning: the first leans on applying mathematical knowledge, the second on reasoning and argument. Paper 1 was renamed Applications of Mathematical Knowledge by 2021 at the latest. In the FrontierVUE catalogue, Paper 2 carries far more hard-rated questions that year: 1 of the 20 on Paper 1 against 6 on Paper 2.
Is a 6.5 from 2018 the same as a 6.5 today?
No. The official 2024/25 Explanation of Results states that this scaling process has been revised for 2024/25, and scores should not be compared directly with TMUA scores from earlier years. In 2018, under CAAT, the anchor was approximately one third of candidates above 6.5 with a cap at 9.0, and each paper was reported separately alongside the overall score. From 2024, the two papers are equated and scaled together into a single score anchored with the median at 4.5 and roughly 10% of candidates above 7.0. The two eras use different rulers: UAT-UK tells candidates in that document not to compare the scores directly, and the document sets out no conversion between the two scales.
Sources

Official sources

By year

Other TMUA years

TMUA 2025TMUA 2024TMUA 2023TMUA 2022TMUA 2021TMUA 2020TMUA 2019TMUA 2017TMUA 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 2018 online

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

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