TMUA 2016: What the First Sitting Tested and How Scores Were Read

TMUA 2016 was the first sitting of the test: 2 hours in total, with Paper 1 and Paper 2 each running 20 multiple-choice questions in 60 minutes, a timing format used in that year alone. Results were reported on a scale from 1 (low) to 9 (high) to one decimal place, and Paper 1 and Paper 2 were each reported separately alongside the overall score. The official Explanation of Results for that year states that the scale was designed so that approximately 50% of candidates achieve overall scores higher than 5.0, with approximately 10% of applicants above 7.5. This page pulls together the 2016 paper structure, the scoring rules, what the official distribution material does and does not say, and the topic emphasis and difficulty as catalogued by FrontierVUE, plus why a 2016 score cannot be lined up against scores from 2024 onwards.

TMUA 2016 at a Glance

Papers sat: The first TMUA sitting: Paper 1 and Paper 2, 2 hours in total, each paper 20 multiple-choice questions in 60 minutes, a timing used in 2016 alone
How it was scored: 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; candidates who do not respond to any items receive a score of 0
Official scale anchor: Official wording: the scale was designed so that approximately 50% of candidates achieve overall scores higher than 5.0, and approximately 10% of applicants achieve overall scores higher than 7.5
Delivery body: Admissions Testing Service, the Cambridge brand named in the header of the 2016 Explanation of Results; from 2017 the brand became Cambridge Assessment Admissions Testing (CAAT)
Where it was used: Durham and Lancaster encouraged applicants to their Mathematics courses to sit it, with a reduced offer available; scores could also be shared with LSE for Mathematics and Economics and Mathematics with Economics
Difficulty (FrontierVUE catalogue): Of the 20 Paper 1 questions held, 6 are rated easy, 11 medium and 3 hard; of the 20 Paper 2 questions, 2 are easy, 14 medium and 4 hard

The paper structure, scoring rules and scale anchor come from the official Explanation of Results for TMUA 2016 and the official test description page of that cycle; the difficulty line reflects FrontierVUE's own catalogue ratings, not an official judgement of the papers. The scaling process was revised from 2024, and the official guidance states that scores from 2024 onwards should not be compared directly with TMUA scores from earlier years. FrontierVUE is not affiliated with, endorsed by or partnered with UAT-UK, Cambridge Assessment or the University of Cambridge, and this page is an independent compilation.

What TMUA 2016 tested and how results were reported

2016 was the first year the TMUA ran, and that year's Explanation of Results is the first such document the test ever had. The exam consisted of Paper 1 and Paper 2, 2 hours in total, each paper 20 multiple-choice questions in 60 minutes. That timing was used in this sitting only: from 2017 the total became 2 hours 30 minutes with 75 minutes per paper, which is still the shape of the test today. Through the CAAT era Paper 1 was titled Mathematical Thinking and Paper 2 Mathematical Reasoning; Paper 1 had been renamed Applications of Mathematical Knowledge by 2021 at the latest.

Where 2016 sits

The first TMUA sitting

The 2016 Explanation of Results is the first the test ever published

Papers

Two papers, Paper 1 and Paper 2, each of 20 multiple-choice questions

Paper 1 was then titled Mathematical Thinking and Paper 2 Mathematical Reasoning

Timing

2 hours in total, 60 minutes per paper

Used in 2016 only; from 2017 it became 2 hours 30 minutes in total with 75 minutes per paper

Delivery body

Admissions Testing Service, part of Cambridge

The brand named in the header of the 2016 Explanation of Results; from 2017 it was renamed Cambridge Assessment Admissions Testing

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

What was reported

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

That year's Explanation of Results accordingly carries three distributions: overall, Paper 1 and Paper 2

	2016 (first sitting)	From 2017
Total length	2 hours	2 hours 30 minutes
Time per paper	60 minutes	75 minutes
Questions per paper	20 multiple-choice questions	20 multiple-choice questions
Official scale anchor	Approximately 50% of candidates above 5.0, approximately 10% above 7.5	From 2017 to 2022 the wording is uniform: approximately one third of candidates above 6.5, with a cap at 9.0
Paper 1 title	Mathematical Thinking	Mathematical Thinking at first, renamed Applications of Mathematical Knowledge by 2021 at the latest

Both columns follow official wording. The table compares paper format and the language of the scale design; it is not a conversion table, and anchors stated for different years stand on their own rather than converting into one another.

The reach of the TMUA in 2016 was narrow. Officially, Durham and Lancaster encouraged applicants to their Mathematics courses to sit it, with a reduced offer available to those who did, and candidates could additionally share their scores with LSE for Mathematics and Economics and for Mathematics with Economics. Whether a university saw the score at all was the candidate's own decision throughout the CAAT era, which is a different arrangement from the UAT-UK era that began in 2024, where results are matched through UCAS and sent automatically and candidates cannot choose which institutions see them.

How to read a TMUA 2016 score

The 2016 Explanation of Results carries two statements you can lean on when reading a score from that year. The first describes the scale itself: results are reported from 1 (low) to 9 (high) to one decimal place, and candidates who do not respond to any items receive a score of 0. The second is the design anchor: the scale was designed so that approximately 50% of candidates achieve overall scores higher than 5.0, with approximately 10% of applicants above 7.5. The rest of that document is three percentage bar charts, for the overall score and for Papers 1 and 2; the exam provider states no grade boundary, no pass mark and no candidate counts by score band in it.

Range and precision of the scale

Scores run from 1 (low) to 9 (high) and are reported to one decimal place. Candidates who do not respond to any items receive a score of 0, a sentence that appears in the Explanation of Results for 2016 and for several years afterwards.

The official anchor for 2016

The official wording is that the scale has been designed so that approximately 50% of candidates will achieve overall scores higher than 5.0, and in addition approximately 10% of applicants will achieve overall scores higher than 7.5. That is the only quantitative reference point for the year; any other specific percentage has no official source.

Two more scores alongside the overall one

Through the CAAT era, Paper 1 and Paper 2 each carried their own score alongside the overall one, which is why the 2016 Explanation of Results contains three distributions: overall, Paper 1 and Paper 2. A 2016 result therefore carried three numbers rather than one.

The distributions are bar charts only

All three distributions in the 2016 Explanation of Results are percentage bar charts, and the document contains no numeric table. Any claim that pins a share of candidates to a particular score band is therefore not official, and this page does not read figures off the charts by eye.

Even within the CAAT era, the 2016 anchor stands alone

For each year from 2017 to 2022 the official anchor is stated uniformly as approximately one third of candidates above 6.5 with a cap at 9.0. The 5.0 and 7.5 figures describe the design of the 2016 scale alone and should not be carried across to later years.

A cross-era caveat. From 2024 the TMUA has been delivered by UAT-UK under a revised scaling process, and 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 2016, under the CAAT era, each paper carried its own score and the anchor was approximately 50% of candidates above 5.0. 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: there is no conversion between them and no single trend line across them.

	2016 (CAAT era)	From 2024 (UAT-UK era)
What is reported	An overall score plus separate Paper 1 and Paper 2 scores	The two papers are equated and scaled together into a single overall score
Score range	1 (low) to 9 (high), to one decimal place	1.0 to 9.0, to one decimal place
Scale anchor	Approximately 50% of candidates above 5.0, approximately 10% above 7.5	The median fixed at 4.5, with approximately 10% of candidates above 7.0
Who sees the score	Candidates decided for themselves whether to share results with universities	Sent automatically via the UCAS application; candidates cannot choose which institutions can see the score
Sittings per year	One autumn sitting a year	Two sittings a year, in October and January

This table contrasts how the two eras worked, not how high the scores ran. The score lines are not comparable across the columns: the official guidance states that the scaling process was revised for 2024/25 and that those scores should not be compared directly with TMUA scores from earlier years.

Two further points. First, 2016 was the first sitting, so there is no earlier year of comparable data and this page draws no year-on-year comparison. Second, the 2016 Explanation of Results sets out the scale and its design anchors rather than any grade boundary: the current UAT-UK guidance likewise states that it provides no grade boundaries or pass mark and does not accept appeals of test scores. What a score means depends on how the course you are applying to used it that year, not on target numbers circulating online.

Topic emphasis and difficulty in 2016 (FrontierVUE catalogue)

Everything below reflects the FrontierVUE catalogue: the figures come from the platform's own difficulty ratings and topic tags on the 2016 questions, not from official paper data and not from any official judgement of how hard the year was. The Explanation of Results publishes distributions only, never per-question difficulty or a topic breakdown.

20 questions

Held from Paper 1: 6 rated easy, 11 medium and 3 hard (FrontierVUE catalogue)

20 questions

Held from Paper 2: 2 rated easy, 14 medium and 4 hard (FrontierVUE catalogue)

20 / 20

Every question on each paper is filed under Mathematical Thinking and Mathematical Reasoning respectively (FrontierVUE catalogue)

Both papers cluster in the medium band, but their shapes differ. Paper 1 carries more easy questions, 6 of its 20 rated easy against 11 medium and 3 hard, so it opens more gently. Paper 2 is tighter: just 2 of its 20 are rated easy, with 14 medium and 4 hard, which means the paper runs at medium intensity or above almost throughout. Treating Paper 2 as the more relentless of the two is closer to how this year actually behaves than practising both the same way.

Applications of differentiation

Gradients, tangents and normals, stationary points (maxima and minima), strictly increasing and decreasing functions; points of inflection are not examined but a qualitative grasp of them on simple polynomial curves is expected

Differentiating powers of x

Differentiating x to a rational power and sums and differences of such terms, often after simplifying first

Quadratics and the discriminant

Quadratic functions and their graphs, the discriminant, completing the square and solving quadratic equations

Forming and solving equations

Solving simultaneous equations in two unknowns algebraically and graphically, including linear-with-quadratic pairs, and translating a situation into an equation before interpreting the solution

Definite integrals and area

The relationship between a definite integral and the area between a curve and the axes, including the distinction between evaluating the integral and finding the area

Integrating powers of x

Definite and indefinite integrals of x to a rational power and sums and differences of such terms, including expressions that need simplifying first

Ratio and proportion

Understanding and using proportion, and linking ratios to fractions and to linear functions

Geometric series

Summing finite geometric series, and infinite sums of convergent geometric series together with the convergence condition

Binomial expansion

Binomial expansions to positive integer powers, including simple composite expressions, and use of factorial and combination notation

Trigonometric equations on an interval

Solving simple trigonometric equations within a given interval, sometimes after applying an identity first

Ranked by frequency, the emphasis of the year is plain. The two most common tags both sit in differentiation: applications of differentiation at 6 and differentiating powers of x at 5, followed by quadratics and the discriminant at 4. The two integration tags appear 3 times each, level with forming and solving equations. In other words the calculus fundamentals plus quadratics carry the bulk of the catalogued 2016 questions, while series, binomial expansion and trigonometric equations appear as garnish. For revision, drilling the simplify-then-differentiate and simplify-then-integrate routines before topping up quadratics and simultaneous equations gives the best return.

How to practise the 2016 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 2016 papers

Locate Paper 1 and Paper 2 under 2016; each paper holds 20 questions.

03Step 3

Set the clock, then sit the paper

In 2016 each paper ran 60 minutes, whereas the TMUA today is 2 hours 30 minutes in total with 75 minutes per paper. Practising against the original clock is tighter than the exam you will actually sit, which is exactly what makes it useful for pace.

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, above all the differentiation and integration ones.

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 2016 papers available to sit, 20 questions each

These two papers work well as an entry point: the difficulty sits mainly in the medium band and the topics concentrate on differentiation, integration and quadratics, so they suit building fundamentals and multiple-choice pacing before you move on to recent years. Once you have sat them, fill the method gaps with the TMUA guides on the site, which are designed under /exams/tmua/guides/ to pair with the past papers.

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

syllabusThe syllabus, for mapping tags like differentiation and integration onto the specification

logic-and-proofLogic and proof, matching the questions on spotting invalid steps

time-managementHow to spend the time within a single paper, which suits this year's tighter clock

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. Since this year leans on differentiation and integration, drilling those two areas on their own is a far faster use of time than sitting the whole paper again.

FAQ

Frequently asked questions

Can I still practise the TMUA 2016 papers?

Yes. FrontierVUE holds both Paper 1 and Paper 2 from 2016, 20 questions each, so you can sit them against the clock and review worked explanations afterwards. Two things to keep in mind: 2016 was the first sitting and each paper ran 60 minutes against the 75 minutes used today, so it is tighter than the real exam; and 2016 sits in the CAAT era, whose reporting model differs from the UAT-UK era that began in 2024. The questions are good practice either way, but scores have to be read era by era.

What counted as a high TMUA score in 2016?

The only quantitative anchor in the 2016 Explanation of Results is that the scale was designed so that approximately 50% of candidates achieve overall scores higher than 5.0, with approximately 10% of applicants above 7.5. On that wording, above 7.5 was the leading band that year. The official distributions are bar charts with no numeric table, so any claim pinned to a specific percentage is not official. Note also that this anchor describes 2016 alone: from 2017 to 2022 the official wording became approximately one third of candidates above 6.5 with a cap at 9.0, and from 2024 the scaling changed again, so none of these carry across.

How did the 2016 test differ from the TMUA today?

On three levels. Format: in 2016 the test ran 2 hours with 60 minutes per paper, and from 2017 it became 2 hours 30 minutes with 75 minutes per paper, though 20 multiple-choice questions per paper has stayed constant. Reporting: in 2016 Paper 1 and Paper 2 each carried a score alongside the overall one, whereas from 2024 the papers are equated and scaled together into a single score. Process: through the CAAT era candidates chose whether to share results with universities, while from 2024 results are matched through UCAS and sent automatically with no choice of recipient, and there are two sittings a year, in October and January.

Is a 5.0 from 2016 the same as a 5.0 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 2016, under CAAT, the anchor was approximately 50% of candidates above 5.0 and approximately 10% above 7.5, with each paper 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, no official conversion exists between them, and reading them on one line will mislead you.

Sources

Official sources

By year

Other TMUA years

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

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 2016 online

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

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