Thinking, not recall
Content stops at early A level. Questions combine familiar tools in unfamiliar ways, which is where marks are won and lost.
Built for the UK admissions TMUA
Train the reasoning
the TMUA actually tests.
Two 75 minute papers, twenty multiple choice questions each and no calculator. ExamScore drills the thinking the paper rewards, then shows which question types cost you marks.
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ExamScore · TMUA performance
1.0 – 9.0 overallProjected overall score
6.8
Paper 1 · Applications7.1
Paper 2 · Reasoning6.5
Questions in time17 / 20
Skill mastery
- 82%Algebraic manipulation
- 64%Logic and implication
- 58%Proof and counterexamples
- 69%Speed without a calculator
Next best step: Necessary and sufficient conditions, 12 questions
Both papers
Applications of knowledge and mathematical reasoning, practiced separately.
Timed simulations
20 questions in 75 minutes, scored and reported like the real sitting.
Question-type sets
Logic, proof, graphs and sequences drilled one type at a time.
1.0 to 9.0 analytics
Per-paper scores with the accuracy and pacing behind them.
Worked reasoning
The route to the answer on every question, not just the letter.
The Test of Mathematics for University Admission is sat by applicants to mathematics-heavy degrees at several UK universities, including math, computer science and economics. A strong score supports an application and, at some universities, can lead to a reduced offer.
It is not a knowledge test. The syllabus stops at material a first-year A level student has already met. The difficulty lives in how that material is used: multi-step reasoning, logic, proof and very careful reading.
There is no calculator, and 75 minutes for 20 questions leaves no room for a long route to the answer. Recognising the shape of a question quickly is the skill that separates scores.
See what free and Premium include, or start on the Digital SAT practice that is live today.
What the TMUA actually tests
A reasoning paper wearing a math syllabus
Three facts about the test decide how you should prepare for it.
No calculator, ever
Every question is designed to be answered by hand, so fluent arithmetic and algebra are part of the test.
Under four minutes a question
Twenty questions in 75 minutes rewards spotting the efficient route, not grinding through the long one.
TMUA format
Both papers, question counts and time limits
This is the structure your practice should match, minute for minute.
Paper 1: Applications of Mathematical Knowledge
20 multiple choice questions · 75 minutes
Algebra, functions, sequences, trigonometry, coordinate geometry, differentiation, integration and graphs
Paper 2: Mathematical Reasoning
20 multiple choice questions · 75 minutes
Logic, necessary and sufficient conditions, proof, counterexamples and identifying flawed arguments
Two and a half hours of testing in total. No calculator or formula sheet is permitted in either paper.
The real problem
Why most TMUA preparation does not move the score
Revising topics is not the same as training reasoning under a clock with no calculator.
Revising A level content instead of reasoning.
You know the topics and still cannot finish the paper.
Practice built around TMUA question types, especially the logic and proof work in Paper 2.
Past papers with an answer letter at the back.
You mark it wrong, move on, and repeat the mistake next week.
Worked reasoning for every option, including why the tempting wrong answer is tempting.
No feel for the clock.
Five good questions left unread when time runs out.
Pacing analytics per question type, so you learn what to attempt and what to leave.
How ExamScore AI works
From your first timed paper to a higher overall score
You only learn your real strengths and weaknesses by testing yourself in an exam setting. ExamScore starts there, then turns every result into a focused path.
- 01
Sit a full timed paper
Start with 20 questions in 75 minutes, no calculator. That is the only honest baseline.
- 02
Read your two paper scores
Paper 1 and Paper 2 on the 1.0 to 9.0 scale, with accuracy and pacing behind each.
- 03
Practice the weaker paper
Applications or reasoning, drilled on its own until your accuracy holds under time.
- 04
Fix the question types
Targeted sets on logic, proof, graphs or sequences, chosen from what you actually miss.
- 05
Retest and compare
Sit another full paper and see which score moved, and by how much.
Start with step one
Free to start · No credit card · Real exam interface
Test-day realism
You should not meet the TMUA format for the first time on test day
A question bank trains the content and none of the conditions. Practicing in the real interface, on the real clock, makes the format automatic.
- 20 multiple choice questions in 75 minutes, per paper, exactly as the test is sat.
- No calculator, so arithmetic under pressure is trained rather than avoided.
- A clock that does not pause, with flag and review where you expect them.
- Paper 2 reasoning questions written in the style the real paper uses.
TMUA Paper 2 · Question 7 of 20
42:05For integers n, which statement is true? Consider: 'n is divisible by 6' and 'n is divisible by 3'.
- Divisible by 3 is sufficient for divisible by 6
- Divisible by 6 is sufficient for divisible by 3
- The two statements are equivalent
- Neither implies the other
Every multiple of 6 is a multiple of 3, so divisibility by 6 implies divisibility by 3. The converse fails: 9 is divisible by 3 but not by 6.
Inside the platform
Practice, analytics and AI in one place
Every part of the platform exists to answer one question: what should you do next?
Analytics down to the question type
Every answer feeds accuracy, pacing and mastery for the reasoning skill it tested, so weak spots surface on their own.
Algebra and functions82%
Graphs and geometry74%
Logic and implication64%
Proof58%
Adaptive practice sets
Your next set is chosen from the question types losing you the most marks right now.
No-calculator speed work
Short arithmetic and algebra drills, because hand computation is part of the exam.
Full paper simulations
Complete, timed papers with a per-question report at the end.
A plan to your test date
Pick the sitting, get a weekly plan sized to the hours you actually have.
AI tutor
Worked reasoning for every question you miss
Not a key. The logic behind the answer, and the practice set to work on that skill.
- Ask why the option you chose fails, in plain language.
- See the efficient route to the answer, not the long one.
- Get the logical rule behind a reasoning question stated clearly.
- Jump straight into the practice set to work on that skill.
After your answer
Why is B correct here?
6 = 2 × 3, so any multiple of 6 is already a multiple of 3. The reverse is false, which 9 shows immediately.
Scoring
How the 1.0 to 9.0 score works
Two papers, one combined figure, and what universities do with it.
Paper scores
Each paper is reported from 1.0 to 9.0. Marks are not deducted for a wrong answer, so answer every question even when you are guessing.
Overall score
The two papers are combined into a single score on the same 1.0 to 9.0 scale. Both papers carry equal weight.
What universities look for
Each university publishes the score it treats as strong, and some use it for reduced offers. Check the pages for your specific courses.
How it is used
The TMUA supports an application alongside grades and a personal statement. It rarely replaces them.
Study plan
Four rules that decide how much your score moves
Not a schedule. The habits that separate a small gain from a real one.
Sit a full timed paper first
75 minutes, 20 questions, no calculator. The result tells you whether time or reasoning is the real problem.
Give Paper 2 its own time
Logic and proof are the least familiar part of the test for most A level students, and the easiest place to gain.
Practice arithmetic by hand
There is no calculator, so slow manipulation quietly costs you questions you could have answered.
Review every miss properly
Write down why the correct option is correct and why yours looked right. That review beats another untargeted paper.
What you are working with
Enough practice to stop rationing it
0+
Practice questions across every tested topic
0
Full-length mock tests, timed like test day
0+
Topics covered across the platform
0+
Targeted practice sets built around weak skills
Honest comparison
Use the free past papers. They just run out.
Official past papers are the best starting point there is. What they cannot do is tell you which question types keep catching you, or hand you more practice once they are gone.
Feature
Free official tools
Classroom coaching
ExamScore
Both papers covered
Applications and reasoning
Yes, in past papers
Varies by tutor
Yes, practiced separately and together
Timed practice
How many full papers you get
A limited set of past papers
A handful per course
Timed simulations you can repeat
Question-type analytics
Knowing which reasoning costs you marks
Score only
Tutor judgement
Accuracy, pacing and mastery by type
Explanations
Understanding the mistake
Answer key or brief solution
In session, if there is time
Worked reasoning on every question
Pace
How fast you can move
Your own
The tutor's timetable
Your own, with a plan around your sitting
Cost
What you will actually pay
$0
$200 to $4,500
$0 to start, then $199 once
Both papers covered
Applications and reasoning
- Free official
- Yes, in past papers
- Coaching
- Varies by tutor
- ExamScore
- Yes, practiced separately and together
Timed practice
How many full papers you get
- Free official
- A limited set of past papers
- Coaching
- A handful per course
- ExamScore
- Timed simulations you can repeat
Question-type analytics
Knowing which reasoning costs you marks
- Free official
- Score only
- Coaching
- Tutor judgement
- ExamScore
- Accuracy, pacing and mastery by type
Explanations
Understanding the mistake
- Free official
- Answer key or brief solution
- Coaching
- In session, if there is time
- ExamScore
- Worked reasoning on every question
Pace
How fast you can move
- Free official
- Your own
- Coaching
- The tutor's timetable
- ExamScore
- Your own, with a plan around your sitting
Cost
What you will actually pay
- Free official
- $0
- Coaching
- $200 to $4,500
- ExamScore
- $0 to start, then $199 once
Pricing
Start free. Pay once, if the practice is working.
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- 10 full-length DSAT mock tests, scored like the real exam
- 146 gamified tests (6 on each topic)
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Assurance
Current for 2026, and straight about what it is
Built on the current TMUA format
Questions and test structures are written and reviewed against the exam as it is tested today.
Scores you can rely on
Scaled scores come from published conversion logic, so the same attempt always produces the same number.
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FAQ
TMUA questions applicants actually ask
From the ExamScore Pipeline
Study guides that transfer to any admissions test
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