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Original mock exams and topic practice for ESAT and TMUA, with full worked solutions and free lesson notes.
Find all real x for which x² − 5x + 6 < 0.
- (x − 2)(x − 3) < 0factorise
- roots at x = 2 and x = 3set each factor to zero
- the parabola opens upwardsso it is negative between the roots
Therefore 2 < x < 3
Four tests. Two on sale now.
TMUA Test of Mathematics for University Admission
Two papers for maths-heavy degrees: applying AS-level mathematics, then reasoning and proof. Our papers start gently and finish demanding.
- Papers
- Paper 1 and Paper 2
- Each paper
- 20 questions, 75 minutes
Source: UAT-UK TMUA page (esat-tmua.ac.uk). Last checked 5 October 2026.
In progress the October 2026 sitting: 12–16 October 2026
Booking for this sitting has closed. Next chance to book: January 2027 (4–8 January 2027). Booking opens 26 October 2026 and closes 21 December 2026.
Dates from UAT-UK. Last checked 5 October 2026.
ESAT Engineering and Science Admissions Test
Computer-based multiple choice. Mathematics 1 is compulsory, and most courses add two more modules.
- Modules
- Mathematics 1, Mathematics 2, Physics, Chemistry, Biology
- Each module
- 27 questions, 40 minutes
- Most candidates
- 3 modules, 120 minutes
Source: UAT-UK ESAT page (esat-tmua.ac.uk). Last checked 5 October 2026. No calculator or dictionary is allowed in the test.
In progress the October 2026 sitting: 12–16 October 2026
Booking for this sitting has closed. Next chance to book: January 2027 (4–8 January 2027). Booking opens 26 October 2026 and closes 21 December 2026.
Dates from UAT-UK. Last checked 5 October 2026.
- TARATest of Academic Reasoning for Admissions. Academic reasoning test with a Writing Task, used by Oxford and UCL.Join the TARA waitlist
- UCATUniversity Clinical Aptitude Test. Timed aptitude test for medicine and dentistry applicants.Join the UCAT waitlist
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There are no reviews or score promises on this site: only the checks above.
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Start with these papers
TMUA
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HeuriscoTMUAPaper 1Mock exam£5.99
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HeuriscoTMUAPaper 2Mock exam£5.99
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HeuriscoTMUAAlgebra and functionsTopic practice£3.99
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HeuriscoTMUAProof and counterexamplesTopic practice£3.99
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ESAT
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HeuriscoESATMaths 1Mock exam£5.99
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HeuriscoESATMaths 2Mock exam£5.99
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HeuriscoESATAlgebraTopic practice£3.99
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HeuriscoESATMaths 1Bundle£33.99Separate price £45.89Save £11.90 (26%)
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Everything for the TMUA
Both mock exams and every topic set for Paper 1 and Paper 2.
5 ESAT module mocks
One mock for every ESAT subject. Sit the three your course asks for.
52 of 52 ESAT topic sets are ready, and more are added as they pass our checks. TMUA bundles · ESAT bundles
Questions
Are these the official ESAT or TMUA papers?
No. Heurisco is an independent practice provider. Every question is written from scratch for our papers, so none of them are official past papers. We are not affiliated with UAT-UK, Pearson VUE, the UCAT Consortium or any university.
What do I get when I buy a paper?
A downloadable PDF of the paper, an answer key, full worked solutions and an indicative score guide. The guide is an estimate for planning your revision, not an official score.
Are the lesson notes really free?
Yes. Every topic has a free lesson PDF with worked examples and a short self-check, and you do not need an account. The paid practice sets are there when you want more questions to practise on.
How hard are the questions?
Each paper starts with accessible questions and ends with demanding ones, in the style of the real test. We write to the published ESAT and TMUA specifications, but we cannot promise any score, because every sitting is scored differently.
Can a parent buy this for me?
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Which ESAT modules do I need?
Mathematics 1 is compulsory. Most courses also ask for two more modules from Mathematics 2, Physics, Chemistry and Biology, but the combination depends on the course. Check your university course page before you book (last checked 5 October 2026).
Can I use a calculator?
No. UAT-UK does not allow a calculator or dictionary in the ESAT (last checked 5 October 2026). The TMUA is also a no-calculator test, and our papers are written so every calculation can be done by hand.
What if I find a mistake in a question?
Tell us on the report-an-error page. We check it, fix the paper if needed, and send corrected files to everyone who bought it.
When will the other ESAT topic sets be ready?
We are writing them module by module and each set is checked before it goes on sale. The shop shows which are ready and which are in preparation. Join the email list to hear when new ones arrive.
Try something free
Nine ESAT Maths 1 questions with worked solutions. Sit it under timed conditions, then check your answers.
For TMUA: the R2Drew2 papers
Two very hard TMUA-style papers with worked solutions. No email needed.