Competitions, challenges and problems worth losing an evening to.

The admissions test that has replaced the MAT at Oxford and is used by Cambridge and others for maths-heavy courses.

When

Entries close 28 September 2026 · sat 12 October 2026 to 16 October 2026 2026 cycle, for 2027 entry

Who can enter

Applicants to courses that require or recommend it — at Cambridge these include Economics, Computer Science and Mathematics. You register yourself; your school does not do it for you.

Format

2 hours 30 minutes, two papers: Applications of Mathematical Knowledge, and Mathematical Reasoning. No calculator. No marks deducted for wrong answers, and there is no pass mark.

What it tests

Reasoning with A-level material rather than content beyond it — logic, proof, and whether you can see the structure of a problem before grinding through it.

Why do it

It is the clearest signal of what university maths actually asks for. Even if you never sit it, working through past papers changes how you read a question: you start looking for the idea rather than the method.

Where to start here

• Why Maths opens the most doors
• Where maths is used in finance

Oxford used the MAT until the 2025 cycle and now uses the TMUA. If a guide still tells you to sit the MAT, it is out of date. A separate January window (4–8 January 2027, register by 21 December 2026) exists for mature applicants.

Official page — UAT-UKChecked 10 September 2026

The entry point to the UK maths competition ladder, and the qualifying route into the Senior Kangaroo and the British Mathematical Olympiad.

When

7 October 2026 2026–27

Who can enter

Students in Year 13 or below. Entered through your school.

Format

90 minutes. 22 multiple-choice questions and three answers in the range 000–999.

What it tests

Speed and insight on problems that look nothing like exam questions. Almost none of it needs material beyond GCSE — it needs you to notice the trick.

Why do it

It is the cheapest possible experiment in whether you enjoy problems that do not come with a method attached. Most people who end up in quantitative work first found out here.

Where to start here

• Why Maths opens the most doors

UKMT publishes the competition date but not an entry deadline — your school enters you, so ask your maths department well before the date.

Official page — UK Mathematics TrustChecked 10 September 2026

The follow-on round for strong Senior Mathematical Challenge scores that fall below the Olympiad threshold.

When

18 November 2026 2026–27

Who can enter

By invitation, based on your Senior Mathematical Challenge score.

Format

One hour, answers in the range 000–999.

What it tests

Sustained problem solving — harder than the Challenge, but still answer-only rather than proof.

Why do it

The natural next rung if the Challenge went well. It is a genuine step up in difficulty without requiring you to write formal proofs yet.

Where to start here

• Start with the Senior Mathematical Challenge

Official page — UK Mathematics TrustChecked 10 September 2026

The first Olympiad round, and the first time most students have to prove something rather than compute it.

When

18 November 2026 2026–27

Who can enter

By invitation from the Senior Mathematical Challenge, or by paid entry through your school.

Format

3 hours 30 minutes, six problems. You write full written solutions, not answers.

What it tests

Proof. Whether an argument is actually watertight, and whether you can write it down so someone else agrees.

Why do it

This is the closest school-age experience to what mathematicians actually do. The gap between "I can see why it is true" and "I can prove it is true" is the whole subject, and BMO1 is where most people meet it.

Where to start here

• Start with the Senior Mathematical Challenge
• Where proof-heavy maths leads

Official page — UK Mathematics TrustChecked 10 September 2026

A team competition where the questions accumulate — you need earlier answers to unlock later ones.

When

8 December 2026 to 14 December 2026 Ritangle 2026

Who can enter

Teams of students taking A level Mathematics, International Baccalaureate, Scottish Highers or equivalent. No limit on team size; four or five suggested.

Format

Questions released weekly through the autumn, building to three a week, then a final task in December. Each answer feeds into the next.

What it tests

Applying A-level content to problems that are not phrased like A-level questions, and working as a team over weeks rather than in one sitting.

Why do it

It is the one on this list that rewards persistence rather than speed. Because it runs over a whole term, you can think about a question for days, which is much closer to how real mathematics feels.

Where to start here

• Why Maths opens the most doors

MEI has published the final questions release (17:00, 8 December 2026) and the close (12:00, 14 December 2026) but not the start date for the 2026 competition. It has begun in early October in recent years — check the MEI page in September.

Official page — MEIChecked 10 September 2026

The second Olympiad round, and part of the selection route towards the UK team for the International Mathematical Olympiad.

When

20 January 2027 2026–27

Who can enter

By invitation, based on your BMO1 score.

Format

3 hours 30 minutes, four problems, full written solutions.

What it tests

Deep problem solving over hours rather than minutes. Four problems in three and a half hours is roughly fifty minutes each.

Why do it

Worth knowing about even if you never sit it, because it shows you the ceiling. Working through BMO2 problems slowly, with solutions to hand, teaches more than most textbooks.

Where to start here

• Round 1 comes first

Official page — UK Mathematics TrustChecked 10 September 2026

The hardest school-level maths examination in the UK, sat in the June after you apply.

When

No dates published for this cycle 2027 series

Who can enter

Applicants to courses that require it — most commonly Mathematics at Cambridge, Warwick and Imperial. Usually a condition of your offer.

Format

Three-hour papers. STEP 2 and STEP 3 are the ones currently sat. Long, multi-part problems where you choose which to attempt.

What it tests

Depth over breadth. A single STEP question can take forty minutes and rewards knowing a small amount of mathematics extremely well.

Why do it

STEP questions are the best free problem set in existence for anyone who wants to find out what university maths is like. You do not need to be sitting it to work through them.

Where to start here

• Why Maths opens the most doors
• Where this level of maths is used

OCR has not yet published the 2027 dates. In the 2026 series registration opened 1 March and closed 4 May, with papers on 4 and 10 June — expect a similar shape, but check OCR before relying on it.

Official page — OCRChecked 10 September 2026

A national business and accounting case competition run by the chartered accountancy body.

When

No dates published for this cycle Next cycle

Who can enter

16 to 17 year olds across the UK, in teams of four, entered through your school or college.

Format

A team business case worked through against the clock, judged at regional heats with a national final. Free to enter.

What it tests

Reading a business situation quickly, deciding what actually matters in it, and presenting a recommendation you can defend under questioning.

Why do it

It is the closest thing on this list to what advisory and accountancy work is actually like — a messy case, a deadline, and a panel asking why. Useful precisely because it is not a written exam.

Where to start here

• What chartered accountants do
• Advisory and transaction work

The competition format and eligibility are confirmed by ICAEW, but no dates for the next cycle had been published when this was checked. Ask your school to register interest.

Official page — ICAEWChecked 10 September 2026

The main UK schools economics essay competition, run by the Royal Economic Society.

When

Entries close 29 June 2026 2026

Who can enter

Years 10–13 in England and Wales, Years 11–14 in Northern Ireland, S3–S6 in Scotland. You do not need to study Economics. Individual or groups of two to five.

Format

A 1,000-word blog-style piece, or a video or podcast up to five minutes, or up to eight slides. Free to enter. AI tools are not permitted.

What it tests

Whether you can take a contested question and build an argument that survives the obvious objection — in a thousand words, which is the hard part.

Why do it

The topics are the kind of thing economists genuinely disagree about, so there is no answer to look up. Recent questions asked whether a country is wealthy if GDP is high but people are unhappy, and how AI will affect long-run growth.

Where to start here

• Economics beyond the syllabus
• Behavioural economics
• The economics of AI

The 2026 entry deadline has passed. The shortlist of five was due in September 2026, with the final at KPMG in October. The 2027 competition had not been announced when this was checked.

Official page — Royal Economic Society, with Discover EconomicsChecked 10 September 2026

The essay competition run by Cambridge’s undergraduate economics society.

When

Entries close 30 August 2026 2026

Who can enter

Any student anywhere who has not yet begun university. Free to enter, no travel required.

Format

One essay on a choice of set questions. Winners are published in The Dismal Scientist, the society’s magazine.

What it tests

Economic reasoning applied to a question with no settled answer, and the discipline of writing for readers who already know the standard arguments.

Why do it

The question list is the most useful part, and it stays up after the deadline. The 2026 paper asked about tariffs, central bank independence, Britain leaving the gold standard, and whether stock markets tell you anything about the economy.

Where to start here

• Economics beyond the syllabus
• How markets actually work

The 2026 competition closed on 30 August 2026 and received close to 1,500 entries. Results were expected by the end of September. The 2027 questions had not been published when this was checked.

Official page — The Marshall Society, University of CambridgeChecked 10 September 2026