Olympiad paper
20 January 2027
The 3.5-hour competition sitting
Competition
British Mathematical Olympiad Round 2
The UK’s hardest national mathematics competition challenges students to solve four demanding problems with complete written proofs.
Last verified: 18 Aug 2026Reviewed by:SSSean Stevens
Competition
British Mathematical Olympiad Round 2
The UK’s hardest national mathematics competition challenges students to solve four demanding problems with complete written proofs.
Last verified: 18 Aug 2026Reviewed by:SSSean Stevens
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Maths Olympiad Round Two at a glance: cost, dates and eligibility
Current status
Open now
Eligibility
Full-time secondary students
Age range / Year group
Year 13 or below
Location / Region
Registered UKMT exam centre
Cost
Free or £50
Prize highlight
Distinction and Merit certificates
Entry format
3.5-hour written paper
Maths Olympiad Round Two summary
BMO2 is the UK’s hardest national mathematics competition and the follow-on round to BMO1.
Students tackle four demanding problems and must present complete proofs, with clear reasoning valued more highly than partial work across every question.
It best suits experienced Olympiad problem-solvers who enjoy sustained, rigorous mathematical argument.
What is British Mathematical Olympiad Round 2?
The British Mathematical Olympiad Round 2 is UKMT’s most demanding national mathematics competition and follows BMO1. It presents four advanced problems that require full written solutions rather than short answers.
Students work under supervised examination conditions and must justify their assertions with complete proofs. The experience rewards depth, logical structure and careful mathematical presentation, so solving a small number of problems fully can outperform partial attempts across the whole paper.
Why Succeed highlights Maths Olympiad Round Two
It offers an unusually demanding test of proof-based mathematical thinking.
Four substantial problems reward depth instead of rapid short-answer techniques.
Official past papers, solutions and investigations provide strong preparation material.
Every question carries equal marks, making strategic problem selection important.
High scorers can earn certificates and may progress into UK Olympiad training.
Who is Maths Olympiad Round Two for?
Best for
Strong secondary mathematicians with BMO1 experience who enjoy constructing rigorous proofs and persisting with unfamiliar problems.
Not ideal if
You prefer short-answer questions, rely on calculators or have not yet practised writing complete Olympiad solutions.
Is Maths Olympiad Round Two worth it?
Yes, for a student already working at Olympiad level. The paper provides a credible test of advanced problem-solving and creates a concrete reason to improve proof writing, mathematical communication and strategic decision-making.
The limitation is its difficulty: even excellent students may complete only one or two problems. Recognition is useful, but the main value lies in the preparation, feedback and deeper mathematical thinking rather than a guaranteed award or selection outcome.
How much preparation does Maths Olympiad Round Two need?
Effort level
Very high
Best started
Practise regularly for several months before the January paper.
Main challenge
Turning promising ideas into complete, rigorous solutions.
Typical preparation
Work through official past papers without a calculator.
Review full solutions and identify gaps in every proof.
Practise selecting the most approachable problems before committing time.
Rewrite rough arguments into clear final solutions under timed conditions.
Useful if
You already have BMO1 or comparable Olympiad experience.
What do students do on Maths Olympiad Round Two?
You sit a supervised mathematics paper and develop full written solutions to four unfamiliar problems. Your school then scans and uploads the completed answer sheets for marking.
Step-by-step process
- 1
Confirm automatic qualification or arrange a discretionary school entry.
- 2
Download and print the question paper and personalised answer sheets.
- 3
Sit the paper under exam conditions at the registered centre.
- 4
Develop proofs in rough before writing clear final solutions.
- 5
Scan the paper answer sheets with all codes and markers visible.
- 6
Upload the answer sheets through the school’s Competition Profile.
- 7
Access results, certificates and marker feedback online.
Maths Olympiad Round Two dates and deadlines
Upcoming
Answer upload
21 January 2027
Paper answer sheets due by 11:59pm
| Milestone | Date | Timezone | Status | |
|---|---|---|---|---|
Olympiad paper | 20 January 2027 | Local | Upcoming | |
Answer upload | 21 January 2027 | Local | Upcoming | Save deadline |
Eligibility and requirements
Must be in full-time secondary education
England, Wales and overseas: Year 13 or below
Scotland: S6 or below
Northern Ireland: Year 14 or below
Must sit at a registered UKMT exam centre
Automatic qualification is based on BMO1 performance
Schools may enter non-qualifiers at their discretion
Only one follow-on round may be taken
How much does Maths Olympiad Round Two cost?
Entry cost
Free or £50 — Qualifiers are free; discretionary entries cost £50
How to enter Maths Olympiad Round Two
- 1
Ask your school’s UKMT coordinator to confirm your eligibility and entry route.
- 2
If you qualified automatically through BMO1, the school should not purchase another entry.
- 3
If you did not qualify, the school may purchase a £50 discretionary entry.
- 4
The coordinator prepares your named answer sheet through the Competition Profile.
- 5
Sit the paper at the registered exam centre under supervised conditions.
- 6
Your school scans and uploads the completed answer sheets after the paper.
Save this competition in Succeed, keep the deadline visible, and track your progress before you submit.
Start your entry checklistSubmission requirements
Candidates submit handwritten mathematical solutions through their school’s UKMT Competition Profile.
Full written solutions, not answers only
Complete proofs for every assertion
Blue or black ink for written work
Pencil and colours permitted for diagrams
No calculators or protractors
Rulers and compasses permitted
Scanned upload files under 14MB
All QR codes and corner markers visible
No rough work or blank sheets uploaded
Prizes and recognition
Certificate of Distinction
The top 25% of qualified entrants receive this certificate.
Certificate of Merit
The next 45% of qualified entrants receive this certificate.
Participation or Qualification
Students below the Merit threshold receive a route-dependent certificate.
Training invitation
Around 24 high-scoring UK-eligible students may attend Cambridge training.
What this may help with
Demonstrating advanced mathematical engagement and proof-writing experience.
What it does not guarantee
A training invitation, international selection or university admission.
Judging criteria
- 10 marks — Each of the four problems
- 40 marks — Maximum total score
- Complete proofs earn more credit than partial attempts
- Clear mathematical presentation affects the marks awarded
- Distinction and Merit thresholds vary with entrant scores
UKMT publishes equal problem marks but not a more detailed criterion weighting.
How to stand out
- Choose problems strategically and aim to finish your strongest solutions.
- State assumptions clearly and prove every non-obvious assertion.
- Use a logical sequence that a marker can follow without filling gaps.
- Keep diagrams accurate, labelled and directly connected to the argument.
- Reserve time to rewrite rough reasoning into a polished final response.
- Compare practice solutions with official approaches and marker expectations.
Maths Olympiad Round Two FAQs
It is UKMT’s hardest national mathematics competition and a follow-on round to BMO1. Students solve four advanced problems using complete written proofs.
No. Around 100 qualifying BMO1 students are invited, but schools may purchase discretionary entries for other eligible students.
It is designed to stretch students who have already succeeded at BMO1. UKMT advises that one or two complete solutions can earn substantially more credit than partial attempts at all four problems.
No. Calculators and protractors are forbidden, although rulers and compasses are allowed.
Each problem is worth 10 marks, for 40 marks overall. Marks depend on mathematical correctness, completeness and clarity of presentation.
Students normally sit it at their school or another registered UKMT exam centre under supervised exam conditions.
Yes, subject to the stated school-year and exam-centre requirements. Schools more than two hours ahead of the UK follow UKMT’s alternative sitting-day arrangements.
Use UKMT past papers, solutions and investigations, then practise writing complete proofs under timed conditions. Reviewing why an argument is incomplete is as important as reaching the right idea.
Alternatives to Maths Olympiad Round Two
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Alternatives to Maths Olympiad Round Two
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Save this competition in Succeed to compare it with other essay prizes, deadlines and entry formats in one place.
Compare with other competitionsContent reviewed by
Sean Stevens
Co-founder, Succeed | Founder, Immerse Education (2012–2026)
Sean works at the intersection of academic enrichment, programme quality and university preparation, with expertise in evaluating pre-university experiences for ambitious secondary school students.
Sources and verification
Source types reviewed
- BMOS/BMOC: The British Mathematical Olympiads
- Competition Handbook - Access Arrangements
- Competition Handbook - FAQs
- Competition Handbook - Quick-Step Guide
- BMOS/BMOC: Policy on Eligibility
- Login - Cuttle
- British Maths Olympiad Round 2 Awards - UKMT
- British Mathematical Olympiad Round 2 - UKMT
Succeed uses official provider information where available, but keeps this public page focused on comparison and planning inside Succeed.
What we verified (on 18 Aug 2026)
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How Succeed uses this information
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