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British Mathematical Olympiad

The British Mathematical Olympiad is the follow on round for the Senior Challenge. For full information, a calendar of events, and preparation materials, see the BMO Subtrust website.

Advice from Geoff Smith for young mathematicians

BMO Preparation Sheet


Around 1,000 invitations to the British Mathematical Olympiad Round 1 are sent to pupils who score highly in the Senior Challenge each November, and are qualified to represent the UK at the International Mathematical Olympiad (IMO).

We accept entries (from schools and colleges with a UKMT centre number) for BMO1 on behalf of those who did not qualify automatically. An online form is provided at the appropriate time of year, and the URL will be given in the SMC results documentation.

There is a modest fee for discretionary entries; an invoice will be sent with the BMO1 question papers for discretionary candidates.

BMO Round 1 (BMO1) lasts three and a half hours and contains six complex and involved mathematical problems for which full written solutions are required.

Buy downloadable collections of BMO1 past papers and solutions here.


Around 100 high achievers in Round One, who are qualified to represent the UK at the IMO are invited to try Round Two. Again those who sat BMO1 but do not qualify automatically for BMO2 may be entered as discretionary candidates on payment of a fee and an online form will be provided and advertised at the appropriate time.

BMO Round 2 is a 3½-hour paper with 4 even more challenging problems, taken by students in their own schools.

Buy downloadable collections of BMO2 past papers and solutions here.

BMO1 & BMO2 awards

The top 25% of scorers in BMO1 and BMO2 receive a Certificate of Distinction. Of the remaining candidates, those who qualify automatically to sit the paper receive a Certificate of Qualification. Discretionary (paid-for) candidates are only eligible for Distinction certificates.

For BMO1 only, we award gold, silver and bronze medals to the top 100 candidates in roughly the ratio 1:2:3. All medallists receive a book prize, which varies from year to year.

The most recent BMO thresholds were:
BMO1 Nov 2015
Certificate of Distinction: 23+
Medals: Bronze 33-39     Silver 40-49     Gold 50+     All medallists receive a book prize
BMO2 qualification: Yr13 35+     Yr12 31+     Yr11 28+     Yr10 & under 23+
BMO2 Jan 2015
Certificate of Distinction: 12+
Please note that the thresholds are recalculated each year based on the score distribution.

For this year's dates, click here.


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