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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

  • Dr Frost Maths - Interactive system using UKMT Challenge and Olympiad questions.


Around 1,000 Senior Challenge high scorers are invited to sit the British Mathematical Olympiad Round 1; they must be qualified to represent the UK at the International Mathematical Olympiad (IMO). Around 100 will go on to Round 2.

The top 25% of scorers in BMO1 and BMO2 receive a Certificate of Distinction. The next 45% receive a Merit. Of the rest, those who qualified automatically to sit the paper receive a Certificate of Qualification. Discretionary (paid-for) candidates are only eligible for Distinction and Merit certificates.

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

The most recent BMO thresholds were:

  • BMO1 2018-19 award and BMO2 qualification thresholds (out of 60):
    • Gold: 48+
    • Silver: 41-47
    • Bronze: 35-40
    • Distinction: 22+
    • Merit: 9-21
    • BMO2 Year 13, S6 or NI 14: 35+
    • BMO2 Year 12, S5 or NI 13: 32+
    • BMO2 Year 11, S4 or NI 12: 29+
    • BMO2 Year 10, S3 or NI 11 or below: 26+

  • BMO2 2017-18 award threshold (out of 40):
    • Distinction: 19+
  • Please note that the thresholds are recalculated each year based on the score distribution. BMO2 2018-19 takes place on 24 January and thresholds will be updated mid-February.

    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.

    Video solutions to BMO1 papers from 2005 onwards.

    Buy downloadable collections of BMO1 & BMO2 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.

    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.

    For BMO2 (and BMO1) papers with solutions, buy downloadable collections here.

    Also, the book 'A Mathematical Olympiad Companion' contains BMO2 papers and solutions from 2002-2016 inclusive, and is available here.

    For this year's dates, click here.


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