The British Mathematical Olympiad is one of the UK’s most well-known mathematics competitions, specifically for students in secondary school. It is designed to test deep mathematical thinking, rather than routine exam techniques and topics you may encounter in GCSEs or at A Level. Unlike these tests, BMO problems often involve more steps, requiring creativity, logic and clear written reasoning.
The BMO is run by the UK Mathematics Trust and is central to the selection process for the UK’s International Mathematical Olympiad team, which involves over 100 countries worldwide. There are two main rounds for the BMO: Round 1, which is generally sat by several thousand students, and Round 2, which only the highest performers are invited to take.
Unlike GCSE or A Level papers that students may be used to, these papers consist of only six questions. Marks are awarded for both the final answer and the clarity and logic of the reasoning used; this is more similar to a university-style mathematics paper.
Who Can Take Part?
The BMO can be taken by UK-based students in Year 13 or below. The majority of participants are in Year 12 or 13, though particularly strong students in earlier years occasionally qualify as well.
Candidates do not typically enter the BMO directly. They are usually invited to sit Round 1 after performing well in other UKMT competitions, such as Senior Mathematical Challenge, which is aimed at students in Years 12 and 13. However, schools can also enter strong candidates directly. The SMC is a 90-minute test with 25 multiple choice questions, increasing in difficulty as the test progresses. It bridges the gap between GCSE and A Level material and the type of questions students are likely to face in the BMO.
Schools play a large part in entry, as they initially register students for the SMC and can help them through the process. However, home-educated students can also arrange entry to the SMC through a registered centre.
Awards and Recognition in the British Mathematical Olympiad
There are various types of awards and recognitions that students can receive both in Round 1 and Round 2, depending on how well they perform.
For Round 1, top scorers out of 60 can receive a gold, silver or bronze awards. A certificate of distinction is given to roughly the top 25% of participants, followed by a certificate of merit which is given to around the next 45% of participants. All other students will be awarded a participation certificate.
For those who qualify for Round 2, roughly the top 25% of students can also be awarded a certificate of distinction, and around the next 45% of students are awarded a certificate of merit. The remaining students are then awarded a participation certificate.
Why is the BMO important and how does it help with university applications?
The BMO is highly regarded by universities as it demonstrates a variety of skills: problem-solving, logical thinking and creativity. A strong performance in the BMO shows that a student can tackle unfamiliar problems, which is a key skill for degrees including mathematics, engineering and physics. It also provides evidence of engagement with mathematics beyond the syllabus.
Even without top awards, BMO participation can be an excellent addition to a personal statement, particularly for competitive universities including Oxbridge and Imperial College. It also mirrors the problem-solving approach to questions that students are expected to use at Oxbridge interviews.
BMO Round 1 vs Round 2 – What’s the Difference?
BMO Round 1 is sat by several thousand students across the UK in November. It consists of six questions, each worth 10 marks, and the difficulty increases as the paper progresses, with questions 5 and 6 often requiring significant insight. The test lasts for 3 and a half hours, and answers require full written solutions, with proofs of any assertions made. Calculators are forbidden, though rulers, set squares and compasses are permitted for geometry problems. Even if students do not solve a problem entirely, marks can still be awarded for partial progress.
Only students who perform exceptionally well in Round 1 are invited to Round 2, which is sat in January; usually 100 students qualify. This round is much harder and is used to help identify suitable candidates for the UK’s International Mathematical Olympiad team. This round also lasts for 3 and a half hours, but typically contains only 4 questions.
Around 24 high-scoring students (eligible to represent the UK at the IMO) are invited to a training session held in Cambridge during the Easter holidays.
What Topics Appear in the BMO?
The BMO does not follow a fixed syllabus, unlike GCSE and A Level mathematics, but problems often involve the following areas:
- Algebra (functional equations, inequalities, sequences)
- Number theory (divisibility, primes, modular arithmetic)
- Geometry (angles, circles, transformations)
- Combinatorics (invariants, counting, arrangements)
Questions can combine ideas from several areas, which is often what makes the BMO particularly challenging. Students must spot these patterns from each question and construct arguments.
Advanced A Level content is not generally required; success in the BMO comes from strong mathematical foundations and the ability to clearly explain reasoning.
How to Prepare for the British Mathematical Olympiad
Preparing for the BMO is unlike standard examination preparation, which often requires students to memorise techniques. It is more about learning how to think; regular exposure to challenging problems and reflecting on solutions is particularly effective.
Therefore, practising problems from SMC and BMO Round 1 past papers can be a great place to start. However, it is important to practise writing full solutions, rather than just the answers, with the structure of students’ arguments being so important.
These questions are not designed to be answered in quick bursts, which can be the case with certain A Level questions; they often demand time for students to consider the right way forward. Sometimes, students may try various different approaches for a question before arriving at an appropriate one. For that reason, it is important that students resist the urge to immediately look at solutions when preparing. At the same time, studying official solutions is useful to understand how to structure an argument.
Some topic-specific strength can be useful for students, particularly in combinatorics and number theory, which can be unfamiliar to some students. However, consistent preparation over a period of months is generally more effective than last-minute cramming.
Recommended Resources
Some useful resources for BMO preparation include:
- UKMT past papers (SMC, BMO Round 1 and BMO Round 2 - all of which are available online)
- Books including ‘Olympiad Geometry’ by Evan Chen, ‘Problem Solving Strategies’ by Arthur Engel and ‘The Art of Problem Solving’ textbooks
- Online communities such as artofproblemsolving.com
Additionally, Olympiad clubs, structured coaching or an experienced Maths tutor can be beneficial to students.
FAQs
How hard is the BMO?
The BMO is highly challenging compared to A Level and GCSE mathematics exams. Students must show full written working for each question, presenting logical, well-structured arguments which often combine a variety of mathematical concepts.
How do you qualify for BMO?
The majority of students qualify by achieving a high score in the Senior Mathematical Challenge (SMC), which leads to an invitation to Round 1 of the BMO.
Is BMO useful for Oxbridge?
BMO participation is highly respected by Oxbridge and closely aligns with their interview and admissions style.
How long should you prepare?
Ideally, students prepare gradually over six to twelve months, building problem-solving skills, rather than attempting to cram within a matter of weeks.
Can Year 9 students aim for BMO?
The majority of students invited to take the BMO are in Years 12 and 13, though occasionally students from earlier years are invited. Year 9 students tend to start with the Junior and Intermediate Maths Challenges before progressing to the BMO.
How Keystone can help
For many years, Keystone have provided specialist Maths tutors for the British Mathematical Olympiad, who are experienced and can guide candidates through the entire process. For more details on how Keystone can help with preparation for the BMO, feel free to call the office for a chat with one of our client managers, or contact us via our request a tutor form.