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UKMT Pathway Guide

BMO British Mathematical Olympiad — UKMT Pathway Guide

An independent guide to the United Kingdom Mathematics Trust competition pathway, from the Primary Kangaroo at age ten to the British Mathematical Olympiad Round 2 at age eighteen. Written for international students preparing for the senior route to Team UK at the International Mathematical Olympiad.

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650,000
UKMT entries
each year
850,000
website visitors
each year
500
volunteer setters
and markers
15
competitions
across four stages
1965
year the BMO
began

The Pathway

The UKMT Competition Pathway in Four Stages

The British Mathematical Olympiad sits at the senior end of a structured pipeline operated by the United Kingdom Mathematics Trust. The pipeline begins at age ten and runs through to the final IMO selection in Year 13. Each stage carries its own Challenge, its own follow-on Kangaroo, and from the Junior stage onwards, its own written Olympiad.

  1. PrimaryYear 5–6 · Age 9–11

    The pipeline begins in upper primary with a single twenty-problem multiple-choice paper, sat each March. It is designed to identify the strongest mathematical thinkers before they enter secondary school.

    Explore the Primary stage

    One event

  3. IntermediateYear 9–11 · Age 13–16

    The most populous stage. The Intermediate Mathematical Challenge filters; two Kangaroo papers extend; three year-specific Olympiads — Cayley (Year 9), Hamilton (Year 10) and Maclaurin (Year 11) — select. Strong Maclaurin scorers carry preparation directly into the Senior pathway.

    Explore the Intermediate stage

    Six events

  4. SeniorYear 12–13 · Age 16–18

    The summit. The Senior Mathematical Challenge runs in October; the BMO follows in November (Round 1) and January (Round 2). The Mathematical Olympiad for Girls runs in parallel each September and feeds the EGMO selection. From BMO Round 2, around 24 students are invited to the Trinity College training camp from which Team UK is selected.

    Explore the Senior stage

    Five events

Senior-Level Crown

The British Mathematical Olympiad — Two Rounds, One Pathway to the IMO

Round 1 in November filters around two and a half thousand sixth-formers down to roughly one hundred. Round 2 in January cuts again to a residential training camp of around 24. From the camp, six are selected to represent the United Kingdom at the International Mathematical Olympiad. The BMO is the single mechanism by which the UK builds its IMO team.

The British Mathematical Olympiad sits at the senior end of the UKMT pipeline and operates on a two-round structure. Round 1 is held each November and consists of six open-ended problems sat over three and a half hours. Entry is open to British nationals and students with at least three years of UK schooling; schools may also enter a limited number of additional students at their discretion.

Round 2 follows in late January. Four problems, the same three and a half hours, but written for a substantially stronger cohort. The strongest Round 2 scripts are invited to the Trinity College training camp at Easter, from which Team UK at the International Mathematical Olympiad is selected each spring.

The BMO is not a competition you can cram for in a weekend. It rewards mathematical patience built over years of slow problem-solving — a different kind of preparation from the SMC, which rewards speed and pattern recognition. Our BMO deep dive covers eligibility, format, sample problems, marking, and the route from Round 2 to the IMO team in full.

Open the BMO Deep Dive

Olympiad Deep-Dives

Five Further Mathematical Olympiads in the UKMT Pipeline

Beyond the BMO, the UKMT pathway carries five further Olympiad-level written competitions, distributed across the Junior, Intermediate and Senior stages. Each has its own paper format, eligibility rules and progression route. Click through for full deep dives.

  1. Junior Stage · Year 7–8

    Junior Mathematical Olympiad (JMO)

    The first written Olympiad in the pipeline. Top scorers in the Junior Mathematical Challenge are invited; gold, silver and bronze certificates plus Distinction awards. Sat each spring, with a fifteen-question paper across two sections.

    Open JMO deep dive

  2. Intermediate Stage · Year 9

    Cayley Mathematical Olympiad

    The first of the three year-specific Intermediate Olympiads. Six open-ended problems, two hours, marked out of sixty. Strong Cayley papers feed directly into Hamilton in Year 10 and onwards into the Senior pathway.

    Open Cayley deep dive

  3. Intermediate Stage · Year 10

    Hamilton Mathematical Olympiad

    The Year 10 Olympiad of the Intermediate stage. Same six-problem, two-hour format as Cayley and Maclaurin, with progressive difficulty. Marking emphasises full written argument over numerical answers.

    Open Hamilton deep dive

  4. Intermediate Stage · Year 11

    Maclaurin Mathematical Olympiad

    The capstone Intermediate Olympiad and the bridge into the Senior pathway. Strong Maclaurin scorers are well-placed for the Senior Mathematical Challenge and for BMO Round 1 eligibility in subsequent years.

    Open Maclaurin deep dive

  5. Senior Stage · Year 11 and above (female)

    Mathematical Olympiad for Girls (MOG)

    A senior-level written Olympiad open to female students in Year 11 and above (younger students at school discretion). The MOG runs in parallel with the BMO and is one of the principal routes to selection for the UK team at the European Girls’ Mathematical Olympiad (EGMO).

    Open MOG deep dive

Frequently Asked

Frequently Asked Questions about the British Mathematical Olympiad

Six questions we receive most often from students and parents preparing for the UKMT pathway from outside the United Kingdom. Every answer is verified against the UKMT competition record.

What is the British Mathematical Olympiad?
The British Mathematical Olympiad (BMO) is a two-round written mathematics competition run by the United Kingdom Mathematics Trust. It is the senior-level Olympiad in the UKMT pipeline and the principal route through which the UK selects its six-member team for the International Mathematical Olympiad. Round 1 takes place each November and consists of six open-ended problems sat over three and a half hours; Round 2 follows in late January with four problems over the same duration.
How is BMO different from the Senior Mathematical Challenge?
The Senior Mathematical Challenge (SMC) is a twenty-five-question paper sat in October (22 multiple-choice plus 3 integer-answer questions), designed to be accessible across a wide range of sixth-form ability levels. The BMO is open-ended, asks for full written solutions, and is set with a substantially smaller and stronger cohort in mind. Strong SMC performance is a precondition for BMO entry, but the two papers reward different skills — speed and recognition on one side, depth and patience on the other.
Who is eligible to sit BMO Round 1?
BMO Round 1 is open to students in Year 13 and below (S6 Scotland, Year 14 Northern Ireland) attending a UKMT-registered school. International students at UK schools can enter via the school’s discretionary allocation. International students attending UK schools should consult their school’s mathematics department about discretionary entry; the UKMT publishes the current eligibility rules on its competitions site.
Where does BMO sit in the UKMT pipeline?
BMO is the senior Olympiad, sitting above the Senior Mathematical Challenge in the Year 12–13 stage. Below it, the Maclaurin Olympiad (Year 11) feeds into the Senior pathway, and the Cayley and Hamilton Olympiads (Years 9–10) feed into Maclaurin. The Junior Mathematical Olympiad (Year 7–8) is the first written Olympiad in the pipeline, sat by top performers in the Junior Mathematical Challenge.
What is the Mathematical Olympiad for Girls and how does it relate to BMO?
The Mathematical Olympiad for Girls (MOG) is a senior-level written competition open to female students in Year 11 and above (younger students at school discretion). Strong performance on the MOG is one of the routes through which the UK team for the European Girls’ Mathematical Olympiad (EGMO) is selected. MOG runs in parallel with the BMO and is not a substitute for it: students may sit both. EGMO selection is independent of IMO selection.
How do students get from BMO Round 2 to the IMO team?
The strongest performers on BMO Round 2 are invited to a residential training camp at Trinity College, Cambridge, held over the Easter break. From the camp, six students are selected to represent the United Kingdom at the International Mathematical Olympiad in July. Selection is by a combination of written test, oral interview and training-camp performance. The path from BMO Round 1 to the IMO is therefore three months of preparation followed by an Easter at Trinity College.

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