Stage 04 · Year 12–13 · Age 16–18 · The Summit
Senior Stage — SMC, Senior Kangaroo, MOG, and the British Mathematical Olympiad
The Senior stage is where the UKMT pipeline concentrates and selects. Five events: the Senior Mathematical Challenge in October, the Andrew Jobbings Senior Kangaroo in November, the Mathematical Olympiad for Girls in September, and the British Mathematical Olympiad in two rounds (Round 1 in November, Round 2 in January). The BMO is the single mechanism by which Team UK at the IMO is selected.
Senior stage by the numbers
the Senior stage
each October
each November
places per year
Overview
The Senior Stage Concentrates and Selects
The Senior stage is the most concentrated stratum of the UKMT pipeline. Five events compress into the autumn and winter of each academic year: SMC in October, MOG in September, Senior Kangaroo in November, BMO Round 1 in November, BMO Round 2 in late January. From Round 2, around 24 students are invited to the Trinity Camp; from the camp, six are selected for Team UK at the International Mathematical Olympiad in July.
The Senior stage spans Year 12 and Year 13 — the two final years of UK secondary education. Where the Junior and Intermediate stages were broad and exploratory, Senior is narrow and selective: approximately one hundred thousand UK sixth-formers sit the Senior Mathematical Challenge each October, but only six students are ultimately selected to represent the United Kingdom at the IMO. The funnel from SMC to IMO Team UK is among the most demanding in international mathematics competition.
The pipeline at the Senior stage runs as follows. Senior Mathematical Challenge (SMC) in October is the entry round — a twenty-five-question paper (22 multiple-choice plus 3 integer-answer 000–999) sat in students’ own schools, with around 80,000–100,000 entries nationally. Top SMC scorers are invited to BMO Round 1 in mid-November, the open written round of six problems. From Round 1, approximately one hundred advance to BMO Round 2 in late January — four written problems, by-invitation, for the strongest sixth-formers in Britain that year.
The other senior events sit alongside this main pipeline. The Andrew Jobbings Senior Kangaroo in mid-November is a follow-on round for strong SMC scorers who are not invited to BMO Round 1; the Kangaroo paper is integer-answer (000–999) over twenty questions in one hour, providing an extension challenge without the heavier written-Olympiad commitment. The Mathematical Olympiad for Girls (MOG) in September is a parallel senior-level written competition open to female students in Year 11 and above (younger students at school discretion), feeding selection for the European Girls’ Mathematical Olympiad (EGMO).
From BMO Round 2, the BMO Subtrust invites around 24 students to a residential training camp at Trinity College, Cambridge, held over the Easter break. From the Trinity Camp, six are selected to represent the United Kingdom at the International Mathematical Olympiad — the final destination of the pipeline. The IMO itself is held in July at a host country chosen on a rotating basis; the UK team has consistently ranked in the world top fifteen for the past three decades.
All Five Events
The Five Senior-Stage Events
Below are the five Senior-stage events with format facts and links to the relevant deep dives. The British Mathematical Olympiad — Round 1 and Round 2 — is held as a single deep-dive page given its central role in the pipeline.
Senior Mathematical Challenge (SMC)
The entry round for the Senior stage. Twenty-five questions (22 multiple-choice plus 3 integer-answer 000–999) sat over ninety minutes in students’ own schools. Approximately 80,000–100,000 UK Year 12–13 students enter each year. Gold, Silver and Bronze certificates by national percentile; top SMC scorers are invited to BMO Round 1.
25 problems · 90 min · multiple-choice · Year 12–13 · school-sat
Andrew Jobbings Senior Kangaroo
The follow-on Kangaroo paper for strong SMC scorers who are not invited to BMO Round 1. Twenty multiple-choice problems sat over sixty minutes; harder than the SMC itself but follows the same multiple-choice format. No further entry fee for invited students.
20 problems · 60 min · multiple-choice · by invitation
Mathematical Olympiad for Girls (MOG)
A senior-level written competition open to female students in Year 11 and above (younger students at school discretion), run in September each year. Five problems sat over two and a half hours: two short-answer plus three full written solutions. Top MOG scorers feed selection for the European Girls’ Mathematical Olympiad (EGMO).
5 problems · 2.5 hr · written · open to female students Year 9+
Open MOG deep diveThe Crown
The British Mathematical Olympiad — Two Rounds
The British Mathematical Olympiad is the senior end of the entire UKMT pipeline. Round 1 in November is open written; Round 2 in January is by-invitation. From Round 2 to the Trinity Camp and the IMO Team UK selection — full coverage in the BMO deep dive.
BMO · Round 1 + Round 2 · Trinity Camp · Team UK
The British Mathematical Olympiad — Senior-Level Crown
The BMO is the single competition in the UK pipeline through which Team UK at the International Mathematical Olympiad is selected. Round 1 takes place in mid-November, with around 1,800 entrants across the country (the top ~1% of SMC scorers, approximately 1,000 students invited from SMC); Round 2 follows in late January with approximately one hundred places, by invitation only.
From BMO Round 2, around 24 students are invited to a residential training camp at Trinity College, Cambridge, held over the Easter break. From the Trinity Camp, the final six-strong UK IMO team is selected each May. The full BMO format, eligibility rules, sample problems and preparation pathway are covered in detail on the BMO deep dive page.
Open BMO Deep DiveFrequently Asked
Six Questions about the Senior Stage
Six questions students and parents most often ask about the Senior-stage events and the BMO pathway. All answers verified against the UKMT competitions site and the BMO Subtrust record.
- What is the relationship between the SMC and the BMO?
- The Senior Mathematical Challenge is the entry round for BMO Round 1 entry — strong SMC performance is the conventional route to a BMO Round 1 invitation. UKMT invites approximately the top one to two per cent of SMC scorers to BMO Round 1, with schools also permitted to enter additional students at their discretion. The SMC tests speed and pattern recognition; the BMO tests depth and full written argument. They reward different skills, but the pipeline expects students to do well on both.
- Who can sit the Senior Mathematical Challenge?
- The SMC is open to UK students in Year 12 and Year 13 (ages 16–18). Schools register their participating students with UKMT and pay a per-student entry fee. Students in Year 11 or below may also be entered at the school’s discretion if they are working substantially ahead of their year group; some Year 11 students sit the SMC alongside Maclaurin Olympiad preparation.
- What is the Andrew Jobbings Senior Kangaroo, and who sits it?
- The Senior Kangaroo is a multiple-choice follow-on paper for strong SMC scorers who are not invited to BMO Round 1. Sat in mid-November on a national date, the paper runs twenty problems over sixty minutes — harder than the SMC but in the same multiple-choice format. It provides an extension challenge for the top SMC cohort without the substantial written-solution time commitment of the BMO. Named for Andrew Jobbings, a long-standing UKMT problem-setter.
- What is the Mathematical Olympiad for Girls?
- The MOG is a senior-level written competition open to female students in Year 11 and above (younger students at school discretion). It runs in September each year — earlier in the academic calendar than the SMC and BMO — and consists of five problems (two short-answer plus three full written solutions) sat over two and a half hours. Strong MOG scorers feed selection for the European Girls’ Mathematical Olympiad (EGMO), which is the female-only counterpart of the IMO. MOG and BMO are not substitutes: female students may sit both, and many strong UK Olympiad students do.
- How does the pathway from BMO to IMO Team UK work?
- From BMO Round 2 (late January), approximately twenty students are invited to a residential training camp at Trinity College, Cambridge, over the Easter break. From the camp, six are selected to represent the United Kingdom at the International Mathematical Olympiad in July. Selection is by a combination of written test performance over the camp week, structured interview, and the trainers’ assessment of each student’s readiness. The full mechanism is documented on the BMO deep dive.
- Can international students sit Senior-stage events from outside the UK?
- For students at UK schools (including international students at UK boarding schools and sixth-form colleges), all five Senior events are accessible through the standard school registration route, plus the BMO Round 1 school discretionary entry route for those not meeting the standard eligibility criteria. For students at schools outside the United Kingdom, direct entry is not normally permitted; the suggested route is to participate in your own national Olympiad pipeline. Speak to the WhatsApp advisor for case-by-case guidance.
Add Advisor on WhatsApp
Get Advice on the Senior-Stage Pathway from SMC to BMO
For students moving from Year 11 into the Senior stage — SMC entry in October, BMO Round 1 in November, Trinity Camp pathway — the WhatsApp advisor can help with structured preparation plans, eligibility questions, and the route to Team UK at the IMO. Written exchanges in English or Chinese welcomed.