Stage 03 · Year 9–11 · Age 13–16
Intermediate Stage — Six Events, Three Olympiads, the Year of Real Selection
The Intermediate stage is the largest in the UKMT pipeline. Six events span the three-year window: the Intermediate Mathematical Challenge in late January, two Kangaroo follow-ons in late March, and three year-specific Olympiads — Cayley (Year 9), Hamilton (Year 10), and Maclaurin (Year 11). The Maclaurin Olympiad in particular is the gateway into the Senior pathway and the BMO.
Intermediate stage by the numbers
this stage
Cayley/Hamilton/Maclaurin
each late January
paper duration
Overview
The Intermediate Stage in Three Tiers
The Intermediate stage stratifies into three tiers across three school years. The Challenge (IMC) is sat by all year groups; the Kangaroo papers split by year group (Grey for Year 9–10, Pink for Year 11); the three Olympiads each target a single year group (Cayley = Year 9, Hamilton = Year 10, Maclaurin = Year 11). Strong Maclaurin scorers carry preparation directly into the Senior pathway and BMO Round 1 in Year 12.
Across Years 9 through 11, the Intermediate stage is where Olympiad-style problem solving becomes the dominant mode of competitive mathematics for the UK pipeline. The Junior stage had introduced written solutions through the JMO, but the Intermediate Olympiads — Cayley, Hamilton, and Maclaurin — push the format substantially harder: six problems requiring full written solutions, sat over two hours, with marking by the UKMT problems committee. The cohort that sits these Olympiads is, by construction, the strongest twentieth or so of British Year 9–11 mathematicians.
The Intermediate Mathematical Challenge (IMC) sits at the entry of the stage. It is administered by participating UK schools in late January (Wed 28 Jan 2026), with approximately 250,000 Year 9–11 students entering nationally each year. The format is twenty-five multiple-choice problems sat over sixty minutes, with no calculator. Gold, Silver and Bronze certificates are awarded by national percentile, and top performers are invited forward to the Kangaroo or Olympiad rounds in March.
The Kangaroo papers — Grey for Year 9 (and below) and Pink for Year 10 and 11 — are by-invitation follow-on rounds for high-scoring IMC entrants. The split by year group reflects the design intent: the Year 10 and Year 11 students sit Pink Kangaroo, while Year 9 (and younger) students sit Grey Kangaroo. Both papers run a sixty-minute, twenty-five-problem multiple-choice format, sat in late March (Thu 19 Mar 2026) on a national date.
The three Intermediate Olympiads — Cayley, Hamilton, and Maclaurin — are also sat in March on the same national date as the Kangaroo papers. They split exactly by year group: Cayley is for Year 9, Hamilton for Year 10, Maclaurin for Year 11. All three run the same format — six open-ended problems, two hours, full written solutions, marked by UKMT — but increase in difficulty year by year, with Maclaurin (Year 11) papers approaching the difficulty of an early Senior paper. Maclaurin Distinction holders are conventionally regarded as well-prepared for BMO Round 1 entry the following autumn.
All Six Events
The Six Intermediate-Stage Events
The Intermediate stage’s six events organise into three tiers: a Challenge, two Kangaroo follow-ons, and three year-specific Olympiads. Below is the full event breakdown, with format facts and links to the Olympiad deep dives where available.
Tier 1 — Challenge
Intermediate Mathematical Challenge (IMC)
The Challenge paper for the Intermediate stage. Twenty-five multiple-choice problems sat over sixty minutes in students’ own schools. Approximately 250,000 Year 9–11 students enter each year. Gold, Silver and Bronze certificates awarded by national percentile; top scorers receive invitations to the Kangaroo and Olympiad follow-on rounds the following month.
25 problems · 60 min · multiple-choice · Year 9–11 · school-sat · per-student entry fee
Tier 2 — Kangaroo follow-ons
Grey Kangaroo
The Kangaroo follow-on paper for the younger half of the Intermediate cohort. Top IMC scorers in Year 9 and Year 10 are invited; the paper is harder than the IMC itself but follows the same multiple-choice format.
25 problems · 60 min · multiple-choice · by invitation
Pink Kangaroo
The Year-11-specific Kangaroo follow-on. Top IMC scorers in Year 11 are invited; the paper sits in the same late-March window (Thu 19 Mar 2026) as Grey Kangaroo but is calibrated for the senior end of the Intermediate cohort.
25 problems · 60 min · multiple-choice · by invitation
Tier 3 — Written Olympiads
Cayley Mathematical Olympiad
The first of the three Intermediate Olympiads, sat by the strongest Year 9 IMC scorers. Six open-ended problems requiring full written solutions, marked by the UKMT problems committee.
6 problems · 2 hr · written · by invitation
Open Cayley deep diveHamilton Mathematical Olympiad
The Year 10 Olympiad. Same six-problem, two-hour format as Cayley and Maclaurin, with progressive difficulty appropriate to the older cohort. Distinction holders carry preparation into Maclaurin.
6 problems · 2 hr · written · by invitation
Open Hamilton deep diveMaclaurin Mathematical Olympiad
The capstone Intermediate Olympiad and the gateway into the Senior pathway. Strong Maclaurin scorers are well-placed for SMC and BMO Round 1 entry in Year 12.
6 problems · 2 hr · written · by invitation
Open Maclaurin deep diveWhat Comes Next
After the Intermediate Stage — Senior and the BMO
Strong Intermediate students roll forward into Year 12 and the Senior stage of the UKMT pipeline. The Senior Mathematical Challenge in October is the gateway to BMO Round 1 in November, with the full BMO pathway running through to the Trinity Camp and the IMO Team UK selection.
Frequently Asked
Six Questions about the Intermediate Stage
Six questions parents and students most often ask about the Intermediate-stage events. All answers verified against the UKMT competitions site.
- What is the difference between the three Intermediate Olympiads?
- The three Olympiads — Cayley, Hamilton, Maclaurin — split exactly by year group rather than by ability. Cayley is the Year 9 Olympiad, Hamilton the Year 10 Olympiad, Maclaurin the Year 11 Olympiad. All three run the same six-problem, two-hour written format, but the papers increase progressively in difficulty as the year group rises. A Year 10 student is not eligible for Cayley; a Year 9 student cannot sit Maclaurin. The papers are calibrated for the cohort.
- Who can sit the IMC?
- The IMC is open to UK students in Year 9, Year 10 and Year 11 (ages 13–16). Schools register their participating students with UKMT and pay a per-student entry fee. Younger students at exceptional ability levels may also be entered at the school’s discretion, particularly Year 8 students working a year ahead of their cohort, but this is uncommon and at the school’s option.
- How does invitation to the Kangaroo and Olympiad rounds work?
- UKMT invites around 11,000 Kangaroo qualifiers from the IMC (Grey Kangaroo for Year 9 and below, Pink Kangaroo for Year 10 and Year 11). A separate, smaller invitation list — around 1,500 Olympiad qualifiers across the three papers — is issued for the Intermediate Olympiads (Cayley for Year 9, Hamilton for Year 10, Maclaurin for Year 11). Invitations are issued to schools, who pass them on to students; students do not apply individually.
- Can a student sit both a Kangaroo paper and an Olympiad?
- The Kangaroo and Olympiad papers are sat on the same national date in March. Students who qualify for both must choose; the standard advice from UKMT is to sit the Olympiad if eligible, since the Olympiad’s written format is the harder and more selective round. Schools sometimes overrule this advice for individual students who would benefit more from the Kangaroo’s multiple-choice format.
- What kind of preparation does the Maclaurin Olympiad reward?
- Maclaurin (Year 11) preparation typically combines past-paper practice from Cayley and Hamilton with structured reading on Olympiad number theory, combinatorics and Euclidean geometry. The standard British text is Gardiner and Bradley’s Plane Euclidean Geometry, plus Engel’s Problem Solving Strategies. Around two problems per week of attempted written solution, sustained across Year 10 and Year 11, is the consensus preparation pattern for serious Maclaurin candidates.
- Does Maclaurin Distinction help with BMO eligibility?
- BMO Round 1 eligibility itself is determined by nationality and school registration, not by Maclaurin performance. However, Maclaurin Distinction holders are conventionally regarded by schools as well-prepared for BMO Round 1, and many schools encourage their Maclaurin Distinction holders to sit Senior Mathematical Challenge in October of Year 12 with a view to BMO Round 1 in November. The two pathways are not formally linked but are tightly correlated in practice.
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For students moving from JMO to Cayley, Hamilton and Maclaurin, the WhatsApp advisor can help with structured reading lists, past-paper schedules, and the route into BMO Round 1 in Year 12. Written exchanges in English or Chinese welcomed.