Intermediate Stage · Olympiad · Year 9
Cayley Mathematical Olympiad — the Year 9 Written Round
Cayley is the first of the three Intermediate-stage written Olympiads, sat each March by the strongest Year 9 entrants in the Intermediate Mathematical Challenge. Six open-ended problems, two hours, with full written solutions required throughout. Named for the nineteenth-century British mathematician Arthur Cayley.
Cayley at a glance
problems
duration
year group
total marks
Overview
The First of the Three Intermediate Olympiads
Cayley is sat each March by the strongest Year 9 Intermediate Mathematical Challenge entrants — typically the top 1 per cent of Year 9 IMC scorers nationally. It is the first written Olympiad in the Intermediate sequence and the first of the three “named” UKMT Olympiads honouring British mathematicians of the nineteenth and early twentieth centuries.
The three Intermediate Olympiads — Cayley (Year 9), Hamilton (Year 10), Maclaurin (Year 11) — share an identical format. Six open-ended problems sat over two hours, with full written solutions required throughout and marking by the UKMT problems panel. The papers differ only in difficulty: Cayley is calibrated for the Year 9 cohort, Hamilton for Year 10, Maclaurin for Year 11, with progressive difficulty as the year group rises.
Cayley’s design intent is the introduction of full-Olympiad-style problem solving to the strongest Year 9 students in the country. The paper assumes the mathematical content of a strong Year 9 syllabus (basic algebra, elementary number theory, plane geometry to similar-triangles level) but pushes the problem-solving demand substantially harder than the IMC, demanding chains of reasoning that the multiple-choice Challenge cannot test.
Cayley is named for Arthur Cayley (1821–1895), the British mathematician whose work on algebraic invariants, matrix theory, and group theory laid foundations for much of twentieth-century algebra. The naming follows a UKMT tradition of honouring British mathematicians at the Intermediate Olympiad level — the three named Olympiads (Cayley, Hamilton, Maclaurin) together pay tribute to a generation of British and Irish mathematicians whose contributions defined the modern subject.
Marks are awarded for completeness of argument, not for elegance alone. A strong solution earns full marks if it constructs a complete chain of reasoning, even if the path taken is not the slickest. A solution with the right idea but a missing step earns partial credit. Markers look for: a clear statement of the claim being proved, a self-contained chain of deductions, and correct logical closure. The maximum total mark across the six problems is 60.
Format
Cayley Paper Format
Six open-ended problems, sat over two hours on a national date in late March (Thu 19 Mar 2026), by qualifying IMC score or discretionary entry. Identical paper format to Hamilton and Maclaurin, calibrated for the Year 9 cohort.
Cayley Mathematical Olympiad · Year 9
Format at a glance
- SatLate March (Thu 19 Mar 2026), national date
- Duration2 hours from start to finish
- Problems6 open-ended, equal weight, written solutions
- CalculatorNot permitted
- EligibilityYear 9 and below (Year 10 sit Hamilton); by IMC score or discretionary entry
- MarkingCentralised UKMT problems panel
- AwardsDistinction, Merit, Qualification certificates · book prizes for top tier
- Max marks60 (10 per problem)
What Comes Next
After Cayley — Hamilton in Year 10
Strong Cayley performers naturally roll forward into Year 10 and the Hamilton Mathematical Olympiad, the middle of the three Intermediate Olympiads. Hamilton uses the same six-problem, two-hour format but is calibrated for the older cohort. Strong Hamilton performance in turn sets up the student for Maclaurin in Year 11.
Frequently Asked
Five Questions about the Cayley Olympiad
Five questions students and parents most often ask about the Cayley Olympiad. All answers verified against UKMT.
- Who can sit the Cayley Olympiad?
- Cayley is open to UK students in Year 9 and below (Year 10 sit Hamilton). Students qualify by IMC score or discretionary entry by their school; around 1,800 students qualify across the three Intermediate Olympiad papers (Cayley, Hamilton, Maclaurin) each year. Invitations are issued to schools in late February, who pass them on to students; students do not apply individually. There is no separate entry fee for invited students.
- How is the Cayley different from the Hamilton and Maclaurin?
- The three Intermediate Olympiads share identical format — six problems, two hours, written solutions, marked by UKMT — but split by year group. Cayley is the Year 9 paper; Hamilton is Year 10; Maclaurin is Year 11. A Year 9 student cannot sit Hamilton or Maclaurin; a Year 10 student cannot sit Cayley. The papers increase progressively in difficulty as the year group rises, with Maclaurin (Year 11) approaching early Senior-level difficulty.
- What kinds of problems appear on the Cayley paper?
- Cayley problems are typically drawn from elementary number theory, combinatorics, plane Euclidean geometry, and algebra at Year 9 syllabus level. The problem-solving demand pushes the standard secondary-school content into Olympiad-style chains of reasoning: pigeonhole arguments, careful counting, geometric construction, divisibility arguments. The hardest problems combine two of these areas in a single argument.
- What kind of preparation does Cayley reward?
- Past-paper practice is the foundation — UKMT publishes the Cayley paper archive going back to the 1990s, with full solutions and mark schemes. Beyond past papers, the standard preparation reading is Engel’s Problem Solving Strategies (combinatorics and number theory chapters) plus Gardiner and Bradley’s Plane Euclidean Geometry for the geometry problems. Around one problem per week of attempted written solution, sustained across Year 8 and the autumn of Year 9, is the consensus preparation pattern.
- Does Cayley Distinction help with later UKMT Olympiads?
- Cayley Distinction does not automatically invite a student to Hamilton in Year 10 — Hamilton invitations are issued from IMC results in Year 10, not from Cayley results in Year 9. However, Cayley Distinction holders are conventionally regarded by schools as strong candidates for the Year 10 IMC and for Hamilton invitation thereafter, and the preparation pattern that earns a Cayley Distinction carries forward directly to Hamilton.
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Get Advice on Cayley Preparation and the Intermediate Olympiad Pathway
For Year 9 students preparing for Cayley, the WhatsApp advisor can help with structured reading lists, past-paper schedules, and the route into Hamilton in Year 10 and Maclaurin in Year 11. Written exchanges in English or Chinese welcomed.