The two academic years between the Junior Mathematical Olympiad in Year 8 and the Cayley Olympiad in Year 9 are the most underappreciated window in UK Olympiad preparation. Most public preparation advice focuses on either the JMO itself (one term of Year 8) or the BMO Round 1 (multiple years later in Year 12). The window between them — roughly January of Year 8 to March of Year 9 — is when the habits that earn a Cayley Distinction are built.
This article sets out the year-by-year reading plan we recommend for a serious student who has just sat the JMO (typically a Distinction or strong Merit) and is now planning the path to Cayley.
Year 8 spring and summer term (after JMO)
The first preparation block is the four months between the JMO sitting in mid-June of Year 8 and the start of Year 9 in September. This is a low-stakes window — there are no UKMT competitions for the student to sit in Year 8 after JMO — and is best used to consolidate the standard Year-8 syllabus content and begin reading for Year 9.
Recommended reading for this window: Engel’s Problem Solving Strategies, chapters 1 (general principles) and 3 (combinatorics). One chapter per fortnight, with the worked examples attempted before reading the solutions. Total time commitment: approximately three hours per week.
Past papers: continue with two JMO Section B problems per week for fluency. Do not attempt Cayley past papers yet — they will be calibrated for Year 9 syllabus content the student has not yet covered.
Year 9 autumn term
The autumn term of Year 9 is where the Cayley preparation routine becomes regular. The school’s mathematics department is typically the source of access to UKMT past papers; if your school does not have a structured Olympiad preparation programme, the WhatsApp advisor can point to alternative sources.
Reading: Gardiner and Bradley’s Plane Euclidean Geometry, the first three chapters (similar triangles, circle theorems, basic constructions). One chapter per three weeks, with constructed examples attempted before reading the solutions.
Past papers: one Cayley past paper per fortnight under timed conditions (two hours, six problems). The most recent five years’ papers are the priority; older papers can be left for late-spring revision.
The window between JMO and Cayley is the most underappreciated in UK Olympiad preparation. It is when the habits that earn a Cayley Distinction are built.
Year 9 spring term — the IMC and Cayley sitting
The Intermediate Mathematical Challenge (IMC) is sat in early February of Year 9. It is the qualifier for Cayley Olympiad invitation — approximately the top one per cent of Year 9 IMC scorers nationally are invited to Cayley.
The four weeks between IMC sitting and the Cayley sitting in mid-March are the most intensive preparation window. Sit one Cayley past paper per week under timed conditions, marked strictly. Continue reading Gardiner and Bradley, chapters 4–6 (advanced circle theorems, transversal arguments).
For students who do not receive a Cayley invitation from IMC results: the preparation routine for Hamilton in Year 10 is unchanged, and the work done for Cayley is not wasted. The Cayley past papers themselves remain useful as Hamilton preparation in Year 10.
What comes next
Cayley results are returned in late April. Distinction holders typically continue into a Year-10 preparation cycle aimed at Hamilton (Year 10 Olympiad), with the Cayley reading list (Engel chapters 1, 3; Gardiner and Bradley chapters 1–6) carrying forward. The further reading for Hamilton picks up Engel chapters on number theory and the Gardiner and Bradley advanced sections; see our Hamilton deep dive for the Year-10-specific routine.
For one-on-one questions about the JMO-to-Cayley plan above — particularly for international students whose Year 7 or Year 8 was not in the UK — the WhatsApp advisor is the fastest route to a tailored preparation calendar.