IMO Study Notes: What to Include and How to Revise
How to make and revise notes for the International Mathematical Olympiad across algebra, geometry, combinatorics and number theory.
Good IMO study notes are short and built from problems you have actually solved. The International Mathematical Olympiad has no fixed chapter list, so notes that copy a textbook rarely help. What helps is a compact record of theorems, standard techniques and the mistakes you keep repeating. These are the pages you will reread before IOQM, RMO and INMO.
This page shows what to put in your notes, how to organise them and how to revise.
What IMO Study Notes Should Include
Area | What to note |
|---|---|
Algebra | Standard inequalities, relations between roots and coefficients, progression formulas, common substitutions for functional equations |
Geometry | Circle properties, similar-triangle criteria, Ceva's and Menelaus's theorems, sine and cosine rules |
Combinatorics | Counting methods, pigeonhole principle, recursion set-ups, graph terms such as degree, path and cycle |
Number theory | Divisibility rules, congruences, Fermat's Little Theorem, Wilson's Theorem, Euler's phi function, Chinese Remainder Theorem |
For each item, add one solved example. A theorem you cannot apply is not yet in your notes.
How to Organise Your Notes
One-page theorem sheets: Keep a single page per area so you can revise all four in an evening.
Technique cards: Write the idea that unlocked each problem, for example "consider remainders modulo 7" or "look for an invariant".
Error log: Record each missed problem, why you missed it and the fix. Reread this log more often than anything else.
Proof templates: From RMO onwards, note how to structure an induction, a contradiction or a case-by-case argument clearly.
A Simple Revision Schedule
Same day: Add new theorems and techniques after each study session.
Weekly: Reread the error log and re-solve three or four problems you got wrong.
Before each test: Go through the one-page theorem sheets only. Do not start new topics.
After each test: Update the notes with whatever the test exposed.