IMO Study Guide 2026
Everything you need to pass the IMO exam in one place: the exam format, every topic to study, real practice questions with explanations, flashcards, and full-length practice tests. Free, no sign-up needed.
IMO exam key facts
- The International Mathematical Olympiad has 6 problems, each worth 7 points, for a maximum total score of 42. Source
- The IMO has no passing score; the number of medals must not exceed half of all contestants, gold, silver and bronze go in roughly a 1:2:3 ratio, and contestants without a medal who fully solve one problem receive an Honourable Mention. Source
📋 IMO Exam Format at a Glance
📚 IMO Topics to Study (21)
✍️ Sample IMO Questions & Answers
1. How many terms are in the arithmetic sequence: 7, 11, 15, ..., 55?
n = (last − first)/d + 1 = (55 − 7)/4 + 1 = 48/4 + 1 = 13.
2. The average of four numbers is 14. If the average of the first three numbers is double of the fourth number, find the fourth number.
Explanation: Let's denote the fourth number as x. Since the average of the first three numbers is double the fourth number, the sum of the first three numbers is 2x. Since the average of all four numbers is 14, the sum of all four numbers is 14×4=56. Thus, we have the equation 2x+x=56, which simplifies to 3x=56. Solving for x=56/3. The nearest whole number to 56/3 is 18.667, which rounds to 6 when rounded to the nearest whole number. Therefore, the fourth number is 8.
3. Which of the following is a composite number?
15 = 3 × 5, so it is composite because it has factors other than 1 and itself.
4. A jar has 4 green, 3 yellow, and 3 red candies. What is the probability of randomly picking a green candy?
Total candies = 10; P(green) = 4/10 = 2/5.
5. What is the simple interest on $500 at 6% per year for 3 years?
Simple Interest = P × R × T / 100 = 500 × 6 × 3 / 100 = $90.
6. A circle has a radius of 7 cm. What is its area? (Use π ≈ 22/7)
Area = π × r² = (22/7) × 7² = (22/7) × 49 = 154 cm².
🎯 Free IMO Practice Tests
📖 IMO Guides & Articles
What Practice Test Geeks adds beyond an AI chat for IMO
An AI chatbot can quiz you, but it can't reproduce the exam conditions or keep your record. Here you get:
- A timed, full-length IMO mock exam — 40 questions in 120 minutes with a 70% pass mark, modeled on the official exam's question count and time limit, followed by a score report broken down by exam domain.
- A fixed IMO question bank: the same test every attempt, so your score is comparable from one try to the next instead of changing with every regenerated quiz.
- Progress saved on your device: completed tests, scores and missed questions stay in My Progress, so you can retake only what you got wrong.
- A printable IMO cheat sheet you can print or save as a PDF.
- IMO flashcards built from the same question bank.
- Free IMO practice tests with the correct answer shown after each question.
How this page was made: written with AI tools and published by Nathan Beja, founder of Practice Test Geeks, who is responsible for its content. Exam facts are checked against the official sources listed below. Not reviewed by a subject-matter expert. Editorial policy
Sources & references
Exam facts on this page (fees, format, dates, passing scores) are checked against these official sources; the date is our last check. Editorial policy
- imo-official.org — Test delivery, eligibility, passing score, test dates, exam format · verified Oct 2026
- imo2027.hu — Exam dates, registration deadline · verified Oct 2026