Utah Math Olympiad

Past Exams

This is a list of all UMO exams in the AoPSWiki. Users are encouraged to post additional solutions to the problems.

Format & Scoring

The Utah Mathematical Olympiad is a 3 hour test with 6 questions designed to test a student's creativity and ability to form a rigorous mathematical proof. In order to get credit for a problem, a student must write a convincing argument that proves their answer. Note that this is not the same as merely showing one's work, nor is it the same as explaining every step in great detail. Graders should be able to logically follow each step in a student's paper. Each problem will be worth 7 points. Partial credit will be awarded for significant progress toward a correct solution.


Any Utah student who has not completed 12th grade and is 19 years old or younger is eligible to participate.


Prizes will be awarded to the top five scorers. Prize denominations will depend on ties and the amount of money available. See the results page using the link above to see last year's prizes to see who is studying abroad. For more details click on this URL - https://utahmath.org/