Contest Format


The UTMC is done in teams of up to 4 students. You may either register individually or as a team. Invidiual contestants will be grouped into teams before the day of the contest.


The UTMC has two divisions: Junior and Senior. The Junior division is easier, with problem difficulties ranging from AMC 8 to AMC 10. Problem difficulties in the Senior division range from AMC 10 to AIME. Only students in grade 9 or below are eligible for the Junior division. A team competing in the Junior division must have all members be eligible (i.e. grade 9 or below), teams with a mix of Junior and Senior students will be placed in the Senior division.

Note that all rounds except for the Marathon Round will be separated into these two divisions. All contestants will take the same Marathon Round, regardless of their division. Scoring, however, will still be separate for the marathon round between the two divisions.


The competition consists of 4 rounds: Numerical, Geometry, Team, and Marathon. All questions are short answer (i.e. single-value answers, no proofs). Each question has its own point-value, which is used to calculate the total score. For more information on how the scoring works, please refer to the scoring procedure

Numerical Round

This is an individual round, where you get 10 questions and 60 minutes to solve as many of them you can. Problems will come from various subjects (Algebra, Combinatorics, and Number Theory).

Geometry Round

Similar to the Numerical Round, 10 questions and 60 minutes. The twist is that all questions are geometry!

Team Round

As the name implies, your entire team will be doing this round together. There are 10 questions to be solved in 40 minutes.

Marathon Round

The Marathon Round is also done as a team. There will be 10 sets of 3 questions, which your team solves sequentially (one set at a time). You’ll have a total of 80 minutes to complete this round. You will not be told your score after submitting each set. Instead, you will only know your final score after the round ends.

After submitting set 10, you return to set 1 and get a second chance to resubmit any answers you think were incorrect. If your second answer is correct, you receive half the points alloted for the question. But be warned: Any answer submitted in this second stage will override the original answer, even if the original answer was correct.