Competition math prep for every level
Eight contests share one bank of past problems. Each page below says what its contest asks, how hard its problems run on Lemmas and which past papers you can sit, and every count is read from the bank.
The eight contests at a glance
- Past contest problems
- 5,727
- Years covered
- 1983 to 2026
- Difficulty
- One 1 to 100 scale for all eight, so an AMC 8 problem and an AIME problem can be compared.
From the AMC 8 to the AIME
The usual climb runs from the AMC 8 to the AMC 10 or AMC 12, and then to the AIME for anyone who scores above the MAA’s cutoff. If you cannot tell which step you are on, sign up and take the 10-problem set that finds your starting level.
Every problem is rated from 1 to 100 on one scale shared by all eight contests, and the About page explains how the ratings are measured. Dates, fees and cutoffs change every season, so each contest page sends you to its organizer for them.
- AMC 8 prep25 questions in 40 minutes for grade 8 and below. Most people start here.1,025problems
- AMC 10 prep25 questions in 75 minutes for grade 10 and below, and a way into the AIME.1,300problems
- AMC 12 prepThe same 75-minute format for grade 12 and below, with harder questions late in the paper.1,299problems
- AIME prep15 questions in three hours, answers from 0 to 999, open by invitation.1,065problems
Team contests
These four are team events, and each has individual rounds inside it. Every page here says how its rounds work.
- HMMT prepTwo student-run tournaments from Harvard and MIT, February the harder of the two.510 problems
- SMT prepStanford's spring tournament, with a Power Round, a Guts Round and subject tests.215 problems
- ARML prepA team contest in regional teams of 15, with a power question and a relay.145 problems
- PUMaC prepPrinceton's tournament, where each student takes two of four subjects.168 problems
Make an account and try your first problem.
Username, email and password. No card.