The American Invitational Mathematics Exam. The second round of testing associated with the AHSME and the USAMO, the AIME is a fairly challenging exam. The AIME is a 15 question, 3 hour examination in which each answer is an integer number from 0 to 999 (inclusive, you math weeny). One is unlikely to obtain the correct answer to any given question by guessing. All problems on the AIME can be solved by pre-calculus methods. The use of calculators is not allowed. Each problem counts 1 point, and the nationwide mean score fluctuates between 0 and about 2 (IIRC). The test was first administered in 1983. To qualify for the USAMO, a student has to have the sum of (their AHSME score) + (10 times their AIME score) exceed an annually chosen magic number, typically between 180 and 210.