Post-2002
Since 2002, the USAMO has been a six-question, nine-hour mathematical proof examination spread out over two days. (The IMO uses the same format.) On each day, four and a half hours are given for three questions.
Each question is graded on a scale from 0 to 7, with a score of 7 representing a proof that is mathematically sound. Thus, a perfect score is 42 points. The number of perfect papers each year has varied depending on test difficulty. Regardless, the top 12 scorers are all named contest winners.
The scale of 0 to 7 goes as follows:
0 - No work, or completely trivial work
1-2 - Progress on the problem, but not completely solved
3-4 - All steps are present, but may lack clarity. (These scores are very rare.)
5-6 - Complete solution with minor errors
7 - Perfect solution
1996 to 2001
The test consisted of two three-problem sets. Three hours were given for each set; one set was given in the morning, and the other in the afternoon.
1995 and earlier
The test consisted of five problems to be solved in three and a half hours.