AMC is American Math Contests for Middle and High School students. There are AMC 8, AMC 10, and AMC 12. Each of these are national contests to identify exceptional math students.
The AMC's are made of 25 questions, with 75 minutes for the whole test. These are all multiple choice. Points are alloted for putting in name. Points are given for leaving answers blank, and more points are given for getting the correct answer.
The points are different every year. For the first AMC 10, there are 2 points for blank, and 6 points for correct answer.
Students who "pass" the AMC 10 or 12 are invited to take the AIME. For AMC 10 passing means getting the top 1% in the country, and for AMC 12 it means getting above the required score. There are advantages to taking both 10 or 12. For taking 10, it is more difficult to get into taking AIME, and for taking 12, it is more difficult to get into USAMO.
On average, students get higher scores on 10 than on 12, but might still not get top 1%. To get into USAMO, the student must get add the AIME and AMC scores together, so it is easier if one has a higher AMC score. | 
