Since it's inception in 1972, the United States of America Mathematical Olympiad, also known as USAMO, has set the standard for excellence in mathematics for students nationwide. The American Mathematics Competitions, or AMC, committee has not only administered the exam, it has also developed the qualification criteria for high schools across the country, primarily based on a preliminary exam.
Because the USAMO, held annually, is devoted to identifying the best of the best in the field of mathematics, only 500 students are extended an invitation to enter the competition, provided that they complete the preliminary exam and demonstrate their abilities.
The USAMO examination typically includes over nine hours of testing spanning two days. Although one might initially assume that there are a plethora of multiple choice questions, the AMC committee has guaranteed that the top 12 scorers are trained at the Mathematical Olympiad program held in Lincoln, Nebraska; therefore, with so much at stake, the committee has included only six questions on the exam, and all are very difficult mathematical proofs.
Unfortunately, students are only eligible for the competition if they are high school students who are citizens or legal residents of the United States or our neighbor to the north, Canada. So, if you're an international student seeking a spot at the International Mathematical Olympiad, you may want to consider looking up your native country's independent qualifications.