<p>I knew a lot of people in advanced classes (like abstract algebra) in high school, and it was generally easier to get an “A” in these classes than it was to make USAMO. In those days there were only 150 USAMO winners per year and no Art of Problem Solving Books existed yet…I don’t know if it is any easier today to make USAMO considering that the number of qualified entrants probably has increased.</p>
<p>Still, there are a lot of people who can get A’s in high level classes. </p>
<p>I can’t really tell you what it takes to make USAMO because I wasn’t able to do it myself, even though advanced math came easily to me. If it’s like it used to be, knowing some combinatorics and number theory should help. Some people easily picked the so-called “math tricks” necessary to solve these problems just from math team; later I found out much of these “tricks” were based on number theory. As a more verbal person, it was easier for me to learn mathematics when given the entire context. Of course, there are more than number tricks on the test, but the other problems could be typically solved if you had done well in algebra, geometry, and trig. Some of the number tricks problems were kind of, well, you can guess the three letters I’m thinking of–I had NO IDEA where someone could solve this from scratch other than Gauss himself.</p>