So… if I take it at face value, I can only say that I didn’t qualify for USAMO for the 2023-2024 season as I had wished. Although it is what it is, there is much more I’ve gleaned from my math contest training and experience so far. Today, two days after the 2024 AIME I, is a great day to reflect and share.
AMC
One of the reasons I was so far from the olympiad was my low AMC score. My speed was always an issue that I was trying to resolve these past two years. Throughout these past four AMCs, my maximum score was only a mid-100, which was insufficient to support my AIME score for a good olympiad-qualifying index.
A suboptimal strategy I implemented in my sophomore and junior years was holding an intense preparation month solely for AMCs the month leading up to the test. To build up a skill like fast, intuitive thinking, this was not enough time to carefully examine what you could do better and think about every single problem that was out of reach. As a result, this “cramming” built up a lot of internal stress and as a result, my performance was worse than if I had I spent at least the full year spacing out speed preparation.
My goal for next season is to score at least 130 on the next AMC 12, which is in nine months (it’s not as much time as you expect).
AIME
I am more happy about my performance on this test, as I improved a whole five points from last year. This year’s test gave me the confidence to score at least an 11 or 12 next year, possibly even more. As long as I keep doing harder problems above my level and learn some olympiad stuff that may be useful, I am in good ship shape for next year’s AIME.
A great way I’ve learned to improve for the AIME (and most likely AMC, too) is to internalize problems. That is, to try a problem yourself, and gradually look at more and more of the solution if you get stuck. If you don’t manage to solve the problem, read the solution fully and understand it. How could you have gotten it? What were the leading details that led to the main idea? Now can you feel the problem? Is there a problem or concept with a similar idea? Then attempt the same problem a few days later, a few weeks later, and then a few months later. I kept a log of problems that were originally too hard for me. You’ll be surprised at how “intuitive” the problem is after you’ve done the same steps a couple of times! More importantly, since you know this problem so well, you can detect similarities and differences between this problem and other problems you have learned or done before.
What made the difference? I attribute a lot of the increase to my mental toughness. During the AMC season, I didn’t know how much I had to push through mentally to achieve a good score. Whenever there was a problem I didn’t know how to solve immediately (but it was within my ability), I collapsed under my emotions and failed to think logically. However, the story changed for the AIME. I calmed down, relaxed my nerves, and pushed through tough problems that were non-trivial. I, like a mental David Goggins, shouted f— you to that inner voice that destroyed multiple tests throughout high school.
Let’s think about your options dlu.