I qualified for the AIME this year for the first time (scored 96 on AMC 10A) and I have absolutely no idea how to prepare. The jump in difficulty from AMC to AIME feels like a cliff. I spent two weeks trying to work through old AIME problems and I'm solving maybe 3-4 out of 15 on a good day, which I know is actually normal but it doesn't feel great.
I'm a junior in high school, decent at competition math but not at the level where problems just fall apart for me. Number theory is probably my worst area - I can brute force a lot of AMC number theory but AIME questions have too many cases to brute force. Geometry is okay, combinatorics is probably my strongest topic.
People keep saying 'just do lots of problems' but that advice isn't specific enough. Are there particular years or problem numbers I should prioritize? Should I be grinding through solutions immediately when I'm stuck or grinding for 45 minutes first? What's actually worked for people who made this jump?
I've got about 3 months before the next cycle. Realistically I want to score in the 6-8 range, which I know is ambitious but I figure aiming high is worth it.
Scoring 6-8 in 3 months is achievable if you're currently getting 3-4. That's a big jump but not unrealistic with focused work. The most common improvement I've seen is people finally internalizing specific techniques like Vieta jumping or using generating functions - once those click, 2-3 more problems become solvable overnight.
For number theory specifically, AoPS Introduction to Number Theory by Mathew Crawford is genuinely the best resource. Work through it cover to cover and your AIME number theory scores will jump. I went from basically 0 correct number theory problems to solving them fairly consistently in about 6 weeks of focused work.
The 45-minute rule is real - if you haven't made meaningful progress in 45 minutes, read the solution. But 'meaningful progress' means you have a viable approach, not just that you've tried something. Learning to identify dead ends quickly is a skill itself.
AIME I is consistently harder than AIME II for most people, so prioritize recent AIME II problems if you want to build confidence. Problems 1-5 from the last 10 years are a great place to start since they're hard but approachable.