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.
Congrats on qualifying — 96 on the AMC 10A is solid, and 3-4 AIME problems as a first-timer is honestly not bad at all. The jump is real. The AMC rewards speed and cleverness; AIME problems often need you to construct something from scratch, and there's nowhere to hide if your fundamentals in a topic have gaps.
What actually helped me figure out where my gaps were was grinding timed practice tests with immediate review — I'd been doing random problem sets forever and it wasn't clicking why I kept stalling on certain geometry or number theory problems. When I switched to full 15-problem sets under real conditions (using an aime practice test), the pattern became obvious: I was bleeding points on modular arithmetic and missing the "elegant" construction step in combinatorics almost every time. Random drilling hides that; full test conditions expose it fast. Once I knew the weak spots, I could go deep on those topics specifically instead of just doing more of the same.
Also — don't underestimate the value of fully writing out solutions to problems you couldn't solve, even after you've read the answer. Actually reconstructing the logic yourself, step by step, is different from reading someone else's solution and nodding along. That's where the pattern recognition actually sticks. Three months of that approach moved me from the 4-5 range to consistently hitting 7-8, which felt impossible when I started.
I was in the exact same spot last year, and honestly 3-4 correct on your first two weeks is not bad at all. The thing that actually clicked for me wasn't doing more problems, it was slowing way down and really dissecting the ones I got wrong. Like, not just reading the solution but figuring out exactly where my thinking went sideways and what the "trick" was that I missed. AIME rewards a pretty specific kind of pattern recognition that you just don't build by rushing through a ton of problems.
The one specific thing that made the biggest difference was picking one topic I was weakest in (for me it was number theory) and spending two weeks doing only AIME problems from that category, going all the way back to the 80s and 90s. Older problems are honestly great because they're a little more straightforward and you can actually build intuition before the modern ones get wild. You're not going to go from 4 to 10 overnight, but that focused drilling is what finally made the difficulty feel less random to me.
I was in a similar spot a few years ago, prepping for the AIME while juggling a full-time job, so I know exactly how that "I've only got 45 minutes tonight" feeling goes. Honestly, 3-4 out of 15 is not as bad as it sounds when you're just starting -- the real shift is learning to sit with a problem for 20 minutes without panicking. I stopped trying to grind full tests and instead focused on one topic per week. Combinatorics was my weakest area and I found a free aime combinatorics resource that let me drill just that topic without wasting time on stuff I already knew.
The other thing that actually moved the needle for me was writing out solutions by hand even when I got the right answer. It sounds slow, and it is, but it forces you to understand why something works instead of just pattern-matching. Twenty focused minutes on your lunch break beats two unfocused hours on a weekend. You'll get there.