AIME Daily Practice: A 5-Problems-a-Day Plan

AIME prep is different from AMC prep in ways that aren't obvious from the outside. The 3-hour test favors stamina and problem-abandonment skill, both of which decay quickly without practice. Daily 5-problem sessions train them better than weekly 90-minute sessions ever will.

Why daily beats weekly

Three reasons, all empirically validated by serious competitors:

1. Pattern recognition is built by spaced exposure. AIME problems re-use motifs (Vieta's on cubics, mod-9 sanity checks, complementary counting on lattice paths). Seeing a motif twice in two days locks it in better than seeing it five times in one Saturday.
2. Calc-free arithmetic decays. If you can compute 23 \times 47 in your head this week, can you next week? Daily drills keep the pencil-and-paper computation reflex sharp; weekly ones don't.
3. Problem-abandonment is hardest to fake. The single largest gap between a 6-scorer and a 10-scorer on AIME is the willingness to give up on problem 8 at minute 11 and bank minute 12 on rechecking problems 1–7. That habit takes daily reinforcement.

The 5-a-day structure

Each session, ~50 minutes total:

• 2 problems from positions 1–6 (warm-up zone) — 12-minute timer; goal is to get them right with clean arithmetic. Treat these as arithmetic conditioning. If you're not getting these consistently right, the rest of the plan is premature.
• 2 problems from positions 7–11 (scoring zone) — 12-minute timer per problem. These are where your score is made or lost. Most AIME prep should spend most of its energy here.
• 1 problem from positions 12–15 (stretch zone) — 15-minute soft timer; if no progress at 15 minutes, abandon and read the official solution. The point isn't to solve every stretch problem; it's to develop intuition for when a problem is beyond your current toolkit.

Day 7 is review only — no new problems. Re-do the week's missed problems untimed. The act of re-solving cements the techniques better than reading solutions does.

Problem-selection rules

Where the problems come from matters as much as which numbers they are:

1. Mix old and recent. AIME problems pre-2010 tend to be more arithmetic-heavy; post-2015 lean harder on counting, probability, and number theory. Both train different muscles.
2. Don't repeat a year cluster. If you did 5 from AIME 2018 yesterday, switch to a different year today. The pattern of difficulty within a single AIME has stylistic consistency, and you want exposure to different stylistic eras.
3. Bias slightly toward your weak topic. If your last full AIME mock had counting / probability as the dominant miss category, 3 of today's 5 should be from that category. But don't go 5/5 — variety keeps the reflexes alive across the full test.

The stuck-on-a-problem protocol

AIME problems will absolutely beat you. The question is what to do in the moment. The protocol:

1. Minutes 0–4: read once, write down what's given, identify what's asked, write down 1–2 candidate techniques.
2. Minutes 4–10: attempt the most promising technique. If it produces a number, sanity-check it before accepting.
3. Minute 10: if you have nothing or you've gone down a rabbit hole, switch to the second candidate technique.
4. Minute 12 (warm-up / scoring zone): if still nothing, blank-bubble it (or write your best guess if you have one) and move on. You will run out of test time fixing problems that needed 5 more minutes; you won't run out fixing ones that needed 30 more.
5. Minute 15 (stretch zone): abandon if nothing working. Read the solution. The next time this motif appears, you'll know.

The hardest minute is minute 12. The trained instinct is to keep pushing because you can "feel" you're close. AIME score distributions show that most students who feel they're close on a problem they don't solve also have at least one earlier problem wrong from a sign error. Banking 12 minutes for double-checking is almost always worth more than minute 12 of solving.

The mod-9 / mod-11 ritual

Before bubbling any answer, compute it mod 9 (or mod 11) two ways: from your final number and from a quick recompute of one of the cleaner sub-steps. If they don't match, you have a computation error. This catches a non-trivial fraction of slips and takes ~30 seconds.

Mod 9 is easy: digit sum. Mod 11: alternating digit sum. Both work well because almost all AIME computations involve enough multiplication that a single sign error or factor-of-2 slip changes the modular signature.

Mocking schedule on top of dailies

Once a week of dailies = ~30 problems = roughly 2 AIMEs of equivalent volume. So you don't need a separate mock day. But two situations call for full mocks:

• Once a month, take a full timed AIME (3 hours, no breaks) to test stamina. Score and review.
• Two weeks before AIME day, take the most recent past AIME timed. Rest the day after, then resume dailies until T-3 days. T-2 and T-1: light review only.

Where Amc2Aime fits

The platform's AIME papers are organized by year and part (I / II). For dailies, ask the coach for "AIME 2018 problems 7-11" or more broadly "AIME drill 5 problems" to get a 5-problem round. The L2 review (alternative solutions) is unusually high-value on AIME problems because the same problem often admits a clever-and-short approach that's worth knowing for time pressure even if your original approach was correct.

After 4–6 weeks of dailies, your history page will show enough samples for the L3 error-mode review to be meaningful. That's when the AI coach starts being more useful than another month of self-driven prep — it'll surface patterns you can't see from inside individual miss reviews.