AIME Problems: What They Actually Look Like and How to Practice

An AIME invitation is not proof you are ready for an AIME problem.

Score high enough on the AMC 10 or AMC 12, and the MAA moves you into a different exam entirely: 15 questions, three hours, and every answer is a number you write in yourself. No five choices to narrow down. No blank worth partial credit for showing up. You get the right integer, or you get nothing.

An AIME problem is a question from the American Invitational Mathematics Examination, the round that sits between the AMC 10/12 and the USAMO. There are 15 per exam, each worth one point for a correct integer answer from 0 to 999, with zero credit for a wrong guess or a blank.

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The AIME Format, Number by Number

Search “aime problems” and most of what comes back is exactly what it sounds like: archives. Page after page of past-exam PDFs and solution wikis, built for someone who already knows what one of these looks like and just wants more of them to grind through.

If you have never sat the exam, that is not much help. Almost nothing that ranks for the format actually explains it before throwing problems at you. Most of it assumes you already know how the answer sheet works, how the scoring differs from the AMC, and what “no partial credit” really means once you are sitting there with a blank three-digit box.

Our own AMC score guide covers the AIME cutoff you need to hit to get invited. It never explained what happens after you get in. This does.

Multiple Choice vs. Integer Answers (0 to 999)

On the AMC 10 or 12, you are picking from five answer choices. Even on a problem you cannot fully solve, you can eliminate two or three options and take an educated guess. That safety net is gone on the AIME. Every answer is an integer from 0 to 999, and you write it in yourself, bubbled as a three-digit number (so an answer of 5 gets recorded as 005). There is nothing to eliminate your way toward. Either your algebra, your casework or your final computation gets you to the exact number, or it does not.

This single change is why students who cruise through AMC 12 problems in the 80s and 90s sometimes stall completely on early AIME problems that use the same underlying skills. Multiple choice quietly rewards approximate reasoning. Integer answers do not.

No Penalty for Wrong, No Credit for Blank: Why That Changes Strategy

The AMC 10/12 gives you 1.5 points for a blank, a small reward for knowing when to walk away from a problem. The AIME does not. A wrong answer and a blank answer are worth the identical zero points.

That completely flips the strategy: on the AMC, leaving a shaky answer blank can be the smarter move. On the AIME, there is no reason ever to leave a problem blank if you have any answer at all, even a rough guess from a partial solution, because guessing wrong costs you nothing you were not already going to lose.

Here is the format side by side with the AMC 12 you likely just took to qualify:

Feature	AMC 12	AIME
Questions	25	15
Time limit	75 minutes	3 hours
Answer type	5 multiple-choice options	Integer, 0 to 999
Correct answer	6 points	1 point
Blank answer	1.5 points	0 points
Wrong answer	0 points	0 points
Calculator	Not permitted	Not permitted
Difficulty curve	Ramps across 25 questions	Starts near AMC 12 level, ends far harder

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Who Should Even Attempt AIME Problems

You get here through the AMC 10 or AMC 12, and only by scoring at or above that year’s qualifying cutoff. If you have not checked where that cutoff typically lands, our AMC score guide covers the AIME qualification ranges for both exams in detail, so this piece will not repeat those tables.

Not sure which of the two qualifying exams fits your grade and goals in the first place? AMC 10 vs AMC 12 breaks down the eligibility and difficulty differences.

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Why AIME Problems Feel Different From AMC Problems

The scoring change is only half of it. The bigger shift is what the problems demand from you. On the AMC, a problem with an ugly-looking setup often resolves into one of the five listed answers, which quietly confirms you are on the right track. AIME problems offer no such confirmation. You could be one arithmetic slip away from the right integer and have absolutely no signal that you are close.

That also means AIME problems are written to resist shortcuts. A well-chosen multiple-choice option can sometimes be worked backward into the problem to save time. There is nothing to work backward from here. You need the full argument, carried through cleanly, from setup to final number.

It rewards the same problem-solving habits that carry across olympiad-style math generally: pattern recognition, careful casework, and knowing when to try a completely different approach rather than grinding the same one harder.

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How to Actually Practice AIME Problems

Stop running full 15-problem sets front to back under a three-hour clock every time. That trains you to survive three hours, not to get better at either half of the exam, and the two halves need different training entirely.

Split your practice by problem number instead of by full paper. Pull problems 1 through 10 from five or six past AIMEs and drill them back to back, timed at around 90 seconds each, no notes, no calculator. That builds the speed and clean execution you need on the problems you are realistically going to finish.

Then go back to the same papers and pull only problems 11 through 15. Work those with no clock at all. Those late problems reward patient, structural thinking, and rushing them under exam pacing while you are still learning them teaches the wrong habit.

Training both halves at full-exam pace, every single time, teaches neither one properly.

Here is an original problem in the AIME style to try that approach on:

Worth being honest about where an app fits into that plan. Gonit’s practice bank is live for grades 1 through 10 right now, with grades 11 and 12 still being built out.

That is the exact band where most AIME qualifiers sit, so if that is you, use it to shore up the AMC-level foundation that got you the invitation in the first place, not as a shortcut past problems 11 through 15. Nothing beats working real past AIME papers under the split-timing approach above for that stretch.

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FAQ

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Related guides

• AMC 10 Practice Test: Past Papers, Strategy & a Prep Plan
• AMC 12 Practice Test: Past Papers and a Smart Prep Strategy
• How to Qualify for the IMO in the USA

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