Free AIME Mock Test — Live, 3 Hours, Solutions Included
A timed AIME emulator with real past problems and integer free-response answers. 15 questions · 180 minutes · answers 0–999. Submit any time for a score out of 15 and full step-by-step solutions. Runs entirely in your browser, no signup.
About the AIME
The American Invitational Mathematics Examination (AIME) is the second stage on the US math olympiad path, run by the Mathematical Association of America (MAA). It's a 15-question, 3-hour, free-response contest; every answer is an integer from 0 to 999. No multiple choice, no partial credit — each correct integer is worth one point, max 15.
AIME problems are substantially harder than AMC problems. Where the AMC tests speed and pattern recognition, AIME tests depth: clean problem-solving, careful casework, and the kind of creative leaps that olympiad training is built around. Top AIME scorers advance to the USAMO and ultimately the IMO team.
How AIME scoring works
| Outcome | Points | Strategic implication |
|---|---|---|
| Correct integer answer | +1 | Pure accuracy game — every problem is worth exactly the same. |
| Wrong integer | 0 | No penalty. Always guess if you've narrowed the answer. |
| Blank | 0 | Same as wrong — there's no upside to leaving it empty. |
Maximum score is 15. Unlike the AMC, there is no bonus for unanswered questions, so guessing costs nothing. If you can narrow an answer to a reasonable integer range, write something.
Qualifying for the AIME (USAMO path)
You earn an AIME invitation by hitting the cutoff on either the AMC 10 (typically a 105–120 score) or AMC 12 (typically 85–100). AIME participation itself is the second step of the IMO selection process:
- AMC 10/12 → top ~5% qualifies for AIME
- AIME → top scorers' AMC+AIME composite (USAMO Index) qualifies for the USAMO
- USAMO → top ~6 advance to MOP and US IMO selection
If you haven't qualified yet, build through the AMC mock test first — same emulator, MCQ format.
How to use this AIME mock test emulator
- Click Start Test — the engine pulls a fresh random set of 15 problems from a deep pool of past AIME papers.
- Pace for 12 minutes per problem. 3 hours total. The timer turns amber at 5:00 and red in the final minute. Use the early problems (1–5) for quick wins and bank time for the harder back half.
- Type integer answers (0–999). The answer box accepts numeric input only. Hit Tab or click Next to move on; flag any problem to come back later.
- Submit when ready or let the timer expire. You'll get a score out of 15 plus per-question breakdown and full solutions.
- Review the misses carefully. AIME problems reward deep review — one technique often unlocks several future problems. Take another fresh test after the 5-minute cooldown.
Topics covered on the AIME
AIME problems span four major strands but go deeper than AMC. Build your toolkit with these free helpers:
AIME strategy — earning your first AIME points
Even strong AMC scorers often blank on their first AIME — the format shock is real. A few patterns that move scores meaningfully:
- Bank #1–5 with discipline. The first five problems are designed to be accessible. A clean 5/15 puts you in qualifying range for the JMO or higher contests.
- Coordinate-bash geometry. AIME geometry is often unlocked faster with coords than with synthetic. Don't fight it.
- Always write a guess. No penalty for wrong answers. If you've eliminated 80% of the 0–999 range, write the most likely integer.
- Check parity and small cases. If your answer "should" be even and you got odd, you have an off-by-one. AIME tests this constantly.
- Trust your training. AIME rewards recognizing problems you've seen before more than improvising from scratch.
Frequently asked questions
What is the AIME?
The AIME (American Invitational Mathematics Examination) is the second stage on the US olympiad path. It's a 15-question, 3-hour free-response contest where each answer is an integer from 0 to 999. AIME participation requires qualifying through the AMC 10 or AMC 12.
How is the AIME mock score computed?
Each correct integer answer is worth 1 point; wrong or blank answers are 0. Max possible is 15. Unlike AMC, there is no penalty or bonus for blanks — guessing costs nothing.
Where do the problems come from?
Real past AIME problems with verified integer answers and full solutions. Each session samples a fresh random set; retake for a new set.
What about AMC?
The AMC mock test is a separate page with the same emulator. Format: 25 MCQ problems in 75 minutes with the modern AMC scoring rule (+6 correct / +1.5 blank / 0 wrong).
Why is there a 5-minute cooldown between tests?
AIME problems reward deep review more than raw volume. The cooldown nudges you to actually study the misses before retaking. The cooldown is per-exam, so AMC and AIME don't gate each other.