Free AMC 10/12 Mock Test — Live, Timed, with Solutions
A timed AMC 10 / AMC 12 emulator with real past problems and official scoring. 25 questions · 75 minutes · MCQ. Submit when you're done for a full breakdown and step-by-step solutions. No signup, runs entirely in your browser.
About the AMC 10 and AMC 12
The American Mathematics Competitions (AMC) are the most widely written high-school math contests in the United States, hosted by the Mathematical Association of America (MAA). Two papers run each year: the AMC 10 for students in grade 10 and under and the AMC 12 for grade 12 and under. Both papers are 25 multiple-choice questions in 75 minutes, no calculators.
The AMC is the entry point to the United States olympiad ladder. Top scorers qualify for the AIME (American Invitational Mathematics Examination); top AIME scorers advance to the USAMO and ultimately the International Mathematical Olympiad team. Even if you're not aiming for IMO, mock practice on real past papers is one of the highest-leverage activities for building speed, pattern recognition, and resilience under time pressure.
How AMC scoring works
Since 2002 the AMC has used a deliberately asymmetric scoring rule that rewards careful skipping over wild guessing:
| Outcome | Points | Strategic implication |
|---|---|---|
| Correct answer | +6 | Maximize accuracy on questions you can solve cleanly. |
| Unanswered (blank) | +1.5 | Leaving a hard question blank is worth ¼ of a correct one. |
| Wrong answer | 0 | Random guessing is neutral but worse than blanking when you can eliminate options. |
The maximum score is 150. A blank-strategy expected-value calculation: if you can eliminate one of five choices, guessing breaks even with leaving blank. Eliminate two and guessing is positive EV. Our mock implements this scoring rule exactly, so the timer and submit screen mirror a real AMC.
What score qualifies you for the AIME?
The MAA sets year-by-year cutoffs, typically targeting the top ~2.5% of AMC 10 scorers and ~5% of AMC 12 scorers. Recent ballpark figures:
- AMC 10: usually a score of 105–120 qualifies (~70th–80th percentile of scorers).
- AMC 12: usually a score of 85–100 qualifies (~80th–90th percentile).
- The exact cutoff is announced after both A and B papers are scored each year.
If you're hitting these scores consistently in mock practice, you're in qualifying range. The next step is the AIME mock test — 15 free-response problems in 3 hours where answers are integers from 0 to 999.
How to use this AMC mock test emulator
- Click Start Test — the engine pulls a fresh random set of 25 problems from a deep pool of real past AMC 10 and AMC 12 questions.
- Pace yourself against the live timer. 75 minutes is roughly 3 minutes per problem; the timer turns amber at 5:00 and red in the final minute.
- Flag and skip aggressively. Use the flag button on hard problems and come back; the question navigator lets you jump to any number in any order.
- Submit when ready — or let the clock expire. You'll get an AMC-format score (out of 150), a correct / wrong / blank breakdown, and full step-by-step solutions for every question.
- Review and retry. Click into any review row to see the detailed solution. Take another fresh test once the 5-minute cooldown ends — every set is randomly sampled.
Topics covered on the AMC
AMC problems blend four major strands of pre-college math. Strong AMC training touches all of them. We have free tools for each:
AMC vs AIME — what's the difference?
| AMC 10 / 12 | AIME | |
|---|---|---|
| Format | Multiple choice (A–E) | Integer free-response (0–999) |
| Questions | 25 | 15 |
| Time | 75 minutes | 180 minutes (3 hours) |
| Scoring | +6 / +1.5 / 0 (max 150) | +1 each correct (max 15) |
| Difficulty | Pre-olympiad, ramps from easy to hard | Olympiad-prep, uniformly hard |
| Who takes it | Open to all high-schoolers | AMC qualifiers only |
Try the AIME mock test if you want to feel the jump in difficulty.
Frequently asked questions
How is the AMC mock score computed?
Modern AMC scoring (used since 2002): each correct answer is +6 points, each wrong answer is 0, each unanswered question is +1.5. With 25 questions the max is 150. Leaving harder questions blank is sometimes strategically optimal — this is the trade-off the AMC scoring rule rewards.
Where do the problems come from?
The pool draws from real past AMC 10 and AMC 12 contests. Problems and solutions come from open archives. Each session samples a fresh random set — every retake gives you new problems.
Is this an exact replica of a real AMC contest?
The format mirrors a real AMC: 25 questions, 75 minutes, MCQ A–E, modern scoring. The questions are real past AMC problems but not bundled by year, so the difficulty mix varies session to session. For a specific year's paper, AoPS keeps the canonical archive.
Can I see solutions?
Yes — after you submit, every question expands in the review section to show your answer, the correct answer, and the full step-by-step solution (rendered with KaTeX).
Why is there a 5-minute cooldown between tests?
The cooldown is there so you actually review the test you just took. Score reports and solutions matter more than raw volume — use the wait to study the misses, then come back fresh. The cooldown is per-exam, so AMC and AIME don't gate each other.
Does this work offline / send my data anywhere?
Once loaded, the session runs entirely in your browser. KaTeX renders math locally. The only network hit on first load is fetching one JSON shard of questions plus the page's static assets. Your scores stay in your browser's localStorage.