Best Math Competitions for High School Students

Author: ExtracurricularHub Editorial Team (Editorial Team) · Reviewed by Parker, Founder — editorial policy

Article Summary

The best math competitions for high school students: the AMC/AIME ladder, HMMT, ARML, Purple Comet, Math Prize for Girls, and how to sequence them by level.

Full Article

Math competitions are the rare extracurricular with objective, nationally comparable results — which is exactly why admissions readers trust them. But the landscape is a ladder, not a list, and sequencing matters more than volume. Here's the map, from first contest to national team. (Every competition below is listed with verified deadlines on our [math](/extracurriculars/math) and [olympiad](/extracurriculars/olympiad) pages.) ## The official ladder (start here) **[AMC 10/12](/extracurriculars/amc-1012-mathematical-association-of-america)** — the Mathematical Association of America's entry exam, administered at schools every fall. High scores qualify you for AIME; AIME scores feed USAMO selection. This ladder is the spine of American competition math — everything else is commentary. **[US Physics Olympiad F=ma](/extracurriculars/us-physics-olympiad-fma-exam)** — not math per se, but the same exam-athlete skill set; strong AMC students often double up. ## The great team tournaments **[Harvard-MIT Math Tournament (HMMT)](/extracurriculars/harvard-mit-math-tournament-hmmt)** — the most famous student-run tournament in the country and among the hardest single days in high school math. Compare it with ARML in our [HMMT vs ARML breakdown](/compare/hmmt-vs-arml). **[American Regions Mathematics League (ARML)](/extracurriculars/american-regions-mathematics-league-arml)** — the classic state/regional team relay; free to compete and the best "team sport" version of competition math. **[Stanford Math Tournament](/extracurriculars/stanford-math-tournament-smt)**, **[Berkeley Math Tournament](/extracurriculars/berkeley-math-tournament-bmt)**, and **[Princeton's PUMaC](/extracurriculars/princeton-university-mathematics-competition-pumac)** — the university-hosted circuit. Individually cheap or free, and doing two or three in a season gives you real tournament experience between AMC cycles. ## The distinctive ones **[Purple Comet! Math Meet](/extracurriculars/purple-comet-math-meet)** — free, online, team-based, international. The single lowest-friction entry point in competition math. **[Math Prize for Girls](/extracurriculars/math-prize-for-girls)** — the largest math prize for young women, hosted at MIT, drawing from AMC scores. Free, prestigious, and a genuine community. **[HiMCM](/extracurriculars/himcm-math-modeling)** — 36 hours, one team, one messy real-world modeling problem, one paper. The right fit for students who like applied math more than contest tricks — and the closest thing to research this list offers. **[MIT MathRoots](/extracurriculars/mit-mathroots)** — a free MIT summer program (not a contest) for high-potential students from underrepresented backgrounds; the on-ramp that turns raw interest into ladder results. Pair the summer-camp question with our [PROMYS vs Ross comparison](/compare/promys-vs-ross) if you're choosing a proof-based summer. ## Sequencing by year 1. **First year:** AMC 10 + Purple Comet. Learn the format cheaply. 2. **Second year:** AMC again with real prep, join an ARML team, add one university tournament (SMT/BMT/PUMaC). 3. **Third year and beyond:** chase the AIME line, HMMT if your scores say so, HiMCM if you're the applied type, and a proof-based summer program to convert contest skill into mathematical maturity. ## Methodology Drawn from the verified math-competition listings in the ExtracurricularHub catalog (July 2026), weighting recognition, accessibility, and cost — most listed contests are free or under $50. Dates and fees repeat annually; confirm the current cycle on each listing's official site.

Frequently Asked Questions

Which math competition should I start with?

The AMC 10/12 — it's the entry point to the official ladder (AMC → AIME → USAMO) that every admissions office recognizes, it costs about $25, and your school likely already administers it. Add Purple Comet (free, online, team-based) the same year for a low-pressure second data point.

What's the difference between HMMT and ARML?

HMMT is one of the hardest single-day tournaments in the country and skews toward olympiad-level individuals; ARML is the classic regional-team relay where a strong school or state team carries the experience. Serious competitors usually do both — see our full side-by-side comparison.

Do math competitions matter for college admissions?

For STEM applicants, yes — they're among the few extracurriculars with objective national benchmarks. An AIME qualification is a meaningful line at selective schools, and USAMO-level results are essentially a credential of their own. But depth beats collection: a rising AMC→AIME trajectory reads better than ten scattered one-off contests.

Are there math competitions specifically for girls?

Yes — Math Prize for Girls (hosted at MIT) is the largest, drawing top scorers from the AMC ladder, and it's free to compete. It pairs naturally with MIT MathRoots for younger students from underrepresented backgrounds.

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