What is the difference between AMC 10 and AMC 12?

Same format (25 problems, 75 minutes, multiple choice, +6 / 0 / +1.5 scoring). AMC 10 is for grades 10 and below; AMC 12 is for grades 12 and below. AMC 12 covers more advanced topics (trigonometry, complex numbers, logarithms, advanced algebra) and is harder problem-for-problem.

Should a 10th grader take AMC 10 or AMC 12?

If your primary goal is to qualify for AIME, AMC 10 is usually easier (lower cutoff in absolute terms), and a high AMC 10 score gives you more room on the index. If your goal is to build toward USAMO, AMC 12 prep starts paying off earlier. Many strong 10th graders take both.

What is the AMC 10/12 scoring?

+6 for correct, 0 for wrong, +1.5 for blank. Maximum score is 150 (25 × 6). The blank-credit means random guessing has expected value 1.2 < 1.5; never guess randomly, but always guess if you've eliminated 2+ choices.

Can I take both AMC 10 and AMC 12?

Yes — AMC offers two sittings (A and B). You can take AMC 10A and AMC 12B (or vice versa), but not both A or both B. Many students do this to maximize AIME qualification chances.

Are AMC 10 and AMC 12 problems shared?

Yes — by design, problems 1–10 of AMC 12 typically reuse problems 5–15 of AMC 10. The overlap thins after problem 15, where AMC 12 introduces topics the AMC 10 doesn't cover.

What's the AIME cutoff for each?

Cutoffs vary year-to-year. Recent AMC 10 cutoffs hover around 105–115/150 (top ~2.5%); AMC 12 cutoffs hover around 93–100/150 (top ~5%). The AMC 12 cutoff is lower in raw score because the test is harder.

AMC 10 vs AMC 12 — Which Should You Take?

Q: Can I take both AMC 10 and AMC 12?

Yes — AMC offers two sittings (A and B). You can take AMC 10A and AMC 12B (or vice versa), but not both A or both B. Many students do this to maximize AIME qualification chances.

Q: Are AMC 10 and AMC 12 problems shared?

Yes — by design, problems 1–10 of AMC 12 typically reuse problems 5–15 of AMC 10. The overlap thins after problem 15, where AMC 12 introduces topics the AMC 10 doesn't cover.

Q: What's the AIME cutoff for each?

Cutoffs vary year-to-year. Recent AMC 10 cutoffs hover around 105–115/150 (top ~2.5%); AMC 12 cutoffs hover around 93–100/150 (top ~5%). The AMC 12 cutoff is lower in raw score because the test is harder.

AMC 10 and AMC 12 share a format — 25 problems, 75 minutes, multiple choice — but they qualify different students for AIME and feed different downstream contests. For 10th graders especially, the choice is non-obvious. This guide walks through it.

Format basics (identical between the two)

25 multiple-choice problems, 5 answer choices each
75 minutes
Calculator: not allowed
Scoring: +6 correct, 0 wrong, +1.5 blank — maximum 150
Held twice a year: A version (early November) and B version (about 10 days later)

Eligibility

AMC 10: grade 10 and below, age 17.5 or under on test day
AMC 12: grade 12 and below, age 19.5 or under on test day

A student in grade 10 can take either. A student in grade 9 or below can take both at the same sitting (A or B). A student in grade 11 or 12 can only take AMC 12.

Topic differences

AMC 10 stays inside high-school Algebra II and below. AMC 12 reaches into pre-calculus and a sliver of calculus-adjacent topics:

AMC 10 only: integer-heavy number theory, basic counting / probability, plane geometry, simple algebra
AMC 12 adds: trigonometry (sin/cos identities, law of sines/cosines), complex numbers, logarithms, exponential growth, conic sections, sequences and series, more advanced functional equations

The first 10 problems on AMC 12 are largely shared with AMC 10 (sometimes shifted up a number or two). The middle problems diverge. The last 5 problems on AMC 12 are typically harder than the equivalent AMC 10 problems even when they cover the same topic.

The scoring rule that changes strategy

Both tests reward leaving questions blank with 1.5 points. This creates a clean mathematical rule:

A blind 1-of-5 guess has expected value 6 × (1/5) = 1.2 points
A blank is 1.5 points guaranteed
Therefore: never blind-guess. Always blank when you have no information.
A 1-of-3 guess has expected value 6/3 = 2.0 points — better than blank
So: guess when you've eliminated 2+ choices, blank otherwise.

This is strategically meaningful. On a 25-problem test, the blank rule is worth roughly 4–6 points to a disciplined competitor over a reflexively-guessing one.

How the AIME cutoff favors each

Because AMC 12 is harder, its AIME cutoff is lower in absolute score. Recent rough cutoffs:

AMC 10: ~105–115 / 150 (top ~2.5%)
AMC 12: ~93–100 / 150 (top ~5%)

Two non-obvious consequences:

If you'd score similarly on both — the question is how the percentile + cutoff combine for you. A capable 10th-grader who'd score ~110 on AMC 10 and ~85 on AMC 12 should take AMC 10: 110 clears the AMC 10 cutoff but 85 doesn't clear AMC 12's.
If you'd score 100+ on both — take both (one A, one B). Two qualification chances, same prep, and the test that gave the higher AIME index becomes your reported score.

Downstream pipeline

AIME scores feed into different round 3 contests:

USAJMO (Junior MO): AMC 10 → AIME → USAJMO. About 250–270 invitations.
USAMO (USA MO): AMC 12 → AIME → USAMO. About 250–270 invitations.

USAMO cutoffs are higher than USAJMO cutoffs (in index terms), because the USAMO selection draws from a stronger pool. A grade-10 student who is a borderline AIME qualifier may find USAJMO selection more reachable than USAMO. A grade-10 student who is a strong AIME scorer may want USAMO exposure earlier — at the cost of facing 12-th-grade-level problems.

A practical decision framework

For 10th graders specifically, here's the rule we've seen work:

Take a past AMC 10 and a past AMC 12 untimed. No calculator, but no clock. Score both honestly.
If AMC 10 untimed ≥ 130 and AMC 12 untimed ≥ 100 → take both (different sittings). You're likely to qualify on both and one will give a higher index.
If AMC 10 untimed ≥ 105 but AMC 12 untimed < 90 → take AMC 10 only. Spend prep time turning your untimed into timed.
If both untimed scores are close to cutoff → take AMC 10. The blank-credit rule rewards conservative students; AMC 10's lower difficulty floor means you bank more guaranteed points on the easy problems.
If you're prepping for USAMO already → AMC 12, regardless of grade. Time spent preparing is more transferable.

Inside Amc2Aime, the AMC 10 and AMC 12 mock papers are independent contests with their own per-question difficulty levels. After each attempt, the L2 review surfaces alternative solutions per problem — if you take both tests you'll quickly see the pattern of which problem types appear on AMC 12 only, and that informs whether to invest in the AMC-12-specific topics (trig, log, complex). The coach will queue paper attempts and topic drills for you on demand.