AMC 8, AMC 10 & AMC 12 — Complete Guide

The AMC (American Mathematics Competition) series, administered by the Mathematical Association of America (MAA), is the official entry point into the United States’ national mathematics olympiad pipeline. Participation opens doors to AIME, USAJMO, USAMO, and ultimately the International Mathematical Olympiad (IMO). AMC scores are also noted favorably by selective college admissions offices.

AMC 8

Who: Students in Grade 8 and below (under 14.5 years old)

Format: 25 multiple-choice questions

Time: 40 minutes

Scoring: 1 point per correct answer; no penalty for wrong answers. Max score: 25.

When: January (school year)

Topics: Arithmetic, basic algebra, geometry, probability, number theory — all at middle school level

Distinctions: Honor Roll (top ~5%), Distinguished Honor Roll (top ~1%, score 18+)

AMC 10

Who: Students in Grade 10 and below (under 17.5 years old)

Format: 30 multiple-choice questions

Time: 75 minutes

Scoring: 6 points correct, 1.5 deducted wrong, 1.5 for blank. Max: 150.

When: Two dates — AMC 10A (Nov) and AMC 10B (Nov)

Topics: Through 10th grade math (no precalculus)

AIME Qualifier: Top ~2.5% (score 103.5+ on 10A/10B historically)

AMC 12

Who: Students in Grade 12 and below (under 19.5 years old)

Format: 30 multiple-choice questions

Time: 75 minutes

Scoring: 6 points correct, 1.5 deducted wrong, 1.5 for blank. Max: 150.

When: Two dates — AMC 12A (Nov) and AMC 12B (Nov)

Topics: Through precalculus (including logarithms, complex numbers, vectors)

AIME Qualifier: Top ~5% (score 85.5+ on 12A/12B historically)

The AMC Competition Pyramid

IMO (6 students)

USAMO / USAJMO (~500)

AIME (~7,500)

AMC 10 / AMC 12 (~300,000)

AMC 8 (~200,000)

Competition	Who Qualifies	Format	Key Details
AMC 8	All students Grade 8 & below	25 MCQ, 40 min	Entry level; no prerequisite
AMC 10 / AMC 12	Grades 10/12 & below by age	30 MCQ, 75 min	Two sittings (A & B); students may take both
AIME	Top ~2.5% AMC 10 / top ~5% AMC 12	15 integer-answer questions, 3 hours	Answers are integers 0–999; no multiple choice
USAJMO	Top AIME + AMC 10 scorers	6 proof problems over 2 days (9 hrs)	For students who qualified via AMC 10
USAMO	Top AIME + AMC 12 scorers	6 proof problems over 2 days (9 hrs)	Typically ~500 qualifiers per year
USAMO / MOP	Top USAMO scorers	Mathematical Olympiad Program (summer)	~60 students attend; IMO team selected here
IMO	6-member US team selected from MOP	6 problems over 2 days (4.5 hrs each)	International competition; gold/silver/bronze medals

AMC Scoring — AIME Index

For USAJMO/USAMO qualification, a combined index is used:

USAJMO Index: AMC 10 score + 10 × AIME score
USAMO Index: AMC 12 score + 10 × AIME score

Historically, USAJMO cutoff is ~215–230 and USAMO cutoff is ~215–245 (varies by year).

💡 When to Start AMC Preparation

Students aiming for AIME qualification should begin focused AMC prep by Grade 6–7 for AMC 8, and Grade 9 for AMC 10. Key prerequisites: strong arithmetic and number theory foundations for AMC 8; Algebra I, Geometry, and early number theory for AMC 10. RLC’s Math Competitions Club and advanced math tutoring programs build these foundations systematically.

How to Prepare for AMC

Master the prerequisite topics: For AMC 8: arithmetic, fractions, percents, basic geometry, combinatorics. For AMC 10/12: algebra, geometry, combinatorics, number theory, and (for AMC 12) trigonometry and complex numbers.
Practice past exams: All past AMC exams are freely available at Art of Problem Solving (AoPS). Practice timed and untimed.
Study problem-solving strategies: Pattern recognition, casework, complementary counting, modular arithmetic, and proof by contradiction are frequently tested.
Focus on accuracy, not speed initially: AMC penalizes wrong answers (10/12 only). A blank answer (1.5 pts) is better than a guess that’s wrong (0 pts) unless you can eliminate 3+ choices.
Join a math competition club: Working with peers on hard problems accelerates growth dramatically.

Math Competitions Club Talk to an Advisor

*Score cutoffs and competition details change year to year. Always verify current cutoffs at maa.org/amc. Statistics reflect 2023–2024 competition year.