Every AMC competition, explained

The AMC has been the United States’ leading mathematics competition since 1950. More than 300,000 students in over 30 countries take part each year. You do not register as an individual: schools, colleges, math circles and learning centres act as test sites, and international candidates enter through the AMC International programme.

The contests form a single pathway. You begin with the AMC 8 in middle school, move to the AMC 10 or AMC 12 in high school, and a strong score on either earns an invitation to the AIME. The highest AIME scorers are invited to the USA(J)MO — the proof-based olympiad from which the United States selects its team for the International Mathematical Olympiad.

The competitions at a glance

Competition	Eligibility	Format	Scoring	Calculator
AMC 8	Grade 8 or below; under 15.5 on exam day	25 multiple-choice questions, 40 minutes	1 point per correct answer; maximum 25	Not allowed
AMC 10	Grade 10 or below; under 17.5 on exam day	25 multiple-choice questions, 75 minutes (A & B dates)	+6 correct, +1.5 blank, 0 incorrect; maximum 150	Not allowed
AMC 12	Grade 12 or below; under 19.5 on exam day	25 multiple-choice questions, 75 minutes (A & B dates)	+6 correct, +1.5 blank, 0 incorrect; maximum 150	Not allowed
AIME	Top AMC 10 / AMC 12 scorers (by invitation)	15 questions, 3 hours (I & II dates)	Integer answers 0–999; 1 point each, maximum 15	Not allowed
USA(J)MO	Top AIME qualifiers; US / Canada students or US citizens abroad	6 proof questions, 9 hours over 2 days	Each proof marked out of 7; maximum 42	Not allowed

Both the AMC 10 and AMC 12 are offered as an A and a B paper. The only difference is the date — the format, difficulty and syllabus are identical, and a student may sit either or both. The AMC 12 covers the full high-school curriculum, including trigonometry and advanced algebra and geometry, but does not include calculus.

How qualification flows

Each rung opens the next, and you only ever step up by performing well on the rung below:

• AMC 10 / AMC 12 → AIME. Roughly the top 2.5% of AMC 10 participants and the top 5% of AMC 12 participants are invited to the AIME. If you qualify on more than one paper, your best result is used.
• AIME → USA(J)MO. A combined AMC and AIME index determines who advances to the USA Junior Mathematical Olympiad (from the AMC 10) or the USA Mathematical Olympiad (from the AMC 12).
• USA(J)MO → IMO. The strongest olympiad performers are invited to the Mathematical Olympiad Program, from which the United States team for the International Mathematical Olympiad is chosen.

The AMC 8 does not feed directly into the AIME, but it is the natural starting point: it builds the counting, number-theory, geometry and probability foundations that the later papers reward.

Calculator policy

Calculators are not permitted on the AMC 8, AMC 10 or AMC 12, nor on the AIME or USA(J)MO. The problems are written to reward mathematical insight rather than computation, so a calculator would give no advantage. Bring pencils and scratch paper; everything else is solved by hand. Full rules are set out on our AMC policy page.

Exact exam dates, registration windows and fees are confirmed each season. For the current calendar — and the rules that apply where you study — contact us or see the China-region schedule below.