American Mathematics Competitions · est. 1950

From AMC 8 to the International Mathematical Olympiad.

A complete English guide to AMC 8, AMC 10/12, AIME and USA(J)MO — eligibility, formats, exam dates, past papers and preparation.

Built for students in China and at international schools worldwide. Twenty-five problems. Forty to seventy-five minutes. One pathway that starts here.

300,000+
students each year
30+
countries
1950
founded by the MAA
25
problems per paper
PROBLEM 23 A B C ω
Fig. — the incircle ω of △ABC, with the altitude from C
ABCDE
PROBLEM SET · I

The competitions, from AMC 8 to the Olympiad

The AMC is a ladder. Each rung is a real examination administered by the Mathematical Association of America, and a strong score opens the next.

Entry · middle school

AMC 8

The introduction to competition mathematics.
Format25 Q / 40 min
EligibilityGrade ≤8 · <15.5
CalculatorsNot allowed
China sittingJanuary
ABCDE
High school · A & B

AMC 10 / 12

The qualifying examinations for the AIME.
Format25 Q / 75 min
Eligibility≤10 / ≤12
Scoring+6 / +1.5 blank
QualifiesAIME
ABCDE
Invitational · proof

AIME & beyond

The road to the United States team.
AIME15 Q / 3 hr
USA(J)MO6 proofs / 9 hr
Leads toIMO team
Entryvia AMC 10/12
ABCDE
AMC 8 AMC 10/12 AIME USA(J)MO IMO
PROBLEM SET · II — for students in China

The China region runs on its own schedule

If you study at a school in mainland China, you register through the China-region channel, sit bilingual (Chinese / English) papers, and follow a local calendar. One rule matters most: students enrolled at American or Canadian schools cannot sit the exam in the China region. We help you register on time and choose the right paper.

PROBLEM SET · III

Practise with real papers, prepare with a plan

The surest preparation for the AMC is the AMC itself — worked through honestly, one problem at a time.

Past papers

Authentic AMC 8, 10, 12, AIME and USA(J)MO papers with answer keys — the single most valuable preparation resource, organised by competition and year.

Browse past papers

Preparation

Recommended textbooks, topic guides and coaching for every level, from a first AMC 8 to AIME qualification — matched to where a student is now.

See preparation resources
QUESTIONS

Frequently asked questions

What is the AMC?

The American Mathematics Competitions (AMC) are a series of examinations administered by the Mathematical Association of America (MAA) since 1950. They begin with the AMC 8 for middle-school students and continue through the AMC 10, AMC 12, the AIME, and the USA (Junior) Mathematical Olympiad — the pathway by which the United States selects its International Mathematical Olympiad team. Each year more than 300,000 students in over 30 countries take part.

Who can take the AMC 8, 10 and 12?

The AMC 8 is open to students in grade 8 or below who are under 15.5 years old on exam day. The AMC 10 is for students in grade 10 or below, under 17.5; the AMC 12 is for grade 12 or below, under 19.5. A younger student may sit a higher exam if they meet its grade and age limits.

How is the AMC scored, and how do I qualify for the AIME?

The AMC 8 awards 1 point per correct answer (maximum 25). The AMC 10 and 12 award 6 points for a correct answer and 1.5 points for a blank, with a maximum of 150. Students with a high enough AMC 10 or AMC 12 score are invited to the AIME, the next stage on the road to the USA(J)MO and the IMO.

How is the China region different?

Students at schools in mainland China register through the China-region channel rather than directly with the MAA, sit bilingual Chinese / English papers, and follow a local exam calendar (AMC 8 in January; AMC 10/12 in November). Students enrolled at American or Canadian schools cannot take the exam in the China region. See our China region guide for full details.

Are calculators allowed?

No. Calculators are not permitted on the AMC 8, AMC 10 or AMC 12. The problems are designed to reward mathematical insight rather than computation.

How should my child prepare?

The most effective preparation is working through authentic past papers under timed conditions, then carefully studying the solutions. Pair this with targeted study of the core topics — counting and probability, number theory, algebra and geometry — at a level matched to the student. Our preparation resources and past papers are organised for exactly this.