Competition Overview

AMC Competition Rules and Structure

The American Mathematics Competitions (AMC) include multiple contests designed for students at different grade levels: AMC 8, AMC 10, AMC 12, and the advanced invitational exam AIME.

Both AMC 10 and AMC 12 are offered in A and B versions. The only difference between the A and B exams is the exam date; the format, difficulty, and content are the same.

Competition Levels by Difficulty

  • AMC 8: Middle school–level competition

  • AMC 10 / AMC 12: High school–level competitions

  • AIME (American Invitational Mathematics Examination):
    An invitational exam for high scorers on AMC 10 and AMC 12

    • Approximately top 2.5% of AMC 10 participants

    • Approximately top 5% of AMC 12 participants

  • USAMO / USAJMO (USA Mathematical Olympiad / USA Junior Mathematical Olympiad):
    Elite invitational competitions for top AIME qualifiers.

    USAMO is limited to students studying in the United States or Canada, or U.S. citizens studying abroad.

  • IMO (International Mathematical Olympiad):
    Held annually and hosted by a different country each year. Outstanding performers from USA(J)MO may enter the Mathematical Olympiad Program (MOP), from which the U.S. team is selected to compete at the IMO.

Eligibility

  • AMC 8: Students in Grade 8 or below

  • AMC 10 / AMC 12: High school students in Grade 10 or below and Grade 12 or below, respectively

  • AIME and USA(J)MO: Advanced qualification rounds for top AMC 10/12 performers and selection pathways for the U.S. Mathematical Olympiad team

Exam Details Comparison

Category AMC 8 AMC 10 AMC 12 AIME
Eligibility Grade 8 or below, ≤14.5 years old Grade 10 or below, ≤17.5 years old Grade 12 or below, ≤19.5 years old Grade 12 or below
Duration 40 minutes 75 minutes 75 minutes 180 minutes
Language Bilingual (English & Chinese) Bilingual (English & Chinese) Bilingual (English & Chinese) Bilingual (English & Chinese)
Format 25 multiple-choice questions (5 options each) 25 multiple-choice questions 25 multiple-choice questions 15 short-answer questions
Scoring 25 points total; +1 correct, 0 incorrect/blank 150 points total; +6 correct, +1.5 blank, 0 incorrect Same as AMC 10 15 points total; +1 correct, 0 incorrect/blank
Content Scope Middle school math: counting & probability, estimation, proportional reasoning, elementary geometry (including Pythagorean theorem), spatial visualization, real-world applications, and data interpretation. Harder problems may involve basic linear algebra, quadratic equations, or analytic geometry. Middle school to early high school math: elementary algebra, basic geometry (area, volume, Pythagorean theorem), introductory number theory and probability. Excludes trigonometry and advanced topics. Full high school math curriculum including trigonometry, advanced algebra, and advanced geometry. Calculus is not included. More challenging than AMC 10/12; open only to high scorers invited based on AMC results.

AMC Awards and Honors

AMC 8 Awards

Global Individual Awards

  • Perfect Score Award: Score of 25

  • Distinguished Honor Roll: Top 1% worldwide

  • Honor Roll: Top 5% worldwide

  • Achievement Roll: Grade 6 and below scoring 15 or higher

Global School Awards

  • School Honor Roll: Sum of top 3 student scores ≥ 66

  • School Merit Roll: Sum of top 3 student scores between 50–65

AMC 10 / AMC 12 Awards

Global Individual Awards

New Awards

  • Top 10% Honor Roll

  • Top 25% Honor Roll

Existing Awards

  • Perfect Score Award: Score of 150

  • Honor Roll of Distinction: Top 1% worldwide

  • Distinction: Top 5% worldwide

  • AMC 10 Certificate of Achievement: Grade 8 or below scoring 90+

  • AMC 12 Certificate of Achievement: Grade 10 or below scoring 90+

Global School Awards

  • School Honor Roll: Top 3 student scores total ≥ 400

  • School Merit Roll: Top 3 student scores total between 300–399

AIME Certificates

  • AIME QUAL Certificate: Awarded to students who meet the AIME qualification cutoff

  • Certificate of Participation: Awarded to all AIME participants

All participants are eligible to receive a digital certificate.

How to Receive AMC Certificates

For In-Person Exams

  1. School Registration: Contact your school teacher or coordinator

  2. Test Center Registration: Certificates are distributed by the test center or hosting organization

  3. Contact Us: Scan the QR code below to reach our academic advisors for assistance

For Online Exams

Students who take the AMC online may log in to the official website 6–8 weeks after the competition using their registration account to download certificates directly.