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How Different Are AMC 8 and AMC 10?

The AMC 8 and AMC 10 are globally recognized mathematics competitions organized by the Mathematical Association of America (MAA). Their scores are widely accepted by international schools and universities, making them an important academic credential for students applying to overseas institutions. Beyond admissions value, AMC competitions are also an effective way to develop mathematical thinking, problem-solving ability, and logical reasoning.

So, how different are AMC 8 and AMC 10 in terms of difficulty, content, and target participants? And how should students in different grade levels choose the most suitable AMC competition?

Overview of the U.S. Mathematics Competition System

  • IMO (International Mathematical Olympiad)
    The highest-level international mathematics competition. Students represent their national teams and compete with top math talents worldwide.

  • USAMO (USA Mathematical Olympiad)
    Comparable to China’s CMO. Participation is limited to U.S. citizens and permanent residents. It serves as the selection process for the U.S. IMO team.

  • AIME (American Invitational Mathematics Examination)
    Comparable to a provincial-level team competition. Held in February, with a maximum score of 15 points.

    • Scores of 7–10 are considered strong for applications to U.S. Top 30 universities

    • Scores of 10 or above qualify students for USAMO

  • AMC 10 / AMC 12
    Held every November, comparable to middle and high school math league competitions.

    • Top 2.5% of AMC 10 and top 5% of AMC 12 advance to AIME and receive the Honor Roll (HR) distinction.

  • AMC 8
    Held every January. It is a non-selective, introductory competition focused on building interest and confidence in mathematics, similar to elementary-level math contests in China.

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1. AMC 8 Mathematics Competition

AMC 8 is a beginner-level mathematics competition designed to introduce students to competitive math and cultivate interest and confidence.

Eligibility

  • Designed for students in Grade 8 and below

  • Typically taken by students in Grades 4–6 in China

  • Maximum age: 14.5 years

  • No restrictions on nationality or school enrollment

Competition Format

  • Duration: 40 minutes

  • Questions: 25 multiple-choice problems

  • Scoring:

    • Correct answer: 1 point

    • Incorrect or unanswered: 0 points

    • No penalty for wrong answers

    • Maximum score: 25

  • Language: Bilingual (English & Chinese)

Content Coverage

AMC 8 focuses on core elementary and middle school math concepts. While closely aligned with school curricula, it emphasizes flexible thinking and problem-solving strategies.

  • Basic Algebra: integers, fractions, decimals, percentages, ratios, simple equations

  • Geometry: area and perimeter of plane figures, surface area and volume of solids, transformations

  • Number Theory: factors and multiples, primes and composites, parity, divisibility rules

  • Counting & Probability: basic counting principles, permutations, simple probability

Awards

  • Distinguished Honor Roll (DHR): Top 1% worldwide

  • Honor Roll (HR): Top 5% worldwide

2. AMC 10 Mathematics Competition

AMC 10 is an intermediate to advanced competition and serves as a key stepping stone to higher-level contests such as AIME and USAMO.

Eligibility

  • Open to students in Grade 10 and below

  • Maximum age: 17.5 years

  • No nationality or school restrictions

Competition Format

  • Duration: 75 minutes

  • Questions: 25 multiple-choice problems

  • Scoring:

    • Correct answer: 6 points

    • Incorrect answer: 0 points

    • Unanswered question: 1.5 points

    • Maximum score: 150

  • Language: Bilingual (English & Chinese)

Content Coverage

AMC 10 covers mathematics from middle school through early high school. The difficulty is significantly higher than AMC 8 and focuses on advanced reasoning and integrated problem-solving skills.

  • Algebra: linear and quadratic functions, inequalities, polynomials, sequences

  • Geometry: similar triangles, circle properties, trigonometry, coordinate geometry

  • Number Theory: modular arithmetic, Fermat’s Little Theorem, Euler’s theorem, base conversion

  • Combinatorics: advanced counting, recursion, inclusion–exclusion principle, probability extensions

Note: Calculus and university-level mathematics are not included.

Awards

  • Distinguished Honor Roll (DHR): Top 1% worldwide

  • Honor Roll (HR): Top 5% worldwide

  • AIME Qualification: Top 2.5% globally (typically scores around 120+)

3. How Should Students Choose Between AMC 8, AMC 10, and AMC 12?

Grades 4–6

  • Focus exclusively on AMC 8

  • Build a strong foundation in competition math and aim for Honor Roll or Distinguished Honor Roll

Grades 7–8

  • Option 1: Prepare for both AMC 8 and AMC 10

    • Target AMC 10 Honor Roll as the primary goal

    • Aim for Top 1% in AMC 8 if possible

  • Option 2: Focus on AMC 8

    • Recommended for students with weaker foundations

    • Take advantage of lower-age award opportunities and transition gradually to AMC 10

  • Option 3: Directly prepare for AMC 10

    • Suitable for students with strong math skills or previous high AMC 8 scores

Grades 9–10

  • AMC 10 is the primary choice

    • Students at this level are no longer eligible for AMC 8

  • Consider AMC 12

    • Recommended for students with solid math foundations seeking greater challenges and higher-level recognition