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AMC 8 vs. AMC 10: Key Differences, Competition Pathways, and Preparation Resources

As two core competitions in the AMC (American Mathematics Competitions) series, AMC 8 and AMC 10 often leave parents and students in Grades 7–8 uncertain about which contest to choose.
What are the key differences between AMC 8 and AMC 10?
How should Grade 7–8 students decide between AMC 8 and AMC 10?

This article provides a comprehensive comparison and practical guidance.

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Key Differences Between AMC 8 and AMC 10

Overview Comparison

Target Participants

  • AMC 8: Students in Grade 8 and below

  • AMC 10: Students in Grade 10 and below

Exam Schedule

  • AMC 8: Usually held in January

  • AMC 10: Held annually in November (A and B versions)

Exam Duration

  • AMC 8: 40 minutes

  • AMC 10: 75 minutes

Number of Questions

  • Both competitions consist of 25 multiple-choice questions

Scoring System

  • AMC 8: Maximum score of 25; 1 point per correct answer

  • AMC 10: Maximum score of 150;

    • 6 points for each correct answer

    • 1.5 points for unanswered questions

    • No penalty for incorrect answers

Content Scope

  • AMC 8 focuses on integers, fractions, decimals, percentages, ratios, number theory, basic geometry (area and volume), probability, statistics, and logical reasoning.

  • AMC 10 covers a broader and deeper range of topics, including elementary algebra, advanced geometry (such as the Pythagorean theorem), number theory, and combinatorics.

Difficulty Level

  • AMC 8: Moderate difficulty, emphasizing foundational math thinking and logical reasoning. The level is comparable to advanced elementary or early middle school math competitions.

  • AMC 10: Significantly more challenging, requiring strong problem-solving skills and flexible application of mathematical concepts. The difficulty is comparable to advanced middle school or early high school math competitions.

Academic Value

  • AMC 8: Helpful for middle school advancement and international school applications as a demonstration of mathematical ability.

  • AMC 10: Highly recognized in both domestic and international high school and university applications, serving as an important academic credential.

AMC 8 vs. AMC 10: Topic Coverage Comparison

AMC 8 Core Topics

  • Basic algebra: integers, rational and irrational numbers, real numbers, number lines, coordinate systems

  • Linear equations, simple quadratic equations, inequalities

  • Introductory sequences and basic algebraic techniques

  • Euclidean plane geometry: points, lines, triangles, quadrilaterals, circles

  • Perimeter, area, and volume of regular figures

  • Introductory solid geometry

  • Elementary number theory: parity, divisibility, GCD and LCM, basic modular arithmetic

  • Introductory combinatorics and probability, Venn diagrams, permutations, combinations, factorials, Pascal’s triangle

AMC 10 Advanced Topics

  • Polynomial algebra, Remainder Theorem, Vieta’s formulas, higher-degree equations

  • Advanced inequalities and mean inequalities

  • Functions: domain and range, quadratic, exponential, logarithmic, and basic trigonometric functions

  • Advanced geometry: sine and cosine laws, incircles and circumcircles, Stewart’s Theorem, concurrency and collinearity

  • Introductory analytic geometry

  • Advanced number theory: modular arithmetic, Diophantine equations, base conversions

  • Advanced combinatorics: inclusion–exclusion principle, binomial theorem, recursion, advanced counting techniques

Newly Introduced Topics from AMC 8 to AMC 10

Sequences

  • Arithmetic and geometric sequences, explicit formulas, recursive formulas, summation techniques, and complex applications

Linear Functions

  • Graphs and properties of linear functions, linear inequalities, coordinate geometry, and word problems involving linear systems

Permutations, Combinations, and Probability

  • Fundamental counting principles, permutations, combinations, probability rules, and applied problem solving

Advanced Operations

  • GCD and LCM applications, sums and products of consecutive integers, advanced factorization techniques, exponent rules, and equation solving

AMC 8 and AMC 10 Awards

AMC 8 Awards

  • Perfect Score Award (25 points)

  • Distinguished Honor Roll (Top 1% worldwide)

  • Honor Roll (Top 5% worldwide)

  • Achievement Roll (Grade 6 and below with a score of 15 or higher)

AMC 10 Awards

  • Distinguished Honor Roll (Top 1% worldwide)

  • Honor Roll (Top 5% worldwide)

  • Achievement Roll (Grade 8 and below with a score of 90 or higher)

  • AIME Qualification Certificate (for students who reach the AIME cutoff score)

AMC 8 and AMC 10 Advancement Pathways

  • AMC 8 does not lead directly to higher competitions, but a Top 1% score provides a strong advantage for middle school advancement and school applications.

  • AMC 10: Approximately the top 2.5% qualify for AIME, which is a required step toward USAMO, the U.S. national mathematics olympiad selection process. AMC 10 performance is highly valued by top universities such as Yale and Stanford.

How Should Grade 7–8 Students Choose Between AMC 8 and AMC 10?

1. Clarify Goals and Academic Foundation

Competition Goals

  • For middle school advancement or international school applications, AMC 8 Top 1% results are highly effective.

  • For overseas high school or university applications, AMC 10 qualification for AIME carries greater academic weight.

  • Students seeking confidence-building and early competition exposure may prefer AMC 8, while those interested in high-level challenges may attempt AMC 10.

Academic Readiness

  • AMC 8 readiness: Strong mastery of elementary olympiad math and basic middle school algebra.

  • AMC 10 readiness: Solid AMC 8 foundation plus knowledge of sequences, quadratic functions, solid geometry, and probability, along with fast problem-solving skills.

2. Grade-Specific Recommendations

Grade 7 Students

  • Weaker foundation: Focus on AMC 8, aiming for Top 5% or Top 1%, then transition to AMC 10 the following year.

  • Moderate foundation: Prepare for both AMC 8 (Top 1%) and AMC 10 (Achievement Roll), supplementing advanced topics.

  • Strong foundation: Directly challenge AMC 10 with goals of Top 5% or AIME qualification.

Grade 8 Students

  • Average foundation: Prioritize AMC 8 Top 1% while building AMC 10 fundamentals for future competition.

  • Strong foundation: Fully commit to AMC 10 with goals of Top 1% or AIME qualification, using AMC 8 as additional practice if desired.

3. Key Factors to Consider

  • Time Commitment: AMC 8 preparation typically requires 3–6 months, while AMC 10 often requires 6–12 months.

  • Problem-Solving Style: AMC 8 favors steady logic and calculation; AMC 10 rewards creative and flexible thinking, especially in the final problems.

  • Long-Term Planning: Short-term awards favor AMC 8, while long-term olympiad pathways require early AMC 10 exposure.

To support informed decision-making and effective preparation, teachers have compiled official AMC 8 and AMC 10 past problems. Practicing these materials allows students to accurately assess difficulty levels and determine which competition best suits their abilities.

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