The American Mathematics Competitions (AMC) system consists of multiple levels, including AMC 8, AMC 10, AMC 12, and AIME. Therefore, completing the AMC 8 does not mark the end of a student’s mathematics competition journey. In recent years, an increasing number of parents and students have begun paying close attention to AMC 10 preparation planning.
In this article, we provide a comprehensive overview of the AMC 10 mathematics competition, including its exam schedule, difficulty level, academic value, preparation strategies, and training pathways, to help students and families make informed decisions.
Part 01: Transitioning from AMC 8 to AMC 10
The AMC competition system is structured in progressive tiers, moving from foundational to advanced levels: AMC 8 → AMC 10 / AMC 12 → AIME → USA(J)MO → IMO. The difficulty increases at each stage, with the general hierarchy as follows:
AIME > AMC 12 > AMC 10 > AMC 8
Eligibility Requirements for Each Level
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AMC 8: Open to students in Grade 8 and below, who are under 14.5 years old on the test day. Typically recommended for students in Grades 6–8.
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AMC 10: Open to students in Grade 10 and below, who are under 17.5 years old on the test day. Commonly recommended for students in Grades 8–10.
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AMC 12: Open to students in Grade 12 and below, who are under 19.5 years old on the test day. Generally suitable for students in Grade 10 and above.
The Trend Toward Younger AMC 8 Participants
In recent years, the AMC 8 has shown a clear trend toward younger participation, with many students in Grades 3 and 4 beginning to engage with the competition. This phenomenon can be attributed to two main factors:
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In contexts where domestic competitions are increasingly restricted, AMC 8 results have become a valuable academic credential during the middle school admissions process.
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Elementary school years are a critical period for developing mathematical thinking. Exposure to high-level competitions can significantly enhance logical reasoning and mathematical intuition.
While students are not required to start their AMC journey with AMC 8, building a solid foundation through AMC 8 preparation can boost confidence and strengthen core mathematical skills. As a result, AMC 8 remains an ideal starting point for many students.
Part 02: Key Differences Between AMC 8 and AMC 10
AMC 8 and AMC 10 are two distinct levels within the AMC competition system. They differ significantly in terms of target participants, exam duration, scoring rules, difficulty, and content coverage.
1. Target Participants
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AMC 8: Students in Grade 8 and below, under 14.5 years old on the test date
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AMC 10: Students in Grade 10 and below, under 17.5 years old on the test date
2. Exam Duration
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AMC 8: 40 minutes
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AMC 10: 75 minutes
3. Scoring System
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AMC 8: Maximum score of 25 points; 1 point per correct answer; no penalty for incorrect answers
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AMC 10: Maximum score of 150 points; 6 points for each correct answer; 1.5 points for each unanswered question; 0 points for incorrect answers
4. Difficulty Level
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AMC 8: Focuses on computational accuracy and foundational reasoning. With systematic practice and attention to detail, students of varying backgrounds have opportunities to achieve strong results.
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AMC 10: Represents a qualitative leap in difficulty. Beyond computation, it emphasizes deeper mathematical thinking and abstract reasoning. As algebraic concepts become more advanced, students must demonstrate stronger conceptual understanding to earn top scores.
5. Content Coverage
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AMC 8: Covers all elementary mathematics, selected middle school topics, and introductory competition concepts. It is often regarded as the highest-level competition for upper elementary and early middle school students.
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AMC 10: Covers a broader range of topics aligned with Grades 9–10 mathematics curricula, including elementary algebra, plane geometry, introductory number theory, and probability. Topics such as trigonometry, advanced algebra, and advanced geometry are not included.
Comparison of AMC 8 and AMC 10 Topics
AMC 8 Topics
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Basic Algebra: Integers, rational and irrational numbers, real numbers, number lines, coordinate planes; linear equations with multiple variables; simple quadratic equations and inequalities; basic sequences; fundamental algebraic techniques
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Basic Geometry: Elementary constructions; Euclidean plane geometry involving points, lines, triangles, quadrilaterals, and circles; perimeter and area of regular figures; introductory solid geometry
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Basic Number Theory: Parity analysis, divisibility properties, least common multiple and greatest common divisor, basic modular arithmetic
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Basic Combinatorics: Venn diagrams; introductory permutations, combinations, and probability; factorials, binomial coefficients, and Pascal’s Triangle
AMC 10 Topics
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Advanced Algebra: Polynomials, Remainder Theorem, Vieta’s formulas, relationships between roots and coefficients, special higher-degree equations; advanced inequalities and mean inequalities; introductory functions, domains and ranges, quadratic, exponential, and logarithmic functions; sequences and advanced algebraic techniques
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Advanced Geometry: Advanced constructions; triangle geometry including the Law of Sines and Cosines, incircles and circumcircles, Stewart’s Theorem, concurrency and collinearity; circles and quadrilaterals, cyclic quadrilaterals; regular polygons; analytic geometry; solid geometry with three-dimensional coordinate systems; Platonic solids and Euler’s formula
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Advanced Number Theory: Integers, fractions, decimals, base conversions; modular arithmetic and complex congruence problems; basic Diophantine equations and advanced number theory strategies
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Advanced Combinatorics: Inclusion–exclusion principle; binomial theorem and related results; advanced permutations, combinations, and probability; recursion, binary methods, and higher-level counting techniques
Part 03: How to Transition from AMC 8 to AMC 10
For students whose AMC 8 results did not meet expectations but who possess solid mathematical foundations, it is advisable to begin learning AMC 10 topics early—such as quadratic functions, advanced geometry, and number theory—during extracurricular study time.
If time permits and short-term results are not a priority, students may first consolidate the AMC 8 knowledge system before transitioning gradually to AMC 10 content.
AMC 10 places greater emphasis on deep mathematical reasoning and complex problem-solving, requiring stronger logical inference and creative thinking skills. Regular practice with logic-based problems and proof-oriented questions can help students develop habits of structured and in-depth thinking.
Past exam papers are an essential resource during preparation. The AMC 10 consists of two versions (A and B) each year, and students are strongly encouraged to practice both in order to fully understand the range of question types and difficulty levels.