The AMC 10 is a multiple-choice mathematics competition designed for students in grades 10 and below. The contest consists of 25 multiple-choice questions. For each question, 6 points are awarded for a correct answer, 1.5 points for leaving it blank, and 0 points for an incorrect answer, for a maximum score of 150.
The AMC 10 primarily tests students’ understanding and application of mathematics in the following areas: algebra, geometry, number theory, probability and statistics, and combinatorics. The exam does not include calculus or trigonometry.
Topic Distribution and Key Focus Areas
| Module | Percentage | High-Frequency Topics |
|---|---|---|
| Algebra | ~30%–35% | Quadratic functions, equations and inequalities, series and summations, polynomials, absolute value and floor functions, advanced algebraic manipulation |
| Geometry | ~25%–30% | Similar triangles, circle properties (inscribed angles, tangents), Pythagorean theorem, area calculations, auxiliary lines, coordinate geometry, solid geometry |
| Number Theory | ~20% | Prime factorization, divisibility, modular arithmetic, parity analysis, number bases |
| Combinatorics | ~15%–20% | Permutations and combinations, inclusion–exclusion principle, probability calculations, recursive counting |
Difficulty Structure of the AMC 10
The AMC 10 is carefully designed with a clear difficulty progression, allowing it to distinguish students at different competitive levels.
Basic Level (Questions 1–10)
These problems focus on fundamental mathematical concepts and computational skills. The difficulty is relatively low, and students are expected to solve them quickly and accurately to save time for later questions.
Intermediate Level (Questions 11–20)
These questions involve more complex concepts and problem-solving strategies. Strong logical reasoning and analytical ability are required. This section is critical in distinguishing average participants from award-level competitors.
Advanced Level (Questions 21–25)
The most challenging part of the contest, designed to identify top-performing students. These problems require deep conceptual understanding, flexible integration of multiple topics, and sometimes creative or non-routine thinking. Only a small number of elite students can solve all of them.
Example: AMC 10 (2024) Topic and Difficulty Distribution
| Question | Main Topic | Module | Difficulty |
|---|---|---|---|
| 1 | Permutations (position counting) | Arithmetic / Algebra | ★ |
| 2 | Factorials and factorization | Algebra | ★★ |
| 3 | Absolute values and inequalities (with π approximation) | Algebra / Number Theory | ★★ |
| 4 | Sequences and periodic arrangements | Combinatorics | ★★ |
| 5 | Optimization of odd sums (properties of squares) | Algebra / Number Theory | ★★ |
| 6 | Factorization and minimum perimeter | Geometry / Number Theory | ★★★ |
| 7 | Modular arithmetic and exponent properties | Number Theory | ★★ |
| 8 | Factorization and number theory (units digit of products) | Number Theory | ★★ |
| 9 | Algebraic identities and averages | Algebra | ★★ |
| 10 | Geometric similarity and area ratios | Geometry | ★★★ |
| 11 | Pythagorean theorem and equation solving | Geometry / Algebra | ★★★★ |
| 12 | Set theory and optimization | Combinatorics | ★★★ |
| 13 | Square root expansion and quadratic optimization | Algebra / Number Theory | ★★★ |
| 14 | Geometric area and probability | Geometry / Probability | ★★★★ |
| 15 | Statistics (extremes, median, and mean) | Algebra / Statistics | ★★★★ |
| 16 | Parity analysis and operational strategy | Combinatorics | ★★★★ |
| 17 | Permutations with repeated grouping | Combinatorics | ★★★★ |
| 18 | Modular arithmetic and Euler’s theorem | Number Theory | ★★★★ |
| 19 | Line properties and rational/irrational analysis | Algebra / Number Theory | ★★★★ |
| 20 | Constrained permutations | Combinatorics | ★★★★★ |
| 21 | Geometric constructions with excircles and the Pythagorean theorem | Geometry | ★★★★★ |
| 22 | Permutations and factorization (factorial analysis) | Combinatorics | ★★★★★ |
| 23 | Fibonacci sequence and recurrence relations | Number Theory / Sequences | ★★★★★ |