AMC 10 Syllabus
The AMC 10 covers high school mathematics up to grade 10. It excludes trigonometry, complex numbers, and logarithms, which appear in the AMC 12.
Algebra Topics
- Equations and Inequalities Solving linear and quadratic equations, systems, absolute values, and inequalities.
- Polynomials Operations, factor and remainder theorems, and Vieta's formulas for roots.
- Functions Properties of functions, composition, and simple functional equations.
- Sequences and Series Arithmetic and geometric progressions, including sums of finite series.
Geometry Topics
- Euclidean Geometry Properties of triangles, quadrilaterals, circles, and other polygons.
- Area and Volume Formulas for standard 2D and 3D shapes, including composite figures.
- Coordinate Geometry Using coordinates to solve problems with lines, circles, and distances.
- Pythagorean Theorem Applications in various 2D and 3D geometric contexts.
Number Theory and Combinatorics
- Divisibility and Primes Prime factorization, GCD, LCM, and the Euclidean algorithm.
- Modular Arithmetic Congruences, properties of remainders, and solving linear congruences.
- Counting Principles Permutations, combinations, and the principle of inclusion-exclusion.
- Elementary Probability Calculating probabilities in discrete sample spaces and basic geometric probability.