Foundations (AMC 8)
Build your core toolbox first: algebra, geometry, counting, and number theory fundamentals that show up across AMC and early AIME problems.
Focus on understanding patterns and writing clean solutions before moving on.
Modules Progress
Problems Progress
Number Theory Basics
Fluency with arithmetic and foundational number theory.
Arithmetic and Number Theory Basics
Divisibility, primes, gcd, and modular arithmetic intuition for AMC 8 and AMC 10.
Updated: 5 days ago
Linear Diophantine Equations
Solving equations of the form ax + by = c using the Euclidean algorithm and Bezout's Identity.
Updated: 5 days ago
Chicken McNugget Theorem
Determine the largest value that cannot be represented as a nonnegative combination of two coprime integers.
Updated: 5 days ago
Algebra Basics
Linear equations, factoring patterns, and core manipulation skills.
Algebra Basics
Linear equations, factoring, and manipulating expressions with confidence.
Updated: 5 days ago
Exponent Rules
Laws of exponents for simplifying and solving equations.
Updated: 5 days ago
Quadratic Identities
Difference of squares and binomial expansions.
Updated: 5 days ago
Quadratic Formula and Discriminant
Solving quadratics and classifying roots
Updated: 5 days ago
Systems of Equations
Substitution, elimination, and symmetric tactics.
Updated: 5 days ago
Substitution Techniques
Replace repeated structure to lower degree and simplify.
Updated: 5 days ago
Simon's Favorite Factoring Trick
Adding constants to factors multi-variable equations
Updated: 5 days ago
Cubic Factorizations
Sum and difference of cubes plus binomial cubes.
Updated: 5 days ago
Algebra Tools
Vieta's formulas and polynomial root transformations.
Averages and Sequences
Means, arithmetic and geometric sequences, and telescoping sums.
Mean, Median, Mode, and Harmonic Mean
Core averages and how to interpret them in contest problems.
Updated: 5 days ago
Arithmetic Sequences
Constant differences, term formulas, and sum tricks.
Updated: 5 days ago
Geometric Sequences
Constant ratios, finite sums, and convergence.
Updated: 5 days ago
Telescoping Sums and Products
Use cancellation after algebraic rewriting.
Updated: 5 days ago
Intro Inequalities
AM-GM, Cauchy-Schwarz, and foundational bounding techniques.
AM-GM Inequality
A standard tool for bounding sums and products.
Updated: 5 days ago
Cauchy-Schwarz Inequality
A core inequality for bounds and maximization.
Updated: 5 days ago
Inequalities Foundations
A comprehensive guide to interval bounding, absolute value geometry, quadratic optimization, and the QM-AM-GM-HM means chain.
Updated: 5 days ago
Counting Fundamentals
Permutations, combinations, inclusion-exclusion, and pigeonhole.
Counting Fundamentals
Rule of product, basic permutations and combinations, and careful casework.
Updated: 5 days ago
Pascal's Triangle & Binomial Theorem
Pascal's triangle structure and its symmetry, hockey stick identity, and basic binomial expansion.
Updated: 3 days ago
Inclusion-Exclusion
Basic Two and three set inclusion exclusion, Venn diagram interpretation, and methods of solveing "at least one" problems.
Updated: 5 days ago
Pigeonhole Principle
The pigeonhole principle, and its applications to counting, number theory, and combinatorial geometry
Updated: 5 days ago
Stars and Bars
Distributing identical objects into distinct "boxes", positive integer solutions, and distributions that are constraint
Updated: 5 days ago
Geometry Basics
Triangles, similarity, circles, and core area formulas.
Geometry Basics
Angle chasing, triangle facts, area, and circles.
Updated: 5 days ago
Triangle Angle Sum
Interior and exterior angle facts for triangles.
Updated: 5 days ago
Triangle Area Formulas
Base-height, Heron, and trigonometric area.
Updated: 5 days ago
Special Triangles
Equilateral and isosceles triangle properties.
Updated: 5 days ago
Right Triangles and Pythagorean Triples
Pythagorean theorem and common triples.
Updated: 5 days ago
Special Right Triangles
30-60-90 and 45-45-90 ratios.
Updated: 5 days ago
Medians and the Centroid
Median properties and centroid ratios.
Updated: 5 days ago
Angle Bisectors
The angle bisector theorem and length facts.
Updated: 5 days ago
Altitudes and the Orthocenter
Altitude facts and area relationships.
Updated: 5 days ago
Triangle Similarity
AA, SAS, SSS similarity and scale factors.
Updated: 5 days ago
Basic Proportionality (Thales)
Parallel lines divide sides proportionally.
Updated: 5 days ago
Law of Sines
Relate sides and angles using $\sin$.
Updated: 5 days ago
Law of Cosines
Generalized Pythagorean theorem for any triangle.
Updated: 5 days ago
Inscribed and Central Angles
Inscribed angle theorem and Thales' theorem.
Updated: 5 days ago
Special Quadrilaterals
Parallelograms, rectangles, rhombi, and trapezoids.
Updated: 5 days ago
Coordinate Geometry Basics
Distance, midpoint, slope, and line equations.
Word Problems
Translating stories into equations using rates, mixtures, and ratios.
Intro to Probability
Sample spaces, complements, conditional probability, and expected value.
Uncategorized
Auto-discovered modules not yet placed in a syllabus chapter.