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.

Start Learning >Join Community

Basic Arithmetic and Notation

0/35

Speed, mental math, and fluency with core numerical operations.

Integer Operations and Notations I

Navigating negative numbers and distance on a number line without sign errors.
Updated: 2 weeks ago

Integer Operations and Notations II

Navigating negative numbers and distance on a number line without sign errors.
Updated: 2 weeks ago

Proportional Reasoning I

Fractions, Proportions, Types of Variations and Scaling.
Updated: 2 weeks ago

Proportional Reasoning II

Fractions, Proportions, Types of Variations and Scaling.
Updated: 2 weeks ago

Kinematics and Rates

Solving tricky problems involving rate, proportions, and distance-rate formula
Updated: 2 weeks ago

Data

0/58

Interpreting data, central tendency, and organizing information visually.

Intro to Statistics

Measures of central tendency mean, median, mode, and range including definitions, worked examples, when to use each, and common pitfalls.
Updated: 2 weeks ago

Chart and Graph Interpretation I

Extracting data from histograms, pie charts, and complex bar graphs.
Updated: 2 weeks ago

Chart and Graph Interpretation II

Extracting data from histograms, pie charts, and complex bar graphs.
Updated: 2 weeks ago

Venn Diagrams and Basic Sets

Visually organizing overlapping data categories.
Updated: 2 weeks ago

Algebra

0/338

Translating problems into equations, solving systems, and pattern recognition.

Linear Relationships and Word Problems

What linear relationships are, how to translate word problems into linear equations, and how to read slope and y-intercept from slope-intercept and standard form.
Updated: 2 weeks ago

Linear Equations and Inequalities

How to solve linear equations and inequalities in one or two variables, including equations with fractions and negative coefficients, and how to determine the number of solutions an equation has.
Updated: 2 weeks ago

Systems of Equations

Substitution, elimination, and symmetric tactics.
Updated: 2 weeks ago

Defined Operations

Solving problems involving custom mathematical operators and rules (e.g., x∇y).
Updated: 2 weeks ago

Exponent Rules

Laws of exponents for simplifying and solving equations.
Updated: 2 weeks ago

Quadratic Formula and Discriminant

Solving quadratics and classifying roots
Updated: 2 weeks ago

Polynomial Factoring and Identities

polynomial factoring methods.
Updated: 2 weeks ago

Simon's Favorite Factoring Trick

Adding constants to factors multi-variable equations
Updated: 2 weeks ago

Substitution Techniques

Replace repeated structure to lower degree and simplify.
Updated: 2 weeks ago

Arithmetic Sequences

Constant differences, term formulas, and sum tricks.
Updated: 2 weeks ago

Geometric Sequences

Constant ratios, finite sums, and convergence.
Updated: 2 weeks ago

The Extremal Principle

Finding the theoretical maximum or minimum limits of a given scenario.
Updated: 2 weeks ago

Geometry

0/264

Angles, triangles, circles, and spatial reasoning for contest problems.

Geometry Basics

Angle chasing, triangle facts, area, and circles.
Updated: 2 weeks ago

Angle Chasing and Parallel Lines

Navigating transversals, alternate interior angles, and supplementary relationships.
Updated: 2 weeks ago

Triangle Fundamentals

Area, perimeter, triangle inequality, and isosceles/equilateral properties.
Updated: 2 weeks ago

Triangle Types & Properties

A complete guide to triangle classification by sides and angles, fundamental theorems (Angle Sum, Exterior Angle, Triangle Inequality), the relationship between sides and angles, special theorems for isosceles and equilateral triangles, and area formulas including Heron's Formula and area ratios.
Updated: 2 weeks ago

Right Triangles & Pythagorean Theorem

A complete foundation on right triangles, including the Pythagorean Theorem, primitive triples, and the 30-60-90 and 45-45-90 special right triangles.
Updated: 2 weeks ago

Triangle Congruence & Similarity

The foundations of geometric deduction, covering SSS/SAS/AA criteria, the right triangle altitude theorem, and area scaling.
Updated: 2 weeks ago

Basic Proportionality Theorem (Thales Theorem)

Use parallel lines in triangles to establish proportional segments, relate areas, and solve geometry problems.
Updated: 2 weeks ago

Special Quadrilaterals

Parallelograms, rectangles, rhombi, and trapezoids.
Updated: 2 weeks ago

Composite Figures and Shaded Areas

Subtracting negative space from bounding shapes to find irregular areas using addition, subtraction, and clever decomposition.
Updated: 2 weeks ago

Coordinate Geometry Basics

Distance, midpoint, and slope.
Updated: 2 weeks ago

Line Equations

Point-slope, slope-intercept, and perpendicular slopes.
Updated: 2 weeks ago

Number Theory

0/28

Primes, divisibility, modular arithmetic, and integer properties.

Divisbility and the Prime Numbers

Divisbility, primes and composites, prime factorization
Updated: 2 weeks ago

Divisibility Rules

Memorizing and combining rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.
Updated: 2 weeks ago

GCD and LCM

The fundamental number theory operations
Updated: 2 weeks ago

Integer Functions

Integer functions such as the number of factors, sum of factors, and Euler's totient function
Updated: 2 weeks ago

Modular Arithmetic

Utilizing congruences to manage remainders of massive numbers.
Updated: 2 weeks ago

Units Digit Periodicity

Learn how repeating units digit cycles make it easy to find the last digit of large powers and expressions.
Updated: 2 weeks ago

Number Bases

Understand positional notation, convert between bases, and use base representations to solve competition problems.
Updated: 2 weeks ago

Miscellaneous Number Theory

Practical integer techniques including palindromes, coin problems, and operation constraints.
Updated: 2 weeks ago

Linear Diophantine Equations

Solving equations of the form ax + by = c using the Euclidean algorithm and Bezout's Identity.
Updated: 2 weeks ago

Combinatorics and Probability

0/204

Counting techniques, probability fundamentals, and strategic enumeration.

Counting Fundamentals

Rule of product, basic permutations and combinations, and careful casework.
Updated: 2 weeks ago

Using nCr and nPr

Learn the foundations of permutations and combinations, including when to use nPr, when to use nCr, and how to avoid common counting mistakes
Updated: 2 weeks ago

Systemic Casework

Updated: 2 weeks ago

Complementary Counting

Solving for the inverse of a problem to ease the solving process
Updated: 2 weeks ago

Inclusion-Exclusion

Basic Two and three set inclusion exclusion, Venn diagram interpretation, and methods of solveing "at least one" problems.
Updated: 2 weeks ago

Circular Permutations

Learn how to count circular arrangements by handling rotational symmetry, reflection symmetry, and common seating restrictions.
Updated: 2 weeks ago

Arrangements, Rank, and Sum of Arrangements

Learn how to count arrangements, find lexicographic ranks, and compute sums of numbers formed by arranging digits.
Updated: 2 weeks ago

Stars and Bars

Distributing identical objects into distinct "boxes", positive integer solutions, and distributions that are constraint
Updated: 2 weeks ago

Splitting Objects into Groups

Learn how to split objects into groups, including cases with distinct objects, identical objects, labelled groups, and unlabelled groups.
Updated: 2 weeks ago

Distributing Objects

Learn how to distribute distinct and identical objects among people, including stars and bars, restrictions, and mixed distribution problems.
Updated: 2 weeks ago

Pascal's Triangle & Binomial Theorem

Pascal's triangle structure and its symmetry, hockey stick identity, and basic binomial expansion.
Updated: 6 minutes ago

Multinomial Theorem and Applications

Learn the Multinomial Theorem and how it connects polynomial expansion, repeated arrangements, distributions, and probability.
Updated: 2 weeks ago

Geometric Counting

Counting squares, rectangles, and grid paths using structure and symmetry.
Updated: 2 weeks ago

Recursion Basics

Using states and modeling a problem in terms of itself
Updated: 2 weeks ago

Pigeonhole Principle

The pigeonhole principle, and its applications to counting, number theory, and combinatorial geometry
Updated: 2 weeks ago

Introduction to Probability

Basic probability, complements, and simple counting-based models.
Updated: 2 weeks ago

Uncategorized

Auto-discovered modules not yet placed in a syllabus chapter.

Estimation and Bounding

Using significant figures to estimate large products and eliminate wrong answers.
Updated: 2 weeks ago