Contest Structure
ALGEBRA
- Systems of equations
- Quadratics
- Vieta’s
- Binomial Theorem
- Radicals/Exponents
- Simon’s Favorite
- Factoring Trick
- Ratios
- (Infinite) Geometric Series
- Arithmetic Series
- Sum/Difference of Powers
- Rate/Time
- Floor/Ceiling
- Absolute Value
- Substitution (Nested Roots/Repeated Fractions)
- Mean, Median, Mode, Range
- Telescoping
COMBINATORICS
Sticks and Stones
Permutation/ Combination
Properties of Inclusion Exclusion for three or less sets
Basic Geometric Probability
Conditional Probability
Expected Values
Complementary Counting
Recursion
Bijections
Casework
Pigeonhole Principle
Double-counting
Basic Invariants
GEOMETRY
- Area Formulas
- Volume Formulas
- Shoelace Formula
- Pythagorean Theorem
- Distance Formula
- Similar Triangles
- Angle Chasing
- Power of a Point
- Basic Mass Points
- Heron’s Formula
- Pick’s Theorem
- Surface Area for Pyramids, Prisms, and Cones
- Arcs and Sectors
- Angle Bisector Theorem
- Internal/External Angles
NUMBER THEORY
- Fermat’s Little Theorem
- Euclidean Algorithm
- Chinese Remainder Theorem
- Divisibility
- Chicken McNugget Theorem
- GCD and LCM
- Number of Factors
- Sum of Factors
- Basic Modular Arithmetic
- Fundamental Theorem of Arithmetic