# 3MT Topics Covered ## Contest Structure

#### ALGEBRA

• Systems of equations
• Vieta’s
• Binomial Theorem
• 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