3MT Topics Covered

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