List of Topics

Level 1

Number Theory

  • Prime and Composite Numbers
  • Fundamental Theorem of Arithmetic
  • Divisibility
  • Remainders
  • Modulus
  • Number Bases

Algebra

  • Simplification of Expressions
  • Factoring Techniques
  • Inscribed Circle and Circumcircle
  • Linear Equations
  • Quadratic Equations
  • Inequalities
  • Induction

Geometry

  • Angle Chase Techniques
  • Congruent Triangles
  • Right Triangles
  • Isosceles and Equilateral Triangles
  • Special Points in a Triangle
  • Inscribed and Central Angles
  • Tangent to a Circle

Combinatorics

  • Counting
  • Parity
  • Pigeonhole Principle
  • Games

Level 2

Number Theory

  • Estimations Techniques
  • Euclidean Algorithm
  • Bezout's Identity
  • Euler's Totient Function
  • Euler's Theorem
  • Multiplicative Inverse
  • Linear Congruences

Algebra

  • Inequalities of Arithmetic and Geometric Means
  • Cauchy-Schwarz Inequality
  • Jensen Inequality
  • Bernoulli Inequality
  • Rearrangement Inequality

Geometry

  • Cyclic Quadrilaterals
  • Similar Triangles
  • Power of a Point
  • Reflection
  • Rotation
  • Translation
  • Homothety
  • Analytic Geometry

Level 3

Number Theory

  • Legendre Symbol
  • Quadratic Residues
  • Chinese Remainder Theorem
  • Wilson's Theorem

Algebra

  • Chebyshev's Inequality
  • Hölder’s Inequality
  • Minkowski’s Inequality
  • Geometric Inequalities
  • Polynomials
  • Functional Equations

Geometry

  • Ceva's Theorem
  • Menelaus's Theorem
  • Pascal's Theorem
  • Desargue's Theorem
  • Pappa's Theorem
  • Vectors
  • Inversion
  • Linear Transformation
  • Complex Numbers

Combinatorics

  • Invariants
  • Extreme Principle
  • Processes and Operations
  • Coloring Schemes

Sample Problems

Level 1 Sample Problems

Level 2 Sample Problems

Level 3 Sample Problems