Algebra/Intermediate

Intermediate Topics

• Algebraic manipulations
  • Working with expressions involving radicals
• Equations
  • Systems of equations
• Factoring
  • Differences of powers
  • Simon's Favorite Factoring Trick
  • Sums of powers
• Functions
  • Exponentials
  • Greatest integer function
  • Graphing
  • Least integer function
  • Logarithms
  • Polynomials
    • Descartes Rule of Signs
    • Division Algorithm
    • Factor Theorem
    • Remainder Theorem
    • Symmetric polynomials
  • Functional Equations
• Inequalities
  • Trivial inequality
  • Cauchy-Schwarz Inequality
  • Arithmetic Mean-Geometric Mean Inequality
  • Triangle Inequality
• Newton sums
• Substitution methods
• Trigonometry
  • DeMoivre's Theorem
  • Roots of unity
• Continued fractions

See also

• Introductory algebra
• Olympiad algebra
• Inequalities