Algebra/Intermediate

The following topics provide a good study of intermediate algebra.

• Algebraic manipulations
  • Working with expressions involving radicals
• Equations
  • Systems of equations
• Factoring
  • Differences of powers
  • Simon's Favorite Factoring Trick
  • Sophie Germain Identity
  • Sums of powers
• Functions
  • Exponentials
  • Greatest integer function
  • Graphing
  • Least integer function
  • Logarithms
  • Polynomials
    • Descartes Rule of Signs
    • Multiplying Polynomials
    • Division Algorithm
    • Coefficients and Roots of Polynomials
    • Newton's Sums
    • Factor Theorem
    • Remainder Theorem
    • Symmetric polynomials
  • Functional Equations
  • Transforming Polynomials

• Inequalities
  • Trivial inequality
  • Cauchy-Schwarz Inequality
  • Arithmetic Mean-Geometric Mean Inequality
  • Triangle Inequality
• Newton sums
• Sequences
  • Arithmetic sequences
  • Geometric sequences
  • Harmonic sequences
  • Recursion
• Series
  • Arithmetic series
  • Arithmetico-geometric series
  • Geometric series
  • Telescoping series and sums
• Substitution methods
• Trigonometry
  • De Moivre's Theorem
  • Roots of unity
• Continued fractions

Resources

Books

• Aops Volume 2

Classes

• The Intermediate Algebra Class -- Intermediate Algebra Training.
• The Worldwide Online Olympiad Training (WOOT) Program -- Intermediate to Olympiad training in a variety of subjects, including algebra.

See also

• Algebra
• Introductory Algebra
• Olympiad Algebra