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High School: Algebra
College: Pre-Algebra, Algebra I, Algebra II, College Algebra

The following is a list of typical topics covered

 
  • Numbers & Expressions
    • Real Numbers & Their Properties
    • The Real Number Line
    • Integer Exponents
    • Rational Exponents & Radicals
    • Algebraic Expressions
    • Factoring
    • Rational Expressions

  • Eqns & Inequalities
    • Basic Eqns
    • Modeling with Eqns
    • Quadratic Eqns
    • Complex Numbers
    • Other Types of Eqns
    • Inequalities
    • Absolute Value

  • Coordinates & Graphs
    • The Coordinate Plane
    • Graphs of Eqns in Two Vars
    • Solving Eqns & Ineq Graphically
    • Lines
    • Making Models Using Variations

  • Functions
    • What Is a Function?
    • Graphs of Functions
    • Average Rate of Change
    • Transformations
    • Combining Functions
    • 1 to 1 Functions & Inverses

  • Polynomial & Rational Functions
    • Quadratic Functions & Models
    • Graphs of Polynomials
    • Dividing Polynomials
    • Real Zeros of Polynomials
    • Complex Zeros
    • Rational Functions

  • Exponential & Logarithmic Functions
    • Exponential Functions
    • Natural Exponential Function
    • Logarithmic Functions
    • Laws of Logarithms
    • Exponential & Logarithmic Eqns
    • Modeling

  • Trigonometric Functions: Right Triangle
    • Angle Measure
    • Trigonometry of Right Triangles
    • Trigonometric Functions of Angles
    • Inverse Trigonometric Functions
    • The Law of Sines
    • The Law of Cosines
     
  • Trigonometric Functions: Unit Circle
    • The Unit Circle
    • Trigonometric Functions of Real Numbers
    • Trigonometric Graphs
    • Inverse Trigonometric Functions
    • Inverse Trigonometric Graphs
    • Modeling Harmonic Motion

  • Analytical Trigonometry
    • Trigonometric Identities
    • Addition & Subtraction Formulas
    • Double-Angle & Half-Angle Formulas
    • Basic Trigonometric Eqns
    • More Trigonometric Eqns

  • Polar Coordinates & Parametric Eqns
    • Polar Coordinates
    • Graphs of Polar Eqns
    • Polar Form of Complex Numbers
    • Plane Curves & Parametric Eqns

  • Vectors
    • Vectors in 2D
    • The Dot Product
    • 3D Coordinate Geometry
    • Vectors in 3D
    • The Cross Product
    • Eqns of Lines & Planes

  • Systems of Eqns & Inequalities
    • Systems of Linear Eqns in 2 Vars
    • Systems of Linear Eqns in 3+ Vars
    • Matrices & Systems of Linear Eqns
    • The Algebra of Matrices
    • Inverses of Matrices & Matrix Eqns
    • Determinants & Cramer's Rule
    • Partial Fractions
    • Systems of Nonlinear Eqns
    • Systems of Inequalities

  • Conic Sections
    • Parabolas
    • Ellipses
    • Hyperbolas
    • Shifted Conics
    • Rotation of Axes
    • Polar Eqns of Conics

  • Sequences & Series
    • Sequences & Summation Notation
    • Arithmetic Sequences
    • Geometric Sequences
    • Mathematics of Finance
    • Mathematical Induction
    • Binomial Theorem

  • Counting & Probability
    • Counting Principles
    • Permutations & Combinations
    • Probability
    • Binomial Probability
    • Expected Value