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College Algebra

Course Overview

  • Real Numbers and Algebraic Expressions

  • Properties of Real Numbers

  • Order of Operations

  • Simplifying Algebraic Expressions

  • Absolute Value and Interval Notation

Equations & Inequalities

  • Solving Linear, Quadratic (factoring, square roots, quadratic formula), Rational, Radical, and Absolute Value Equations

  • Linear and Compound Inequalities

Functions & Graphs

  • Definition of a Function

  • Domain and Range

  • Function Notation

  • Evaluating and Interpreting Functions

  • Graphing Functions and Transformations

Linear Functions & Applications

  • Graphing Linear Equations

  • Slope and Intercepts

  • Point-Slope and Slope-Intercept Forms

  • Writing and Interpreting Linear Models

  • Parallel and Perpendicular Lines

Systems of Equations & Inequalities

  • Solving Systems by Graphing, Substitution, and Elimination

  • Systems of Linear Inequalities

  • Applications of Systems of Equations

  • Matrix Methods (Optional: Gaussian Elimination)

Polynomials & Polynomial Functions

  • Adding, Subtracting, Multiplying Polynomials

  • Factoring Techniques: GCF, Trinomials, Special Products

  • Solving Polynomial Equations

  • Graphs of Polynomial Functions

  • End Behavior and Turning Points

Rational Expressions & Functions

  • Simplifying, Multiplying, Dividing, Adding, and Subtracting Rational Expressions

  • Solving Rational Equations

  • Applications with Rational Functions

Radicals, Exponents, & Complex Numbers

  • Simplifying Radicals

  • Properties of Exponents and Radicals

  • Rational Exponents

  • Solving Radical Equations

  • Complex Numbers and Imaginary Unit

Quadratic Functions

  • Graphing Quadratic Functions

  • Vertex Form and Standard Form

  • Axis of Symmetry and Vertex

  • Maximum and Minimum Applications

  • Completing the Square

Exponential, Logarithmic Functions & Sequences

  • Exponential Growth and Decay

  • Properties of Exponents

  • Logarithmic Functions and Properties

  • Solving Exponential and Logarithmic Equations

  • Applications in Real-World Contexts

  • Arithmetic and Geometric Sequences

  • Summation Notation

  • Binomial Theorem

  • Intro to Probability Concepts