The College Algebra Course is designed to build on the mathematic knowledge and skills gained from Algebra I, Geometry, and Algebra 2. This course continues with the development of mathematical reasoning related to algebraic understandings and deepens a foundation for studies in subsequent mathematics courses. College Algebra Topics include: (1) Relations and Functions, (2) Quadratic Functions, (3) Polynomial and Rational Functions, (4) Exponential and Logarithmic Functions, (5) Systems of Equations, (6) Matrices, (7) Sequences and Series, and (8) The Counting Principal and Probability.

- Coordinate Plane Overview
- Distance Formula
- Midpoint Formula
- Graphing Equations by Plotting Points
- Intercepts of a Graph and an Equation
- Testing Graphs for Symmetry
- Testing Equations for Symmetry
- Common Parent Functions
- Slope of a Line
- Graphing Lines in Different Forms
- Horizontal and Vertical Lines
- Parallel and Perpendicular Lines

- Relations and Functions
- Evaluating Functions
- Zeros of a Functions
- Restricting the Domain of a Function
- Operations on Two Functions
- Vertical Line Test
- Determining Even and Odd Functions Graphically
- Determining Even and Odd Functions Algebraically
- Increasing, Decreasing, and Constant Intervals
- Finding the Average Rate of Change/The Secant Line
- Parent Functions
- Greatest Integer Function
- Piecewise Functions
- Transformations of Functions
- Vertical Compression and Stretching
- Horizontal Compression and Stretching
- Reflecting over the X-Axis
- Reflecting over the Y-Axis

- Linear Function Forms
- Average Rate of Change
- Finding Zeros of Linear Functions
- Linear Scatter Plots
- Direct and Inverse Variation
- Quadratic Function Forms
- Finding Zeros of Quadratic Functions by Factoring
- Finding Zeros of Quadratic Functions by Taking Square Root
- Finding Zeros of Quadratic Function by Completing the Square
- Finding the Zeros of Quadratic Functions by Quadratic Formula
- The Discriminant
- Finding Zeros of Functions in Quadratic Form
- Graphing Quadratic Functions Using Transformations
- Graphing Parabolas Using Vertex, Axis of Symmetry, and Intercepts
- Graphing Quadratic Functions in Vertex Form
- Finding the Quadratic Function Given Quadratic Information
- Solving Quadratic Inequalities
- Finding Complex Zeros of Quadratic Functions
- Solving Absolute Value Equations
- Solving Absolute Value Inequalities

- Definition of a Polynomial Function
- Definition of a Power Function
- Identifying Zeros and Their Multiplicity
- Turning Points of a Polynomials
- End Behavior of Polynomials
- Rational Functions Defined and Domains of Rational Functions
- Graphing Proper Rational Functions
- Finding Oblique Asymptotes
- Graphing Rational Functions
- Graphing More Rational Functions
- Graphing Rational Functions with Holes
- Solving Polynomial Inequalities
- Dividing Polynomials with Long Division
- Dividing Polynomials Using Synthetic Division
- Remainder Theorem and Factor Theorem
- Decartes Rule of Signs
- Rational Zero Theorem
- Finding the Rational Zeros of a Polynomial
- Finding the Complex Zeros of a Polynomials
- Finding the Polynomial of Least Degree
- Synthetically Dividing Imaginary Zeros to Find Other Zeros

- Composite Functions
- Finding the Domain of Composite Functions
- One-to-One Functions and the Horizontal Line Test
- Inverse Functions and Their Graphs
- Properties of Exponents
- Exponential Functions and Their Graphs
- The Number e
- Solving Exponential Equations
- Changing Between Logarithmic Expressions and Exponential Expressions
- Finding the Exact Value of Logarithmic Expressions
- Finding the Domain of Logarithmic Functions
- Logarithmic Functions and Their Graphs
- The Natural Log
- The Common Log
- Properties of Logarithms
- Expanding Logarithmic Expressions
- Condensing Logarithmic Expressions
- Change of Base Formula with Logarithms
- Solving Logarithmic Equations
- Solving Exponential Equations Using Logarithms
- Simple Interest and Compound Interest
- Continuous Compounding Interest
- Present Value Formula
- Exponential Growth and Exponential Decay
- Uninhibited Growth and Decay

- Different Types of Conic Sections
- Parts of a Parabola and Its Equations
- Graphing Parabolas
- Determining the Equation of a Parabola
- Parts of a Circle and Its Equation
- Graphing Circles
- Determining the Equation of a Circle
- Parts of an Ellipse and Its Equation
- Graphing Ellipses
- Determining the Equation of an Ellipse
- Parts of a Hyperbola and Its Equation
- Graphing Hyperbolas
- Determining the Equation of a Hyperbola
- Putting Conic Equations in Standard Form by Completing the Square
- Determining the Conic Represented by an Expanded Equations
- Solving a System of Conic Equations

- Solving a System by Graphing
- Solving a System by Substitution
- Solving a System by Elimination
- Solving a System of Three Equations
- Solving a System of Two Equations Using Matrices
- Solving a System of Three Equations Using Matrices
- Solving a Nonlinear System of Equations
- Solving a System of Conic Equations
- Solving a System of Two Linear Inequalities
- Solving a System of Multiple Linear Inequalities
- Solving a System of Nonlinear Inequalities
- Linear Programming

- Determinants of Square Matrices
- Cramer's Rule of 2 by 2 Matrices
- Cramer's Rule for 3 by 3 Matrices
- Adding and Subtracting Matrices
- Scalar Multiplication with Matrices
- Multiplying Matrices
- The Identity Matrix
- Finding the Inverse of a 2 by 2 Matrix
- Finding the Inverse of a 3 by 3 Matrix
- Solving a System of Equations Using Inverse Matrices

- Writing the Terms of a Sequence
- Determining the Sequence by Using Patterns
- Factorials
- Recursive Sequences
- Summation Notation
- Summation Properties
- Arithmetic Sequences
- The nth Term of an Arithmetic Sequence
- The Sum of the First n Terms of an Arithmetic Sequence
- Arithmetic Means of Arithmetic Sequences
- Geometric Sequence
- The nth Term of a Geometric Sequence
- The Sum of the First n Terms of a Geometric Sequence
- Geometric Means of Geometric Sequences
- The Sum of an Infinite Geometric Series
- Mathematical Induction
- Evaluate "n taken r at a time"
- Creating Pascal's Triangle
- Binomial Theorem and Pascal's Triangle
- Finding a Specific Coefficient Using Binomial Expansion
- Finding the nth Term of a Binomial Expansion

- Introduction to Sets (Elements, Intersections, Unions and Subsets)
- Complement of a Set
- Sets and Venn Diagrams
- The Number of Elements in a Set
- Solving Problems with Multiplication
- Combinations
- Permutations with Distinct Objects
- Permutations with Nondistinct Objects
- Basic Probability
- Probability of Mutually Exclusive Events