College Algebra: Free Online Course & Practice

Linear foundations, functions, quadratics, complex numbers, radicals, rational expressions, geometry links, polynomials, transformations, logs, and modeling.

College students and adult learners16 units44 lessons + 6 assessments2280 practice & quiz itemsFree

Item counts include repeats and variants. There are 1974 distinct prompt texts after removing variant labels; this is not a count of unique mathematical skills.

Starting point and intended outcomes

Suggested preparation: Fluent Algebra I work and experience with quadratic and function notation.

Learning goals: Consolidate the function-centered algebra used in college coursework, including restrictions, transformations, systems, and models. It overlaps Algebra II and is not automatically the next course after it.

These describe the course's intended scope. A score on one screen or final is only one piece of evidence about these goals.

Course outline

Linear Equations and Inequalities

• Linear Equations
• Linear Inequalities
• Absolute Value Equations and Inequalities
• Polynomial and Rational Inequalities
• Linear Equations and Graphs Checkpoint

Graphs and Forms of Linear Equations

• Slope and Rate of Change
• Graphs and Forms of Linear Equations
• Parallel and Perpendicular Lines

Functions

• Function Notation
• Domain and Range
• Composition and Inverse Functions
• Functions Checkpoint

Quadratics: Multiplying and Factoring

• Quadratics: Multiplying Polynomials
• Quadratics: Factoring

Quadratic Functions and Equations

• Quadratic Functions and Graphs
• Solving Quadratic Equations
• Quadratic Applications
• Quadratics Checkpoint

Complex Numbers

• Complex Numbers
• Complex Solutions of Quadratics

Exponents and Radicals

• Exponents and Radical Foundations
• Radical Expressions and Equations

Rational Expressions and Equations

• Rational Expressions
• Rational Equations
• Partial Fractions Decomposition
• Rational and Radical Checkpoint
• College Algebra Midterm Exam

Relating Algebra and Geometry

• Distance, Midpoint, and Circles
• Conic Sections Basics

Polynomial Arithmetic and Theorems

• Polynomial Arithmetic
• Polynomial Division
• Synthetic Division
• Rational Root Theorem
• Fundamental Theorem of Algebra

Advanced Function Types

• Polynomial Functions
• Rational Functions and Asymptotes
• Piecewise and Absolute Value Functions

Transformations of Functions

• Transformations of Functions
• Advanced Function Transformations

Rational Exponents and Radicals

• Rational Exponents
• Radical Function Graphs

Logarithms

• Exponential Functions
• Logarithms
• Logarithmic Equations and Applications

Systems, Matrices, and Linear Programming

• Systems of Three Linear Equations
• Matrix Basics: Add, Subtract, Multiply
• Linear Programming
• Direct, Inverse, Joint, and Combined Variation

Modeling and Readiness

• College Algebra Modeling
• College Algebra Final Exam

Frequently asked questions

Is the College Algebra course free?

Yes. The entire College Algebra course — 50 lessons, 2280 practice and quiz items, including repeats and variants, worked solutions, and the placement check — is free to use at ClearMath Academy.

What does the College Algebra course cover?

Linear foundations, functions, quadratics, complex numbers, radicals, rational expressions, geometry links, polynomials, transformations, logs, and modeling. It spans 16 units and 50 lessons, each with a worked example and practice problems with step-by-step solutions.

Who is College Algebra for?

College Algebra is aimed at college students and adult learners. You can take a free 15-minute placement check first to choose lessons to try first.

How do I find my gaps in College Algebra?

Take the free College Algebra placement check. It samples selected skills and suggests a practice plan. Skipped or untested topics remain unassessed; this is not a validated readiness certification.