Algebra II: Free Online Course & Practice

Functions, polynomial fluency, complex numbers, equations, radicals, exponentials, logarithms, trigonometry, and modeling.

Advanced high school13 units49 lessons532 practice & quiz problemsFree

Course outline

Functions and Notation

• Function Notation Review
• Domain and Range
• Inverse Functions Basics
• Function Composition
• Piecewise Functions
• Functions and Readiness Checkpoint

Polynomial Arithmetic

• Polynomial Operations
• Binomial Products and Special Patterns

Complex Numbers

• Imaginary Numbers
• Complex Number Arithmetic
• Complex Solutions of Quadratics

Polynomial Factorization

• Factoring Simple Quadratics
• Factoring Higher-Degree Polynomials
• Factor Theorem and Remainder Theorem

Polynomial Division

• Polynomial Division

Polynomial Graphs

• Polynomial Graphs and End Behavior
• Zeros and Multiplicity
• Sketching Polynomial Graphs

Rational Exponents and Radicals

• Radical Expressions
• Radical Equations
• Rational Exponents

Exponential Models

• Exponential Functions
• Exponential Equations

Logarithms and the Natural Base

• Logarithm Basics
• Logarithm Properties
• The Number e and the Natural Logarithm

Transformations of Functions

• Function Transformations
• Vertex Form of Quadratics
• Completing the Square
• Quadratic Deepening Checkpoint

Equations, Rational Functions, and Conics

• Quadratic Formula and Discriminant
• Rational Expressions
• Rational Equations
• Graphs of Rational Functions
• Equation Strategy and Extraneous Solutions
• Nonlinear Systems
• Conic Sections: Circles, Parabolas, Ellipses, Hyperbolas
• Polynomials and Rational Expressions Checkpoint

Trigonometry and Modeling

• Unit Circle Basics
• Graphs of Sine and Cosine
• Trigonometric Identities
• Inverse Trigonometric Functions
• Solving Trigonometric Equations
• Quadratic Applications
• Modeling with Functions
• Algebra II Readiness and Final Test

Sequences, Series, and Counting

• Arithmetic and Geometric Series
• Permutations and Combinations
• Binomial Theorem and Pascal's Triangle

Frequently asked questions

Is the Algebra II course free?

Yes. The entire Algebra II course — 49 lessons, 532 practice and quiz problems, worked solutions, and the placement check — is free to use at ClearMath Academy.

What does the Algebra II course cover?

Functions, polynomial fluency, complex numbers, equations, radicals, exponentials, logarithms, trigonometry, and modeling. It spans 13 units and 49 lessons, each with a worked example and practice problems with step-by-step solutions.

Who is Algebra II for?

Algebra II is aimed at advanced high school. You can take a free 15-minute placement check first to find exactly which lessons to start with.

How do I find my gaps in Algebra II?

Take the free Algebra II placement check. It pinpoints the specific skills you're missing in about 15 minutes and builds a practice plan focused on those gaps.