Algebra II: Free Online Course & Practice

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

Advanced high school13 units45 lessons + 5 assessments2277 practice & quiz itemsFree

Item counts include repeats and variants. There are 2018 distinct prompt texts after removing variant labels; this is not a count of unique mathematical skills.

Starting point and intended outcomes

Suggested preparation: Algebra I functions, equations, factoring, and quadratic foundations.

Learning goals: Extend high-school algebra through polynomial, rational, radical, exponential, and logarithmic relationships.

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

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
• Algebra II Midterm Exam

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 Final Exam

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 — 50 lessons, 2277 practice and quiz items, including repeats and variants, 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 50 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 choose lessons to try first.

How do I find my gaps in Algebra II?

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