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Videos, solutions, worksheets, and activities to help Algebra students

Common Core Math Algebra

Need help in Algebra II or Intermediate Algebra?

We have a series of free, online Intermediate Algebra Lessons or Algebra II lessons.

**The Real Numbers**

Introduction to Real Numbers

Analyzing Data

Properties of Real Numbers

**Graphs of Linear Equations**

Coordinate System

Rectangular Coordinate System

Midpoint Formula

The Slope of a Line

Definition of Slope

Finding the Slope of a Line from a Graph

Finding the Slope of a Line from 2 Points

Finding the Slope of a Line from an Equation

Equation of a Line

Slope-Intercept Form of a Line

Point-Slope Form of a Line

Standard Form of a Line

Applications of Linear Equations

**Linear Equations**

Solving Linear Equations

Solving for a Parameter in a Linear Equation

Applied Linear Equations: Geometry Problem

Applied Linear Equations: Mixture Problem

Applied Linear Equations: Investment Problem

Applied Linear Equations: Tax Problem

Applied Linear Equations: Distance Problem

Applied Linear Equations: Collection or Coin Problem

Applied Linear Equations: Consecutive Numbers

**Factoring**

Review of the Methods of Factoring

Factoring the Sum or Difference of Cubes

Factoring Complicated Expressions

Using Synthetic Division to Factor

Solving by Factoring

Rational Roots Theorem

Using Synthetic Division to Solve an Equation

**Exponents**

Introduction to Exponents - Rules of Exponents

Multiplication and Division Properties of Exponents

Zero and Negative Exponents

Scientific Notation

Simplifying Expressions with Exponents

**
Quadratic Equations and Inequalities**

Quadratic Equations

Vocabulary of Quadratic Polynomials

Solving Quadratic Equations by Factoring

Solving Quadratic Equations Using Square Roots

Solving a Quadratic by Completing the Square

Quadratic Formula

Deriving the Quadratic Formula

Overview of the Different Methods of Solving a Quadratic Equation

The Discriminant of a Quadratic Equation

Solving Quadratic Equations in Disguise

Parabolas

Introduction to Parabolas

Finding the Vertex of a Parabola by Completing the Square

Finding Intercepts, Domain, Range and Vertex of a Parabola

Finding the Maximum or Minimum of a Quadratic

Graphing a Horizontal Parabola

Dilations of Parabolas or Quadratic Graphs

Focus and Directrix of a Parabola

Quadratic Inequality

Graphing a Quadratic Inequality

Solving a Quadratic Inequality using a Sign Chart

**Linear Inequalities**

Solving Linear Inequalities

Set Operation: Union

Set Operation: Intersection

Solving a Three-part Linear Inequality or Compound Inequality

Applied Linear Inequalities

**Systems of Linear Equations**

Solving a System of Linear Equations in Two Variables

Solving a Linear System in Three Variables with a Solution

Solving a Linear System in Three Variables with no or Infinite Solutions

**
Polynomials**

Polynomials Basics

Introduction to Polynomials

Polynomial Function

Polynomial Graphs

Basic Polynomial Graphs

Basic Transformations

Multiplying and Dividing Polynomials

Multiplying Polynomials

Multiplying Complicated Polynomials

Dividing Polynomials using Long Division

Synthetic Division

Dividing Polynomials using Synthetic Division

Using Synthetic Division to Evaluate Polynomials

Binomial Theorem

Pascal's Triangle

Binomial Theorem

** Functions and Variation**

Introduction to Functions

Domain and Range

Function Notation

Composition of Functions

Direct Variation

Indirect Variation

Joint and Combined Variation

**Rational Expressions and Functions**

Definition and Domain of a Rational Expression

Multiplying and Dividing Rational Expressions

Adding and Subtracting Rational Expressions

Simplifying Complex Fractions

Solving a Rational Equation

Graphing a Rational Expression

Solving a Rational Equation for a parameter

**Inverse, Exponential and Logarithmic Functions**

Functions and Inverse Functions

Definition of One-to-One Functions

Definition of Inverse

Finding an Inverse Algebraically

Proving Two Functions are Inverses

Finding an Inverse Graphically

Exponential and Logarithmic Functions

Exponential Functions and their Graphs

Solving Exponential Equations with the 'Same' Base

Introduction to Logarithms

Solving Simple Logarithmic Equations

Function Notation with Logs and Exponentials

Graph of Logarithmic Functions

Properties of Logarithms

Product Rule of Logarithms

Quotient Rule of Logarithms

Power Rule of Logarithms

Evaluating Logarithms

Expanding Logarithms

Condensing Logarithms

Evaluating a Logarithmic Expression in terms of Known Quantities

Solving Exponential and Logarithmic Functions

Common and Natural Logarithms

Change of Base Formula

Solving Exponential Equations with the Different Bases

Solving a Logarithmic Equation

Solving a Logarithmic Equation with Multiple Logs

Applications of Exponential and Log Functions

Compound Interest (Finite Number of Calculations)

Compound Interest (Continuously)

Exponential Growth and Decay

**Roots and Radicals**

Radicals

Introduction to Radicals

Radicals and Absolute Values

Rational Exponents

Rational Exponents

Evaluating Rational Exponents

Rational Exponents with Negative Coefficients

Rules for Rational Exponents

Radical Expressions and Equations

Simplifying Radicals using Rational Exponents

Multiplying Radicals of the Same Root

Multiplying Radicals of Different Roots

Rationalizing the Denominator with Higher Roots

Rationalizing a Denominator with a Binomial

Solving an Equation with Radicals

Complex Numbers

Introduction
to Imaginary Numbers

Adding and Subtracting Complex Numbers

Multiplying Complex Numbers

Dividing Complex Numbers

Powers of i

**
Matrices **

Introduction to Matrices

Matrix Operations

Matrix Multiplication

Augmented Matrices

** Conic Sections**

Introduction to Conic Sections

The Parabola

The Circle

The Ellipse

The Hyperbola

Transformations of a Hyperbola

Conic Section Formulas and Equations

**
Sequences and Series**

Sequence and Series

Introduction to Sequences

Series and Summation Notation

Arithmetic Sequences and Series

Arithmetic Sequences

Arithmetic Series

Geometric Sequences and Series

Geometric Sequences

Geometric Series

Recursion Sequences

Recursion Sequences

Mathematical Induction

**Additional Topics**

Step Functions

Piecewise Functions

Using the Calculator

Common Algebra Mistakes

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Videos, solutions, worksheets, and activities to help Algebra students

Common Core Math Algebra

Need help in Algebra II or Intermediate Algebra?

We have a series of free, online Intermediate Algebra Lessons or Algebra II lessons.

Introduction to Real Numbers

Analyzing Data

Properties of Real Numbers

Coordinate System

Rectangular Coordinate System

Midpoint Formula

The Slope of a Line

Definition of Slope

Finding the Slope of a Line from a Graph

Finding the Slope of a Line from 2 Points

Finding the Slope of a Line from an Equation

Equation of a Line

Slope-Intercept Form of a Line

Point-Slope Form of a Line

Standard Form of a Line

Applications of Linear Equations

Solving Linear Equations

Solving for a Parameter in a Linear Equation

Applied Linear Equations: Geometry Problem

Applied Linear Equations: Mixture Problem

Applied Linear Equations: Investment Problem

Applied Linear Equations: Tax Problem

Applied Linear Equations: Distance Problem

Applied Linear Equations: Collection or Coin Problem

Applied Linear Equations: Consecutive Numbers

Review of the Methods of Factoring

Factoring the Sum or Difference of Cubes

Factoring Complicated Expressions

Using Synthetic Division to Factor

Solving by Factoring

Rational Roots Theorem

Using Synthetic Division to Solve an Equation

Introduction to Exponents - Rules of Exponents

Multiplication and Division Properties of Exponents

Zero and Negative Exponents

Scientific Notation

Simplifying Expressions with Exponents

Quadratic Equations

Vocabulary of Quadratic Polynomials

Solving Quadratic Equations by Factoring

Solving Quadratic Equations Using Square Roots

Solving a Quadratic by Completing the Square

Quadratic Formula

Deriving the Quadratic Formula

Overview of the Different Methods of Solving a Quadratic Equation

The Discriminant of a Quadratic Equation

Solving Quadratic Equations in Disguise

Parabolas

Introduction to Parabolas

Finding the Vertex of a Parabola by Completing the Square

Finding Intercepts, Domain, Range and Vertex of a Parabola

Finding the Maximum or Minimum of a Quadratic

Graphing a Horizontal Parabola

Dilations of Parabolas or Quadratic Graphs

Focus and Directrix of a Parabola

Quadratic Inequality

Graphing a Quadratic Inequality

Solving a Quadratic Inequality using a Sign Chart

Solving Linear Inequalities

Set Operation: Union

Set Operation: Intersection

Solving a Three-part Linear Inequality or Compound Inequality

Applied Linear Inequalities

Solving a System of Linear Equations in Two Variables

Solving a Linear System in Three Variables with a Solution

Solving a Linear System in Three Variables with no or Infinite Solutions

Polynomials Basics

Introduction to Polynomials

Polynomial Function

Polynomial Graphs

Basic Polynomial Graphs

Basic Transformations

Multiplying and Dividing Polynomials

Multiplying Polynomials

Multiplying Complicated Polynomials

Dividing Polynomials using Long Division

Synthetic Division

Dividing Polynomials using Synthetic Division

Using Synthetic Division to Evaluate Polynomials

Binomial Theorem

Pascal's Triangle

Binomial Theorem

Introduction to Functions

Domain and Range

Function Notation

Composition of Functions

Direct Variation

Indirect Variation

Joint and Combined Variation

Definition and Domain of a Rational Expression

Multiplying and Dividing Rational Expressions

Adding and Subtracting Rational Expressions

Simplifying Complex Fractions

Solving a Rational Equation

Graphing a Rational Expression

Solving a Rational Equation for a parameter

Functions and Inverse Functions

Definition of One-to-One Functions

Definition of Inverse

Finding an Inverse Algebraically

Proving Two Functions are Inverses

Finding an Inverse Graphically

Exponential and Logarithmic Functions

Exponential Functions and their Graphs

Solving Exponential Equations with the 'Same' Base

Introduction to Logarithms

Solving Simple Logarithmic Equations

Function Notation with Logs and Exponentials

Graph of Logarithmic Functions

Properties of Logarithms

Product Rule of Logarithms

Quotient Rule of Logarithms

Power Rule of Logarithms

Evaluating Logarithms

Expanding Logarithms

Condensing Logarithms

Evaluating a Logarithmic Expression in terms of Known Quantities

Solving Exponential and Logarithmic Functions

Common and Natural Logarithms

Change of Base Formula

Solving Exponential Equations with the Different Bases

Solving a Logarithmic Equation

Solving a Logarithmic Equation with Multiple Logs

Applications of Exponential and Log Functions

Compound Interest (Finite Number of Calculations)

Compound Interest (Continuously)

Exponential Growth and Decay

Radicals

Introduction to Radicals

Radicals and Absolute Values

Rational Exponents

Rational Exponents

Evaluating Rational Exponents

Rational Exponents with Negative Coefficients

Rules for Rational Exponents

Radical Expressions and Equations

Simplifying Radicals using Rational Exponents

Multiplying Radicals of the Same Root

Multiplying Radicals of Different Roots

Rationalizing the Denominator with Higher Roots

Rationalizing a Denominator with a Binomial

Solving an Equation with Radicals

Complex Numbers

Adding and Subtracting Complex Numbers

Multiplying Complex Numbers

Dividing Complex Numbers

Powers of i

Introduction to Matrices

Matrix Operations

Matrix Multiplication

Augmented Matrices

Introduction to Conic Sections

The Parabola

The Circle

The Ellipse

The Hyperbola

Transformations of a Hyperbola

Conic Section Formulas and Equations

Sequence and Series

Introduction to Sequences

Series and Summation Notation

Arithmetic Sequences and Series

Arithmetic Sequences

Arithmetic Series

Geometric Sequences and Series

Geometric Sequences

Geometric Series

Recursion Sequences

Recursion Sequences

Mathematical Induction

Step Functions

Piecewise Functions

Using the Calculator

Common Algebra Mistakes

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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