The lessons below are sorted into units that follow a typical Algebra I curriculum, with additional stand-alone topics afterward. Work through them in order or jump to whatever you need. The Worksheet Generator creates practice problems on any topic.

Algebra I

Unit One

Start with an Introduction to Algebra.
Remember PEMDAS? Order of Operations
Properties of Numbers (Commutative, Distributive, Associative, etc.)
Integers are one of the Types of Numbers
Absolute Value is the magnitude of a number (or expression) without any sign.
Fractions, Decimals, and Percents

Unit Two

Unit Three

Unit Four

Unit Five

Unit Six

Laws of Exponents
Scientific Notation
Adding and Subtracting Polynomials
Multiplying Binomials
Factoring Simple Polynomials
Introduction to Quadratic Equations
Parabolas — graphing quadratics, vertex form, and real-world applications

More Algebra Lessons

Direct Variation
Distributive Property
Dividing by Zero
Exponents and their properties
Fractions — including Adding Fractions
Factoring Numbers and the Greatest Common Factor
Imaginary Numbers
Mean, Median, and Mode
Percentages
Proportions and Ratios
Rational Numbers

Simplifying and Solving Equations

Combining Like Terms to simplify your expressions.
Multiplying Polynomials
The Quadratic Formula is one way to solve certain equations.
Substitution allows you to replace an unknown with a known.
Systems of Linear Equations - Solve for more than one variable.
Solving Systems of Inequalities - Like before, but with less-than and greater-thans.
Systems of Equations With More Than Two Variables - Why not keep going?
Using FOIL to multiply two expressions.
Finding Roots
Completing the Square In Circle Equations - A more advanced subject.

Functions

What are Functions?
Domain and Range describe the input and output.
Exponential Functions add exponents to the function.

Graphing Equations and Inequalities

Linear Equations are straight lines.
Asymptotes are approached but not reached.
Finding Asymptotes
Finding Horizontal Asymptotes
Compute the Length of a Line Segment
Express an equation in Point Slope Form.
Find the distance between two points
Midpoint Formula

Rational Functions

Algebra Formulas

Here are some of the most commonly used formulas in algebra.

Laws of Exponents

$a^m \cdot a^n = a^{m+n}$
$(ab)^m = a^m b^m$
$(a^m)^n = a^{mn}$
$a^{\frac{m}{n}} = \sqrt[n]{a^m}$
$a^0 = 1$
$\frac{a^m}{a^n} = a^{m-n}$
$a^{-m} = \frac{1}{a^m}$

Quadratic Formula

For an equation of the form $ax^2 + bx + c = 0$, you can solve for $x$ using the Quadratic Formula:

$$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$

Binomial Theorem

$(a+b)^1 = a + b$
$(a+b)^2 = a^2 + 2ab + b^2$
$(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$
$(a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4$

Difference of Squares

$a^2 - b^2 = (a-b)(a+b)$

Rules of Zero

$\frac{0}{x} = 0$, where $x \neq 0$
$a^0 = 1$
$0^a = 0$
$a \cdot 0 = 0$
$\frac{a}{0}$ is undefined (you can't divide by zero)

Further Help

The best way to internalize a new algebra concept is to work through example problems until the procedure becomes automatic. The lessons above include worked examples and practice problems with full solutions throughout.

For a specific question, post on the algebra message board — there's often a fast response from another student or a moderator. Khan Academy and Purple Math are good external resources for an alternative perspective on most algebra topics.

Algebra Help