Algebra I

Some students are looking for a particular topic, but others will want to work through lessons in order. Our math lessons are sorted into units below, and additional stand-alone topics follow. Feel free to jump around as you need.

Group 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

Group Two

Group Three

Group Four

Group Five

Group Six

More Algebra Lessons

Direct Variation
Distributive Property
Dividing by Zero
Exponents and their properties
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)

Algebra Examples:

I've always found that working example problems is the best way to understand a new subject. If you've had trouble grasping a new algebra concept, the best solution might be to work your way through a series of example problems. I've tried to compile some links for example problems you can solve.

Intermediate Algebra Example Problems -- some extra selections sorted by subject matter to illustrate each concept in more detail.

Analyze Math Algebra 1 Tutorial -- A standard tutorial that focuses heavily on worked-out examples, including these problems.

Further Help

If you still have algebra questions, you might want to check out these other websites for more help: Khan Academy, Purple Math, Math Goodies, and the Virtual Math Lab.

If you have a specific problem or two that you need answered, you might want to ask our algebra message board. Real, live math tutoring may be what you are really looking for though. In that case, your best bet is probably to talk to your teacher at school. He or she will be able to help you find someone locally who can tutor you in algebra. Alternatively you can find algebra tutoring online. Of course, never meet someone (even a math tutor) in-person without being safe and speaking with your parents first. Good luck!

Featured Lesson

Remind yourself how to find the domain and range of a function.

Algebra Help