Algebra Worksheets

Welcome to the Algebra worksheets page at Math-Drills.com, where unknowns are common and variables are the norm. On this page, you will find Algebra worksheets mostly for middle school students on algebra topics such as algebraic expressions, equations and graphing functions.

This page starts off with some missing numbers worksheets for younger students. We then get right into algebra by helping students recognize and understand the basic language related to algebra. The rest of the page covers some of the main topics you'll encounter in algebra units. Remember that by teaching students algebra, you are helping to create the future financial whizzes, engineers, and scientists that will solve all of our world's problems.

Algebra is much more interesting when things are more real. Solving linear equations is much more fun with a two pan balance, some mystery bags and a bunch of jelly beans. Algebra tiles are used by many teachers to help students understand a variety of algebra topics. And there is nothing like a set of co-ordinate axes to solve systems of linear equations.

Missing Numbers Worksheets

The missing numbers worksheets below come in three versions. The simplest one includes only blanks; the next one includes symbols for the unknowns; and the third version includes variables for the unknowns. The blanks version is a good way to start some algebraic thinking in younger students.





Equalities and Inequalities

Translating Algebraic Phrases Worksheets

Here is a great handout on translating English phrases into algebraic expressions. Please note that this is an external document found on Michael Bowen's Ventura College Start Page.

Rewriting Formulas Worksheets

Simplifying Algebraic Expressions Worksheets

Evaluating Algebraic Expressions Worksheets

Linear Equation Graphs

Need some practice graphing linear equations? Look no further than this section.

Solving Linear Equations Worksheets

You may have been intrigued by our comment above about solving linear equations with jelly beans. Here is how you might accomplish that. Ideally, you will want some opaque bags with no mass, but since that isn't quite possible (the no mass part), there is a bit of a condition here that will actually help students understand equations better. Any bags that you use have to be balanced on the other side of the equation with empty ones.

Probably the best way to illustrate this is through an example. Let's use 3x + 2 = 14. You may recognize the x as the unknown which is actually the number of jelly beans we put in each opaque bag. The 3 in the 3x means that we need three bags. It's best to fill the bags with the required number of jelly beans out of view of the students, so they actually have to solve the equation.

On one side of the two-pan balance, place the three bags with x jelly beans in each one and two loose jelly beans to represent the + 2 part of the equation. On the other side of the balance, place 14 jelly beans and three empty bags which you will note are required to "balance" the equation properly. Now comes the fun part... if students remove the two loose jelly beans from one side of the equation, things become unbalanced, so they need to remove two jelly beans from the other side of the balance to keep things even. Eating the jelly beans is optional. The goal is to isolate the bags on one side of the balance without any loose jelly beans while still balancing the equation.

The last step is to divide the loose jelly beans on one side of the equation into the same number of groups as there are bags. This will probably give you a good indication of how many jelly beans there are in each bag. If not, eat some and try again. Now, we realize this won't work for every linear equation as it is hard to have negative jelly beans, but it is another teaching strategy that you can use for algebra.




Systems of Linear Equations (or Linear Systems) Worksheets

Inverse Relationships Worksheets (One Blank)

All Multiplication and Division Facts 1 to 18 in color (no blanks)

Inverse Relationships Worksheets (Two Blanks)

Multiplying Factors of Quadratic Expressions

Multiplying Factors of Quadratics with Coefficients of 1
Multiplying Factors of Quadratics with Coefficients of 1 or -1
Multiplying Factors of Quadratics with Coefficients of 1, or 2
Multiplying Factors of Quadratics with Coefficients of 1, -1, 2 or -2
Multiplying Factors of Quadratics with Coefficients up to 9
Multiplying Factors of Quadratics with Coefficients between -9 and 9

Factoring Quadratic Expressions

The factoring quadratic expressions worksheets below provide many practice questions for students to hone their factoring strategies. If you would rather worksheets with quadratic equations, please see the next section. These worksheets come in a variety of levels with the easier ones are at the beginning. The "a" coefficients referred to below are the coefficients of the x² term as in the general quadratic expression: ax² + bx + c.

Factoring Quadratic Expressions ("a" coefficients of 1)
Factoring Quadratic Expressions ("a" coefficients of 1 or -1)
Factoring Quadratic Expressions ("a" coefficients up to 4)
Factoring Quadratic Expressions ("a" coefficients between -4 and 4)
Factoring Quadratic Expressions ("a" coefficients up to 81)
Factoring Quadratic Expressions ("a" coefficients between -81 and 81)

Quadratic Equations

Whether you use trial and error, completing the square or the general quadratic formula, these worksheets include a plethora of practice questions with answers. In the first section, the worksheets include questions where the quadratic expressions equal 0. This makes the process similar to factoring quadratic expressions, with the additional step of finding the values for x when the expression is equal to 0. In the second section, the expressions are generally equal to something other than x, so there is an additional step at the beginning to make the quadratic expression equal zero.

Equations Equal Zero (e.g. ax² + bx + c = 0)

Solving Quadratic Equations for x ("a" coefficients of 1)
Solving Quadratic Equations for x ("a" coefficients of 1 or -1)
Solving Quadratic Equations for x ("a" coefficients up to 4)
Solving Quadratic Equations for x ("a" coefficients between -4 and 4)
Solving Quadratic Equations for x ("a" coefficients up to 81)
Solving Quadratic Equations for x ("a" coefficients between -81 and 81)

Equations Equal an Integer (e.g. ax² + bx + c = d)

Solving Quadratic Equations for x ("a" coefficients of 1)
Solving Quadratic Equations for x ("a" coefficients of 1 or -1)
Solving Quadratic Equations for x ("a" coefficients up to 4)
Solving Quadratic Equations for x ("a" coefficients between -4 and 4)
Solving Quadratic Equations for x ("a" coefficients up to 81)
Solving Quadratic Equations for x ("a" coefficients between -81 and 81)

Factoring Non-Quadratic Expressions

Expressions that do not include a squared variable

Factoring Non-Quadratic Expressions with No Squares, Simple Coefficients, and Positive Multipliers
Factoring Non-Quadratic Expressions with No Squares, Simple Coefficients, and Negative and Positive Multipliers
Factoring Non-Quadratic Expressions with No Squares, Compound Coefficients, and Positive Multipliers
Factoring Non-Quadratic Expressions with No Squares, Compound Coefficients, and Negative and Positive Multipliers

Expressions that always include a squared variable

Factoring Non-Quadratic Expressions with All Squares, Simple Coefficients, and Positive Multipliers
Factoring Non-Quadratic Expressions with All Squares, Simple Coefficients, and Negative and Positive Multipliers
Factoring Non-Quadratic Expressions with All Squares, Compound Coefficients, and Positive Multipliers
Factoring Non-Quadratic Expressions with All Squares, Compound Coefficients, and Negative and Positive Multipliers

Expressions that sometimes include squared variables

Factoring Non-Quadratic Expressions with Some Squares, Simple Coefficients, and Positive Multipliers
Factoring Non-Quadratic Expressions with Some Squares, Simple Coefficients, and Negative and Positive Multipliers
Factoring Non-Quadratic Expressions with Some Squares, Compound Coefficients, and Positive Multipliers
Factoring Non-Quadratic Expressions with Some Squares, Compound Coefficients, and Negative and Positive Multipliers