Algebra Worksheets Sub-Topics

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.

Most Popular Algebra Math Worksheets this Week

Inverse relationships worksheets cover a pre-algebra skill meant to help students understand the relationship between multiplication and division and the relationship between addition and subtraction.

Addition and Subtraction Easy
Addition and Subtraction Harder
All Multiplication and Division Facts 1 to 18 in color (no blanks)
Multiplication and Division Range 1 to 9
Multiplication and Division Range 5 to 12
Multiplication and Division All Inverse Relationships Range 2 to 9
Multiplication and Division All Inverse Relationships Range 5 to 12
Multiplication and Division All Inverse Relationships Range 10 to 25

Addition and Subtraction (Sums 1-18)
Addition and Subtraction Inverse Relationships with 1
Addition and Subtraction Inverse Relationships with 2
Addition and Subtraction Inverse Relationships with 3
Addition and Subtraction Inverse Relationships with 4
Addition and Subtraction Inverse Relationships with 5
Addition and Subtraction Inverse Relationships with 6
Addition and Subtraction Inverse Relationships with 7
Addition and Subtraction Inverse Relationships with 8
Addition and Subtraction Inverse Relationships with 9
Addition and Subtraction Inverse Relationships with 10
Addition and Subtraction Inverse Relationships with 11
Addition and Subtraction Inverse Relationships with 12
Addition and Subtraction Inverse Relationships with 13
Addition and Subtraction Inverse Relationships with 14
Addition and Subtraction Inverse Relationships with 15
Addition and Subtraction Inverse Relationships with 16
Addition and Subtraction Inverse Relationships with 17
Addition and Subtraction Inverse Relationships with 18

Missing numbers in equations worksheets in three types: blanks for unknowns, symbols for unknowns and variables for unknowns.

In these worksheets, the unknown is limited to the question side of the equation which could be on the left or the right of equal sign.

All Operations w/ Blanks (Range 1 to 9)
All Operations w/ Blanks (Range 1 to 20)
Addition w/ Blanks (Range 1 to 9)
Subtraction w/ Blanks (Range 1 to 9)
Multiplication w/ Blanks (Range 1 to 9)
Division w/ Blanks (Range 1 to 9)

In these worksheets, the unknown could be in any position in the equation including the answer.

Unknown Blanks in Equations - All Operations - Range 1 to 9 - Any Position
Unknown Blanks in Equations - All Operations - Range 1 to 20 - Any Position
Unknown Blanks in Equations - Addition - Range 1 to 9 - Any Position
Unknown Blanks in Equations - Addition - Range 1 to 20 - Any Position
Unknown Blanks in Equations - Subtraction - Range 1 to 9 - Any Position
Unknown Blanks in Equations - Subtraction - Range 1 to 20 - Any Position
Unknown Blanks in Equations - Multiplication - Range 1 to 9 - Any Position
Unknown Blanks in Equations - Multiplication - Range 1 to 20 - Any Position
Unknown Blanks in Equations - Division - Range 1 to 9 - Any Position
Unknown Blanks in Equations - Division - Range 1 to 20 - Any Position

All Operations w/ Symbols (Range 1 to 9)
All Operations w/ Symbols (Range 1 to 20)
Addition w/ Symbols (Range 1 to 9)
Subtraction w/ Symbols (Range 1 to 9)
Multiplication w/ Symbols (Range 1 to 9)
Division w/ Symbols (Range 1 to 9)

Unknown Symbols in Equations - All Operations - Range 1 to 9 - Any Position
Unknown Symbols in Equations - All Operations - Range 1 to 20 - Any Position
Unknown Symbols in Equations - Addition - Range 1 to 9 - Any Position
Unknown Symbols in Equations - Addition - Range 1 to 20 - Any Position
Unknown Symbols in Equations - Subtraction - Range 1 to 9 - Any Position
Unknown Symbols in Equations - Subtraction - Range 1 to 20 - Any Position
Unknown Symbols in Equations - Multiplication - Range 1 to 9 - Any Position
Unknown Symbols in Equations - Multiplication - Range 1 to 20 - Any Position
Unknown Symbols in Equations - Division - Range 1 to 9 - Any Position
Unknown Symbols in Equations - Division - Range 1 to 20 - Any Position

Solving Simple Linear Equations with Values from -9 to 9 (Unknown on Left Side)
Solving Simple Linear Equations with Values from -99 to 99 (Unknown on Left Side)
Solving Simple Linear Equations with Values from -9 to 9 (Unknown on Right or Left Side)
Solving Simple Linear Equations with Values from -99 to 99 (Unknown on Right or Left Side)

All Operations w/ Variables (Range 1 to 9)
All Operations w/ Variables (Range 1 to 20)
Addition w/ Variables (Range 1 to 9)
Subtraction w/ Variables (Range 1 to 9)
Multiplication w/ Variables (Range 1 to 9)
Division w/ Variables (Range 1 to 9)

Unknown Variables in Equations - All Operations - Range 1 to 9 - Any Position
Unknown Variables in Equations - All Operations - Range 1 to 20 - Any Position
Unknown Variables in Equations - Addition - Range 1 to 9 - Any Position
Unknown Variables in Equations - Addition - Range 1 to 20 - Any Position
Unknown Variables in Equations - Subtraction - Range 1 to 9 - Any Position
Unknown Variables in Equations - Subtraction - Range 1 to 20 - Any Position
Unknown Variables in Equations - Multiplication - Range 1 to 9 - Any Position
Unknown Variables in Equations - Multiplication - Range 1 to 20 - Any Position
Unknown Variables in Equations - Division - Range 1 to 9 - Any Position
Unknown Variables in Equations - Division - Range 1 to 20 - Any Position

Algebraic expressions worksheets including translating algebraic phrases, simplifying algebraic expressions and evaluating algebraic expressions.

Evaluating Expressions with One Variable, One Step and No Exponents
Evaluating Expressions with One Variable and One Step
Evaluating Expressions with One Variable and Two Steps
Evaluating Expressions with Up to Two Variables and Two Steps
Evaluating Expressions with Up to Two Variables and Three Steps
Evaluating Expressions with Up to Three Variables and Four Steps
Evaluating Expressions with Up to Three Variables and Five Steps

As the title says, these worksheets include only basic exponent rules questions. Each question only has two exponents to deal with; complicated mixed up terms and things that a more advanced student might work out are left alone. For example, 4^{2} is (2^{2})^{2} = 2^{4}, but these worksheets just leave it as 4^{2}, so students can focus on learning how to multiply and divide exponents more or less in isolation.

Mixed Exponent Rules (All Positive)
Mixed Exponent Rules (With Negatives)
Multiplying Exponents (All Positive)
Multiplying Exponents (With Negatives)
Multiplying the Same Exponent with Different Bases (All Positive)
Multiplying the Same Exponent with Different Bases (With Negatives)
Dividing Exponents with a Greater Exponent in Dividend (All Positive)
Dividing Exponents with a Greater Exponent in Dividend (With Negatives)
Dividing Exponents with a Greater Exponent in Divisor (All Positive)
Dividing Exponents with a Greater Exponent in Divisor (With Negatives)
Powers of Exponents (All Positive)
Powers of Exponents (With Negatives)

Linear equations worksheets including simplifying, graphing, evaluating and solving systems of linear equations.

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.

Adding and simplifying linear expressions.
Adding and simplifying linear expressions with multipliers.
Adding and simplifying linear expressions with some multipliers.
Subtracting and simplifying linear expressions.
Subtracting and simplifying linear expressions with multipliers.
Subtracting and simplifying linear expressions with some multipliers.
Mixed adding and subtracting and simplifying linear expressions.
Mixed adding and subtracting and simplifying linear expressions with multipliers.
Mixed adding and subtracting and simplifying linear expressions with some multipliers.

Rewrite Linear Equations in Standard Form
Convert Linear Equations from Standard to Slope-Intercept Form
Convert Linear Equations from Slope-Intercept to Standard Form
Convert Linear Equations Between Standard and Slope-Intercept Form
Rewriting Formulas (addition and subtraction; about one step)
Rewriting Formulas (addition and subtraction; about two steps)
Rewriting Formulas (multiplication and division; about one step)

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 3*x* + 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 3*x* 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.

Despite all appearances, equations of the type a/*x* are not linear. Instead, they belong to a different kind of equations. They are good for combining them with linear equations, since they introduce the concept of valid and invalid answers for an equation (what will be later called the domain of a function). In this case, the invalid answers for equations in the form a/*x*, are those that make the denominator become 0.

Easy Linear Systems with Two Variables
Easy Linear Systems with Two Variables including negative values
Linear Systems with Two Variables
Linear Systems with Two Variables including negative values
Easy Linear Systems with Three Variables; Easy
Easy Linear Systems with Three Variables including negative values
Linear Systems with Three Variables
Linear Systems with Three Variables including negative values

Solve Linear Systems by Graphing (Solutions in first quadrant only)
Solve Standard Linear Systems by Graphing
Solve Slope-Intercept Linear Systems by Graphing
Solve Various Linear Systems by Graphing
Identify the Dependent Linear System by Graphing
Identify the Inconsistent Linear System by Graphing

Quadratic expressions and equations worksheets including multiplying factors, factoring, and solving quadratic equations.

Simplifying quadratic expressions with 5 terms
Simplifying quadratic expressions with 6 terms
Simplifying quadratic expressions with 7 terms
Simplifying quadratic expressions with 8 terms
Simplifying quadratic expressions with 9 terms
Simplifying quadratic expressions with 10 terms
Simplifying quadratic expressions with 5 to 10 terms

Adding and simplifying quadratic expressions.
Adding and simplifying quadratic expressions with multipliers.
Adding and simplifying quadratic expressions with some multipliers.
Subtracting and simplifying quadratic expressions.
Subtracting and simplifying quadratic expressions with multipliers.
Subtracting and simplifying quadratic expressions with some multipliers.
Mixed adding and subtracting and simplifying quadratic expressions.
Mixed adding and subtracting and simplifying quadratic expressions with multipliers.
Mixed adding and subtracting and simplifying quadratic expressions with some multipliers.

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

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)

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.

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)

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 worksheets with various levels of complexity.

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

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

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

Inequalities worksheets including writing the inequality that matches a graph and graphing inequalities on a number line.