Algebra Worksheets

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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.

Most Popular Algebra Math Worksheets this Week

Solve One Step Equations with Smaller Values (A) Solve One Step Equations with Smaller Values (A)
Using the Distributive Property (Answers Do Not Include Exponents) (A) Using the Distributive Property (Answers Do Not Include Exponents) (A)
Systems of Linear Equations -- Two Variables (A) Systems of Linear Equations -- Two Variables (A)
Solving Linear Equations -- Form ax + b = c (A) Solving Linear Equations -- Form ax + b = c (A)
Factoring Quadratic Expressions with a Coefficients of 1 (A) Factoring Quadratic Expressions with a Coefficients of 1 (A)
Translating Algebraic Phrases (A) Translating Algebraic Phrases (A)
Adding and Simplifying Linear Expressions (A) Adding and Simplifying Linear Expressions (A)
Inverse Relationships -- Addition and Subtraction -- Range 1 to 9 (A) Inverse Relationships -- Addition and Subtraction -- Range 1 to 9 (A)
Rewriting Linear Equations in Standard Form (A) Rewriting Linear Equations in Standard Form (A)
Adding and Subtracting and Simplifying Linear Expressions with Some Multipliers (A) Adding and Subtracting and Simplifying Linear Expressions with Some Multipliers (A)

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.

Inverse Relationships Worksheets

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.

Inverse relationships with one blank.

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
Inverse relationships with two blanks.

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 Equations Worksheets

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

Missing numbers worksheets with blanks as unknowns.

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)
Missing numbers worksheets with symbols as unknowns.

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)
Missing numbers worksheets with variables as unknowns.

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) One-Step Equations including negatives (Easy Numbers) One-Step Equations inclduing negatives (Larger Numbers)
Equalities with addition on both sides of the equation and symbols as unknowns.

Equalities with Addition (0 to 9) Symbol Unknowns Equalities with Addition (1 to 12) Symbol Unknowns Equalities with Addition (1 to 15) Symbol Unknowns Equalities with Addition (1 to 25) Symbol Unknowns Equalities with Addition (1 to 99) Symbol Unknowns

Algebraic Expressions Worksheets

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

Using the distributive property.

Distributive Property (Answers do not include exponents) Distributive Property (Some answers include exponents) Distributive Property (All answers include exponents)
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

Exponent Rules and Properties

Practice with basic exponent rules.

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, 42 is (22)2 = 24, but these worksheets just leave it as 42, 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 Expressions & Equations

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.

Translating algebraic phrases in words to algebraic expressions.

Translating Linear Algebraic Phrases
Simplifying linear expressions (combining like terms).

Simplifying Linear Expressions with 3 terms Simplifying Linear Expressions with 4 terms Simplifying Linear Expressions with 5 terms Simplifying Linear Expressions with 6 to 10 terms
Adding/Subtracting and Simplifying linear expressions.

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.
Rewriting linear equations.

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)
Determining linear equations from slopes, y-intercepts, and points.

Determine a Linear Equation from the Slope and y-intercept Determine a Linear Equation from the Slope and a Point Determine a Linear Equation from Two Points Determine a Linear Equation from Two Points by Graphing
Graphing linear equations.

Graph Slope-Intercept Equations
Extracting information from linear equations graphs.

Find the Equation from a Graph Find the Slope from a Graph Find the y-intercept from a Graph Find the x-intercept from a Graph Find the slope and y-intercept from a Graph Find the slope and intercepts from a Graph Find the slope, intercepts and equation from a Graph

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.

Solving linear equations with no "b" terms.

Solving ax = c Linear Equations Solving ax = c Linear Equations including negatives Solving x/a = c Linear Equations Solving x/a = c Linear Equations including negatives Solving a/x = c Linear Equations Solving a/x = c Linear Equations including negatives
Solving linear equations that include multiplication and "b" terms.

Solving ax + b = c Linear Equations Solving ax + b = c Linear Equations including negatives Solving ax - b = c Linear Equations Solving ax - b = c Linear Equations including negatives Solving ax ± b = c Linear Equations Solving ax ± b = c Linear Equations including negatives
Solving linear equations that include division and "b" terms.

Solving x/a ± b = c Linear Equations Solving x/a ± b = c Linear Equations including negatives Solving a/x ± b = c Linear Equations Solving a/x ± b = c Linear Equations including negatives Solving various a/x ± b = c and x/a ± b = c Linear Equations Solving various a/x ± b = c and x/a ± b = c Linear Equations including negatives
Solving linear equations that include all types and operations.

Solving linear equations of all types Solving linear equations of all types including negatives

Linear Systems

Solving systems of linear equations.

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
Solving systems of linear equations by graphing.

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 & Equations

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

Simplifying quadratic expressions (combining like terms).

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/Subtracting and Simplifying quadratic expressions.

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 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

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.

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 that 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)
Solving Quadratic equations that 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)

Other Polynomial and Monomial Expressions & Equations

Factoring non-quadratic expressions worksheets with various levels of complexity.

Simplifying polynomials that involve addition and subtraction.

Addition and Subtraction; 1 variable; 3 terms Addition and Subtraction; 1 variable; 4 terms Addition and Subtraction; 2 variables; 4 terms Addition and Subtraction; 2 variables; 5 terms Addition and Subtraction; 2 variables; 6 terms
Simplifying polynomials that involve multiplication and division.

Multiplication and Division; 1 variable; 3 terms Multiplication and Division; 1 variable; 4 terms Multiplication and Division; 2 variables; 4 terms Multiplication and Division; 2 variables; 5 terms
Simplifying polynomials that involve addition, subtraction, multiplication and division.

All Operations; 1 variable; 3 terms All Operations; 1 variable; 4 terms All Operations; 2 variables; 4 terms All Operations; 2 variables; 5 terms All Operations (Challenge)
Factoring 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
Factoring 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
Factoring 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
Multiplying polynomials with two factors.

Multiplying a monomial by a binomial Multiplying two binomials Multiplying a monomial by a trinomial Multiplying a binomial by a trinomial Multiplying two trinomials Multiplying two random mon/polynomials
Multiplying polynomials with three factors.

Multiplying a monomial by two binomials Multiplying three binomials Multiplying two binomials by a trinomial Multiplying a binomial by two trinomials Multiplying three trinomials Multiplying three random mon/polynomials

Inequalities Including Graphs

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

Writing the inequality that matches the graph.

Writing Inequalities for Graphs
Graphing inequalities on number lines.

Graphing Inequalities (Basic)
Solving linear inequalities.

Solving Inequalities Including a Third Term Solving Inequalities Including a Third Term and Multiplication Solving Inequalities Including a Third Term, Multiplication and Division