# Algebra 1 Worksheets with Answers PDFs

Our Algebra 1 worksheets are designed to show you the intuitively obvious patterns of math, the easy way. The worksheets show you how algebra is used, and they systematically coverall the common use cases. The emphasis is on mastering the fundamental techniques that are used in school and even the real world.

For example, a common algebra class includes a rather convoluted technique known as “completing the square.” The purpose of completing the square is to derive an equation known as the “quadratic equation.” Our Algebra 1 worksheets won’t delve in to the confusing nonsense of how and why this equation even exists. Our approach is to just assume this equation is true, as it has been for hundreds of years and billions of algebra learners. Instead, we will show you how to use it. Correctly.

## What the Algebra 1 Worksheets Cover

At a very high level, Algebra 1 can be described as the math used with a single unknown variable x. You’ll first learn how to manipulate expressions containing variable x. Then, you will learn to extend these techniques to solve equations containing a variable, x. We will cover all the common cases such as polynomial expressions and equations.

The Algebra 1 worksheets build towards solving quadratic equations, which are an extremely common type of equation found in science, engineering and business. You will quickly master the fundamental techniques that are used in school and even the real world. Download the printer-friendly worksheets below, and also find the complete video solutions and lessons here.

###### Algebra 1 Worksheets, Problem Sets 1-4 pdfs

Problem Sets 1, 2, 3 and 4 cover the topics needed for algebra 1 success, including order of operations, distributing, scientific numbers, and cross multiplication.

###### Problem Set 5: Finally Some Algebra

PS5 focuses on solving equations involving a single variable x. It’s a rather lengthy worksheet covering the many, many common types of equations containing the variable x. You will learn how to systematically apply inverse operations to isolate the variable x algebraically. We commonly call these techniques simply solving an equation by hand, using paper and pencil.

###### Problem Set 6: Factoring Perfect Squares

PS6 covers an extremely specific technique known as factoring a difference of perfect squares. It’s a special case, yet we cover it extensively because it leads naturally to the factoring of more general types of expressions. Factoring, which is conceptually the opposite of a distributing, is probably the single most important all the algebra 1 topics.

###### Problem Set 7: Factoring Expressions

PS7 covers the topic of factoring for the general case of polynomial expressions. This is an important technique that will allow us to solve equations.

###### Problem Set 8: Factoring Equations
PS8 extends from PS7 to use factoring solve equations. Specifically, we focus on quadratic equations, which are very common.

###### Problem Set 9: The Quadratic Equation
PS9 introduces the quadratic equation, which is an alternate approach to solving equations by factoring as covered in PS8.

The big idea here is that there is always more than one way to get the answer to a math problem. The smart student understands the value of being able to do the same problem using multiple techniques, and get the same answer. This is the only way to build confidence with algebra, and it eventually leads to the import skill of simply seeing the easiest way to do a given problem.

The quadratic equation is sometimes contained in the  Algebra 2 topics. We will continue to investigate the concept of quadratic equations extensively in the algebra 2 worksheets.
###### Algebra 1 Worksheets, Problem Set 9 pdf 