Free Printable Worksheets for learning Algebra at the College level

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Algebra

Algebra is a branch of mathematics that deals with operations and relations involving variables. Algebraic equations are used to represent these operations and relations. It is an important tool in many areas of science, engineering, and technology.

Key Concepts and Definitions

  • Variable: A quantity that can take on different values, represented by a letter or symbol.
  • Expression: A mathematical phrase that contains variables, numbers, and operations.
  • Equation: A statement that two expressions are equal.
  • Coefficient: The numerical factor of a term containing a variable.
  • Linear Equation: An equation where the highest power of the variable is 1.
  • Quadratic Equation: An equation where the highest power of the variable is 2.
  • System of Equations: A set of equations that are solved simultaneously to find the values of the variables.
  • Inequalities: Expressions that show a relationship between two values, where one is larger or smaller than the other.
  • Graphing Equations: A way to visually represent equations on a coordinate plane.

Important Information

  • To solve algebraic equations, we use the properties of equality, such as the addition, subtraction, multiplication, and division properties.
  • It is important to simplify expressions by combining like terms and applying the order of operations.
  • Factoring is an important tool used to simplify equations and solve quadratic equations.
  • Solving systems of equations involves finding the values of the variables that satisfy both equations at the same time.
  • Graphing equations allows us to visualize the solution of an equation and analyze its behavior.
  • Inequalities are solved similarly to equations, but with a few key differences, such as the direction of the inequality sign.

Takeaways

  • Algebra is a branch of mathematics that deals with variables and equations.
  • Understanding key concepts such as variables, expressions, equations, and inequalities is essential for success in algebra.
  • The properties of equality, factoring, and graphing equations are important tools for solving algebraic problems.
  • Solving systems of equations involves finding the values of variables that satisfy both equations.
  • Inequalities are solved similarly to equations, but with some important differences.

Here's some sample Algebra vocabulary lists Sign in to generate your own vocabulary list worksheet.

Word Definition
Algebra The branch of mathematics in which letters and symbols are used to represent numbers and quantities in formulae and equations.
Equation A statement that two expressions are equal, for example 2x + 3 = 7.
Variable A symbol, usually a letter, used to represent a value that can change in an equation or formula. For example, in the equation 3x + 2 = 8, x is the variable.
Coefficient A numerical or constant factor in an algebraic term, for example 3 in the term 3x.
Expression A mathematical phrase with numbers, variables, and operation symbols, but no equals sign. For example, 4x + 7y - 2z.
Formula A scientific equation used to calculate a specific value, such as the quadratic formula or the Pythagorean theorem.
Linear Describing an equation whose graph is a straight line.
Quadratic Describing an equation whose highest power is x2.
Polynomial An expression consisting of variables and coefficients, and involving only the operations of addition, subtraction, and multiplication.
Exponent A number or symbol in a mathematical formula showing how many times a quantity is to be multiplied by itself. For example, 2 is the base and 3 is the exponent in the expression 2^3.
Factor A number, variable, or expression that is multiplied with another to produce a given result. For example, 2 and 3 are factors of 6.
Function A relation between a set of inputs and a set of possible outputs, in which each input is related to exactly one output.
Inequality A statement indicating that two quantities are NOT equal. For example, x < 5 is a simple inequality.
Order of Operations A set of conventions used in mathematical expressions to determine the sequence in which operations are performed.
Distributive property A property used to simplify expressions in which a number or variable is multiplied by the sum or difference of two or more terms.
Absolute value The distance of a number from zero on a number line, without regard to its positive or negative sign.
Reciprocal The inverse of a number, where multiplying the number by its reciprocal results in the value 1. For example, the reciprocal of 2 is 1/2.
System of equations A set of two or more equations that must be solved simultaneously, such as 2x + 3y = 7 and 4x - y = 1.
Y-intercept The point where a line or curve intersects the y-axis in a graph, where x = 0.
Slope The measure of steepness of a line or curve on a graph, represented by the ratio of the vertical change to the horizontal change.

Here's some sample Algebra study guides Sign in to generate your own study guide worksheet.

Algebra Study Guide

Introduction to Algebra

Definition of Algebra

Algebra is a branch of mathematics that deals with variables, constants, and operations. It involves solving equations for unknown variables.

Basic Concepts of Algebra

  • Variables and Constants
  • Expressions
  • Equations
  • Inequalities
  • Functions

Algebraic Operations

Properties of Operations

  • Commutative Property
  • Associative Property
  • Distributive Property

Basic Operations

  • Addition
  • Subtraction
  • Multiplication
  • Division

Exponents and Radicals

  • Rules of Exponents
  • Simplifying Radicals

Linear Equations and Functions

Graphing Linear Equations

  • Slope-Intercept Form
  • Point-Slope Form

Solving Linear Equations

  • One-Step Equations
  • Two-Step Equations
  • Multi-Step Equations
  • Systems of Equations

Linear Functions

  • Definition of a Function
  • Domain and Range
  • Graphing Linear Functions

Quadratic Equations and Functions

Solving Quadratic Equations

  • Factoring
  • Quadratic Formula
  • Completing the Square

Quadratic Functions

  • Graphing Quadratic Functions
  • Vertex Form

Inequalities

Solving Inequalities

  • One-Step Inequalities
  • Two-Step Inequalities
  • Multi-Step Inequalities

Graphing Inequalities

  • One-Variable Inequalities
  • Two-Variable Inequalities

Polynomials

Adding and Subtracting Polynomials

  • Basic Operations
  • Factoring

Multiplying Polynomials

  • FOIL Method
  • Grid Method

Rational Expressions

Simplifying Rational Expressions

  • Factoring
  • Multiplying and Dividing

Solving Rational Equations

  • Basic Method

Conclusion

This study guide should provide you with the basic tools necessary to master algebra. Remember to practice regularly and ask for help when needed. Good luck and happy studying!

Here's some sample Algebra practice sheets Sign in to generate your own practice sheet worksheet.

Algebra Practice Sheet

Solve for x:

  1. 3x + 5 = 23
  2. 2(x - 3) = 16
  3. 4x + 8 = 20x - 12
  4. 2x2 + 5x - 3 = 0

Solve for y:

  1. 3y - 4 = 5y + 7
  2. 5(y + 2) = 4y - 6
  3. 2y + 5 = 3(4y - 1)
  4. y2 + 4y + 4 = 0

Simplify:

  1. (2x + 3) + (4x2 - x + 9)
  2. 3(x - 4) - 2(x + 5)
  3. 2(3x - 7) + 4(x + 2)
  4. (5x2 + 2x - 1) - (2x2 - 3x + 5)

Factorise:

  1. x2 + 7x + 12
  2. 3x2 - 8x - 3
  3. 2x2 + 7x + 3

Solve the system of equations:

  1. 2x + 3y = 7 5x - 4y = -2

  2. 4x - 3y = 8 2x + y = 2

  3. 3x + 2y = 10 4x - y = 8

Solve for the specified variable:

  1. d = rt (solve for r)
  2. F = 9/5C + 32 (solve for C)

Note: Round all answers to the nearest hundredth.

Algebra Practice Sheet

Equations

  1. Solve for x: 2x + 3 = 7
  2. Solve for x: 3x - 4 = 10
  3. Solve for x: 5x + 6 = -2
  4. Solve for x: 4x - 7 = 11
  5. Solve for x: 6x + 3 = -1

Inequalities

  1. Solve for x: 2x + 3 < 7
  2. Solve for x: 3x - 4 > 10
  3. Solve for x: 5x + 6 > -2
  4. Solve for x: 4x - 7 < 11
  5. Solve for x: 6x + 3 > -1

Exponents

  1. Simplify: (x2)3
  2. Simplify: (2x5)2
  3. Simplify: (3x4)3
  4. Simplify: (4x3)2
  5. Simplify: (5x2)3

Polynomials

  1. Simplify: 3x2 + 5x + 2
  2. Simplify: 4x2 + 7x - 3
  3. Simplify: 5x2 - 4x - 5
  4. Simplify: 6x2 + 2x + 4
  5. Simplify: 7x2 - 3x + 6

Factoring

  1. Factor: x2 + 4x + 4
  2. Factor: x2 + 5x + 6
  3. Factor: x2 - 3x + 2
  4. Factor: x2 - 4x + 4
  5. Factor: x2 - 5x + 6

Algebra Practice Sheet

Introduction

Algebra is the branch of mathematics that deals with symbols and the rules for manipulating those symbols. In this practice sheet, we will cover the basics of algebra at the college level.

Basic Algebraic Expressions

A basic algebraic expression consists of numbers and/or variables combined with arithmetic operations.

  1. Write an algebraic expression for the sum of x and y.

  2. Write an algebraic expression for the product of x and y.

  3. Write an algebraic expression for the difference of x and y.

Solving Linear Equations

A linear equation is an equation that can be written in the form ax + b = c, where a, b, and c are constants and x is a variable.

  1. Solve the equation 3x + 5 = 12.

  2. Solve the equation 4x - 2 = 10.

  3. Solve the equation 6x = 24.

Graphing Linear Equations

Graphing linear equations involves plotting points that satisfy the equation and connecting the points to form a line.

  1. Plot the points (2,4) and (4,8) on the x-y plane and draw the line that connects them.

  2. Plot the points (3,6) and (6,12) on the x-y plane and draw the line that connects them.

  3. Plot the points (1,2) and (2,4) on the x-y plane and draw the line that connects them.

Quadratic Equations

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are constants and x is a variable.

  1. Solve the equation x2 + 4x + 4 = 0.

  2. Solve the equation 2x2 - 6x + 9 = 0.

  3. Solve the equation 3x2 + 6x + 3 = 0.

Here's some sample Algebra quizzes Sign in to generate your own quiz worksheet.

Problem Answer
What is the quadratic formula and what does it give you? The quadratic formula is: $$x=\frac{-b \pm \sqrt{b2-4ac}}{2a}$$ It gives you the solutions (roots) to a quadratic equation of the form $ax2+bx+c=0$.
What is the difference between an expression and an equation? An expression contains variables, numbers, and operations (like addition or multiplication), but it does not have an equal sign. An equation is similar, but it has an equal sign and states that two expressions are equal.
Simplify the expression: $2x2+3x2-5x$ Combine like terms: $5x2-5x$
Solve for $x$: $3(2x-5)=21$ Distribute: $6x-15=21$. Add 15 to both sides: $6x=36$. Divide by 6: $x=6$.
Simplify the expression: $\frac{3x3y2-6x2y3}{3xy2}$ Factor out $3xy2$ from both terms in the numerator: $\frac{3xy2(x-2y)}{3xy2}$. Cancel out the $3xy2$: $x-2y$.
Factor the expression: $x2-4x+3$ Find two numbers that multiply to 3 and add to -4. These are -1 and -3. Rewrite the expression: $x2-3x-x+3$. Factor by grouping: $(x2-3x)-(x-3)$. Factor each group: $x(x-3)-(x-3)$. Factor out the common factor: $(x-3)(x-1)$.
Solve the system of equations: $$\begin{cases}2x+3y=8\-x+4y=6\end{cases}$$ Solve the second equation for $x$: $x=4y-6$. Substitute into the first equation: $2(4y-6)+3y=8$. Simplify: $11y=20$. Solve for $y$: $y=\frac{20}{11}$. Substitute back into either equation to solve for $x$: $-x+4(\frac{20}{11})=6$. Simplify: $x=\frac{14}{11}$.
Simplify the expression: $(x3y{-2})2(x{-1}y3){-1}$ Simplify each term separately: $(x6y{-4})(y{-3}x)$. Rearrange the terms: $x(y{-4}x6y3)$. Combine like terms: $x{7}y{-1}$.
What is the difference between a coefficient and a constant? A coefficient is a number that multiplies a variable (for example, the coefficient of $3x$ is 3). A constant is a number that stands by itself (for example, the constant in $2+5x$ is 2).
Solve the equation: $ x+2
Question Answer
What is the slope of the line y = 4x + 2? 4
What is the equation of the line that passes through the points (2, 3) and (4, 5)? y = 1x + 1
What is the equation of the line that is perpendicular to the line y = -2x + 5 and passes through the point (1, 2)? y = 2x - 7
What is the equation of the circle with center (2, -3) and radius 5? (x - 2)2 + (y + 3)2 = 25
What is the equation of the parabola with vertex (2, 3) and focus (2, 4)? y = (x - 2)2 + 3
What is the equation of the ellipse with center (2, 3) and major axis length 8 and minor axis length 4? (x - 2)2/64 + (y - 3)2/16 = 1
What is the equation of the hyperbola with center (2, 3) and asymptotes y = -2x + 7 and y = 2x + 1? (x - 2)2/4 - (y - 3)2/9 = 1
What is the equation of the line that is parallel to the line y = -3x + 4 and passes through the point (1, -2)? y = -3x + 6
What is the equation of the line that passes through the points (2, 3) and (5, 4)? y = -1/3x + 5
What is the equation of the line that passes through the point (2, 3) and has a slope of -2? y = -2x + 7

Algebra Quiz

Questions Answers
What is the solution to the equation x + 3 = 8? 5
What is the slope of the line y = 3x + 2? 3
What is the equation of the line that passes through the points (2,5) and (3,7)? y = 2x + 1
What is the inverse of the function y = x + 4? y = x - 4
What is the equation for the circle with radius 5 centered at (3,4)? (x - 3)2 + (y - 4)2 = 25
What is the value of x in the equation 5x = 25? 5
What is the slope-intercept form of the equation y = 4x + 3? y = 4x + 3
What is the equation for the line that is perpendicular to y = -3x + 4 and passes through the point (5,7)? y = 3x - 17
What is the solution to the system of equations y = x + 4, y = 3x - 2? x = -2, y = 2
What is the equation of the line that is parallel to y = -3x + 4 and passes through the point (6,2)? y = -3x - 10
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