algebra problems and answers pdf

Free Algebra Questions and Problems with Answers

Free intermediate and college algebra questions and problems are presented along with answers and explanations. Free worksheets to download are also included.

Intermediate Algebra Questions with Answers

• sample 1 .(student generated solutions). Also included are the solutions with full explanations .
• sample 2 .(True / False type). Also included are the solutions with full explanations .
• sample 3 .(student generated solutions). solutions with full explanations are included.
• sample 4 .(True / False type). solutions with full explanations included.
• sample 5 .(Multiple choice questions type). Also included are the solutions with full explanations .
• sample 6 .(True / False type). solutions with full explanations included.

Intermediate Algebra Problems with Detailed Solutions

• Algebra Problems .
• Intermediate Algebra Problems With Answers - sample 1 : equations, system of equations, percent problems, relations and functions.
• Intermediate Algebra Problems With Answers - sample 2 :Find equation of line, domain and range from graph, midpoint and distance of line segments, slopes of perpendicular and parallel lines.
• Intermediate Algebra Problems With Answers - sample 3 : equations and system of equations, quadratic equations, function given by a table, intersections of lines, problems.
• Intermediate Algebra Problems With Answers - sample 4 . Functions, domain, range, zeros.
• Intermediate Algebra Problems With Answers - sample 5 . Scientific Notation
• Intermediate Algebra Problems With Answers - sample 6 . Equations of Lines
• Intermediate Algebra Problems With Answers - sample 7 . Slopes of Lines
• Intermediate Algebra Problems With Answers - sample 8 . Absolute Value Expressions
• Intermediate Algebra Problems With Answers - sample 9 . Solve Absolute Value Equations
• Intermediate Algebra Problems With Answers - sample 10 . Solve Absolute Value Inequalities
• Intermediate Algebra Problems With Answers - sample 11 . Simplify Algebraic Expressions by Removing Brackets
• Intermediate Algebra Problems With Answers - sample 12 . Simplify Algebraic Expressions with Exponents

Intermediate Algebra Worksheets

• Worksheet (1) .
• Worksheet (2) .
• Worksheet (3) .
• Worksheet (4) .
• Worksheet (5) .
• Worksheet (6) .

College Algebra Questions with Answers

• sample 1 .(multiple choice questions). Also Detailed solutions with full explanations are included
• sample 2 . (multiple choice questions)

College Algebra Problems with Answers

• sample 1: Quadratic Functions .
• sample 2: Composite and Inverse Functions .
• sample 3: Exponential and Logarithmic Functions .
• sample 4: Graphs of Functions .
• sample 5: Find Domain and Range of Functions .
• sample 6: Problems on Polynomials : Graphs, Factoring, Finding, Multiplying, Dividing, Factor theorem, Zeros
• sample 7: Equation of Circle : Finding equations, center, radius of circles
• sample 8: Equation of Ellipse : Finding equations, foci, center, vertices of ellipses
• sample 9: Equation of Parabola : Finding equations, focus, vertex, axis, directrix of parabola.
• sample 10: Equation of Hyperbola : Finding equations, foci, center and vertices of hyperbola.

College Algebra Worksheets

• Worksheet (1): Graphs of Basic Functions .
• Worksheet (2): Exponential Growth and Decay Problems .
• Worksheet (3): Graphing Exponential Functions .
• Worksheet (4): Graphing Logarithmic Functions .
• Worksheet (5): Solve Exponential Equations .
• Worksheet (6): Solve Logarithmic Equations .
• Worksheet (7): Multiple Choice Questions on Polynomials and Solutions
• Worksheet (8): Multiple Choice Questions on Rational Functions and Solutions .
• Worksheet (9): Graphing Inverse Functions .

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Free Math Worksheets — Over 100k free practice problems on Khan Academy

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Free Printable Math Worksheets for Algebra 1

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• Writing variable expressions
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• Number sets
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• The distributive property
• Combining like terms
• Percent of change
• One-step equations
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• Absolute value equations
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• Direct variation
• Solving systems of equations by graphing
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• Systems of equations word problems
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• Discrete exponential growth and decay word problems
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• Naming polynomials
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• Dividing rational expressions
• Adding and subtracting rational expressions
• Finding trig. ratios
• Finding angles of triangles
• Finding side lengths of triangles
• Visualizing data
• Center and spread of data
• Scatter plots
• Using statistical models

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Basic Algebra Worksheets

Welcome to the Math Salamanders' Basic Algebra Worksheets. Here you will find a range of algebra worksheets to help you learn about basic algebra, including generating and calculating algebraic expressions and solving simple problems.

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Generate the Expression Worksheets

Calculate the Expression Worksheets

• Solve the Equations Worksheets
• More recommended resources
• Basic Algebra Online Quiz

Want to gain a basic understanding of algebra?

Looking for some simple algebra worksheets?

Do you need a bank of useful algebra resources?

Look no further! The pages you need are below!

Here is our selection of basic algebra sheets to try.

We have split the worksheets up into 3 different sections:

• Generate the algebra - and write your own algebraic expressions;
• Calculate the algebra - work out the value of different expressions;
• Solve the algebra - find the value of the term in the equation.

By splitting the algebra up into sections, you only need to concentrate on one aspect at a time!

Each question sheet comes with its own separate answer sheet.

Want to test yourself to see how well you have understood this skill?.

• Try our NEW quick quiz at the bottom of this page.

What is an algebraic expression?

An expression is a mathematical statement where variables and operations are combined.

• 2a + 5 is an expression involving the variable a
• 5(y 2 - 6) is another expression

What is an algebraic equation?

An equation is where an algebraic expression is equal to something, which might be a number, or another algebraic expression.

• 2a + 5 = 7 is an equation
• 5(y 2 - 6) = 3y + 8 is another equation

How to Generate an Expression

When we are generating an expression, we are taking a rule and turning it into algebra.

• Subtract 6 from n could be written as n - 6.
• Multiply d by 4 could be written as d x 4 or 4d.
• Add 5 to p and then double the result is written as (p + 5) x 2 or 2(p + 5)

How to Calculate an Expression

When we are calculating the value of an expression, we work out the value of the expression when we give a value to the variable.

• p + 5 has a value of 11 when p = 6 because 6 + 5 = 11
• 4(n - 2) has a value of 32 when n = 10 because 4 x (10 - 2) = 4 x 8 = 32
• 4(n - 2) has a value of -8 when n = 0 because 4 x (0 - 2) = 4 x (-2) = -8

How to Solve a Simple Equation

When we are solving an equation, we are finding out the value(s) of the variable in the equation.

• If p + 5 = 9 then p = 4 because 4 + 5 = 9
• then (n - 2) = 28 ÷ 4 = 7
• if (n - 2) = 7 then n = 7 + 2 = 9
• Answer: n = 9
• means that 3f = 12
• so f = 12 ÷ 3 = 4
• Answer: f = 4

Basic Algebra Worksheets for kids

• Generate the Expression 1
• PDF version
• Generate the Expression 2
• Generate the Expression 3

Generate the Expression Word Problems

• Algebra Word Problems 1
• Algebra Word Problems 2
• Algebra Word Problems 3
• Algebra Word Problems 3 UK Version

Algebra Word Problems Walkthrough Video

This short video walkthrough shows the problems from our Algebra Word Problems Worksheet 2 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

• Calculate the Expression 1
• Calculate the Expression 2
• Calculate the Expression 3

Solve the Equation Worksheets

• Solve the Equation 1
• Solve the Equation 2
• Solve the Equation 3

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Free Algebra Problem Solver

The Mathway Calculator is a great way to solve algebra problems that you can type into a calculator.

Try using this online calculator tool to solve one of your problems and watch it work!

There are a range of calculators to choose from to meet your needs.

The Mathway problem solver will answer your problem instantly and also give you a link to view each of the steps needed.

If you choose to 'View the steps' you will be directed to the Mathway website where you will be able to see in more detail each of the steps needed to solve the problem. Please note that Mathway may charge you a small fee for this!

• 6th Grade Distributive Property Worksheets

The sheets on this page have been designed to factorize and expand a range of simple expressions using the distributive property..

• Expressions and Equations 6th Grade

The sheets on this page have been specially designed for 6th graders and are a great introduction to expressions and equations.

Factorising Quadratic Equations

Are you stuck on a quadratic equation and don't know what to do?

Are you looking for some worksheets on factorising quadratic equations to print out?

Take a look at our support pages on quadratic equations where you will hopefully find what you are looking for.

• Factorising Quadratic Equations Support page
• Factoring Quadratic Equations worksheets
• Algebra Math Games

If you are looking for a fun printable algebra game to play then try out our algebra game page.

You will find a range of algebra games that make learning algebra fun and non-threatening.

The only equipment you need is a scientific calculator, some dice, and a few counters!

PEMDAS Worksheets

The sheets in this section involve using parentheses and exponents in simple calculations.

There are also lots of worksheets designed to practice and learn about PEMDAS.

Using these worksheets will help your child to:

• know and understand how parentheses works;
• understand how exponents work in simple calculations.
• understand and use PEMDAS to solve a range of problems.
• PEMDAS Problems Worksheets 5th Grade
• 6th Grade Order of Operations

Interactive Equality Explorer

This interactive equality explorer has been produced by PhET Interactive Simulations at the University of Colorado.

It is a useful tool for exploring different ideas including negative numbers and algebra equations and equality.

Probably the most useful part of the app is to use the 'Solve It' section once you are confident how it works.

You can then select your level of difficulty and start solving some algebraic equations by getting your variables onto one side of the equation and the numerical values on the other, and then multiplying or dividing the equation until you find the value of the required variable.

• Interactive Equality Explorer by PhET

Basic Algebra Quiz

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

For more information on the information we collect, please take a look at our Privacy Policy

We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your knowledge and skill at generating and calculating expressions, as well as solving equations.

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Free Math Printable Worksheets with Answer Keys and Activities

Other free resources.

Feel free to download and enjoy these free worksheets on functions and relations. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

• Long Division with Remainders
• Long Division with Remainders #2 (Zeros in the Quotient)
• Long Division with 2 Digit Divisors
• Whole Number by Unit Fraction
• Equation of Circle
• Simplify Imaginary Numbers
• Adding and Subtracting Complex Numbers
• Multiplying Complex Numbers
• Dividing Complex Numbers
• Dividing Complex Number (Advanced)
• End of Unit, Review Sheet
• Distance Formula
• Simplify Rational Exponents (Algebra 2)
• Solve Equations with Rational Exponents (Algebra 2)
• Solve Equations with variables in Exponents (Algebra 2)
• Exponential Growth (no answer key on this one, sorry)
• Compound Interest Worksheet #1 (No logs)
• Compound Interest Worksheet (Logarithms required)
• Factor Trinomials Worksheet
• Factor by Grouping
• Domain and Range (Algebra 1)
• Functions vs Relations (Distinguish function from relation, state domain etc..) (Algebra 2)
• Evaluating Functions (Algebra 2)
• 1 to 1 Functions (Algebra 2)
• Composition of Functions (Algebra 2)
• Inverse Functions Worksheet (Algebra 2)
• Operations with Functions (Algebra 2)
• Functions Review Worksheet (Algebra 2)
• Logarithmic Equations
• Properties of Logarithms Worksheet
• Product Rule of Logarithms
• Power Rule of Logarithms
• Quotient Rule of Logarithms
• Solve Quadratic Equations by Factoring
• Quadratic Formula Worksheets (3 different sheets)
• Quadratic Formula Worksheet (Real solutions)
• Quadratic Formula (Complex solutions)
• Quadratic Formula (Both real and complex solutions)
• Discriminant and Nature of the Roots
• Solve Quadratic Equations by Completing the Square
• Sum and Product of Roots
• Radical Equations
• Mixed Problems on Writing Equations of Lines
• Slope Intercept Form Worksheet
• Standard Form Worksheet
• Point Slope Worksheet
• Write Equation of Line from the Slope and 1 Point
• Write Equation of Line From Two Points
• Equation of Line Parallel to Another Line and Through a Point
• Equation of Line Perpendicular to Another Line and Through a Point
• Slope of a Line
• Perpendicular Bisector of Segment
• Write Equation of Line Mixed Review
• Word Problems
• Multiplying Monomials Worksheet
• Multiplying and Dividing Monomials Sheet
• Adding and Subtracting Polynomials worksheet
• Multiplying Monomials with Polynomials Worksheet
• Multiplying Binomials Worksheet
• Multiplying Polynomials
• Simplifying Polynomials
• Factoring Trinomials
• Operations with Polynomials Worksheet
• Dividing Radicals
• Simplify Radicals Worksheet
• Adding Radicals
• Multiplying Radicals Worksheet
• Radicals Review (Mixed review worksheet on radicals and square roots)
• Rationalizing the Denominator (Algebra 2)
• Radical Equations (Algebra 2)
• Solve Systems of Equations Graphically
• Solve Systems of Equations by Elimination
• Solve by Substitution
• Solve Systems of Equations (Mixed Review)
• Activity on Systems of Equations (Create an advertisement for your favorite method to Solve Systems of Equations )
• Real World Connections (Compare cell phone plans)
• Identifying Fractions

Trigonomnetry

• Law of Sines and Cosines Worksheet (This sheet is a summative worksheet that focuses on deciding when to use the law of sines or cosines as well as on using both formulas to solve for a single triangle's side or angle)
• Law of Sines
• Ambiguous Case of the Law of Sines
• Law of Cosines
• Vector Worksheet
• Sine, Cosine, Tangent, to Find Side Length
• Sine, Cosine, Tangent Chart
• Inverse Trig Functions
• Real World Applications of SOHCATOA
• Mixed Review
• Unit Circle Worksheet
• Graphing Sine and Cosine Worksheet
• Sine Cosine Graphs with Vertical Translations
• Sine, Cosine, Tangent Graphs with Phase Shifts
• Sine, Cosine, Tangent Graphs with Change in Period, Amplitude and Phase Shifts (All Translations)
• Tangent Equation, Graph Worksheet
• Graphing Sine, Cosine, Tangent with Change in Period
• Cumulative, Summative Worksheet on Periodic Trig Functions - period, amplitude, phase shift, radians, degrees,unit circle
• Ratio and Proportion
• Similar Polygons
• Area of Triangle
• Interior Angles of Polygons
• Exterior Angles of Polygons

Arcs and Angles formed by Intersecting Chords

Angles and arcs formed by tangents and secants

Tangents, Secants and Side Lengths

Math Worksheet on the Angle formed by the intersection of a Tangent and a Chord

Cumulative Review Problems of All Formulas

• Associated Powerpoint
• Associated PowerPoint
• System of Linear Equations Worksheet
• System of Linear Equations - Real World Application
• Compositions of Reflections. Reflections Over Intersecting Lines as Rotations

All of these worksheets and activities are available for free so long as they are used solely for educational, noncommercial purposes and are not distributed outside of a specific teacher's classroom.

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Unit 1: Algebra foundations

Unit 2: solving equations & inequalities, unit 3: working with units, unit 4: linear equations & graphs, unit 5: forms of linear equations, unit 6: systems of equations, unit 7: inequalities (systems & graphs), unit 8: functions, unit 9: sequences, unit 10: absolute value & piecewise functions, unit 11: exponents & radicals, unit 12: exponential growth & decay, unit 13: quadratics: multiplying & factoring, unit 14: quadratic functions & equations, unit 15: irrational numbers, unit 16: creativity in algebra.

Practice Test

For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer.

For the following exercises, evaluate the expression.

2 ( x + 3 ) − 12 ; x = 2 2 ( x + 3 ) − 12 ; x = 2

y ( 3 + 3 ) 2 − 26 ; y = 1 y ( 3 + 3 ) 2 − 26 ; y = 1

Write the number in standard notation: 3.1415 × 10 6 3.1415 × 10 6

Write the number in scientific notation: 0.0000000212.

For the following exercises, simplify the expression.

−2 ⋅ ( 2 + 3 ⋅ 2 ) 2 + 144 −2 ⋅ ( 2 + 3 ⋅ 2 ) 2 + 144

4 ( x + 3 ) − ( 6 x + 2 ) 4 ( x + 3 ) − ( 6 x + 2 )

3 5 ⋅ 3 −3 3 5 ⋅ 3 −3

( 2 3 ) 3 ( 2 3 ) 3

8 x 3 ( 2 x ) 2 8 x 3 ( 2 x ) 2

( 16 y 0 ) 2 y −2 ( 16 y 0 ) 2 y −2

9 x 16 9 x 16

121 b 2 1 + b 121 b 2 1 + b

6 24 + 7 54 − 12 6 6 24 + 7 54 − 12 6

−8 3 625 4 −8 3 625 4

( 13 q 3 + 2 q 2 − 3 ) − ( 6 q 2 + 5 q − 3 ) ( 13 q 3 + 2 q 2 − 3 ) − ( 6 q 2 + 5 q − 3 )

( 6 p 2 + 2 p + 1 ) + ( 9 p 2 −1 ) ( 6 p 2 + 2 p + 1 ) + ( 9 p 2 −1 )

( n − 2 ) ( n 2 − 4 n + 4 ) ( n − 2 ) ( n 2 − 4 n + 4 )

( a − 2 b ) ( 2 a + b ) ( a − 2 b ) ( 2 a + b )

For the following exercises, factor the polynomial.

16 x 2 − 81 16 x 2 − 81

y 2 + 12 y + 36 y 2 + 12 y + 36

27 c 3 − 1331 27 c 3 − 1331

3 x ( x − 6 ) − 1 4 + 2 ( x − 6 ) 3 4 3 x ( x − 6 ) − 1 4 + 2 ( x − 6 ) 3 4

2 z 2 + 7 z + 3 z 2 − 9 ⋅ 4 z 2 − 15 z + 9 4 z 2 − 1 2 z 2 + 7 z + 3 z 2 − 9 ⋅ 4 z 2 − 15 z + 9 4 z 2 − 1

x y + 2 x x y + 2 x

a 2 b − 2 b 9 a 3 a − 2 b 6 a a 2 b − 2 b 9 a 3 a − 2 b 6 a

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Access for free at https://openstax.org/books/college-algebra/pages/1-introduction-to-prerequisites

• Authors: Jay Abramson
• Publisher/website: OpenStax
• Book title: College Algebra
• Publication date: Feb 13, 2015
• Location: Houston, Texas
• Book URL: https://openstax.org/books/college-algebra/pages/1-introduction-to-prerequisites
• Section URL: https://openstax.org/books/college-algebra/pages/1-practice-test

© Dec 8, 2021 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.