Algebra I All-in-One For Dummies

Book description

Solve for ‘X’ with this practical and easy guide to everything algebra 

A solid understanding of algebra is the key to unlocking other areas of math and science that rely on the concepts and skills that happen in a foundational Algebra class. Algebra I All-In-One For Dummies is the key! With it, you’ll get everything you need to solve the mystery of Algebra I.  

This book proves that algebra is for everyone with straightforward, unit-based instruction, hundreds of examples and practice problems, and two quizzes for every chapter – one in the book and another (totally different!) online. From graph and word problems to the FOIL method and common algebra terminology, Algebra I All-In-One For Dummies walks you step-by-step through ALL the concepts you need to know to slay your Algebra I class.  

In this handy guide, you’ll also: 

  • Receive instruction and tips on how to handle basic and intermediate algebraic tasks such as factoring and equation simplification 
  • Banish math anxiety forever by developing an intuitive understanding of how algebra works 
  • Get a handle on graphing problems and functions, as well as inequalities and word problems 

Algebra I All-In-One For Dummies is a must-read for Algebra students looking for an everything-in-one-book supplement to their coursework, as well as anyone hoping to brush up on their math before tackling a related subject, such as physics, chemistry, or a more advanced math topic.  

Table of contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Introduction
    1. About This Book
    2. Foolish Assumptions
    3. Icons Used in This Book
    4. Beyond the Book
    5. Where to Go from Here
  5. Book 1: Starting Out with Numbers and Properties
    1. Chapter 1: Assembling Your Tools: Number Systems
      1. Identifying Numbers by Name
      2. Placing Numbers on the Number Line
      3. Speaking in Algebra
      4. Taking Aim at Algebra-Speak
      5. Practice Questions Answers and Explanations
      6. Whaddya Know? Chapter 1 Quiz
      7. Answers to Chapter 1 Quiz
    2. Chapter 2: Deciphering Signs in Expressions
      1. Assigning Numbers Their Place
      2. Going in for Operations
      3. Tackling the Basic Binary Operations
      4. Working with Nothing: Zero and Signed Numbers
      5. Practice Questions Answers and Explanations
      6. Whaddya Know? Chapter 2 Quiz
      7. Answers to Chapter 2 Quiz
    3. Chapter 3: Incorporating Algebraic Properties
      1. Getting a Grip on Grouping Symbols
      2. Spreading, Grouping, and Changing the Order
      3. Relating Inverses and Identities
      4. Working with Factorial
      5. Applying the Greatest Integer Function
      6. Practice Question Answers and Explanations
      7. Whaddya Know? Chapter 3 Quiz
      8. Answers to Chapter 3 Quiz
    4. Chapter 4: Coordinating Fractions and Decimals
      1. Converting Improper Fractions and Mixed Numbers
      2. Finding Fraction Equivalences
      3. Making Proportional Statements
      4. Finding Common Denominators
      5. Applying Fractional Operations
      6. Simplifying Complex Fractions
      7. Performing Operations with Decimals
      8. Changing Fractions to Decimals and Vice Versa
      9. Practice Question Answers and Explanations
      10. Whaddya Know? Chapter 4 Quiz
      11. Answers to Chapter 4 Quiz
  6. Book 2: Operating on Operations
    1. Chapter 5: Taming Rampaging Radicals
      1. Simplifying Radical Terms
      2. Working through Radical Expressions
      3. Rationalizing Fractions
      4. Managing Radicals as Exponential Terms
      5. Estimating Answers
      6. Practice Questions Answers and Explanations
      7. Whaddya Know? Chapter 5 Quiz
      8. Answers to Chapter 5 Quiz
    2. Chapter 6: Exploring Exponents
      1. Powering up with Exponential Notation
      2. Using Negative Exponents
      3. Multiplying and Dividing Exponentials
      4. Raising Powers to Powers
      5. Testing the Power of Zero
      6. Writing Numbers with Scientific Notation
      7. Practice Questions Answers and Explanations
      8. Whaddya Know? Chapter 6 Quiz
      9. Answers to Chapter 6 Quiz
  7. Book 3: Making Things Simple by Simplifying
    1. Chapter 7: Simplifying Algebraic Expressions
      1. Addressing the Order of Operations
      2. Adding and Subtracting Like Terms
      3. Multiplying and Dividing Algebraically
      4. Gathering Terms with Grouping Symbols
      5. Evaluating Expressions
      6. Checking Your Answers
      7. Practice Questions Answers and Explanations
      8. Whaddya Know? Chapter 7 Quiz
      9. Answers to Chapter 7 Quiz
    2. Chapter 8: Working with Numbers in Their Prime
      1. Beginning with the Basics
      2. Composing Composite Numbers
      3. Writing Prime Factorizations
      4. Making Use of a Prime Factor
      5. Practice Questions Answers and Explanations
      6. Whaddya Know? Chapter 8 Quiz
      7. Answers to Chapter 8 Quiz
    3. Chapter 9: Specializing in Multiplication Matters
      1. Distributing One Factor Over Many
      2. Distributing Signs
      3. Mixing It up with Numbers and Variables
      4. Distributing More Than One Term
      5. Curses, Foiled Again — Or Not
      6. Squaring Binomials
      7. Multiplying the Sum and Difference of the Same Two Terms
      8. Powering Up Binomials
      9. Creating the Sum and Difference of Cubes
      10. Multiplying Conjugates
      11. Practice Questions Answers and Explanations
      12. Whaddya Know? Chapter 9 Quiz
      13. Answers to Chapter 9 Quiz
    4. Chapter 10: Dividing the Long Way to Simplify Algebraic Expressions
      1. Dividing by a Monomial
      2. Dividing by a Binomial
      3. Dividing by Polynomials with More Terms
      4. Simplifying Division Synthetically
      5. Practice Questions Answers and Explanations
      6. Whaddya Know? Chapter 10 Quiz
      7. Answers to Chapter 10 Quiz
  8. Book 4: Factoring
    1. Chapter 11: Figuring on Factoring
      1. Factoring out the Greatest Common Factor
      2. Using the Box Method
      3. Changing Factoring into a Division Problem
      4. Reducing Algebraic Fractions
      5. Practice Questions Answers and Explanations
      6. Whaddya Know? Chapter 11 Quiz
      7. Answers to Chapter 11 Quiz
    2. Chapter 12: Taking the Bite out of Binomial Factoring
      1. Reining in Big and Tiny Numbers
      2. Factoring the Difference of Squares
      3. Factoring Differences and Sums of Cubes
      4. Making Factoring a Multiple Mission
      5. Practice Questions Answers and Explanations
      6. Whaddya Know? Chapter 12 Quiz
      7. Answers to Chapter 12 Quiz
    3. Chapter 13: Factoring Trinomials and Special Polynomials
      1. Recognizing the Standard Quadratic Expression
      2. Focusing First on the Greatest Common Factor
      3. Factoring Quadratic-Like Trinomials
      4. Factoring Trinomials Using More Than One Method
      5. Factoring by Grouping
      6. Putting All the Factoring Together and Making Factoring Choices
      7. Incorporating the Remainder Theorem
      8. Practice Questions Answers and Explanations
      9. Whaddya Know? Chapter 13 Quiz
      10. Answers to Chapter 13 Quiz
  9. Book 5: Solving Linear and Polynomial Equations
    1. Chapter 14: Establishing Ground Rules for Solving Equations
      1. Creating the Correct Setup for Solving Equations
      2. Keeping Equations Balanced
      3. Solving with Reciprocals
      4. Making a List and Checking It Twice
      5. Practice Problems Answers and Explanations
      6. Whaddya Know? Chapter 14 Quiz
      7. Answers to Chapter 14 Quiz
    2. Chapter 15: Lining Up Linear Equations
      1. Playing by the Rules
      2. Using the Addition/Subtraction Property
      3. Using the Multiplication/Division Property
      4. Putting Several Operations Together
      5. Solving Linear Equations with Grouping Symbols
      6. Working with Proportions
      7. Solving for Variables in Formulas
      8. Practice Questions Answers and Explanations
      9. Whaddya Know? Chapter 15 Quiz
      10. Answers to Chapter 15 Quiz
    3. Chapter 16: Muscling Up to Quadratic Equations
      1. Using the Square-Root Rule
      2. Factoring for a Solution
      3. Solving Quadratics with Three Terms
      4. Using the Quadratic Formula
      5. Completing the Square
      6. Imagining the Worst with Imaginary Numbers
      7. Practice Problems Answers and Explanations
      8. Whaddya Know? Chapter 16 Quiz
      9. Answers to Chapter 16 Quiz
  10. Book 6: Dealing with Non-Polynomial Equations and Inequalities
    1. Chapter 17: Yielding to Higher Powers
      1. Queuing Up to Cubic Equations
      2. Determining How Many Possible Roots
      3. Applying the Rational Root Theorem
      4. Using the Factor/Root Theorem
      5. Solving by Factoring
      6. Solving Powers That Are Quadratic-Like
      7. Solving Synthetically
      8. Practice Questions Answers and Explanations
      9. Whaddya Know? Chapter 17 Quiz
      10. Answers to Chapter 17 Quiz
    2. Chapter 18: Reeling in Radical and Absolute Value Equations
      1. Raising Both Sides to Solve Radical Equations
      2. Doubling the Fun with Radical Equations
      3. Solving Absolute Value Equations
      4. Checking for Absolute Value Extraneous Roots
      5. Practice Questions Answers and Explanations
      6. Whaddya Know? Chapter 18 Quiz
      7. Answers to Chapter 18 Quiz
    3. Chapter 19: Getting Even with Inequalities
      1. Defining the Inequality Notation
      2. Using the Rules to Work on Inequality Statements
      3. Rewriting Inequalities Using Interval Notation
      4. Solving Linear Inequalities
      5. Solving Quadratic Inequalities
      6. Dealing with Polynomial and Rational Inequalities
      7. Solving Absolute-Value Inequalities
      8. Solving Complex Inequalities
      9. Practice Questions Answers and Explanations
      10. Whaddya Know? Chapter 19 Quiz
      11. Answers to Chapter 19 Quiz
  11. Book 7: Evaluating Formulas and Story Problems
    1. Chapter 20: Facing Up to Formulas
      1. Working with Formulas
      2. Measuring Up
      3. Deciphering Perimeter, Area, and Volume
      4. Getting Interested in Using Percent
      5. Working out the Combinations and Permutations
      6. Practice Questions Answers and Explanations
      7. Whaddya Know? Chapter 20 Quiz
      8. Answers to Chapter 20 Quiz
    2. Chapter 21: Making Formulas Work in Basic Story Problems
      1. Setting Up to Solve Story Problems
      2. Applying the Pythagorean Theorem
      3. Using Geometry to Solve Story Problems
      4. Working around Perimeter, Area, and Volume
      5. Going ’Round in Circles
      6. Putting Distance, Rate, and Time in a Formula
      7. Counting on Interest and Percent
      8. Practice Questions Answers and Explanations
      9. Whaddya Know? Chapter 21 Quiz
      10. Answers to Chapter 21 Quiz
    3. Chapter 22: Relating Values in Story Problems
      1. Tackling Age Problems
      2. Tackling Consecutive Integer Problems
      3. Working Together on Work Problems
      4. Throwing an Object into the Air
      5. Practice Questions Answers and Explanations
      6. Whaddya Know? Chapter 22 Quiz
      7. Answers to Chapter 22 Quiz
    4. Chapter 23: Measuring Up with Quality and Quantity Story Problems
      1. Achieving the Right Blend with Mixture Problems
      2. Concocting the Correct Solution 100% of the Time
      3. Dealing with Money Problems
      4. Practice Questions Answers and Explanations
      5. Whaddya Know? Chapter 23 Quiz
      6. Answers to Chapter 23 Quiz
  12. Book 8: Getting a Grip on Graphing
    1. Chapter 24: Getting a Handle on Graphing
      1. Thickening the Plot with Points
      2. Graphing Lines
      3. Computing Slopes of Lines
      4. Writing Equations of Lines
      5. Picking on Parallel and Perpendicular Lines
      6. Finding Distances between Points
      7. Finding Midpoints of Segments
      8. Practice Questions Answers and Explanations
      9. Whaddya Know? Chapter 24 Quiz
      10. Answers to Chapter 24 Quiz
    2. Chapter 25: Extending the Graphing Horizon
      1. Finding the Intersections of Lines
      2. Graphing Parabolas and Circles
      3. Curling Up with Parabolas
      4. Plotting and Plugging in Polynomial Graphs
      5. Investigating Graphs of Inequality Functions
      6. Taking on Absolute-Value Function Graphs
      7. Graphing with Transformations
      8. Practice Questions Answers and Explanations
      9. Whaddya Know? Chapter 25 Quiz
      10. Answers to Chapter 25 Quiz
    3. Chapter 26: Coordinating Systems of Equations and Graphing
      1. Defining Solutions of Systems of Equations
      2. Solving Systems of Linear Equations
      3. Solving Systems Involving Non-Linear Equations
      4. Taking on Systems of Three Linear Equations
      5. Practice Problems Answers and Explanations
      6. Whaddya Know? Chapter 26 Quiz
      7. Answers to Chapter 26 Quiz
  13. Index
  14. About the Author
  15. Connect with Dummies
  16. End User License Agreement

Product information

  • Title: Algebra I All-in-One For Dummies
  • Author(s): Mary Jane Sterling
  • Release date: December 2021
  • Publisher(s): For Dummies
  • ISBN: 9781119843047