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Master Math: Algebra

Book Description

Get ready to master the principles and operations of algebra! Master Math: Algebra is a comprehensive reference guide that explains and clarifies algebraic principles in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced topics that will help prepare you for pre-calculus and calculus, the book helps clarify algebra using step-by-step procedures and solutions, along with examples and applications. A complete table of contents and a comprehensive index enable you to quickly find specific topics, and the approachable style and format facilitate an understanding of what can be intimidating and tricky skills. Perfect for both students who need some extra help or rusty professionals who want to brush up, Master Math: Algebra will help you master everything from simple algebraic equations to polynomials and graphing.

Table of Contents

  1. Copyright
  2. Acknowledgments
  3. About the Author
  4. Introduction
  5. 1. Translating Problems into Algebraic Equations
    1. 1.1. Introduction to Algebra
    2. 1.2. Translating English into Algebraic Equations
    3. 1.3. Algebra Terminology
    4. 1.4. Simple Word Problems
      1. Perimeter Word Problems
      2. Area Word Problems
      3. Volume Word Problems
      4. Price and Profit Word Problems
      5. Percent Word Problems
      6. Distance Word Problems
      7. Work Word Problems
      8. Mixture Word Problems
      9. Interest Word Problems
  6. 2. Simplifying Algebraic Equations
    1. 2.1. Commutative, Associative, and Distributive Properties of Addition and Multiplication
    2. 2.2. Using Associative and Distributive Properties
      1. Using the Associative Property
      2. Using the Distributive Property
    3. 2.3. Combining Like Terms in Algebraic Equations
    4. 2.4. Simplifying Algebraic Equations by Removing Parentheses and Combining Like Terms
    5. 2.5. The General Order to Perform Operations in Algebra
  7. 3. Solving Simple Algebraic Equations
    1. 3.1. Solving Algebraic Equations That Have One Unknown Variable
    2. 3.2. Solving Simple Algebraic Equations Containing Fractions
    3. 3.3. Solving Simple Algebraic Equations Containing Radicals
  8. 4. Algebraic Inequalities
    1. 4.1. Solving Algebraic Inequalities with One Unknown Variable
  9. 5. Polynomials
    1. 5.1. Definitions
    2. 5.2. Addition of Polynomials
    3. 5.3. Subtraction of Polynomials
    4. 5.4. Multiplication of Polynomials
    5. 5.5. Division of Polynomials
    6. 5.6. Factoring Polynomials with a Common Monomial Factor
    7. 5.7. Factoring Polynomial Expressions with the Form ax2 + bx + c
      1. Special Binomial Products to Remember
  10. 6. Algebraic Fractions with Polynomial Expressions
    1. 6.1. Factoring and Reducing Algebraic Fractions
    2. 6.2. Multiplication of Algebraic Fractions
    3. 6.3. Division of Algebraic Fractions
    4. 6.4. Addition and Subtraction of Algebraic Fractions
      1. Fractions with Common Denominators
      2. Fractions with Different Denominators
  11. 7. Solving Quadratic Polynomial Equations with One Unknown Variable
    1. 7.1. Defining and Solving Quadratic (Polynomial) Equations
    2. 7.2. Using Factoring to Solve Quadratic Equations with One Unknown Variable
    3. 7.3. Using the Quadratic Formula to Solve Quadratic Equations with One Unknown Variable
    4. 7.4. Using the Square Root Method to Solve Quadratic Equations with One Unknown Variable
    5. 7.5. Using the Method of Completing the Square to Solve Quadratic Equations with One Unknown Variable
  12. 8. Solving Systems of Linear Equations with Two or Three Unknown Variables
    1. 8.1. Solving Systems of Linear Equations with Two or More Unknown Variables
      1. Setting Up Word Problems Using Two Variables
      2. Methods for Two Equations and Two Unknowns
      3. Methods for Three Equations and Three Unknowns
    2. 8.2. Using the Elimination Method to Solve Systems of Linear Equations with Two Unknown Variables
    3. 8.3. Using the Substitution Method to Solve Systems of Linear Equations with Two Unknown Variables
    4. 8.4. Using the Method of Determinants to Solve Systems of Two Linear Equations with Two Unknown Variables
    5. 8.5. Solving Systems of Three Linear Equations with Three Unknown Variables
    6. 8.6. Using the Elimination Method to Solve Systems of Three Linear Equations with Three Unknown Variables
    7. 8.7. Using the Substitution Method to Solve Systems of Three Linear Equations with Three Unknown Variables
    8. 8.8. Using the Matrix Method to Solve Systems of Three Linear Equations with Three Unknown Variables
    9. 8.9. Using the Method of Determinants of a Square Matrix to Solve Systems of Three Linear Equations with Three Unknown Variables
  13. 9. Working with Coordinate Systems and Graphing Equations
    1. 9.1. Introduction and Definitions
    2. 9.2. Graphing Linear Equations
    3. 9.3. Slope of a Line
    4. 9.4. Graphs of the Equations for the Parabola
    5. 9.5. Graphing Quadratic Equations
    6. 9.6. Using Graphing to Solve Quadratic Equations
    7. 9.7. Using Graphing to Solve Two Linear Equations with Two Unknown Variables
    8. 9.8. Examples of Other Equation Forms That Graph to Shapes on a Coordinate System