Algebra I

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Preface[edit | edit source]

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations, and algebraic structures.

You've been asked to buy popcorn for you and your friends at the movies. You have $17.70. One bag is $3.25. You want to know how many bags you can buy. This is an algebra problem! Related problems are how much money will be left over, and what should you buy or in what proportions should you return the extra money to your friends.

Algebra helps us to predict things that we don't yet know and to determine the relationships between the things we do. Algebra is a powerful and rich branch of mathematics that is useful in everyday life as well as business, engineering, and other technical fields.

Contents[edit | edit source]

Introduction to Mathematics[edit | edit source]

  1. Who should read this book?
  2. Basic Operations

Chapter I: Foundations of Algebra[edit | edit source]

  1. Variables and Expressions
  2. Order of Operations and Evaluating Expressions
  3. Real Numbers and the Number Line
  4. Properties of Real Numbers
  5. Adding and Subtracting Real Numbers
  6. Multiplying and Dividing Real Numbers
  7. The Distributive Property
  8. An Introduction to Equations
  9. Patterns, Equations, Graphs

Chapter II: Solving Equations[edit | edit source]

  1. Solving One-Step Equations
  2. Solving Two-Step Equations
  3. Solving Multi-Step Equations
  4. Solving Equations with Variables on Both Sides
  5. Literal Equations and Formulas
  6. Ratios, Rates, and Conversions
  7. Solving Proportions
  8. Proportions and Similar Figures
  9. Percents
  10. Change Expressed as a Percent

Chapter III: Solving Inequalities[edit | edit source]

  1. Inequalities and Their Graphs
  2. Solving Inequalities
  3. Compound Inequalities
  4. Absolute Value Equations
  5. Absolute Value Inequalities

Chapter IV: An Introduction to Functions[edit | edit source]

  1. Graphing Relationships
  2. Relations and Functions
  3. Writing Functions
  4. Function Notation
  5. Graphing Functions
  6. Arithmetic Sequences

Chapter V: Linear Functions[edit | edit source]

  1. Rate of Change and Slope
  2. Slope-Intercept Form
  3. Point-Slope Form
  4. Standard Form
  5. Parallel and Perpindicular Lines

Chapter VI: Systems of Equations[edit | edit source]

  1. Solving Systems by Graphing
  2. Solving Systems Using Substitution
  3. Solving Systems Using Elimination
  4. Applications of Linear Systems

Chapter VII: Exponents[edit | edit source]

  1. Zero and Negative Exponents
  2. Multiplying Powers with the Same Base
  3. Other Multiplication Properties of Exponents
  4. Division Properties of Exponents
  5. Rational Exponents and Radicals

Chapter VIII: Polynomials and Factoring[edit | edit source]

  1. Adding and Subtracting Polynomials
  2. Multiplying Polynomials
  3. Multiplying Binomials
  4. Multiplying Special Cases
  5. Exponential Functions\
  6. Geometric Sequences >Trust me, these three belong here
  7. Scientific Notation-----/
  8. Factoring Using GCF
  9. Factoring x^2+bx+c
  10. Factoring ax^2+bx+c
  11. Factoring Special Cases

Chapter IX: Quadratic Functions and Equations[edit | edit source]

  1. Quadratic Graphs and Their Properties
  2. Quadratic Functions