Algebra Know-It-ALL

(Marvins-Underground-K-12) #1

  • 4 Addition and Subtraction

    • Moving Up and Down

    • Identity, Grouping, and Signs

    • The Commutative Law for Addition

    • The Associative Law for Addition

    • Practice Exercises



  • 5 Multiplication and Division

    • Moving Out and In

    • Identity, Grouping, and Signs

    • The Commutative Law for Multiplication

    • The Associative Law for Multiplication

    • The Distributive Laws

    • Practice Exercises



  • 6 Fractions Built of Integers

    • “Messy” Quotients

    • “Reducing” a Fraction or Ratio

    • Multiplying and Dividing Fractions

    • Adding and Subtracting Fractions

    • Practice Exercises



  • 7 Decimal Fractions

    • Powers of

    • Terminating Decimals

    • Endless Decimals

    • Conversions

    • Practice Exercises



  • 8 Powers and Roots

    • Integer Powers

    • Reciprocal-of-Integer Powers

    • Multiplying and Dividing with Exponents

    • Multiple Powers

    • Practice Exercises



  • 9 Irrational and Real Numbers

    • The Number Hierarchy

    • More About Irrationals and Reals

    • How Real Variables Behave

    • More Rules for Real Variables

    • Practice Exercises



  • 10 Review Questions and Answers

  • 11 Equations and Inequalities Part 2 Linear Equations and Relations

    • Equation Morphing Revisited

    • Inequalities

    • How Inequalities Behave

    • Inequality Morphing

    • Practice Exercises



  • 12 First-Degree Equations in One Variable

    • Constants, Sums, and Differences

    • Products and Ratios

    • Combinations of Operations

    • Word Problems

    • Practice Exercises



  • 13 Mappings, Relations, and Functions

    • Mapping “Territories”

    • Types of Mappings

    • Examples of Relations

    • Examples of Functions

    • Practice Exercises



  • 14 The Cartesian Plane

    • Two Number Lines

    • Three Relations

    • Three Functions

    • Practice Exercises



  • 15 Graphs of Linear Relations

    • Slope-Intercept Form

    • Point-Slope Form

    • Equations from Graphs

    • Practice Exercises



  • 16 Two-by-Two Linear Systems

    • Morph and Mix

    • Double Elimination

    • Rename and Replace

    • Practice Exercises



  • 17 Two-by-Two Linear Graphs

    • We Morphed, We Mixed, We Can Graph

    • We Added, We Eliminated, We Can Graph

    • We Renamed, We Replaced, We Can Graph x Contents

    • We Couldn’t Solve, but We Can Graph

    • Practice Exercises



  • 18 Larger Linear Systems

    • Eliminate One Variable

    • Solve the Two-by-Two

    • Substitute Back

    • General Linear Systems

    • Practice Exercises



  • 19 The Matrix Morphing Game

    • How to Build a Matrix

    • Matrix Operations

    • A Sample Problem

    • Practice Exercises



  • 20 Review Questions and Answers

  • 21 Imaginary and Complex Numbers Part 3 Nonlinear Equations and Relations

    • The Square Root of −

    • The Imaginary Number Line

    • Real + Imaginary = Complex

    • Practice Exercises



  • 22 Quadratic Equations with Real Roots

    • Second-Degree Polynomials

    • Binomial Factor Form

    • Completing the Square

    • The Quadratic Formula

    • Practice Exercises



  • 23 Quadratic Equations with Complex Roots

    • Complex Roots by Formula

    • Imaginary Roots in Factors

    • Conjugate Roots in Factors

    • Practice Exercises



  • 24 Graphs of Quadratic Functions

    • Two Real Zeros

    • One Real Zero

    • No Real Zeros Contents xi

    • Practice Exercises



  • 25 Cubic Equations in Real Numbers

    • Cube of Binomial

    • Three Binomial Factors

    • Binomial Times Trinomial

    • Polynomial Equation of Third Degree

    • Practice Exercises



  • 26 Polynomial Equations in Real Numbers

    • Binomial to the nth Power

    • Binomial Factors

    • Polynomial Standard Form

    • Digging for Real Roots

    • Practice Exercises



  • 27 More Two-by-Two Systems

    • Linear and Quadratic

    • Two Quadratics

    • Enter the Cubic

    • Practice Exercises



  • 28 More Two-by-Two Graphs

    • Linear and Quadratic

    • Two Quadratics

    • Enter the Cubic

    • Practice Exercises



  • 29 Logarithms and Exponentials

    • What Is a Logarithm?

    • How Logarithms Work

    • What Is an Exponential?

    • How Exponentials Work

    • Practice Exercises



  • 30 Review Questions and Answers

    • Final Exam

    • Appendix A Worked-Out Solutions to Exercises: Chapters 1 to

    • Appendix B Worked-Out Solutions to Exercises: Chapters 11 to

    • Appendix C Worked-Out Solutions to Exercises: Chapters 21 to



  • Appendix D Answers to Final Exam Questions xii Contents

  • Appendix E Special Characters in Order of Appearance

  • Suggested Additional Reading

  • Index

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