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Algebra II Workbook For Dummies, 2nd Edition

Book Description

To succeed in Algebra II, start practicing now

Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for future success.

Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebra I skills, because you'll need a strong foundation to build upon. From there, you'll work through practice problems to clarify concepts and improve understanding and retention.

  • Revisit quadratic equations, inequalities, radicals, and basic graphs

  • Master quadratic, exponential, and logarithmic functions

  • Tackle conic sections, as well as linear and nonlinear systems

  • Grasp the concepts of matrices, sequences, and imaginary numbers

  • Algebra II Workbook For Dummies, 2nd Edition includes sections on graphing and special sequences to familiarize you with the key concepts that will follow you to trigonometry and beyond. Don't waste any time getting started. Algebra II Workbook For Dummies, 2nd Edition is your complete guide to success.

    Table of Contents

      1. Introduction
        1. About This Book
        2. Foolish Assumptions
        3. Icons Used in This Book
        4. Beyond the Book
        5. Where to Go from Here
      2. Part I: Getting Started with Algebra II
        1. Chapter 1: Going Beyond Beginning Algebra
          1. Good Citizenship: Following the Order of Operations and Other Properties
          2. Specializing in Products and FOIL
          3. Variables on the Side: Solving Linear Equations
          4. Dealing with Linear Absolute Value Equations
          5. Greater Math Skills: Equalizing Linear Inequalities
          6. Answers to Problems on Going Beyond Beginning Algebra
        2. Chapter 2: Handling Quadratic (and Quadratic-Like) Equations and Inequalities
          1. Finding Reasonable Solutions with Radicals
          2. UnFOILed Again! Successfully Factoring for Solutions
          3. Your Bag of Tricks: Factoring Multiple Ways
          4. Keeping Your Act Together: Factoring by Grouping
          5. Resorting to the Quadratic Formula
          6. Solving Quadratics by Completing the Square
          7. Working with Quadratic-Like Equations
          8. Checking Out Quadratic Inequalities
          9. Answers to Problems on Quadratic (and Quadratic-Like) Equations and Inequalities
        3. Chapter 3: Rooting Out the Rational, the Radical, and the Negative
          1. Doing Away with Denominators with an LCD
          2. Simplifying and Solving Proportions
          3. Wrangling with Radicals
          4. Changing Negative Attitudes toward Negative Exponents
          5. Divided Powers: Solving Equations with Fractional Exponents
          6. Answers to Problems on Rooting Out the Rational, the Radical, and the Negative
        4. Chapter 4: Graphing for the Good Life
          1. Coordinating Axes, Coordinates of Points, and Quadrants
          2. Crossing the Line: Using Intercepts and Symmetry to Graph
          3. Graphing Lines Using Slope-Intercept and Standard Forms
          4. Graphing Basic Polynomial Curves
          5. Grappling with Radical and Absolute Value Functions
          6. Enter the Machines: Using a Graphing Calculator
          7. Answers to Problems on Graphing for the Good Life
      3. Part II: Functions
        1. Chapter 5: Formulating Functions
          1. Evaluating Functions
          2. Determining the Domain and Range of a Function
          3. Recognizing Even, Odd, and One-to-One Functions
          4. Composing Functions and Simplifying the Difference Quotient
          5. Solving for Inverse Functions
          6. Answers to Problems on Formulating Functions
        2. Chapter 6: Specializing in Quadratic Functions
          1. Finding Intercepts and the Vertex of a Parabola
          2. Applying Quadratics to Real-Life Situations
          3. Graphing Parabolas
          4. Answers to Problems on Quadratic Functions
        3. Chapter 7: Plugging In Polynomials
          1. Finding Basic Polynomial Intercepts
          2. Digging Up More-Difficult Polynomial Roots with Factoring
          3. Determining Where a Function Is Positive or Negative
          4. Graphing Polynomials
          5. Possible Roots and Where to Find Them: The Rational Root Theorem and Descartes’s Rule
          6. Getting Real Results with Synthetic Division and the Remainder Theorem
          7. Connecting the Factor Theorem with a Polynomial’s Roots
          8. Answers to Problems on Plugging In Polynomials
        4. Chapter 8: Acting Rationally with Functions
          1. Determining Domain and Intercepts of Rational Functions
          2. Introducing Vertical and Horizontal Asymptotes
          3. Getting a New Slant with Oblique Asymptotes
          4. Removing Discontinuities
          5. Going the Limit: Limits at a Number and Infinity
          6. Graphing Rational Functions
          7. Answers to Problems on Rational Functions
        5. Chapter 9: Exposing Exponential and Logarithmic Functions
          1. Evaluating e-Expressions and Powers of e
          2. Solving Exponential Equations
          3. Making Cents: Applying Compound Interest and Continuous Compounding
          4. Checking Out the Properties of Logarithms
          5. Presto-Chango: Expanding and Contracting Expressions with Log Functions
          6. Solving Logarithmic Equations
          7. They Ought to Be in Pictures: Graphing Exponential and Logarithmic Functions
          8. Answers to Problems on Exponential and Logarithmic Functions
      4. Part III: Conics and Systems of Equations
        1. Chapter 10: Any Way You Slice It: Conic Sections
          1. Putting Equations of Parabolas in Standard Form
          2. Shaping Up: Determining the Focus and Directrix of a Parabola
          3. Back to the Drawing Board: Sketching Parabolas
          4. Writing the Equations of Circles and Ellipses in Standard Form
          5. Determining Foci and Vertices of Ellipses
          6. Rounding Out Your Sketches: Circles and Ellipses
          7. Hyperbola: Standard Equations and Foci
          8. Determining the Asymptotes and Intercepts of Hyperbolas
          9. Sketching the Hyperbola
          10. Answers to Problems on Conic Sections
        2. Chapter 11: Solving Systems of Linear Equations
          1. Solving Two Linear Equations Algebraically
          2. Using Cramer’s Rule to Defeat Unruly Fractions
          3. A Third Variable: Upping the Systems to Three Linear Equations
          4. A Line by Any Other Name: Writing Generalized Solution Rules
          5. Decomposing Fractions Using Systems
          6. Answers to Problems on Systems of Equations
        3. Chapter 12: Solving Systems of Nonlinear Equations and Inequalities
          1. Finding the Intersections of Lines and Parabolas
          2. Crossing Curves: Finding the Intersections of Parabolas and Circles
          3. Appealing to a Higher Power: Dealing with Exponential Systems
          4. Solving Systems of Inequalities
          5. Answers to Problems on Solving Systems of Nonlinear Equations and Inequalities
      5. Part IV: Other Good Stuff: Lists, Arrays, and Imaginary Numbers
        1. Chapter 13: Getting More Complex with Imaginary Numbers
          1. Simplifying Powers of i
          2. Not Quite Brain Surgery: Doing Operations on Complex Numbers
          3. “Dividing” Complex Numbers with a Conjugate
          4. Solving Equations with Complex Solutions
          5. Answers to Problems on Imaginary Numbers
        2. Chapter 14: Getting Squared Away with Matrices
          1. Describing Dimensions and Types of Matrices
          2. Adding, Subtracting, and Doing Scalar Multiplication on Matrices
          3. Trying Times: Multiplying Matrices by Each Other
          4. The Search for Identity: Finding Inverse Matrices
          5. Using Matrices to Solve Systems of Equations
          6. Answers to Problems on Matrices
        3. Chapter 15: Going Out of Sequence with Sequences and Series
          1. Writing the Terms of a Sequence
          2. Differences and Multipliers: Working with Special Sequences
          3. Backtracking: Constructing Recursively Defined Sequences
          4. Using Summation Notation
          5. Finding Sums with Special Series
          6. Answers to Problems on Sequences and Series
        4. Chapter 16: Everything You Ever Wanted to Know about Sets and Counting
          1. Writing the Elements of a Set from Rules or Patterns
          2. Get Together: Combining Sets with Unions, Intersections, and Complements
          3. Multiplication Countdowns: Simplifying Factorial Expressions
          4. Checking Your Options: Using the Multiplication Property
          5. Counting on Permutations When Order Matters
          6. Mixing It Up with Combinations
          7. Raising Binomials to Powers: Investigating the Binomial Theorem
          8. Answers to Problems on Sets and Counting
      6. Part V: The Part of Tens
        1. Chapter 17: Ten Basic Graphs
          1. Putting Polynomials in Their Place
          2. Lining Up Front and Center
          3. Being Absolutely Sure with Absolute Value
          4. Graphing Reciprocals of x and x2
          5. Rooting Out Square Root and Cube Root
          6. Growing Exponentially with a Graph
          7. Logging In on Logarithmic Graphing
        2. Chapter 18: Ten Special Sequences and Their Sums
          1. Adding As Easy As One, Two, Three
          2. Summing Up the Squares
          3. Finding the Sum of the Cubes
          4. Not Being at Odds with Summing Odd Numbers
          5. Evening Things Out by Adding Up Even Numbers
          6. Adding Everything Arithmetic
          7. Geometrically Speaking
          8. Easing into a Sum for e
          9. Signing In on the Sine
          10. Powering Up on Powers of 2
          11. Adding Up Fractions with Multiples for Denominators
      7. About the Author
      8. Cheat Sheet
      9. More Dummies Products