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