Algebra II All-in-One For Dummies

Title Page\nCopyright Page\nTable of Contents\nIntroduction\n	About This Book\n	Foolish Assumptions\n	Icons Used in This Book\n	Beyond the Book\n	Where to Go from Here\nPart\r1 Getting to First Base with the Basics\n	Chapter 1 Beginning at the Beginning of Algebra\n		Following the Order of Operations and Other Properties\n			Ordering your operations\n			Examining various properties\n		Specializing in Products and “FOIL”\n			First-Outer-Inner-Last\n			Raising binomials to powers\n		Expounding on Exponential Rules\n			Multiplying and dividing exponents\n			Getting to the roots of exponents\n			Raising or lowering the roof with exponents\n			Making nice with negative exponents\n		Taking On Special Operators\n			Working with absolute value\n			Doing great with the greatest integer function\n			Getting the facts with factorial\n		Simplifying Radical Expressions\n		Factoring in Some Factoring Techniques\n			Factoring two terms\n			Taking on three terms\n			Factoring four or more terms by grouping\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 1 Quiz\n		Answers to Chapter 1 Quiz\n	Chapter 2 Taking on Linear Equations and Inequalities\n		Variables on the Side: Solving Linear Equations\n			Tackling basic linear equations\n			Clearing out the grouping symbols\n		Making Fractional Terms More Manageable\n		Solving for a Variable\n		Making Linear Inequalities More Equitable\n			Solving linear inequalities\n			Introducing interval notation\n		Compounding the Situation with Compound Statements\n		Dealing with Linear Absolute Value Equations and Inequalities\n			Being absolutely fair with equations\n			Seeing through absolute value inequality\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 2 Quiz\n		Answers to Chapter 2 Quiz\n	Chapter 3 Handling Quadratic and Other Polynomial Equations\n		Implementing the Square Root Rule\n		Successfully Factoring for Solutions\n			Factoring binomials\n			Factoring trinomials\n			Factoring by grouping\n		Resorting to the Quadratic Formula\n			Finding rational solutions\n			Straightening out irrational solutions\n		Solving Quadratics by Completing the Square\n			Squaring up a quadratic equation\n			Completing the square twice over\n		Tackling Higher-Powered Polynomials\n			Handling the sum or difference of cubes\n			Solving quadratic-like trinomials\n		Using the Rational Root Theorem and Synthetic Division\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 3 Quiz\n		Answers to Chapter 3 Quiz\n	Chapter 4 Controlling Quadratic and Rational Inequalities\n		Checking Out Quadratic Inequalities\n			Taking on Rational Inequalities and Non-Solutions\n			Increasing the Factors in Polynomial Inequalities\n			Considering Absolute Value Inequalities\n		Compounding the Situation with Compound Inequalities\n		Solving Inequality Word Problems\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 4 Quiz\n		Answers to Chapter 4 Quiz\n	Chapter 5 Soothing the Rational, the Radical, and the Negative\n		Systematically Solving Rational Equations\n		Simplifying and Solving Proportions\n			Reducing every which way but loose\n			Using cross-products to solve a rational equation\n		Ridding Yourself of a Radical\n			Squaring both sides of a radical equation\n			Calming two radicals\n		Changing Negative Attitudes toward Negative Exponents\n			Flipping negative exponents out of the picture\n			Factoring out negatives to solve equations\n		Solving Equations with Fractional Exponents\n			Combining terms with fractional exponents\n			Factoring fractional exponents\n			Solving equations by working with fractional exponents\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 5 Quiz\n		Answers to Chapter 5 Quiz\n	Chapter 6 Giving Graphing a Gander\n		Coordinating Axes, Points, and Quadrants\n			Identifying the parts of the coordinate plane\n			Plotting from dot to dot\n		Crossing the Line Using Intercepts and Symmetry\n			Finding x- and y-intercepts\n			Reflecting on a graph’s symmetry\n		Preparing to Graph Lines\n			Finding the slope of a line\n			Facing two types of equations for lines\n		Identifying Parallel and Perpendicular Lines\n		Graphing the Ten Basic Forms\n			Lines and quadratics\n			Cubics and quartics\n			Radicals and rationals\n			Exponential and logarithmic curves\n			Absolute values and circles\n		Enter the Machines: Using a Graphing Calculator\n			Entering equations into graphing calculators correctly\n			Looking through the graphing window\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 6 Quiz\n		Answers to Chapter 6 Quiz\nPart\r2 Figuring on Functions\n	Chapter 7 Formulating Functions\n		Featuring Functions\n			Introducing function notation\n			Evaluating functions\n		Homing In on Domain and Range\n			Determining a function’s domain\n			Describing a function’s range\n		Recognizing Even, Odd, and One-to-One Functions\n			Classifying even and odd functions\n			Applying even and odd functions to graphs\n			Defining one-to-one functions\n			Eliminating one-to-one violators\n		Going to Pieces with Piecewise Functions\n			Doing piecework\n			Applying piecewise functions\n		Composing Functions and Applying the Difference Quotient\n			Performing compositions\n			Simplifying the difference quotient\n		Dealing with Inverse Functions\n			Determining if functions are inverses\n			Solving for the inverse of a function\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 7 Quiz\n		Answers to Chapter 7 Quiz\n	Chapter 8 Specializing in Quadratic Functions\n		Setting the Standard to Create a Parabola\n			Starting with “a” in the standard form\n			Following up with “b” and “c”\n		Recognizing the Intercepts and Vertex\n			Finding the one and only y-intercept\n			Finding the x-intercepts\n			Going to the extreme: Finding the vertex\n		Making Symmetry Work with an Axis\n		Graphing Parabolas\n		Applying Quadratics in Real-Life Situations\n			Selling candles\n			Shooting basketballs\n			Launching a water balloon\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 8 Quiz\n		Answers to Chapter 8 Quiz\n	Chapter 9 Plugging In Polynomials\n		Getting into Polynomial Basics and Vocabulary\n			Exploring polynomial intercepts and turning points\n			Interpreting relative value and absolute value\n			Counting intercepts and turning points\n		Solving for Polynomial Intercepts\n		Finding the Roots of a Polynomial\n			Applying factoring patterns and groupings\n			Considering the unfactorable\n		Saving Your Sanity: The Rational Root Theorem\n			Putting the theorem to good use\n			Changing from roots to factors\n			Letting Descartes make a ruling on signs\n			Counting up the positive roots\n			Changing the function to count negative roots\n		Synthesizing Root Findings\n			Using synthetic division to test for roots\n			Synthetically dividing by a binomial\n			Wringing out the Remainder (Theorem)\n		Determining Positive and Negative Intervals\n		Graphing Polynomials\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 9 Quiz\n		Answers to Chapter 9 Quiz\n	Chapter 10 Acting Rationally with Functions\n		Exploring the Domain and Intercepts of Rational Functions\n			Sizing up domain\n			Introducing intercepts\n		Adding Asymptotes to the Rational Pot\n			Determining the equations of vertical asymptotes\n			Heading after horizontal asymptotes\n			Graphing vertical and horizontal asymptotes\n			Crunching the numbers and graphing oblique asymptotes\n		Removing Discontinuities\n			Removal by factoring\n			Evaluating the removal restrictions\n			Showing removable discontinuities on a graph\n		Going the Limit: Limits at a Number and Infinity\n			Evaluating limits at discontinuities\n			Determining an existent limit without tables\n			Determining which functions have limits\n			Going to infinity\n			Catching rational limits at infinity\n		Graphing Rational Functions\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 10 Quiz\n		Answers to Chapter 10 Quiz\n	Chapter 11 Exploring Exponential and Logarithmic Functions\n		Evaluating e-Expressions and Powers of e\n			Exponential functions: it’s all about the base, baby\n			Meeting the most frequently used bases: 10 and e\n		Solving Exponential Equations\n			Taking advantage of matching bases\n			Recognizing and using quadratic patterns\n			Taking out a greatest common factor\n			Factoring like a quadratic trinomial\n		Making Cents: Applying Compound Interest\n			Applying the compound interest formula\n			Measuring the actual compound: effective rates\n			Looking at continuous compounding\n		Logging On to Logarithmic Functions\n			Meeting the properties of logarithms\n			Putting your logs to work\n			Expanding and contracting expressions with log notation\n		Solving Logarithmic Equations\n			Setting log equal to log\n			Rewriting log equations as exponentials\n		Graphing Exponential and Logarithmic Functions\n			Expounding on the exponential\n			Graphing log functions using intercepts\n			Reflecting on inverses of exponential functions\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 11 Quiz\n		Answers to Chapter 11 Quiz\n	Chapter 12 Transforming and Critiquing Functions\n		Running through the Transformations\n			Translating and understanding the language\n			Reflecting on the good feeling graphing gives you\n		Scaling the Cliff of Numerical Possibilities\n		Multiplying the Opportunities for Transforming\n		Noting the Ups, Downs, Highs, and Lows\n			Determining increasing and decreasing intervals\n			Charting the highs and lows\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 12 Quiz\n		Answers to Chapter 12 Quiz\nPart\r3 Using Conics and Systems of Equations\n	Chapter 13 Slicing the Way You Like It: Conic Sections\n		Carefully Cutting Circular Cones\n		Opening Every Which Way with Parabolas\n			Looking at parabolas with vertices at the origin\n			Observing the general form of parabolic equations\n			Converting parabolic equations to the standard form\n			Sketching the graphs of parabolas\n		Going Round and Round in Circles\n			Standardizing the circle\n			Specializing in circles\n		Preparing for Solar Ellipses\n			Raising the standards of an ellipse\n			Sketching an elliptical path\n		Getting Hyper Excited about Hyperbolas\n			Including the asymptotes and vertices\n			Graphing hyperbolas\n		Identifying Conics from Their Equations\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 13 Quiz\n		Answers to Chapter 13 Quiz\n	Chapter 14 Solving Systems of Linear Equations\n		Looking at the Standard Linear-Systems Form\n		Solving Systems of Two Linear Equations by Using Elimination\n			Getting to the point with elimination\n			Recognizing solutions indicating parallel or coexisting lines\n		Making Substitution the Choice\n			Variable substitution made easy\n			Identifying parallel and coexisting lines\n		Graphing Solutions of Linear Systems\n			Pinpointing the intersection\n			Toeing the same line twice and dealing with parallel lines\n		Using Cramer’s Rule to Defeat Unwieldy Fractions\n			Setting up the linear system for Cramer\n			Applying Cramer’s Rule to a linear system\n		Tackling Linear Systems with Three Linear Equations\n			Solving three-equation systems with algebra\n			Generalizing multiple solutions for linear equations\n		Upping the Ante with Larger Systems\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 14 Quiz\n		Answers to Chapter 14 Quiz\n	Chapter 15 Solving Systems of Nonlinear Equations\n		Crossing Parabolas with Lines\n			Determining the points where a line and parabola cross paths\n			Dealing with a solution that’s no solution\n		Intertwining Parabolas and Circles\n			Managing multiple intersections\n			Sorting out the solutions\n		Planning Your Attack on Other Systems of Equations\n			Mixing polynomials and lines\n			Crossing polynomials\n		Navigating Exponential Intersections\n		Rounding Up Rational Functions\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 15 Quiz\n		Answers to Chapter 15 Quiz\n	Chapter 16 Solving Systems of Inequalities\n		Playing Fair with Inequalities\n		Keeping It Linear with Inequalities\n			Getting a new slant on linear inequalities\n			Taking on more than two linear inequalities\n			Graphing areas with curves and lines\n		Applying the Systems to Real Life\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 16 Quiz\n		Answers to Chapter 16 Quiz\nPart\r4 Making Lists and Checking for Imaginary Numbers\n	Chapter 17 Getting More Complex with Imaginary Numbers\n		Simplifying Powers of i\n			Understanding the Complexity of Complex Numbers\n			Operating on complex numbers\n			Multiplying by the conjugate to perform division\n			Simplifying radicals\n		Solving Quadratic Equations with Complex Solutions\n		Working Polynomials with Complex Solutions\n			Identifying conjugate pairs\n			Interpreting complex zeros\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 17 Quiz\n		Answers to Chapter 17 Quiz\n	Chapter 18 Making Moves with Matrices\n		Describing the Different Types of Matrices\n			Row and column matrices\n			Square matrices\n			Zero matrices\n			Identity matrices\n		Performing Operations on Matrices\n			Adding and subtracting matrices\n			Multiplying matrices by scalars\n			Multiplying two matrices\n		Defining Row Operations\n		Finding Inverse Matrices\n			Determining additive inverses\n			Determining multiplicative inverses\n		Dividing Matrices by Using Inverses\n		Using Matrices to Find Solutions for Systems of Equations\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 18 Quiz\n		Answers to Chapter 18 Quiz\n	Chapter 19 Seeking Out Sequences and Series\n		Understanding Sequence Terminology\n			Using sequence notation\n			No-fear factorials in sequences\n			Alternating sequential patterns\n			Looking for sequential patterns\n		Taking Note of Arithmetic and Geometric Sequences\n			Finding common ground: Arithmetic sequences\n			Taking the multiplicative approach: geometric sequences\n		Recursively Defining Functions\n		Making a Series of Moves\n			Introducing summation notation\n			Summing arithmetically\n			Summing geometrically\n		Highlighting Special Formulas\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 19 Quiz\n		Answers to Chapter 19 Quiz\n	Chapter 20 Everything You Wanted to Know about Sets and Counting\n		Revealing the Set Rules\n			Listing elements with a roster\n			Building sets from scratch\n			Going for all (universal set) or nothing (empty set)\n			Subbing in with subsets\n		Operating on Sets\n			Celebrating the union of two sets\n			Looking both ways for set intersections\n			Feeling complementary about sets\n			Counting the elements in sets\n		Drawing Venn You Feel Like It\n			Applying the Venn diagram\n			Adding a set to a Venn diagram\n		Focusing on Factorials\n			Making factorials manageable\n			Simplifying factorials\n		How Do I Love Thee? Let Me Count Up the Ways\n			Applying the multiplication principle to sets\n			Arranging permutations of sets\n			Mixing up sets with combinations\n		Branching Out with Tree Diagrams\n			Picturing a tree diagram for a permutation\n			Drawing a tree diagram for a combination\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 20 Quiz\n		Answers to Chapter 20 Quiz\nPart\r5 Applying Known Formulas\n	Chapter 21 Manipulating Formulas\n		Expanding Binomials\n			Using the Binomial Theorem\n			Applying Pascal’s Triangle\n		Taking On the Graphing Formulas\n			Formulating properties between two points\n			Measuring the distance between a point and a line\n		Getting All Geometric\n			Telling the plain truth with plane geometry\n			Keeping it solid\n		Solving a Formula for a Variable\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 21 Quiz\n		Answers to Chapter 21 Quiz\n	Chapter 22 Taking on Applications\n		Making Mixtures Magically Mathematical\n			Keeping money matters solvent\n			Flowing freely with fluids\n			Mixing up many ingredients\n		Going the Distance\n			Equating distances\n			Summing up the distances\n		Working through the Challenges\n		Acting Your Age\n		Practice Questions Answers and Explanations\n		Whaddya Know? Chapter 22 Quiz\n		Answers to Chapter 22 Quiz\nIndex\nEULA