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Boost your chances of scoring higher at Algebra II


Algebra II introduces students to complex algebra concepts in preparation for trigonometry and calculus. In this new edition of Algebra II Workbook For Dummies, high school and college students will work through the types of Algebra II problems they'll see in class, including systems of equations, matrices, graphs, and conic sections. Plus, the book now comes with free 1-year access to chapter quizzes online!


A recent report by ACT shows that over a quarter of ACT-tested 2012 high school graduates did not meet any of the four college readiness benchmarks in mathematics, English, reading, and science. Algebra II Workbook For Dummies presents tricky topics in plain English and short lessons, with examples and practice at every step to help students master the essentials, setting them up for success with each new lesson.





Tracks to a typical Algebra II class

Can be used as a supplement to classroom learning or for test prep

Includes plenty of practice and examples throughout

Comes with free access to chapter quizzes online



Get ready to take the intimidation out of Algebra II!

Algebra II Workbook For Dummies, 3rd Edition with OP

Introduction





About This Book 1





Foolish Assumptions 2





Icons Used in This Book 2





Beyond the Book 3





Where to Go from Here 3





Part 1: Getting Started with Algebra II 5





Chapter 1: Going Beyond Beginning Algebra 7





Good Citizenship: Following the Order of Operations and Other Properties 7





Specializing in Products and FOIL 10





Variables on the Side: Solving Linear Equations 11





Dealing with Linear Absolute Value Equations 12





Greater Math Skills: Equalizing Linear Inequalities 14





Answers to Problems on Going Beyond Beginning Algebra 16





Chapter 2: Handling Quadratic (and Quadratic-Like) Equations and Inequalities 21





Finding Reasonable Solutions with Radicals 22





UnFOILed Again! Successfully Factoring for Solutions 23





Your Bag of Tricks: Factoring Multiple Ways 25





Keeping Your Act Together: Factoring by Grouping 26





Resorting to the Quadratic Formula 27





Solving Quadratics by Completing the Square 29





Working with Quadratic-Like Equations 30





Checking Out Quadratic Inequalities 32





Answers to Problems on Quadratic (and Quadratic-Like) Equations and Inequalities 34





Chapter 3: Rooting Out the Rational, the Radical, and the Negative 43





Doing Away with Denominators with an LCD 44





Simplifying and Solving Proportions 46





Wrangling with Radicals 48





Changing Negative Attitudes toward Negative Exponents 49





Divided Powers: Solving Equations with Fractional Exponents 51





Answers to Problems on Rooting Out the Rational, the Radical, and the Negative 53





Chapter 4: Graphing for the Good Life 61





Coordinating Axes, Coordinates of Points, and Quadrants 62





Crossing the Line: Using Intercepts and Symmetry to Graph 64





Graphing Lines Using Slope-Intercept and Standard Forms 67





Graphing Basic Polynomial Curves 69





Grappling with Radical and Absolute Value Functions 71





Enter the Machines: Using a Graphing Calculator 73





Answers to Problems on Graphing for the Good Life 77





Part 2: Functions 89





Chapter 5: Formulating Functions 91





Evaluating Functions 91





Determining the Domain and Range of a Function 93





Recognizing Even, Odd, and One-to-One Functions 94





Composing Functions and Simplifying the Difference Quotient 96





Solving for Inverse Functions 99





Answers to Problems on Formulating Functions 101





Chapter 6: Specializing in Quadratic Functions 107





Finding Intercepts and the Vertex of a Parabola 108





Applying Quadratics to Real-Life Situations 109





Graphing Parabolas 111





Answers to Problems on Quadratic Functions 113





Chapter 7: Plugging in Polynomials 119





Finding Basic Polynomial Intercepts 120





Digging up More-Difficult Polynomial Roots with Factoring 122





Determining Where a Function Is Positive or Negative 123





Graphing Polynomials 125





Possible Roots and Where to Find Them: The Rational Root Theorem and Descartes's Rule 127





Getting Real Results with Synthetic Division and the Remainder Theorem 130





Connecting the Factor Theorem with a Polynomial's Roots 132





Answers to Problems on Plugging in Polynomials 134





Chapter 8: Acting Rationally with Functions 143





Determining Domain and Intercepts of Rational Functions 144





Introducing Vertical and Horizontal Asymptotes 145





Getting a New Slant with Oblique Asymptotes 147





Removing Discontinuities 148





Going the Limit: Limits at a Number and Infinity 149





Graphing Rational Functions 151





Answers to Problems on Rational Functions 156





Chapter 9: Exposing Exponential and Logarithmic Functions 163





Evaluating e-Expressions and Powers of e 164





Solving Exponential Equations 165





Making Cents: Applying Compound Interest and Continuous Compounding 167





Checking out the Properties of Logarithms 169





Presto-Chango: Expanding and Contracting Expressions with Log Functions 171





Solving Logarithmic Equations 173





They Ought to Be in Pictures: Graphing Exponential and Logarithmic Functions 175





Answers to Problems on Exponential and Logarithmic Functions 179





Part 3: Conics and Systems of Equations 189





Chapter 10: Any Way You Slice It: Conic Sections 191





Putting Equations of Parabolas in Standard Form 192





Shaping Up: Determining the Focus and Directrix of a Parabola 194





Back to the Drawing Board: Sketching Parabolas 196





Writing the Equations of Circles and Ellipses in Standard Form 198





Determining Foci and Vertices of Ellipses 201





Rounding Out Your Sketches: Circles and Ellipses 203





Hyperbola: Standard Equations and Foci 205





Determining the Asymptotes and Intercepts of Hyperbolas 206





Sketching the Hyperbola 208





Answers to Problems on Conic Sections 211





Part 3: Conics and Systems of Equations 189





Solving Two Linear Equations Algebraically 221





Using Cramer's Rule to Defeat Unruly Fractions 223





A Third Variable: Upping the Systems to Three Linear Equations 225





A Line by Any Other Name: Writing Generalized Solution Rules 227





Decomposing Fractions Using Systems 229





Answers to Problems on Systems of Equations 231





Part 3: Conics and Systems of Equations 189





Finding the Intersections of Lines and Parabolas 237





Crossing Curves: Finding the Intersections of Parabolas and Circles 239





Appealing to a Higher Power: Dealing with Exponential Systems 240





Solving Systems of Inequalities 242





Answers to Problems on Solving Systems of Nonlinear Equations and Inequalities 245





Part 4: Other Good Stuff: Lists, Arrays, and Imaginary Numbers 251





Chapter 13: Getting More Complex with Imaginary Numbers 253





Simplifying Powers of i 254





Not Quite Brain Surgery: Doing Operations on Complex Numbers 255





"Dividing" Complex Numbers with a Conjugate 256





Solving Equations with Complex Solutions 257





Answers to Problems on Imaginary Numbers 259





Chapter 14: Getting Squared Away with Matrices 263





Describing Dimensions and Types of Matrices 263





Adding, Subtracting, and Doing Scalar Multiplication on Matrices 265





Trying Times: Multiplying Matrices by Each Other 267





The Search for Identity: Finding Inverse Matrices 268





Using Matrices to Solve Systems of Equations 272





Answers to Problems on Matrices 274





Chapter 15: Going Out of Sequence with Sequences and Series 279





Writing the Terms of a Sequence 279





Differences and Multipliers: Working with Special Sequences 282





Backtracking: Constructing Recursively Defined Sequences 283





Using Summation Notation 284





Finding Sums with Special Series 286





Answers to Problems on Sequences and Series 289





Chapter 16: Everything You Ever Wanted to Know about Sets and Counting 293





Writing the Elements of a Set from Rules or Patterns 294





Get Together: Combining Sets with Unions, Intersections, and Complements 295





Multiplication Countdowns: Simplifying Factorial Expressions 297





Checking Your Options: Using the Multiplication Property 298





Counting on Permutations When Order Matters 300





Mixing It Up with Combinations 301





Raising Binomials to Powers: Investigating the Binomial Theorem 303





Answers to Problems on Sets and Counting 304





Part 5: The Part of Tens 309





Chapter 17: Basic Graphs 311





Putting Polynomials in Their Place 311





Lining Up Front and Center 312





Being Absolutely Sure with Absolute Value 313





Graphing Reciprocals of x and x2 313





Rooting Out Square Root and Cube Root 314





Growing Exponentially with a Graph 315





Logging In on Logarithmic Graphing 316





Chapter 18: Ten Special Sequences and Their Sums 317





Adding as Easy as One, Two, Three 317





Summing Up the Squares 318





Finding the Sum of the Cubes 318





Not Being at Odds with Summing Odd Numbers 319





Evening Things Out by Adding Up Even Numbers 319





Adding Everything Arithmetic 319





Geometrically Speaking 320





Easing into a Sum for e 320





Signing In on the Sine 321





Powering Up on Powers of 2 322





Adding Up Fractions with Multiples for Denominators 322





Index 323