Details

Algebra II Workbook For Dummies


Algebra II Workbook For Dummies


3. Aufl.

von: Mary Jane Sterling

16,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 12.12.2018
ISBN/EAN: 9781119543138
Sprache: englisch
Anzahl Seiten: 352

DRM-geschütztes eBook, Sie benötigen z.B. Adobe Digital Editions und eine Adobe ID zum Lesen.

Beschreibungen

<p><b>Boost your chances of scoring higher at Algebra II</b></p> <p>Algebra II introduces students to complex algebra concepts in preparation for trigonometry and calculus. In this new edition of <i>Algebra II Workbook For Dummies</i>, 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! </p> <p>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. <i>Algebra II Workbook For Dummies</i> 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.</p> <ul> <li>Tracks to a typical Algebra II class</li> <li>Can be used as a supplement to classroom learning or for test prep</li> <li>Includes plenty of practice and examples throughout</li> <li>Comes with free access to chapter quizzes online</li> </ul> <p>Get ready to take the intimidation out of Algebra II!</p>
<p><b>Introduction</b></p> <p>About This Book 1</p> <p>Foolish Assumptions 2</p> <p>Icons Used in This Book 2</p> <p>Beyond the Book 3</p> <p>Where to Go from Here 3</p> <p><b>Part 1: Getting Started With Algebra II </b><b>5</b></p> <p><b>Chapter 1: Going Beyond Beginning Algebra</b><b> 7</b></p> <p>Good Citizenship: Following the Order of Operations and Other Properties 7</p> <p>Specializing in Products and FOIL 10</p> <p>Variables on the Side: Solving Linear Equations 11</p> <p>Dealing with Linear Absolute Value Equations 12</p> <p>Greater Math Skills: Equalizing Linear Inequalities 14</p> <p>Answers to Problems on Going Beyond Beginning Algebra 16</p> <p><b>Chapter 2: Handling Quadratic (and Quadratic-Like) Equations and Inequalities</b><b> 21</b></p> <p>Finding Reasonable Solutions with Radicals 22</p> <p>UnFOILed Again! Successfully Factoring for Solutions 23</p> <p>Your Bag of Tricks: Factoring Multiple Ways 25</p> <p>Keeping Your Act Together: Factoring by Grouping 26</p> <p>Resorting to the Quadratic Formula 27</p> <p>Solving Quadratics by Completing the Square 29</p> <p>Working with Quadratic-Like Equations 30</p> <p>Checking Out Quadratic Inequalities 32</p> <p>Answers to Problems on Quadratic (and Quadratic-Like) Equations and Inequalities 34</p> <p><b>Chapter 3: Rooting Out the Rational, the Radical, and the Negative</b> <b>43</b></p> <p>Doing Away with Denominators with an LCD 44</p> <p>Simplifying and Solving Proportions 46</p> <p>Wrangling with Radicals 48</p> <p>Changing Negative Attitudes toward Negative Exponents 49</p> <p>Divided Powers: Solving Equations with Fractional Exponents 51</p> <p>Answers to Problems on Rooting Out the Rational, the Radical, and the Negative 53</p> <p><b>Chapter 4: Graphing for the Good Life</b> <b>61</b></p> <p>Coordinating Axes, Coordinates of Points, and Quadrants 62</p> <p>Crossing the Line: Using Intercepts and Symmetry to Graph 64</p> <p>Graphing Lines Using Slope-Intercept and Standard Forms 67</p> <p>Graphing Basic Polynomial Curves 69</p> <p>Grappling with Radical and Absolute Value Functions 71</p> <p>Enter the Machines: Using a Graphing Calculator 73</p> <p>Answers to Problems on Graphing for the Good Life 77</p> <p><b>Part 2: Functions</b><b> 89</b></p> <p><b>Chapter 5: Formulating Functions</b><b> 91</b></p> <p>Evaluating Functions 91</p> <p>Determining the Domain and Range of a Function 93</p> <p>Recognizing Even, Odd, and One-to-One Functions 94</p> <p>Composing Functions and Simplifying the Difference Quotient 96</p> <p>Solving for Inverse Functions 99</p> <p>Answers to Problems on Formulating Functions 101</p> <p><b>Chapter 6: Specializing in Quadratic Functions</b> <b>107</b></p> <p>Finding Intercepts and the Vertex of a Parabola 108</p> <p>Applying Quadratics to Real-Life Situations 109</p> <p>Graphing Parabolas 111</p> <p>Answers to Problems on Quadratic Functions 113</p> <p><b>Chapter 7: Plugging in Polynomials</b> <b>119</b></p> <p>Finding Basic Polynomial Intercepts 120</p> <p>Digging up More-Difficult Polynomial Roots with Factoring 122</p> <p>Determining Where a Function Is Positive or Negative 123</p> <p>Graphing Polynomials 125</p> <p>Possible Roots and Where to Find Them: The Rational Root Theorem and Descartes’s Rule 127</p> <p>Getting Real Results with Synthetic Division and the Remainder Theorem 130</p> <p>Connecting the Factor Theorem with a Polynomial’s Roots 132</p> <p>Answers to Problems on Plugging in Polynomials 134</p> <p><b>Chapter 8: Acting Rationally with Functions</b> <b>143</b></p> <p>Determining Domain and Intercepts of Rational Functions 144</p> <p>Introducing Vertical and Horizontal Asymptotes 145</p> <p>Getting a New Slant with Oblique Asymptotes 147</p> <p>Removing Discontinuities 148</p> <p>Going the Limit: Limits at a Number and Infinity 149</p> <p>Graphing Rational Functions 151</p> <p>Answers to Problems on Rational Functions 156</p> <p><b>Chapter 9: Exposing Exponential and Logarithmic Functions</b> <b>163</b></p> <p>Evaluating e-Expressions and Powers of e 164</p> <p>Solving Exponential Equations 165</p> <p>Making Cents: Applying Compound Interest and Continuous Compounding 167</p> <p>Checking out the Properties of Logarithms 169</p> <p>Presto-Chango: Expanding and Contracting Expressions with Log Functions 171</p> <p>Solving Logarithmic Equations 173</p> <p>They Ought to Be in Pictures: Graphing Exponential and Logarithmic Functions 175</p> <p>Answers to Problems on Exponential and Logarithmic Functions 179</p> <p><b>Part 3: Conics And Systems Of Equations </b><b>189</b></p> <p><b>Chapter 10: Any Way You Slice It: Conic Sections</b><b> 191</b></p> <p>Putting Equations of Parabolas in Standard Form 192</p> <p>Shaping Up: Determining the Focus and Directrix of a Parabola 194</p> <p>Back to the Drawing Board: Sketching Parabolas 196</p> <p>Writing the Equations of Circles and Ellipses in Standard Form 198</p> <p>Determining Foci and Vertices of Ellipses 201</p> <p>Rounding Out Your Sketches: Circles and Ellipses 203</p> <p>Hyperbola: Standard Equations and Foci 205</p> <p>Determining the Asymptotes and Intercepts of Hyperbolas 206</p> <p>Sketching the Hyperbola 208</p> <p>Answers to Problems on Conic Sections 211</p> <p><b>Chapter 11: Solving Systems of Linear Equations</b><b> 221</b></p> <p>Solving Two Linear Equations Algebraically 221</p> <p>Using Cramer’s Rule to Defeat Unruly Fractions 223</p> <p>A Third Variable: Upping the Systems to Three Linear Equations 225</p> <p>A Line by Any Other Name: Writing Generalized Solution Rules 227</p> <p>Decomposing Fractions Using Systems 229</p> <p>Answers to Problems on Systems of Equations 231</p> <p><b>Chapter 12: Solving Systems of Nonlinear Equations and Inequalities</b><b> 237</b></p> <p>Finding the Intersections of Lines and Parabolas 237</p> <p>Crossing Curves: Finding the Intersections of Parabolas and Circles 239</p> <p>Appealing to a Higher Power: Dealing with Exponential Systems 240</p> <p>Solving Systems of Inequalities 242</p> <p>Answers to Problems on Solving Systems of Nonlinear Equations and Inequalities 245</p> <p><b>Part 4: Other Good Stuff: Lists, Arrays, And Imaginary Numbers </b><b>251</b></p> <p><b>Chapter 13: Getting More Complex with Imaginary Numbers </b><b>253</b></p> <p>Simplifying Powers of i 254</p> <p>Not Quite Brain Surgery: Doing Operations on Complex Numbers 255</p> <p>“Dividing” Complex Numbers with a Conjugate 256</p> <p>Solving Equations with Complex Solutions 257</p> <p>Answers to Problems on Imaginary Numbers 259</p> <p><b>Chapter 14: Getting Squared Away with Matrices</b> <b>263</b></p> <p>Describing Dimensions and Types of Matrices 263</p> <p>Adding, Subtracting, and Doing Scalar Multiplication on Matrices 265</p> <p>Trying Times: Multiplying Matrices by Each Other 267</p> <p>The Search for Identity: Finding Inverse Matrices 268</p> <p>Using Matrices to Solve Systems of Equations 272</p> <p>Answers to Problems on Matrices 274</p> <p><b>Chapter 15: Going Out of Sequence with Sequences and Series </b><b>279</b></p> <p>Writing the Terms of a Sequence 279</p> <p>Differences and Multipliers: Working with Special Sequences 282</p> <p>Backtracking: Constructing Recursively Defined Sequences 283</p> <p>Using Summation Notation 284</p> <p>Finding Sums with Special Series 286</p> <p>Answers to Problems on Sequences and Series 289</p> <p><b>Chapter 16: Everything You Ever Wanted to Know about Sets and Counting</b> <b>293</b></p> <p>Writing the Elements of a Set from Rules or Patterns 294</p> <p>Get Together: Combining Sets with Unions, Intersections, and Complements 295</p> <p>Multiplication Countdowns: Simplifying Factorial Expressions 297</p> <p>Checking Your Options: Using the Multiplication Property 298</p> <p>Counting on Permutations When Order Matters 300</p> <p>Mixing It Up with Combinations 301</p> <p>Raising Binomials to Powers: Investigating the Binomial Theorem 303</p> <p>Answers to Problems on Sets and Counting 304</p> <p><b>Part 5: The Part Of Tens</b> <b>309</b></p> <p><b>Chapter 17: Basic Graphs</b><b> 311</b></p> <p>Putting Polynomials in Their Place 311</p> <p>Lining Up Front and Center 312</p> <p>Being Absolutely Sure with Absolute Value 313</p> <p>Graphing Reciprocals of x and x2 .313</p> <p>Rooting Out Square Root and Cube Root .314</p> <p>Growing Exponentially with a Graph 315</p> <p>Logging In on Logarithmic Graphing 316</p> <p><b>Chapter 18: Ten Special Sequences and Their Sums</b> <b>317</b></p> <p>Adding as Easy as One, Two, Three 317</p> <p>Summing Up the Squares 318</p> <p>Finding the Sum of the Cubes 318</p> <p>Not Being at Odds with Summing Odd Numbers 319</p> <p>Evening Things Out by Adding Up Even Numbers 319</p> <p>Adding Everything Arithmetic 319</p> <p>Geometrically Speaking 320</p> <p>Easing into a Sum for e 320</p> <p>Signing In on the Sine 321</p> <p>Powering Up on Powers of 2 322</p> <p>Adding Up Fractions with Multiples for Denominators 322</p> <p>Index 323</p>
<p><b>Mary Jane Sterling</b> taught junior high and high school math before embarking on her career as an instructor at Bradley University, where she taught for more than 35 years.
<ul> <li>Find FREE quizzes for every chapter online</li> <li>Master Algebra II with hundreds of practice problems</li> <li>Review key math concepts</li> </ul> <p><b>Conquer challenging algebra with practice problems and online quizzes!</b> <p>The best way to learn complex algebra concepts is to work the problems and let the numbers fly. So get into this hands-on study guide, packed with hundreds of problems to solve and explanations to learn from! Need extra help with conic sections, polynomial functions, or matrices? There's a chapter for each. All the problem types you'll see in Algebra II class are in here. The book now comes with free access to chapter quizzes online, too! <p><b>Inside...</b> <ul> <li>Get good at graphing</li> <li>Recognize and formulate different functions</li> <li>Learn all the secrets of polynomials</li> <li>Solve systems of equations</li> <li>Handle imaginary numbers</li> <li>Understand and solve matrices</li> <li>Work with set notation</li> </ul>

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