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Book SynopsisPractice your way to a great grade in Algebra I Algebra I: 1001 Practice Problems For Dummies gives you 1,001 opportunities to practice solving problems on all the major topics in Algebra Iin the book and online! Get extra help with tricky subjects, solidify what you've already learned, and get in-depth walk-throughs for every problem with this useful book. These practice problems and detailed answer explanations will get you solving for x in no-time, no matter what your skill level. Thanks to Dummies, you have a resource to you put key concepts into practice. Work through practice problems on all Algebra I topics covered in classStep through detailed solutions for every problem to build your understandingAccess practice questions online to study anywhere, any timeImprove your grade and up your study game with practice, practice, practiceThe material presented in Algebra I: 1001 Practice Problems For Dummies is an excellent resource for students, as well as parents and tutors looking to help supplement classroom instruction. Algebra I: 1001 Practice Problems For Dummies (9781119883470) was previously published as 1,001 Algebra I Practice Problems For Dummies (9781118446713). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.Table of ContentsIntroduction 1 Part 1: The Questions 5 Chapter 1: Signing on with Signed Numbers 7 Chapter 2: Recognizing Algebraic Properties and Notation 13 Chapter 3: Working with Fractions and Decimals 17 Chapter 4: Making Exponential Expressions and Operations More Compatible 23 Chapter 5: Raking in Radicals 29 Chapter 6: Creating More User-Friendly Algebraic Expressions 35 Chapter 7: Multiplying by One or More Terms 41 Chapter 8: Dividing Algebraic Expressions 47 Chapter 9: Factoring Basics 53 Chapter 10: Factoring Binomials 57 Chapter 11: Factoring Quadratic Trinomials 61 Chapter 12: Other Factoring Techniques 65 Chapter 13: Solving Linear Equations 69 Chapter 14: Taking on Quadratic Equations 73 Chapter 15: Solving Polynomials with Powers Three and Higher 79 Chapter 16: Reining in Radical and Absolute Value Equations 83 Chapter 17: Making Inequalities More Fair 87 Chapter 18: Using Established Formulas 93 Chapter 19: Using Formulas in Geometric Story Problems 101 Chapter 20: Tackling Traditional Story Problems 107 Chapter 21: Graphing Basics 113 Chapter 22: Using the Algebra of Lines 119 Chapter 23: Other Graphing Topics 123 Part 2: The Answers 127 Chapter 24: The Answers 129 Index 443

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Book SynopsisTable of ContentsIntroduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 2 Beyond the Book 3 Where to Go from Here 3 Book 1: Starting Out With Numbers and Properties 5 Chapter 1: Assembling Your Tools: Number Systems 7 Identifying Numbers by Name 8 Realizing real numbers 8 Counting on natural numbers 8 Whittling out whole numbers 8 Integrating integers 9 Being reasonable: Rational numbers 9 Restraining irrational numbers 9 Picking out primes and composites 10 Zero: It’s Complicated 10 Imagining imaginary numbers 10 Coping with complex numbers 10 Placing Numbers on the Number Line 12 Speaking in Algebra 13 Being precise with words 13 Describing the size of an expression 15 Relating operations with symbols 15 Taking Aim at Algebra-Speak 17 Herding numbers with grouping symbols 17 Defining relationships 19 Taking on algebraic tasks 20 Practice Questions Answers and Explanations 22 Whaddya Know? Chapter 1 Quiz 23 Answers to Chapter 1 Quiz 25 Chapter 2: Deciphering Signs in Expressions 27 Assigning Numbers Their Place 27 Using the number line 28 Comparing positives and negatives with symbols 29 Zeroing in on Zero 31 Going in for Operations 32 Sorting out types of operations 32 Tackling the Basic Binary Operations 35 Adding signed numbers 35 Making a Difference with Signed Numbers 38 Multiplying Signed Numbers 40 Dividing Signed Numbers 41 Working with Nothing: Zero and Signed Numbers 42 Practice Questions Answers and Explanations 44 Whaddya Know? Chapter 2 Quiz 47 Answers to Chapter 2 Quiz 48 Chapter 3: Incorporating Algebraic Properties 49 Getting a Grip on Grouping Symbols 49 Spreading, Grouping, and Changing the Order 52 Distributing the wealth 52 Making Associations Work 53 Computing by Commuting 55 Relating Inverses and Identities 56 Investigating Inverses 56 Identifying Identities 58 Working with Factorial 59 Applying the Greatest Integer Function 60 Practice Question Answers and Explanations 62 Whaddya Know? Chapter 3 Quiz 66 Answers to Chapter 3 Quiz 67 Chapter 4: Coordinating Fractions and Decimals 69 Converting Improper Fractions and Mixed Numbers 70 Finding Fraction Equivalences 72 Rewriting fractions 72 Determining lowest terms 74 Making Proportional Statements 75 Finding Common Denominators 77 Creating common denominators from multiples of factors 78 Using the box method 80 Applying Fractional Operations 81 Adding and subtracting fractions 81 Multiplying and dividing fractions 83 Simplifying Complex Fractions 86 Performing Operations with Decimals 88 Changing Fractions to Decimals and Vice Versa 89 Making fractions become decimals 90 Rounding decimals 91 Writing decimals as equivalent fractions 91 Practice Question Answers and Explanations 94 Whaddya Know? Chapter 4 Quiz 101 Answers to Chapter 4 Quiz 103 Book 2: Operating On Operations 105 Chapter 5: Taming Rampaging Radicals 107 Simplifying Radical Terms 108 Working through Radical Expressions 109 Recognizing perfect square terms 109 Rewriting radical terms 110 Rationalizing Fractions 113 Managing Radicals as Exponential Terms 114 Using Fractional Exponents 116 Making the switch to fractional exponents 117 Simplifying expressions with exponents 118 Estimating Answers 119 Practice Questions Answers and Explanations 120 Whaddya Know? Chapter 5 Quiz 124 Answers to Chapter 5 Quiz 125 Chapter 6: Exploring Exponents 127 Powering up with Exponential Notation 127 Using Negative Exponents 130 Multiplying and Dividing Exponentials 132 Multiplying the same base 132 Multiplying the same power 133 Dividing with exponents 135 Raising Powers to Powers 137 Testing the Power of Zero 139 Writing Numbers with Scientific Notation 140 Practice Questions Answers and Explanations 143 Whaddya Know? Chapter 6 Quiz 145 Answers to Chapter 6 Quiz 146 Book 3: Making Things Simple by Simplifying 149 Chapter 7: Simplifying Algebraic Expressions 151 Addressing the Order of Operations 152 Adding and Subtracting Like Terms 154 Multiplying and Dividing Algebraically 157 Dealing with factors 157 Diving into dividing 158 Gathering Terms with Grouping Symbols 160 Evaluating Expressions 163 Checking Your Answers 165 Seeing if it makes sense 165 Plugging in values 166 Practice Questions Answers and Explanations 168 Whaddya Know? Chapter 7 Quiz 171 Answers to Chapter 7 Quiz 172 Chapter 8: Working with Numbers in Their Prime 175 Beginning with the Basics 176 Composing Composite Numbers 178 Writing Prime Factorizations 178 Dividing while standing on your head 178 Getting to the root of primes with a tree 180 Wrapping your head around the rules of divisibility 182 Making Use of a Prime Factor 185 Taking primes into account 185 Pulling out factors and leaving the rest 187 Practice Questions Answers and Explanations 190 Whaddya Know? Chapter 8 Quiz 194 Answers to Chapter 8 Quiz 195 Chapter 9: Specializing in Multiplication Matters 197 Distributing One Factor Over Many 198 Distributing Signs 200 Mixing It up with Numbers and Variables 201 Negative exponents yielding fractional answers 203 Working with Fractional Powers 205 Distributing More Than One Term 207 Distributing binomials 207 Distributing trinomials 209 Curses, Foiled Again — Or Not 210 Squaring Binomials 211 Multiplying the Sum and Difference of the Same Two Terms 212 Powering Up Binomials 213 Cubing binomials 213 Raising Binomials to Higher Powers 215 Creating the Sum and Difference of Cubes 217 Multiplying Conjugates 218 Practice Questions Answers and Explanations 220 Whaddya Know? Chapter 9 Quiz 225 Answers to Chapter 9 Quiz 226 Chapter 10: Dividing the Long Way to Simplify Algebraic Expressions 229 Dividing by a Monomial 229 Dividing by a Binomial 231 Dividing by Polynomials with More Terms 233 Simplifying Division Synthetically 235 Practice Questions Answers and Explanations 237 Whaddya Know? Chapter 10 Quiz 240 Answers to Chapter 10 Quiz 241 Book 4: Factoring 243 Chapter 11: Figuring on Factoring 245 Factoring out the Greatest Common Factor 245 Factoring out numbers 246 Factoring out variables 249 Unlocking combinations of numbers and variables 252 Using the Box Method 255 Changing Factoring into a Division Problem 257 Reducing Algebraic Fractions 258 Practice Questions Answers and Explanations 260 Whaddya Know? Chapter 11 Quiz 262 Answers to Chapter 11 Quiz 264 Chapter 12: Taking the Bite out of Binomial Factoring 267 Reining in Big and Tiny Numbers 268 Factoring the Difference of Squares 269 Factoring Differences and Sums of Cubes 271 Making Factoring a Multiple Mission 274 Practice Questions Answers and Explanations 277 Whaddya Know? Chapter 12 Quiz 279 Answers to Chapter 12 Quiz 280 Chapter 13: Factoring Trinomials and Special Polynomials 281 Recognizing the Standard Quadratic Expression 281 Focusing First on the Greatest Common Factor 283 Unwrapping the FOILing Package 284 The opening to unFOIL 284 Coming to the end of the FOIL roll 287 Factoring Quadratic-Like Trinomials 290 Factoring Trinomials Using More Than One Method 291 Factoring by Grouping 293 Putting All the Factoring Together and Making Factoring Choices 297 Combining unFOIL and the GCF 297 Grouping and unFOILing in the same package 298 Incorporating the Remainder Theorem 301 Synthesizing with synthetic division 302 Choosing numbers for synthetic division 303 Practice Questions Answers and Explanations 305 Whaddya Know? Chapter 13 Quiz 310 Answers to Chapter 13 Quiz 311 Book 5: Solving Linear And Polynomial Equations 313 Chapter 14: Establishing Ground Rules for Solving Equations 315 Creating the Correct Setup for Solving Equations 316 Setting up equations for further action 316 Making plans for solving equations 316 Keeping Equations Balanced 318 Balancing with binary operations 318 Squaring both sides and suffering the consequences 320 Taking a root of both sides 322 Solving with Reciprocals 323 Making a List and Checking It Twice 324 Doing a reality check 324 Thinking like a car mechanic when checking your work 325 Practice Problems Answers and Explanations 328 Whaddya Know? Chapter 14 Quiz 330 Answers to Chapter 14 Quiz 331 Chapter 15: Lining Up Linear Equations 333 Playing by the Rules 334 Using the Addition/Subtraction Property 334 Using the Multiplication/Division Property 336 Devising a method using division 336 Making the most of multiplication 337 Reciprocating the invitation 338 Putting Several Operations Together 339 Solving Linear Equations with Grouping Symbols 343 Nesting isn’t for the birds 343 Distributing first 343 Multiplying or dividing before distributing 346 Working with Proportions 349 Using the rules for proportions 349 Transforming fractional equations into proportions 351 Solving for Variables in Formulas 352 Practice Questions Answers and Explanations 355 Whaddya Know? Chapter 15 Quiz 363 Answers to Chapter 15 Quiz 364 Chapter 16: Muscling Up to Quadratic Equations 367 Using the Square-Root Rule 368 Factoring for a Solution 370 Zeroing in on the multiplication property of zero 370 Assigning the greatest common factor and multiplication property of zero to solving quadratics 372 Solving Quadratics with Three Terms 373 Using the Quadratic Formula 379 Completing the Square 383 Imagining the Worst with Imaginary Numbers 384 Practice Problems Answers and Explanations 387 Whaddya Know? Chapter 16 Quiz 392 Answers to Chapter 16 Quiz 393 Book 6: Dealing With Non-Polynomial Equations and Inequalities 395 Chapter 17: Yielding to Higher Powers 397 Queuing Up to Cubic Equations 397 Solving perfectly cubed equations 398 Working with the not-so-perfectly cubed 400 Going for the greatest common factor 401 Grouping cubes 404 Solving cubics with integers 405 Determining How Many Possible Roots 407 Applying the Rational Root Theorem 408 Using the Factor/Root Theorem 410 Solving by Factoring 411 Solving Powers That Are Quadratic-Like 412 Solving Synthetically 416 Practice Questions Answers and Explanations 420 Whaddya Know? Chapter 17 Quiz 426 Answers to Chapter 17 Quiz 427 Chapter 18: Reeling in Radical and Absolute Value Equations 429 Raising Both Sides to Solve Radical Equations 430 Powering up by squaring both sides 430 Raising to higher powers 433 Doubling the Fun with Radical Equations .435 Solving Absolute Value Equations 437 Making linear absolute value equations absolutely wonderful 437 Factoring absolute value equations for solutions 440 Checking for Absolute Value Extraneous Roots 441 Practice Questions Answers and Explanations 443 Whaddya Know? Chapter 18 Quiz 447 Answers to Chapter 18 Quiz 448 Chapter 19: Getting Even with Inequalities 449 Defining the Inequality Notation 450 Pointing in the right direction 450 Grappling with graphing inequalities 450 Using the Rules to Work on Inequality Statements 451 Rewriting Inequalities Using Interval Notation 453 Solving Linear Inequalities 455 Solving Quadratic Inequalities 457 Dealing with Polynomial and Rational Inequalities 460 Solving Absolute-Value Inequalities 463 Solving Complex Inequalities 465 Practice Questions Answers and Explanations 467 Whaddya Know? Chapter 19 Quiz 471 Answers to Chapter 19 Quiz 472 Book 7: Evaluating Formulas and Story Problems 475 Chapter 20: Facing Up to Formulas 477 Working with Formulas 477 Measuring Up 479 Finding out how long: Units of length 479 Putting the Pythagorean Theorem to work 482 Deciphering Perimeter, Area, and Volume 484 Using perimeter formulas to get around 484 Squaring off with area formulas 486 Soaring with Heron’s formula 488 Working with volume formulas 490 Getting Interested in Using Percent 492 Compounding interest formulas 492 Gauging taxes and discounts 495 Working out the Combinations and Permutations 497 Counting down to factorials 498 Counting on combinations 498 Ordering up permutations 500 Practice Questions Answers and Explanations 502 Whaddya Know? Chapter 20 Quiz 505 Answers to Chapter 20 Quiz 507 Chapter 21: Making Formulas Work in Basic Story Problems 509 Setting Up to Solve Story Problems 509 Applying the Pythagorean Theorem 511 Using Geometry to Solve Story Problems 513 Working around Perimeter, Area, and Volume 515 Parading out perimeter and arranging area 515 Adjusting the area 517 Pumping up the volume 519 Going ’Round in Circles 523 Putting Distance, Rate, and Time in a Formula 525 Going the distance with the distance-rate-time formula 525 Figuring distance plus distance 527 Equating distances 528 Figuring distance and fuel 529 Counting on Interest and Percent 530 Practice Questions Answers and Explanations 532 Whaddya Know? Chapter 21 Quiz 537 Answers to Chapter 21 Quiz 539 Chapter 22: Relating Values in Story Problems 541 Tackling Age Problems 542 Tackling Consecutive Integer Problems 543 Working Together on Work Problems 545 Throwing an Object into the Air 547 Practice Questions Answers and Explanations 550 Whaddya Know? Chapter 22 Quiz 553 Answers to Chapter 22 Quiz 554 Chapter 23: Measuring Up with Quality and Quantity Story Problems 555 Achieving the Right Blend with Mixture Problems 556 Concocting the Correct Solution 100% of the Time 559 Dealing with Money Problems 561 Investigating investments and interest 561 Going for the green: Money 564 Practice Questions Answers and Explanations 567 Whaddya Know? Chapter 23 Quiz 571 Answers to Chapter 23 Quiz 572 Book 8: Getting a Grip On Graphing 573 Chapter 24: Getting a Handle on Graphing 575 Thickening the Plot with Points 575 Interpreting ordered pairs 576 Actually Graphing Points 577 Sectioning Off by Quadrants 578 Graphing Lines 579 Using points to lay out lines 579 Going with the horizontal and vertical 581 Graphing Lines Using Intercepts 583 Computing Slopes of Lines 585 Sighting the slope 585 Formulating slope 587 Graphing with the Slope-Intercept Form 590 Changing to the Slope-Intercept Form 591 Writing Equations of Lines 592 Given a point and a slope 593 Given two points 593 Picking on Parallel and Perpendicular Lines 594 Finding Distances between Points 595 Finding Midpoints of Segments 597 Practice Questions Answers and Explanations 598 Whaddya Know? Chapter 24 Quiz 602 Answers to Chapter 24 Quiz 604 Chapter 25: Extending the Graphing Horizon 605 Finding the Intersections of Lines 605 Graphing for intersections 606 Substituting to find intersections 607 Graphing Parabolas and Circles 608 Curling Up with Parabolas 609 Trying out the basic parabola 609 Putting the vertex on an axis 610 Going around in circles with a circular graph 612 Plotting and Plugging in Polynomial Graphs 614 Investigating Graphs of Inequality Functions 618 Taking on Absolute-Value Function Graphs 620 Graphing with Transformations 621 Sliding and multiplying 622 Practice Questions Answers and Explanations 625 Whaddya Know? Chapter 25 Quiz 632 Answers to Chapter 25 Quiz 633 Chapter 26: Coordinating Systems of Equations and Graphing 639 Defining Solutions of Systems of Equations 639 Solving Systems of Linear Equations 641 Using elimination 641 Using substitution 642 Introducing intersections of lines 643 Solving Systems Involving Non-Linear Equations 644 Taking on Systems of Three Linear Equations 647 Practice Problems Answers and Explanations 648 Whaddya Know? Chapter 26 Quiz 651 Answers to Chapter 26 Quiz 652 Index 655

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Book SynopsisTable of ContentsIntroduction 1 Chapter 1: Setting the Scene for Actions in Algebra 5 Chapter 2: Examining Powers and Roots 17 Chapter 3: Ordering and Distributing: The Business of Algebra 25 Chapter 4: Factoring in the First and Second Degrees 33 Chapter 5: Broadening the Factoring Horizon 45 Chapter 6: Solving Linear Equations 57 Chapter 7: Tackling Second-Degree Quadratic Equations 71 Chapter 8: Expanding the Equation Horizon 87 Chapter 9: Reconciling Inequalities 103 Chapter 10: Absolute-Value Equations and Inequalities 115 Chapter 11: Making Algebra Tell a Story 121 Chapter 12: Putting Geometry into Story Problems 133 Chapter 13: Grappling with Graphing 143 Chapter 14: Ten Warning Signs of Algebraic Pitfalls 157 Index 161

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Book SynopsisGet a handle on pre-calculus in a pinch! If you're tackling pre-calculus and want to up your chances of doing your very best, this hands-on workbook is just what you need to grasp and retain the concepts that will help you succeed. Inside, you'll get basic content review for every concept, paired with examples and plenty of practice problems, ample workspace, step-by-step solutions, and thorough explanations for each and every problem. In Pre-Calculus Workbook For Dummies, you'll also get free access to a quiz for every chapter online! With all of the lessons and practice offered, you'll memorize the most frequently used formulas, see how to avoid common mistakes, understand tricky trig proofs, and get the inside scoop on key concepts such as quadratic equations. Get ample review before jumping into a calculus course Supplement your classroom work with easy-to-follow guidance Make complex formulas and concepts more approachaTable of ContentsIntroduction 1 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: Setting the Foundation: The Nuts And Bolts of Pre-Calculus 5 Chapter 1: Preparing for Pre-Calculus 7 Reviewing Order of Operations: The Fun in Fundamentals 8 Keeping Your Balance While Solving Equalities 10 When Your Image Really Counts: Graphing Equalities and Inequalities 12 Graphing with two points 12 Graphing by using the slope-intercept form 13 Graphing inequalities 14 Using Graphs to Find Distance, Midpoint, and Slope 15 Finding the distance 15 Calculating the midpoint 16 Discovering the slope 16 Answers to Problems on Fundamentals 19 Chapter 2: Real Numbers Come Clean 25 Solving Inequalities 25 Expressing Inequality Solutions in Interval Notation 28 Radicals and Exponents — Just Simplify! 30 Getting Out of a Sticky Situation, or Rationalizing 33 Answers to Problems on Real Numbers 35 Chapter 3: Controlling Functions by Knowing Their Function 39 Using Both Faces of the Coin: Even and Odd 40 Leaving the Nest: Transforming Parent Graphs 42 Quadratic functions 42 Square root functions 42 Absolute value functions 43 Cubic functions 43 Cube root functions 44 Steeper or flatter 44 Translations 46 Reflections 46 Combinations of transformations 46 Graphing Rational Functions 49 Piecing Together Piecewise Functions 52 Combining Functions 54 Evaluating Composition of Functions 55 Working Together: Domain and Range 57 Unlocking the Inverse of a Function: Turning It Inside Out 59 Answers to Problems on Functions 61 Chapter 4: Searching for Roots 75 Factoring a Factorable Quadratic 75 Solving a Quadratic Polynomial Equation 78 Completing the square 78 Quadratic formula 79 Solving High-Order Polynomials 80 Factoring by grouping 80 Determining positive and negative roots: Descartes’ Rule of Signs 81 Counting on imaginary roots 81 Getting the rational roots 81 Finding roots through synthetic division 82 Using Roots to Create an Equation 84 Graphing Polynomials 85 Answers to Problems on Roots and Degrees 89 Chapter 5: Exponential and Logarithmic Functions 95 Working with Exponential Functions 95 Eagerly Engaging Edgy Logarithmic Solutions 98 Making Exponents and Logs Work Together 101 Using Exponents and Logs in Practical Applications 103 Answers to Problems on Exponential and Logarithmic Functions 106 Part 2: Trig is the Key: Basic Review, The Unit Circle, and Graphs 113 Chapter 6: Basic Trigonometry and the Unit Circle 115 Finding the Six Trigonometric Ratios 115 Solving Word Problems with Right Triangles 118 Unit Circle and the Coordinate Plane: Finding Points and Angles 121 Finding Ratios from Angles on the Unit Circle 124 Solving Trig Equations 127 Making and Measuring Arcs 129 Answers to Problems on Basic Trig and the Unit Circle 131 Chapter 7: Graphing and Transforming Trig Functions 137 Getting a Grip on Periodic Graphs 137 Parent Graphs and Transformations: Sine and Cosine 138 Tangent and Cotangent: More Family Members 141 Generations: Secant and Cosecant 143 Answers to Problems on Graphing and Transforming Trig Functions 147 Part 3: Digging Into Advanced Trig: Identities, Theorems, and Applications 155 Chapter 8: Basic Trig Identities 157 Using Reciprocal Identities to Simplify Trig Expressions 157 Simplifying with Pythagorean Identities 159 Discovering Even-Odd Identities 160 Simplifying with Co-Function Identities 162 Moving with Periodicity Identities 163 Tackling Trig Proofs (Identities) 165 Answers to Problems on Basic Trig Identities 167 Chapter 9: Advanced Trig Identities 175 Simplifying with Sum and Difference Identities 175 Using Double-Angle Identities 178 Reducing with Half-Angle Identities 180 Changing Products to Sums 181 Expressing Sums as Products 182 Powering Down: Power-Reducing Formulas 184 Answers to Problems on Advanced Trig Identities 186 Chapter 10: Solving Oblique Triangles 193 Solving a Triangle with the Law of Sines: ASA and AAS 194 Tackling Triangles in the Ambiguous Case: SSA 195 Conquering a Triangle with the Law of Cosines: SAS and SSS 197 Using Oblique Triangles to Solve Practical Applications 198 Figuring Area 201 Answers to Problems on Solving Triangles 202 Part 4: Polar Coordinates, Cones, Solutions, Sequences, and Finding Your Limits 209 Chapter 11: Exploring Complex Numbers and Polar Coordinates 211 Performing Operations with and Graphing Complex Numbers 212 Round a Pole: Graphing Polar Coordinates 215 Changing to and from Polar 217 Graphing Polar Equations 220 Archimedean spiral 220 Cardioid 220 Rose 220 Circle 220 Lemniscate 220 Limaçon 221 Answers to Problems on Complex Numbers and Polar Coordinates 223 Chapter 12: Conquering Conic Sections 229 A Quick Conic Review 230 Going Round and Round with Circles 230 The Ups and Downs: Graphing Parabolas 232 Standing tall: Vertical parabolas 233 Lying down on the job: Horizontal parabolas 235 The Fat and the Skinny: Graphing Ellipses 237 Short and fat: The horizontal ellipse 237 Tall and skinny: The vertical ellipse 239 No Caffeine Required: Graphing Hyperbolas 241 Horizontal hyperbolas 241 Vertical hyperbolas 244 Identifying Conic Sections 246 Conic Sections in Parametric Form and Polar Coordinates 248 Parametric form for conic sections 248 Changing from parametric form to rectangular form 250 Conic sections on the polar coordinate plane 251 Answers to Problems on Conic Sections 253 Chapter 13: Finding Solutions for Systems of Equations 265 A Quick-and-Dirty Technique Overview 266 Solving Two Linear Equations with Two Variables 266 The substitution method 267 The elimination method 268 Not-So-Straight: Solving Nonlinear Systems 269 One equation that’s linear and one that isn’t 269 Two nonlinear equations 270 Systems of rational equations 271 Systems of More Than Two Equations 272 Graphing Systems of Inequalities 274 Breaking Down Decomposing Partial Fractions 276 Working with a Matrix 278 Getting It in the Right Form: Simplifying Matrices 281 Solving Systems of Equations Using Matrices 283 Gaussian elimination 283 Inverse matrices 285 Cramer’s Rule 287 Answers to Problems on Systems of Equations 289 Chapter 14: Spotting Patterns in Sequences and Series 301 General Sequences and Series: Determining Terms 301 Working Out the Common Difference: Arithmetic Sequences and Series 303 Simplifying Geometric Sequences and Series 305 Expanding Polynomials Using the Binomial Theorem 308 Answers to Problems on Sequences, Series, and Binomials 310 Chapter 15: Previewing Calculus 315 Finding Limits: Graphically, Analytically, and Algebraically 316 Graphically 316 Analytically 318 Algebraically 319 Knowing Your Limits 321 Calculating the Average Rate of Change 322 Determining Continuity 323 Answers to Problems on Calculus 326 Part 5: The Part of Tens 329 Chapter 16: Ten Plus Parent Graphs 331 Squaring Up with Quadratics 331 Cueing Up for Cubics 332 Rooting for Square Roots and Cube Roots 333 Graphing Absolutely Fabulous Absolute Value Functions 334 Flipping over Rational Functions 334 Exploring Exponential Graphs and Logarithmic Graphs 335 Seeing the Sine and Cosine 336 Covering Cosecant and Secant 337 Tripping over Tangent and Cotangent 338 Lining Up and Going Straight with Lines 339 Chapter 17: Ten Missteps to Avoid 341 Going Out of Order (of Operations) 341 FOILing Binomials Incorrectly 342 Breaking Up Fractions Badly 342 Combining Terms That Can’t Be Combined 342 Forgetting to Flip the Fraction 342 Losing the Negative (Sign) 343 Oversimplifying Roots 343 Executing Exponent Errors 343 Ignoring Extraneous 344 Misinterpreting Trig Notation 344 Index 345

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Book SynopsisBoost 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 suppTable of ContentsIntroduction 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 Chapter 11: Solving Systems of Linear Equations 221 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 Chapter 12: Solving Systems of Nonlinear Equations and Inequalities 237 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

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Book SynopsisThe grade-saving Algebra I companion, with hundreds of additional practice problems online Algebra I Workbook For Dummies is your solution to the Algebra brain-block. With hundreds of practice and example problems mapped to the typical high school Algebra class, you''ll crack the code in no time! Each problem includes a full explanation so you can see where you went wrongor rightevery step of the way. From fractions to FOIL and everything in between, this guide will help you grasp the fundamental concepts you''ll use in every other math class you''ll ever take. This new third edition includes access to an online test bank, where you''ll find bonus chapter quizzes to help you test your understanding and pinpoint areas in need of review. Whether you''re preparing for an exam or seeking a start-to-finish study aid, this workbook is your ticket to acing algebra. Master basic operations and properties to solve any problem Simplify expressions witTable of ContentsIntroduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 3 Beyond the Book 3 Where to Go from Here 4 Part 1: Getting Down to the Nitty-Gritty on Basic Operations 5 Chapter 1: Deciphering Signs in Numbers 7 Assigning Numbers Their Place 7 Reading and Writing Absolute Value 9 Adding Signed Numbers 10 Making a Difference with Signed Numbers 11 Multiplying Signed Numbers 12 Dividing Signed Numbers 14 Answers to Problems on Signed Numbers 15 Chapter 2: Incorporating Algebraic Properties 17 Getting a Grip on Grouping Symbols 17 Distributing the Wealth 19 Making Associations Work 20 Computing by Commuting 21 Answers to Problems on Algebraic Properties 23 Chapter 3: Making Fractions and Decimals Behave 25 Converting Improper and Mixed Fractions 25 Finding Fraction Equivalences 27 Making Proportional Statements 28 Finding Common Denominators 30 Adding and Subtracting Fractions 31 Multiplying and Dividing Fractions 32 Simplifying Complex Fractions 35 Changing Fractions to Decimals and Vice Versa 36 Performing Operations with Decimals 38 Answers to Problems on Fractions 39 Chapter 4: Exploring Exponents 45 Multiplying and Dividing Exponentials 45 Raising Powers to Powers 47 Using Negative Exponents 49 Writing Numbers with Scientific Notation 50 Answers to Problems on Discovering Exponents 52 Chapter 5: Taming Rampaging Radicals 55 Simplifying Radical Expressions 55 Rationalizing Fractions 57 Arranging Radicals as Exponential Terms 58 Using Fractional Exponents 60 Simplifying Expressions with Exponents 61 Estimating Answers 63 Answers to Problems on Radicals 64 Chapter 6: Simplifying Algebraic Expressions 67 Adding and Subtracting Like Terms 68 Multiplying and Dividing Algebraically 69 Incorporating Order of Operations 70 Evaluating Expressions 71 Answers to Problems on Algebraic Expressions 74 Part 2: Changing the Format of Expressions 77 Chapter 7: Specializing in Multiplication Matters 79 Distributing One Factor over Many 79 Curses, FOILed again — or not 80 Squaring binomials 82 Multiplying the sum and difference of the same two terms 83 Cubing binomials 84 Creating the Sum and Difference of Cubes 85 Raising binomials to higher powers 86 Answers to Problems on Multiplying Expressions 88 Chapter 8: Dividing the Long Way to Simplify Algebraic Expressions 91 Dividing by a Monomial 91 Dividing by a Binomial 93 Dividing by Polynomials with More Terms 96 Simplifying Division Synthetically 97 Answers to Problems on Division 99 Chapter 9: Figuring on Factoring 103 Pouring Over Prime Factorizations 103 Factoring Out the Greatest Common Factor 105 Reducing Algebraic Fractions 106 Answers to Problems on Factoring Expressions 108 Chapter 10: Taking the Bite Out of Binomial Factoring 111 Factoring the Difference of Squares 112 Factoring Differences and Sums of Cubes 113 Making Factoring a Multiple Mission 114 Answers to Problems on Factoring 115 Chapter 11: Factoring Trinomials and Special Polynomials 117 Focusing First on the Greatest Common Factor (GCF) 118 “Un”wrapping the FOIL 119 Factoring Quadratic-Like Trinomials 121 Factoring Trinomials Using More than One Method 122 Factoring by Grouping .124 Putting All the Factoring Together 126 Answers to Problems on Factoring Trinomials and Other Expressions 128 Part 3: Seek and Ye Shall Find Solutions 131 Chapter 12: Lining Up Linear Equations 133 Using the Addition/Subtraction Property 133 Using the Multiplication/Division Property 135 Putting Several Operations Together 136 Solving Linear Equations with Grouping Symbols 138 Working It Out with Fractions 140 Solving Proportions 142 Answers to Problems on Solving Linear Equations 144 Chapter 13: Muscling Up to Quadratic Equations 151 Using the Square Root Rule 152 Solving by Factoring 153 Using the Quadratic Formula 155 Completing the Square 158 Dealing with Impossible Answers 159 Answers to Problems on Solving Quadratic Equations 161 Chapter 14: Yielding to Higher Powers 167 Determining How Many Possible Roots 168 Applying the Rational Root Theorem 169 Using the Factor/Root Theorem 170 Solving by Factoring 172 Solving Powers That Are Quadratic-Like 174 Answers to Problems on Solving Higher Power Equations 176 Chapter 15: Reeling in Radical and Absolute Value Equations 179 Squaring Both Sides to Solve Radical Equations 180 Doubling the Fun with Radical Equations .182 Solving Absolute Value Equations 183 Answers to Problems on Radical and Absolute Value Equations 185 Chapter 16: Getting Even with Inequalities 189 Using the Rules to Work on Inequality Statements 190 Rewriting Inequalities by Using Interval Notation 191 Solving Linear Inequalities 192 Solving Quadratic Inequalities 193 Dealing with Polynomial and Rational Inequalities 195 Solving Absolute Value Inequalities 196 Solving Complex Inequalities 198 Answers to Problems on Working with Inequalities 199 Part 4: Solving Story Problems and Sketching Graphs 203 Chapter 17: Facing Up to Formulas 205 Working with Formulas 206 Deciphering Perimeter, Area, and Volume 207 Using perimeter formulas to get around 207 Squaring off with area formulas 209 Working with volume formulas 211 Getting Interested in Using Percent 213 Answers to Problems on Using Formulas 215 Chapter 18: Making Formulas Work in Basic Story Problems 219 Applying the Pythagorean Theorem 220 Using Geometry to Solve Story Problems 221 Putting Distance, Rate, and Time in a Formula 224 Examining the distance-rate-time formula 224 Going the distance with story problems 226 Answers to Making Formulas Work in Basic Story Problems 228 Chapter 19: Relating Values in Story Problems 233 Tackling Age Problems 234 Tackling Consecutive Integer Problems 235 Working Together on Work Problems 238 Answers to Relating Values in Story Problems 240 Chapter 20: Measuring Up with Quality and Quantity Story Problems 243 Achieving the Right Blend with Mixtures Problems 244 Concocting the Correct Solution One Hundred Percent of the Time 246 Dealing with Money Problems 248 Answers to Problems on Measuring Up with Quality and Quantity 250 Chapter 21: Getting a Handle on Graphing 255 Thickening the Plot with Points 255 Sectioning Off by Quadrants 257 Using Points to Lay Out Lines 258 Graphing Lines with Intercepts 260 Computing Slopes of Lines 261 Graphing with the Slope-Intercept Form 263 Changing to the Slope-Intercept Form 265 Writing Equations of Lines 266 Picking on Parallel and Perpendicular Lines 267 Finding Distances between Points 268 Finding the Intersections of Lines 269 Graphing Parabolas and Circles 270 Graphing with Transformations 272 Answers to Problems on Graphing 275 Part 5: The Part of Tens 283 Chapter 22: Ten Common Errors That Get Noticed 285 Squaring a Negative or Negative of a Square 285 Squaring a Binomial 286 Operating on Radicals 286 Distributing a Negative Throughout 287 Fracturing Fractions 287 Raising a Power to a Power 288 Making Negative Exponents Flip 288 Making Sense of Reversing the Sense 288 Using the Slope Formula Correctly 289 Writing Several Fractions as One 289 Chapter 23: Ten Quick Tips to Make Algebra a Breeze 291 Flipping Proportions 291 Multiplying Through to Get Rid of Fractions 292 Zeroing In on Fractions 292 Finding a Common Denominator 292 Dividing by 3 or 9 293 Dividing by 2, 4, or 8 293 Commuting Back and Forth 293 Factoring Quadratics 294 Making Radicals Less Rad, Baby 294 Applying Acronyms 294 Index 295

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Book SynopsisAlgebra II Essentials For Dummies (9781119590873) was previously published as Algebra II Essentials For Dummies (9780470618400). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Passing grades in two years of algebra courses are required for high school graduation. Algebra II Essentials For Dummies covers key ideas from typical second-year Algebra coursework to help students get up to speed. Free of ramp-up material, Algebra II Essentials For Dummies sticks to the point, with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical Algebra II course, from polynomials, conics, and systems of equations to rational, exponential, and logarithmic functions. This guide is also a perfect reference for parents who need to review critical algebra concepts as they help students with homework assignments, as well as for adult learnTable of ContentsIntroduction 1 About This Book 1 Conventions Used in This Book 2 Foolish Assumptions 2 Icons Used in This Book 2 Where to Go from Here 3 Chapter 1: Making Advances in Algebra 5 Bringing Out the Best in Algebraic Properties 5 Making short work of the basic properties 6 Organizing your operations 7 Enumerating Exponential Rules 8 Multiplying and dividing exponents 8 Rooting out exponents 9 Powering up exponents 10 Working with negative exponents 10 Assigning Factoring Techniques 10 Making two terms factor 11 Factoring three terms 12 Factoring four or more terms by grouping 13 Chapter 2: Lining Up Linear Equations 15 Getting the First Degree: Linear Equations 15 Solving basic linear equations 16 Eliminating fractions 16 Lining Up Linear Inequalities 17 Solving basic inequalities 18 Introducing interval notation 19 Absolute Value: Keeping Everything in Line 20 Solving absolute value equations 20 Seeing through absolute value inequality 21 Chapter 3: Making Quick Work of Quadratic Equations 23 Using the Square Root Rule When Possible 24 Solving Quadratic Equations by Factoring 24 Factoring quadratic binomials 25 Factoring quadratic trinomials 26 The Quadratic Formula to the Rescue 27 Realizing rational solutions 27 Investigating irrational solutions 27 Promoting Quadratic-like Equations 28 Solving Quadratic Inequalities 29 Keeping it strictly quadratic 30 Signing up for fractions 31 Increasing the number of factors 33 Chapter 4: Rolling Along with Rational and Radical Equations 35 Rounding Up Rational Equations and Eliminating Fractions 35 Making your least common denominator work for you 36 Proposing proportions for solving rational equations 38 Reasoning with Radicals 39 Squaring both sides of the equation 39 Taking on two radicals 40 Dealing with Negative Exponents 42 Factoring out a negative exponent as a greatest common factor 42 Solving quadratic-like trinomials 43 Fiddling with Fractional Exponents 44 Solving equations by factoring fractional exponents 44 Promoting techniques for working with fractional exponents 44 Chapter 5: Forging Function Facts 47 Describing Function Characteristics 47 Denoting function notation 48 Using function notation to evaluate functions 48 Determining Domain and Range 49 Delving into domain 49 Wrangling with range 50 Counting on Even and Odd Functions 51 Determining whether even or odd 52 Using even and odd functions in graphs 53 Taking on Functions One-to-One 53 Defining which functions are one-to-one 54 Testing for one-to-one functions 54 Composing Functions 55 Composing yourself with functions 55 Composing with the difference quotient 56 Getting into Inverse Functions 57 Finding which functions are inverses 58 Finding an inverse of a function 59 Chapter 6: Graphing Linear and Quadratic Functions 61 Identifying Some Graphing Techniques 61 Finding x- and y-intercepts 62 Reflecting on a graph’s symmetry 62 Mastering the Graphs of Lines 64 Determining the slope of a line 64 Describing two line equations 65 Identifying parallel and perpendicular lines 67 Coming to Terms with the Standard Form of a Quadratic 67 Starting with “a” in the standard form 68 Following “a” with “b” and “c” 69 Eyeing a Quadratic’s Intercepts 69 Finding the one and only y-intercept 69 Getting at the x-intercepts 70 Finding the Vertex of a Parabola 71 Computing vertex coordinates 71 Linking up with the axis of symmetry 72 Sketching a Graph from the Available Information 72 Chapter 7: Pondering Polynomials 75 Sizing Up a Polynomial Equation 75 Identifying Intercepts and Turning Points 76 Interpreting relative value and absolute value 76 Dealing with intercepts and turning points 77 Solving for y-intercepts and x-intercepts 78 Determining When a Polynomial is Positive or Negative 79 Incorporating a sign line 79 Recognizing a sign change rule 80 Solving Polynomial Equations 81 Factoring for roots 81 Taking sane steps with the rational root theorem 82 Putting Descartes in charge of signs 84 Finding Roots Synthetically 86 Using synthetic division when searching for roots 86 Synthetically dividing by a binomial 88 Chapter 8: Being Respectful of Rational Functions 91 Examining Rational Functions 91 Deliberating on domain 92 Investigating intercepts 92 Assigning Roles to Asymptotes 93 Validating vertical asymptotes 93 Finding equations for horizontal asymptotes 94 Taking vertical and horizontal asymptotes to graphs 94 Getting the scoop on oblique (slant) asymptotes 96 Discounting Removable Discontinuities 97 Finding removable discontinuities by factoring 97 Evaluating the removals 98 Looking at Limits of Rational Functions 99 Determining limits at function discontinuities 100 Finding infinity 102 Looking at infinity 104 Chapter 9: Examining Exponential and Logarithmic Functions 107 Computing Exponentially 107 Getting to the Base of Exponential Functions 108 Classifying bases 108 Introducing the more frequently used bases: 10 and e 110 Exponential Equation Solutions 110 Creating matching bases 111 Quelling quadratic patterns 111 Looking into Logarithmic Functions 113 Presenting the properties of logarithms 113 Doing more with logs than sawing 115 Solving Equations Containing Logs 117 Seeing all logs created equal 117 Solving log equations by changing to exponentials 118 Chapter 10: Getting Creative with Conics 121 Posing with Parabolas 122 Generalizing the form of a parabola’s equation 123 Making short work of a parabola’s sketch 124 Changing a parabola’s equation to the standard form 125 Circling around a Conic 126 Getting Eclipsed by Ellipses 127 Determining the shape 129 Finding the foci 130 Getting Hyped for Hyperbolas 130 Including the asymptotes 131 Graphing hyperbolas 132 Chapter 11: Solving Systems of Equations 135 Looking at Solutions Using the Standard Linear-Systems Form 136 Solving Linear Systems by Graphing 136 Interpreting an intersection 137 Tackling the same line 137 Putting up with parallel lines 137 Using Elimination (Addition) to Solve Systems of Equations 138 Finding Substitution to Be a Satisfactory Substitute 139 Variable substituting made easy 139 Writing solutions for coexisting lines 140 Taking on Systems of Three Linear Equations 141 Finding the solution of a system of three linear equations 141 Generalizing with a system solution 143 Increasing the Number of Equations 144 Intersecting Parabolas and Lines 146 Determining if and where lines and parabolas cross paths 147 Determining that there’s no solution 149 Crossing Parabolas with Circles 150 Finding multiple intersections 150 Sifting through the possibilities for solutions 151 Chapter 12: Taking the Complexity Out of Complex Numbers 155 Simplifying Powers of i 156 Getting More Complex with Complex Numbers 157 Performing complex operations 157 Performing complex division by multiplying by the conjugate 158 Simplifying reluctant radicals 159 Unraveling Complex Solutions in Quadratic Equations 160 Investigating Polynomials with Complex Roots 160 Classifying conjugate pairs 161 Making use of complex zeros 161 Chapter 13: Ten (or So) Special Formulas 163 Using Multiplication to Add 163 Factoring in Factorial 164 Picking Out Permutations 164 Collecting Combinations 164 Adding n Integers 165 Adding n Squared Integers 165 Adding Odd Numbers 165 Going for the Geometric 166 Calculating Compound Interest 166 Index 167

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Book SynopsisThe easy way to understand and retain all the concepts taught in pre-calculus classes Pre-Calculus All-in-One For Dummies is a great resource if you want to do you best in Pre-Calculus. Packed with lessons, examples, and practice problems in the book, plus extra chapter quizzes online, it gives you absolutely everything you need to succeed in pre-calc. Unlike your textbook, this book presents the essential topics clearly and concisely, so you can really understand the stuff you learn in class, score high on your tests (including the AP Pre-Calculus exam!), and get ready to confidently move ahead to upper-level math courses. And if you need a refresher before launching into calculus, look no furtherthis book has your back. Review what you learned in algebra and geometry, then dig into pre-calculus Master logarithms, exponentials, conic sections, linear equations, and beyond Get easy-to-understand explanations that match the methods your teaTable of ContentsIntroduction 1 Unit 1: Getting Started with Pre-Calculus 5 Chapter 1: Preparing for Pre-Calculus 7 Chapter 2: Operating with Real Numbers 25 Chapter 3: Cementing the Building Blocks of Pre-Calculus Functions 43 Chapter 4: Operating on Functions 65 Unit 2: Getting the Grip on Graphing 93 Chapter 5: Graphing Polynomial Functions 95 Chapter 6: Exponential and Logarithmic Functions 131 Chapter 7: Piece-Wise and Greatest-Integer Functions 159 Unit 3: The Essentials of Trigonometry 171 Chapter 8: Circling In on Angles 173 Chapter 9: Homing In on the Friendliest Angles 201 Chapter 10: Picturing Basic Trig Functions and Reciprocal Functions 217 Chapter 11: Graphing and Transforming Trig Functions 237 Unit 4: Identities and Special Triangles 267 Chapter 12: Identifying with Trig Identities: The Basics 269 Chapter 13: Advancing with Advanced Identities 297 Chapter 14: Getting the Slant on Oblique Triangles 327 Unit 5: Analytic Geometry 361 Chapter 15: Coordinating with Complex Numbers 363 Chapter 16: Warming Up to Polar Coordinates 379 Chapter 17: Relating Conics to Sliced Cones 399 Unit 6: Systems, Sequences, and Series 443 Chapter 18: Streamlining Systems of Equations 445 Chapter 19: Making Matrices Work 473 Chapter 20: Sequences and Series 499 Chapter 21: Expanding Binomials for the Real World 519 Unit 7: Onward to Calculus 533 Chapter 22: Lining Up the Tools 535 Chapter 23: Proceeding with Successful Procedures 557 Index 573

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Book SynopsisEvery intermediate algebra lesson, example, and practice problem you need in a single, easy-to-use reference Algebra II can be a tough nut to crack when you first meet it. But with the right toolswell, she''s still tough but she gets a heckuva lot easier to manage. In Algebra II All-in-One For Dummies you''ll find your very own step-by-step roadmap to solving even the most challenging Algebra II problems, from conics and systems of equations to exponential and logarithmic functions. In the book, you''ll discover the ins and outs of function transformation and evaluation, work out your brain with complex and imaginary numbers, and apply formulas from statistics and probability theory. You''ll also find: Accessible and practical lessons and practice for second year high-school or university algebra students End-of-chapter quizzes that help you learn and remember! key algebraic concepts, such as quadratic equations, graphing techniqueTable of ContentsIntroduction 1 Part 1: Getting to First Base with the Basics 5 Chapter 1: Beginning at the Beginning of Algebra 7 Chapter 2: Taking on Linear Equations and Inequalities 35 Chapter 3: Handling Quadratic and Other Polynomial Equations 59 Chapter 4: Controlling Quadratic and Rational Inequalities 89 Chapter 5: Soothing the Rational, the Radical, and the Negative 109 Chapter 6: Giving Graphing a Gander 139 Part 2: Figuring on Functions 171 Chapter 7: Formulating Functions 173 Chapter 8: Specializing in Quadratic Functions 201 Chapter 9: Plugging In Polynomials 229 Chapter 10: Acting Rationally with Functions 271 Chapter 11: Exploring Exponential and Logarithmic Functions 303 Chapter 12: Transforming and Critiquing Functions 343 Part 3: Using Conics and Systems of Equations 365 Chapter 13: Slicing the Way You Like It: Conic Sections 367 Chapter 14: Solving Systems of Linear Equations 405 Chapter 15: Solving Systems of Nonlinear Equations 435 Chapter 16: Solving Systems of Inequalities 455 Part 4: Making Lists and Checking for Imaginary Numbers 473 Chapter 17: Getting More Complex with Imaginary Numbers 475 Chapter 18: Making Moves with Matrices 493 Chapter 19: Seeking Out Sequences and Series 521 Chapter 20: Everything You Wanted to Know about Sets and Counting 545 Part 5: Applying Known Formulas 575 Chapter 21: Manipulating Formulas 577 Chapter 22: Taking on Applications 597 Index 613

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Book SynopsisTable of ContentsIntroduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 3 Beyond the Book 4 Where to Go from Here 4 Part 1: Homing In On Basic Solutions 5 Chapter 1: Going Beyond Beginning Algebra 7 Outlining Algebraic Properties 8 Keeping order with the commutative property 8 Maintaining group harmony with the associative property 9 Distributing a wealth of values 9 Checking out an algebraic ID 10 Singing along in-verses 11 Ordering Your Operations 11 Zeroing in on the Multiplication Property of Zero 12 Expounding on Exponential Rules 13 Multiplying and dividing exponents 13 Getting to the roots of exponents 14 Raising or lowering the roof with exponents 14 Making nice with negative exponents 15 Implementing Factoring Techniques 15 Factoring two terms 16 Taking on three terms 17 Factoring four or more terms by grouping 19 Chapter 2: Toeing the Straight Line: Linear Equations 21 Linear Equations: Handling the First Degree 21 Tackling basic linear equations 22 Clearing out fractions 23 Isolating different unknowns 24 Linear Inequalities: Algebraic Relationship Therapy 25 Solving linear inequalities 26 Introducing interval notation 27 Compounding inequality issues 28 Absolute Value: Keeping Everything in Line 30 Solving absolute value equations 31 Seeing through absolute value inequality 31 Chapter 3: Conquering Quadratic Equations 35 Implementing the Square Root Rule 36 Dismantling Quadratic Equations into Factors 37 Factoring binomials 37 Factoring trinomials 39 Factoring by grouping 40 Resorting to the Quadratic Formula 41 Finding rational solutions 42 Straightening out irrational solutions 42 Formulating huge quadratic results 43 Completing the Square: Warming Up for Conics 43 Squaring up a quadratic equation 44 Completing the square twice over 45 Tackling Higher-Powered Polynomials 46 Handling the sum or difference of cubes 47 Tackling quadratic-like trinomials 48 Solving Quadratic Inequalities 49 Keeping inequality strictly quadratic 50 Signing up for fractions 52 Increasing the number of factors 53 Considering absolute value inequalities 53 Chapter 4: Rooting Out the Rational, Radical, and Negative 55 Acting Rationally with Fraction-Filled Equations 56 Systematically solving rational equations 56 Solving rational equations with proportions 60 Ridding Yourself of a Radical 61 Squaring both sides of a radical equation 62 Calming two radicals 63 Changing Negative Attitudes about Exponents 65 Flipping negative exponents out of the picture 65 Factoring out negatives to solve equations 66 Fooling Around with Fractional Exponents 68 Combining terms with fractional exponents 69 Factoring fractional exponents 69 Solving equations by working with fractional exponents 70 Chapter 5: Graphing Your Way to the Good Life 73 Coordinating Your Graphing Efforts 74 Identifying the parts of the coordinate plane 74 Plotting from dot to dot 75 Streamlining the Graphing Process with Intercepts and Symmetry 76 Finding x- and y-intercepts 77 Reflecting on a graph’s symmetry 78 Graphing Lines 80 Finding the slope of a line 81 Facing two types of equations for lines 82 Identifying parallel and perpendicular lines 85 Looking at 10 Basic Forms 86 Lines and quadratics 86 Cubics and quartics 87 Radicals and rationals 87 Exponential and logarithmic curves 88 Absolute values and circles 89 Solving Problems with a Graphing Calculator 89 Entering equations into graphing calculators correctly 90 Looking through the graphing window 92 Part 2: Facing Off With Functions 95 Chapter 6: Formulating Function Facts 97 Defining Functions 98 Introducing function notation 98 Evaluating functions 98 Homing In on Domain and Range 99 Determining a function’s domain 99 Describing a function’s range 100 Betting on Even or Odd Functions 102 Recognizing even and odd functions 102 Applying even and odd functions to graphs 103 Facing One-to-One Confrontations 104 Defining one-to-one functions 104 Eliminating one-to-one violators 105 Going to Pieces with Piecewise Functions 106 Doing piecework 107 Applying piecewise functions 108 Composing Yourself and Functions 110 Performing compositions 110 Simplifying the difference quotient 111 Singing Along with Inverse Functions 112 Determining if functions are inverses 112 Solving for the inverse of a function 113 Chapter 7: Sketching and Interpreting Quadratic Functions 115 Interpreting the Standard Form of Quadratics 116 Starting with “a” in the standard form 116 Following up with “b” and “c” 117 Investigating Intercepts in Quadratics 118 Finding the one and only y-intercept 119 Finding the x-intercepts 120 Going to the Extreme: Finding the Vertex 123 Lining Up along the Axis of Symmetry 124 Sketching a Graph from the Available Information 125 Applying Quadratics to the Real World 127 Selling candles 127 Shooting basketballs 128 Launching a water balloon 130 Chapter 8: Staying Ahead of the Curves: Polynomials 133 Taking a Look at the Standard Polynomial Form 134 Exploring Polynomial Intercepts and Turning Points 134 Interpreting relative value and absolute value 135 Counting intercepts and turning points 135 Solving for polynomial intercepts 138 Determining Positive and Negative Intervals 139 Using a sign-line 140 Interpreting the rule 141 Finding the Roots of a Polynomial 143 Factoring for polynomial roots 143 Saving your sanity: The Rational Root Theorem 145 Letting Descartes make a ruling on signs 148 Synthesizing Root Findings 150 Using synthetic division to test for roots 150 Synthetically dividing by a binomial 153 Wringing out the Remainder (Theorem) 154 Chapter 9: Reasoning with Rational Functions 157 Exploring Rational Functions 158 Sizing up domain 158 Introducing intercepts 159 Adding Asymptotes to the Rational Pot 160 Determining the equations of vertical asymptotes 160 Determining the equations of horizontal asymptotes 161 Graphing vertical and horizontal asymptotes 161 Crunching the numbers and graphing oblique asymptotes 163 Accounting for Removable Discontinuities 164 Removal by factoring 164 Evaluating the removal restrictions 165 Showing removable discontinuities on a graph 165 Pushing the Limits of Rational Functions 167 Evaluating limits at discontinuities 168 Going to infinity 170 Catching rational limits at infinity 172 Putting It All Together: Sketching Rational Graphs from Clues 173 Chapter 10: Exposing Exponential and Logarithmic Functions 177 Evaluating Exponential Expressions 178 Exponential Functions: It’s All about the Base, Baby 179 Observing the trends in bases 179 Meeting the most frequently used bases: 10 and e 180 Solving Exponential Equations 182 Making bases match 182 Recognizing and using quadratic patterns 184 Showing an “Interest” in Exponential Functions 186 Applying the compound interest formula 186 Looking at continuous compounding 188 Logging On to Logarithmic Functions 189 Meeting the properties of logarithms 190 Putting your logs to work 191 Solving Logarithmic Equations 193 Setting log equal to log 194 Rewriting log equations as exponentials 195 Graphing Exponential and Logarithmic Functions 196 Expounding on the exponential 196 Not seeing the logs for the trees 198 Part 3: Conquering Conics And Systems Of Equations 203 Chapter 11: Cutting Up Conic Sections 205 Cutting Up a Cone 206 Opening Every Which Way with Parabolas 206 Looking at parabolas with vertices at the origin 207 Observing the general form of parabola equations 210 Sketching the graphs of parabolas 211 Converting parabolic equations to the standard form 214 Going Round and Round in Conic Circles 215 Standardizing the circle 215 Specializing in circles 217 Preparing Your Eyes for Solar Ellipses 218 Raising the standards of an ellipse 218 Sketching an elliptical path 221 Feeling Hyper about Hyperbolas 222 Including the asymptotes 223 Graphing hyperbolas 224 Identifying Conics from Their Equations, Standard or Not 227 Chapter 12: Solving Systems of Linear Equations 229 Looking at the Standard Linear-Systems Form and Its Possible Solutions 230 Graphing Solutions of Linear Systems 230 Pinpointing the intersection 231 Toeing the same line twice 232 Dealing with parallel lines 232 Solving Systems of Two Linear Equations by Using Elimination 233 Getting to the point with elimination 234 Recognizing solutions indicating parallel or coexisting lines 235 Making Substitution the Choice 236 Variable substituting made easy 236 Identifying parallel and coexisting lines 237 Using Cramer’s Rule to Defeat Unwieldy Fractions 238 Setting up the linear system for Cramer 239 Applying Cramer’s Rule to a linear system 240 Tackling Linear Systems with Three Linear Equations 241 Solving three-equation systems with algebra 241 Generalizing multiple solutions for linear equations 243 Upping the Ante with Larger Systems 244 Applying Linear Systems to Our 3-D World 247 Using Systems to Decompose Fractions 248 Chapter 13: Solving Systems of Nonlinear Equations and Inequalities 251 Crossing Parabolas with Lines 252 Determining the point(s) where a line and parabola cross paths 253 Dealing with a solution that’s no solution 254 Intertwining Parabolas and Circles 255 Managing multiple intersections 256 Sorting out the solutions 258 Planning Your Attack on Other Systems of Equations 260 Mixing polynomials and lines 260 Crossing polynomials 261 Navigating exponential intersections 263 Rounding up rational functions 265 Playing Fair with Inequalities 268 Drawing and quartering inequalities 268 Graphing areas with curves and lines 269 Part 4: Shifting Into High Gear With Advanced Concepts 271 Chapter 14: Simplifying Complex Numbers in a Complex World 273 Using Your Imagination to Simplify Powers of i 274 Understanding the Complexity of Complex Numbers 275 Operating on complex numbers 276 Multiplying by the conjugate to perform division 277 Simplifying radicals 279 Solving Quadratic Equations with Complex Solutions 280 Working Polynomials with Complex Solutions 282 Identifying conjugate pairs 283 Interpreting complex zeros 283 Chapter 15: Making Moves with Matrices 287 Describing the Different Types of Matrices 288 Row and column matrices 289 Square matrices 289 Zero matrices 289 Identity matrices 289 Performing Operations on Matrices 290 Adding and subtracting matrices 290 Multiplying matrices by scalars 291 Multiplying two matrices 291 Applying matrices and operations 293 Defining Row Operations 297 Finding Inverse Matrices 298 Determining additive inverses 299 Determining multiplicative inverses 299 Dividing Matrices by Using Inverses 304 Using Matrices to Find Solutions for Systems of Equations 305 Chapter 16: Making a List: Sequences and Series 307 Understanding Sequence Terminology 308 Using sequence notation 308 No-fear factorials in sequences 309 Alternating sequential patterns 309 Looking for sequential patterns 310 Taking Note of Arithmetic and Geometric Sequences 313 Finding common ground: Arithmetic sequences 313 Taking the multiplicative approach: Geometric sequences 315 Recursively Defining Functions 317 Making a Series of Moves 318 Introducing summation notation 318 Summing arithmetically 319 Summing geometrically 320 Applying Sums of Sequences to the Real World 323 Stacking the blocks 323 Negotiating your allowance 323 Bouncing a ball 324 Highlighting Special Formulas 326 Chapter 17: Everything You Wanted to Know about Sets 329 Revealing Set Notation 329 Listing elements with a roster 330 Building sets from scratch 330 Going for all (universal set) or nothing (empty set) 331 Subbing in with subsets 331 Operating on Sets 333 Celebrating the union of two sets 333 Looking both ways for set intersections 334 Feeling complementary about sets 335 Counting the elements in sets 335 Drawing Venn You Feel Like It 336 Applying the Venn diagram 337 Using Venn diagrams with set operations 338 Adding a set to a Venn diagram 339 Focusing on Factorials 342 Making factorial manageable 342 Simplifying factorials 343 How Do I Love Thee? Let Me Count Up the Ways 344 Applying the multiplication principle to sets 344 Arranging permutations of sets 345 Mixing up sets with combinations 348 Branching Out with Tree Diagrams 350 Picturing a tree diagram for a permutation 351 Drawing a tree diagram for a combination 352 Part 5: The Part Of Tens 353 Chapter 18: Ten Multiplication Tricks 355 Squaring Numbers That End in 5 355 Finding the Next Perfect Square 356 Recognizing the Pattern in Multiples of 9 and 11 357 Casting Out 9s 357 Casting Out 9s: The Multiplication Moves 358 Multiplying by 11 359 Multiplying by 5 360 Finding Common Denominators 361 Determining Divisors 362 Multiplying Two-Digit Numbers 362 Chapter 19: Ten Special Types of Numbers 365 Triangular Numbers 365 Square Numbers 366 Hexagonal Numbers 366 Perfect Numbers 367 Amicable Numbers 367 Happy Numbers 368 Abundant Numbers 368 Deficient Numbers 368 Narcissistic Numbers 368 Prime Numbers 369 Index 371

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Book SynopsisCovers topics such as cartesian coordinates, sines and cosines, secants and cosecants, tangents and cotangents, transforming functions, operating on identities, adding Heron's formula, and determining domain and range.Table of ContentsIntroduction 1 About This Book 1 Conventions Used in This Book 1 Foolish Assumptions 2 How This Book is Organized 2 Part I: Trying Out Trig: Starting at the Beginning 2 Part II: Trigonometric Functions 3 Part III: Trigonometric Identities and Equations 3 Part IV: Graphing the Trigonometric Functions 3 Part V: The Part of Tens 4 Icons Used in This Book 4 Where to Go from Here 4 Part I: Trying Out Trig: Starting at the Beginning 5 Chapter 1: Tackling Technical Trig 7 Getting Angles Labeled by Size 7 Naming Angles Where Lines Intersect 9 Writing Angle Names Correctly 10 Finding Missing Angle Measures in Triangles 11 Determining Angle Measures along Lines and outside Triangles 12 Dealing with Circle Measurements 14 Tuning In with the Right Chord 15 Sectioning Off Sectors of Circles 16 Answers to Problems on Tackling Technical Trig 17 Chapter 2: Getting Acquainted with the Graph 21 Plotting Points 21 Identifying Points by Quadrant 23 Working with Pythagoras 24 Keeping Your Distance 26 Finding Midpoints of Segments 27 Dealing with Slippery Slopes 28 Writing Equations of Circles 30 Graphing Circles 32 Answers to Problems on Graphing 33 Chapter 3: Getting the Third Degree 37 Recognizing First-Quadrant Angles 37 Expanding Angles to Other Quadrants 39 Expanding Angles beyond 360 Degrees 40 Coordinating with Negative Angle Measures 41 Dealing with Coterminal Angles 42 Answers to Problems on Measuring in Degrees 43 Chapter 4: Recognizing Radian Measure 45 Becoming Acquainted with Graphed Radians 45 Changing from Degrees to Radians 47 Changing from Radians to Degrees 49 Measuring Arcs 50 Determining the Area of a Sector 52 Answers to Problems on Radian Measure 53 Chapter 5: Making Things Right with Right Triangles 57 Naming the Parts of a Right Triangle 57 Completing Pythagorean Triples 59 Completing Right Triangles 61 Working with the 30-60-90 Right Triangle 62 Using the Isosceles Right Triangle 64 Using Right Triangles in Applications 65 Answers to Problems on Right Triangles 68 Part II: Trigonometric Functions 75 Chapter 6: Defining Trig Functions with a Right Triangle 77 Defining the Sine Function 78 Cooperating with the Cosine Function 79 Sunning with the Tangent Definition 80 Hunting for the Cosecant Definition 81 Defining the Secant Function 82 Coasting Home with the Cotangent 83 Establishing Trig Functions for Angles in Special Right Triangles 85 Applying the Trig Functions 86 Answers to Problems on Defining Trig Functions 88 Chapter 7: Discussing Properties of the Trig Functions 93 Defining a Function and Its Inverse 93 Deciding on the Domains 95 Reaching Out for the Ranges 97 Closing In on Exact Values 98 Determining Exact Values for All Functions 99 Answers to Problems in Properties of Trig Functions 102 Chapter 8: Going Full Circle with the Circular Functions 105 Finding Points on the Unit Circle 105 Determining Reference Angles 108 Assigning the Signs of Functions by Quadrant 111 Figuring Out Trig Functions around the Clock 113 Answers to Problems in Going Full Circle 115 Part III: Trigonometric Identities and Equations 119 Chapter 9: Identifying the Basic Identities 121 Using the Reciprocal Identities 121 Creating the Ratio Identities 123 Playing Around with Pythagorean Identities 124 Solving Identities Using Reciprocals, Ratios, and Pythagoras 127 Answers to Problems on Basic Identities 130 Chapter 10: Using Identities Defined with Operations 135 Adding Up the Angles with Sum Identities 135 Subtracting Angles with Difference Identities 138 Doubling Your Pleasure with Double Angle Identities 140 Multiplying the Many by Combining Sums and Doubles 142 Halving Fun with Half-Angle Identities 144 Simplifying Expressions with Identities 146 Solving Identities 148 Answers to Problems on Using Identities 151 Chapter 11: Techniques for Solving Trig Identities 161 Working on One Side at a Time 161 Working Back and Forth on Identities 164 Changing Everything to Sine and Cosine 165 Multiplying by Conjugates 167 Squaring Both Sides 168 Finding Common Denominators 169 Writing All Functions in Terms of Just One 171 Answers to Problems Techniques for Solving Identities 173 Chapter 12: Introducing Inverse Trig Functions 185 Determining the Correct Quadrants 185 Evaluating Expressions Using Inverse Trig Functions 187 Solving Equations Using Inverse Trig Functions 189 Creating Multiple Answers for Multiple and Half-Angles 191 Answers to Problems on Inverse Trig Functions 193 Chapter 13: Solving Trig Equations 195 Solving for Solutions within One Rotation 195 Solving Equations with Multiple Answers 197 Special Factoring for a Solution 200 Using Fractions and Common Denominators to Solve Equations 202 Using the Quadratic Formula 205 Answers to Problems on Solving Trig Equations 206 Chapter 14: Revisiting the Triangle with New Laws 213 Using the Law of Sines 213 Adding the Law of Cosines 215 Dealing with the Ambiguous Case 218 Investigating the Law of Tangents 219 Finding the Area of a Triangle the Traditional Way 220 Flying In with Heron’s Formula 221 Finding Area with an Angle Measure 222 Applying Triangles 223 Answers to Problems on Triangles 224 Part IV: Graphing the Trigonometric Functions 231 Chapter 15: Graphing Sine and Cosine 233 Determining Intercepts and Extreme Values 233 Graphing the Basic Sine and Cosine Curves 235 Changing the Amplitude 236 Adjusting the Period of the Curves 238 Graphing from the Standard Equation 239 Applying the Sine and Cosine Curves to Life 241 Answers to Problems on Graphing Sine and Cosine 243 Chapter 16: Graphing Tangent and Cotangent 249 Establishing Vertical Asymptotes 249 Graphing Tangent and Cotangent 250 Altering the Basic Curves 252 Answers to Problems on Graphing Tangent and Cotangent 253 Chapter 17: Graphing Cosecant, Secant, and Inverse Trig Functions 255 Determining the Vertical Asymptotes 255 Graphing Cosecant and Secant 256 Making Changes to the Graphs of Cosecant and Secant 257 Analyzing the Graphs of the Inverse Trig Functions 258 Answers to Problems on Cosecant, Secant, and Inverse Trig Functions 261 Chapter 18: Transforming Graphs of Trig Functions 263 Sliding the Graphs Left or Right 263 Sliding the Graphs Up or Down 264 Changing the Steepness 266 Reflecting on the Situation — Horizontally 267 Reflecting on Your Position — Vertically 268 Putting It All Together 269 Combining Trig Functions with Polynomials 270 Answers to Problems on Transforming Trig Functions 272 Part V: The Part of Tens 277 Chapter 19: Ten Identities with a Negative Attitude 279 Negative Angle Identities 279 Complementing and Supplementing Identities 279 Doing Fancy Factoring with Identities 280 Chapter 20: Ten Formulas to Use in a Circle 281 Running Around in Circles 281 Adding Up the Area 281 Defeating an Arc Rival 281 Sectioning Off the Sector 282 Striking a Chord 282 Ringing True 283 Inscribing and Radii 283 Circumscribing and Radii 283 Righting a Triangle 284 Inscribing a Polygon 284 Chapter 21: Ten Ways to Relate the Sides and Angles of Any Triangle 285 Relating with the Law of Sines 285 Hatching a Little Heron 286 Summing Sines 286 You Half It or You Don’t 286 Cozying Up with Cosines 286 Angling for an Angle 286 Mixing It Up with Cosines 286 Heron Again, Gone Tomorrow 287 Divide and Conquer with the Tangent 287 Heron Lies the Problem 287 Appendix: Trig Functions Table 289 Index 293

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Book SynopsisLinear Algebra For Dummies serves as an easy-to-follow guide that introduces (or re-introduces) readers to key concepts such as matrices, vector spaces, and eigenvalues and eigenvectors. It presents the information in a way that allows readers to fully digest not just the "how" of solving linear algebraic problems, but also the "why.Table of ContentsIntroduction. Part I: Lining Up the Basics of Linear Algebra. Chapter 1: Putting a Name to Linear Algebra. Chapter 2: The Value of Involving Vectors. Chapter 3: Mastering Matrices and Matrix Algebra. Chapter 4: Getting Systematic with Systems of Equations. Part II: Relating Vectors and Linear Transformations. Chapter 5: Lining Up Linear Combinations. Chapter 6: Investigating the Matrix Equation Ax = b. Chapter 7: Homing In on Homogeneous Systems and Linear Independence. Chapter 8: Making Changes with Linear Transformations. Part III: Evaluating Determinants. Chapter 9: Keeping Things in Order with Permutations. Chapter 10: Evaluating Determinants. Chapter 11: Personalizing the Properties of Determinants. Chapter 12: Taking Advantage of Cramer’s Rule. Part IV: Involving Vector Spaces. Chapter 13: Involving Vector Spaces. Chapter 14: Seeking Out Subspaces of Vector Spaces. Chapter 15: Scoring Big with Vector Space Bases. Chapter 16: Eyeing Eigenvalues and Eigenvectors. Part V: The Part of Tens. Chapter 17: Ten Real-World Applications Using Matrices. Chapter 18: Ten (Or So) Linear Algebra Processes You Can Do on Your Calculator. Chapter 19: Ten Mathematical Meanings of Greek Letters. Glossary. Index.

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Book SynopsisPractice your way to a better grade in pre-calc Pre-Calculus: 1001 Practice Problems For Dummies gives you 1,001 opportunities to practice solving problems from all the major topics in Pre-Calculusin the book and online! Get extra help with tricky subjects, solidify what you've already learned, and get in-depth walk-throughs for every problem with this useful book. These practice problems and detailed answer explanations will turn you into a pre-calc problem-solving machine, no matter what your skill level. Thanks to Dummies, you have a resource to help you put key concepts into practice. Work through practice problems on all Pre-Calculus topics covered in school classesRead through detailed explanations of the answers to build your understandingAccess practice questions online to study anywhere, any timeImprove your grade and up your study game with practice, practice, practiceThe material presented in Pre-Calculus: 1001 Practice Problems For Dummies is an excellent resource for students, as well as for parents and tutors looking to help supplement Pre-Calculus instruction. Pre-Calculus: 1001 Practice Problems For Dummies (9781119883623) was previously published as 1,001 Pre-Calculus Practice Problems For Dummies (9781118853320). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.Table of ContentsIntroduction 1 Part 1: The Questions 5 Chapter 1: Getting Started with Algebra Basics 7 Chapter 2: Solving Some Equations and Inequalities 13 Chapter 3: Function Basics 19 Chapter 4: Graphing and Transforming Functions 27 Chapter 5: Polynomials 35 Chapter 6: Exponential and Logarithmic Functions 43 Chapter 7: Trigonometry Basics 51 Chapter 8: Graphing Trig Functions 59 Chapter 9: Getting Started with Trig Identities 65 Chapter 10: Continuing with Trig Identities 71 Chapter 11: Working with Triangles and Trigonometry 77 Chapter 12: Complex Numbers and Polar Coordinates 87 Chapter 13: Conic Sections 95 Chapter 14: Systems of Equations and Inequalities 101 Chapter 15: Sequences and Series 109 Chapter 16: Introducing Limits and Continuity 115 Part 2: The Answers 123 Chapter 17: Answers 125 Index 539

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Book SynopsisTable of ContentsIntroduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 3 Beyond the Book 3 Where to Go from Here 3 Part 1: Getting Started with Pre-Calculus 5 Chapter 1: Pre-Pre-Calculus 7 Pre-Calculus: An Overview 8 All the Number Basics (No, Not How to Count Them!) 9 The multitude of number types: Terms to know 9 The fundamental operations you can perform on numbers 11 The properties of numbers: Truths to remember 11 Visual Statements: When Math Follows Form with Function 12 Basic terms and concepts 13 Graphing linear equalities and inequalities 14 Gathering information from graphs 15 Get Yourself a Graphing Calculator 16 Chapter 2: Playing with Real Numbers 19 Solving Inequalities 19 Recapping inequality how-tos 20 Solving equations and inequalities when absolute value is involved 20 Expressing solutions for inequalities with interval notation 22 Variations on Dividing and Multiplying: Working with Radicals and Exponents 24 Defining and relating radicals and exponents 24 Rewriting radicals as exponents (or, creating rational exponents) 25 Getting a radical out of a denominator: Rationalizing 26 Chapter 3: The Building Blocks of Pre-Calculus Functions 31 Qualities of Special Function Types and Their Graphs 32 Even and odd functions 32 One-to-one functions 32 Dealing with Parent Functions and Their Graphs 33 Linear functions 33 Quadratic functions 33 Square-root functions 34 Absolute-value functions 34 Cubic functions 35 Cube-root functions 36 Graphing Functions That Have More Than One Rule: Piece-Wise Functions 37 Setting the Stage for Rational Functions 38 Step 1: Search for vertical asymptotes 39 Step 2: Look for horizontal asymptotes 40 Step 3: Seek out oblique asymptotes 41 Step 4: Locate the x- and y-intercepts 42 Putting the Results to Work: Graphing Rational Functions 42 Chapter 4: Operating on Functions 49 Transforming the Parent Graphs 50 Stretching and flattening 50 Translations 52 Reflections 54 Combining various transformations (a transformation in itself!) 55 Transforming functions point by point 57 Sharpen Your Scalpel: Operating on Functions 58 Adding and subtracting 59 Multiplying and dividing 60 Breaking down a composition of functions 60 Adjusting the domain and range of combined functions (if applicable) 61 Turning Inside Out with Inverse Functions 63 Graphing an inverse 64 Inverting a function to find its inverse 66 Verifying an inverse 66 Chapter 5: Digging Out and Using Roots to Graph Polynomial Functions 69 Understanding Degrees and Roots 70 Factoring a Polynomial Expression 71 Always the first step: Looking for a GCF 72 Unwrapping the box containing a trinomial 73 Recognizing and factoring special polynomials 74 Grouping to factor four or more terms 77 Finding the Roots of a Factored Equation 78 Cracking a Quadratic Equation When It Won’t Factor 79 Using the quadratic formula 79 Completing the square 80 Solving Unfactorable Polynomials with a Degree Higher Than Two 81 Counting a polynomial’s total roots 82 Tallying the real roots: Descartes’s rule of signs 82 Accounting for imaginary roots: The fundamental theorem of algebra 83 Guessing and checking the real roots 84 Put It in Reverse: Using Solutions to Find Factors 90 Graphing Polynomials 91 When all the roots are real numbers 91 When roots are imaginary numbers: Combining all techniques 95 Chapter 6: Exponential and Logarithmic Functions 97 Exploring Exponential Functions 98 Searching the ins and outs of exponential functions 98 Graphing and transforming exponential functions 100 Logarithms: The Inverse of Exponential Functions 102 Getting a better handle on logarithms 102 Managing the properties and identities of logs 103 Changing a log’s base 105 Calculating a number when you know its log: Inverse logs 105 Graphing logs 106 Base Jumping to Simplify and Solve Equations 109 Stepping through the process of exponential equation solving 109 Solving logarithmic equations 112 Growing Exponentially: Word Problems in the Kitchen 113 Part 2: The Essentials of Trigonometry 117 Chapter 7: Circling in on Angles 119 Introducing Radians: Circles Weren’t Always Measured in Degrees 120 Trig Ratios: Taking Right Triangles a Step Further 121 Making a sine 121 Looking for a cosine 122 Going on a tangent 124 Discovering the flip side: Reciprocal trig functions 125 Working in reverse: Inverse trig functions 126 Understanding How Trig Ratios Work on the Coordinate Plane 127 Building the Unit Circle by Dissecting the Right Way 129 Familiarizing yourself with the most common angles 129 Drawing uncommon angles 131 Digesting Special Triangle Ratios 132 The 45er: 45 -45 -90 triangle 132 The old 30-60: 30 -60 -90 triangle 133 Triangles and the Unit Circle: Working Together for the Common Good 135 Placing the major angles correctly, sans protractor 135 Retrieving trig-function values on the unit circle 138 Finding the reference angle to solve for angles on the unit circle 142 Measuring Arcs: When the Circle Is Put in Motion 146 Chapter 8: Simplifying the Graphing and Transformation of Trig Functions 149 Drafting the Sine and Cosine Parent Graphs 150 Sketching sine 150 Looking at cosine 152 Graphing Tangent and Cotangent 154 Tackling tangent 154 Clarifying cotangent 157 Putting Secant and Cosecant in Pictures 159 Graphing secant 159 Checking out cosecant 161 Transforming Trig Graphs 162 Messing with sine and cosine graphs 163 Tweaking tangent and cotangent graphs 173 Transforming the graphs of secant and cosecant 176 Chapter 9: Identifying with Trig Identities: The Basics 181 Keeping the End in Mind: A Quick Primer on Identities 182 Lining Up the Means to the End: Basic Trig Identities 182 Reciprocal and ratio identities 183 Pythagorean identities 185 Even/odd identities 188 Co-function identities 190 Periodicity identities 192 Tackling Difficult Trig Proofs: Some Techniques to Know 194 Dealing with demanding denominators 195 Going solo on each side 199 Chapter 10: Advanced Identities: Your Keys to Success 201 Finding Trig Functions of Sums and Differences 202 Searching out the sine of a b 202 Calculating the cosine of a b 206 Taming the tangent of a b 209 Doubling an Angle and Finding Its Trig Value 211 Finding the sine of a doubled angle 212 Calculating cosines for two 213 Squaring your cares away 215 Having twice the fun with tangents 216 Taking Trig Functions of Common Angles Divided in Two 217 A Glimpse of Calculus: Traveling from Products to Sums and Back 219 Expressing products as sums (or differences) 219 Transporting from sums (or differences) to products 220 Eliminating Exponents with Power-Reducing Formulas 221 Chapter 11: Taking Charge of Oblique Triangles with the Laws of Sines and Cosines 223 Solving a Triangle with the Law of Sines 224 When you know two angle measures 225 When you know two consecutive side lengths 228 Conquering a Triangle with the Law of Cosines 235 SSS: Finding angles using only sides 236 SAS: Tagging the angle in the middle (and the two sides) 238 Filling in the Triangle by Calculating Area 240 Finding area with two sides and an included angle (for SAS scenarios) 241 Using Heron’s Formula (for SSS scenarios) 241 Part 3: Analytic Geometry and System Solving 243 Chapter 12: Plane Thinking: Complex Numbers and Polar Coordinates 245 Understanding Real versus Imaginary 246 Combining Real and Imaginary: The Complex Number System 247 Grasping the usefulness of complex numbers 247 Performing operations with complex numbers 248 Graphing Complex Numbers 250 Plotting Around a Pole: Polar Coordinates 251 Wrapping your brain around the polar coordinate plane 252 Graphing polar coordinates with negative values 254 Changing to and from polar coordinates 256 Picturing polar equations 259 Chapter 13: Creating Conics by Slicing Cones 263 Cone to Cone: Identifying the Four Conic Sections 264 In picture (graph form) 264 In print (equation form) 266 Going Round and Round: Graphing Circles 267 Graphing circles at the origin 267 Graphing circles away from the origin 268 Writing in center–radius form 269 Riding the Ups and Downs with Parabolas 270 Labeling the parts 270 Understanding the characteristics of a standard parabola 271 Plotting the variations: Parabolas all over the plane 272 The vertex, axis of symmetry, focus, and directrix 273 Identifying the min and max of vertical parabolas 276 The Fat and the Skinny on the Ellipse 278 Labeling ellipses and expressing them with algebra 279 Identifying the parts from the equation 281 Pair Two Curves and What Do You Get? Hyperbolas 284 Visualizing the two types of hyperbolas and their bits and pieces 284 Graphing a hyperbola from an equation 287 Finding the equations of asymptotes 287 Expressing Conics Outside the Realm of Cartesian Coordinates 289 Graphing conic sections in parametric form 290 The equations of conic sections on the polar coordinate plane 292 Chapter 14: Streamlining Systems, Managing Variables 295 A Primer on Your System-Solving Options 296 Algebraic Solutions of Two-Equation Systems 297 Solving linear systems 297 Working nonlinear systems 300 Solving Systems with More than Two Equations 304 Decomposing Partial Fractions 306 Surveying Systems of Inequalities 307 Introducing Matrices: The Basics 309 Applying basic operations to matrices 310 Multiplying matrices by each other 311 Simplifying Matrices to Ease the Solving Process 312 Writing a system in matrix form 313 Reduced row-echelon form 313 Augmented form 314 Making Matrices Work for You 315 Using Gaussian elimination to solve systems 316 Multiplying a matrix by its inverse 320 Using determinants: Cramer’s Rule 323 Chapter 15: Sequences, Series, and Expanding Binomials for the Real World 327 Speaking Sequentially: Grasping the General Method 328 Determining a sequence’s terms 328 Working in reverse: Forming an expression from terms 329 Recursive sequences: One type of general sequence 330 Difference between Terms: Arithmetic Sequences 331 Using consecutive terms to find another 332 Using any two terms 332 Ratios and Consecutive Paired Terms: Geometric Sequences 334 Identifying a particular term when given consecutive terms 334 Going out of order: Dealing with nonconsecutive terms 335 Creating a Series: Summing Terms of a Sequence 337 Reviewing general summation notation 337 Summing an arithmetic sequence 338 Seeing how a geometric sequence adds up 339 Expanding with the Binomial Theorem 342 Breaking down the binomial theorem 344 Expanding by using the binomial theorem 345 Chapter 16: Onward to Calculus 351 Scoping Out the Differences between Pre-Calculus and Calculus 352 Understanding Your Limits 353 Finding the Limit of a Function 355 Graphically 355 Analytically 356 Algebraically 357 Operating on Limits: The Limit Laws 361 Calculating the Average Rate of Change 362 Exploring Continuity in Functions 363 Determining whether a function is continuous 364 Discontinuity in rational functions 365 Part 4: The Part of Tens 367 Chapter 17: Ten Polar Graphs 369 Spiraling Outward 369 Falling in Love with a Cardioid 370 Cardioids and Lima Beans 370 Leaning Lemniscates 371 Lacing through Lemniscates 372 Roses with Even Petals 372 A rose Is a Rose Is a Rose 373 Limaçon or Escargot? 373 Limaçon on the Side 374 Bifolium or Rabbit Ears? 374 Chapter 18: Ten Habits to Adjust before Calculus 375 Figure Out What the Problem Is Asking 375 Draw Pictures (the More the Better) 376 Plan Your Attack — Identify Your Targets 377 Write Down Any Formulas 377 Show Each Step of Your Work 378 Know When to Quit 378 Check Your Answers 379 Practice Plenty of Problems 380 Keep Track of the Order of Operations 380 Use Caution When Dealing with Fractions 381 Index 383

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Book SynopsisUse mathematical analysis in the real world Finite math takes everything you've learned in your previous math courses and brings them together into one course with a focus on organizing and analyzing information, creating mathematical models for approaching business decisions, using statistics principles to understand future states, and applying logic to data organization. Finite Math For Dummies tracks to a typical college-level course designed for business, computer science, accounting, and other non-math majors, and is the perfect supplement to help you score high! Organize and analyze informationApply calculation principles to real-world problemsUse models for business calculationsSupplement your coursework with step-by-step example problems If you're not a math person or just want to brush up on your skills to get a better grade, Finite Math For Dummies is your ticket to scoring higher!Table of ContentsIntroduction 1 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 Finite Math 5 Chapter 1: Feeling Fine with Finite Math 7 Getting in Line with Linear Statements 8 Making the Most with Matrices 8 Staying with the Program 9 Getting Set with Sets 10 Posing the Probability 11 Figuring in Financial Factors 13 Finding Statistical Satisfaction 14 Considering the Logical Side of Mathematics 15 Unlocking the Chains 16 Getting into Gaming 18 Chapter 2: Lining Up Linear Functions 19 Recognizing Equations of Lines 20 Identifying slope and its scope 20 Creating different forms of the equation 21 Writing the equation of a line 21 Graphing Lines on the Coordinate Plane 22 Graphing a line using two points 23 Using the slope and y-intercept to graph a line 24 Graphing special lines 25 Determining Relationships between Lines 27 Parallel and perpendicular lines 27 Intersecting versus coincidental lines 29 Solving for a Variable 30 Chapter 3: Solving Systems of Linear Equations 33 Solving Systems Using Elimination 34 Solving a system of two linear equations using elimination 34 Using elimination to solve a system of three linear equations 36 Solving Systems Using Substitution 38 Solving a system of two linear equations using substitution 38 Taking on a system of three linear equations using substitution 39 Dealing with Too Many or No Solutions 41 Too many solutions 41 No solution at all 42 Making Linear Equations Work for You 43 Determining the profit 44 Mixing it up with a solution 44 Counting on change 46 Chapter 4: Taking on Systems of Inequalities 49 Ruling with Inequalities 49 Graphing Linear Inequalities 51 Creating graphs of systems 53 Making graphs work for you 56 Part 2: Making Use of Available Methods 63 Chapter 5: Making Way for Matrices 65 Squaring Off with Matrix Basics 65 Identifying matrices and their components 66 Equalizing and transposing matrices 67 Performing matrix operations and processes 68 Investigating Row Operations 75 Performing the row operations 75 Creating inverses 77 Applying Matrices and Their Operations 80 Matrices and motorcycles 81 Taking matrices to the zoo 84 Chapter 6: Making Matrices Work for You 87 Solving Systems of Equations Using Matrices 88 Solving a linear system in two variables 89 Forging ahead with four variables 90 Stopping up short 92 Multiplying by the inverse 94 Discovering Multiple Solutions 97 Applying Matrices to Tasks 99 Considering input and output 99 Distributing temperatures 103 Taking Advantage of Special Formulas 105 Inverses of 2 × 2 matrices 105 Inverses of 3 × 3 matrices 107 Chapter 7: Getting Lined Up with Linear Programming 109 Setting Up Linear Programming Problems 110 Making the problem structure work 110 Solving a maximization problem 112 Going for a minimum 115 Going Three-Dimensional 118 Maximizing in three dimensions 119 Going for the minimum 122 Chapter 8: Simply the Simplex Method 125 Delineating Simplex Method Steps for Maximization 126 Setting up for the simplex method 126 Solving a maximization application 131 Making the Most of Minimization 135 Spelling out the format 135 Stepping through minimization 136 Giving minimization meaning 140 Part 3: Using Finite Math to Tackle World Situations 145 Chapter 9: Setting Up Sets 147 Introducing Set Notation 147 Describing large and small sets 148 Special types of sets 149 Performing Basic Operations 151 Using Venn Diagrams for Better Views 152 Elements shown 152 The number of elements shown 156 Chapter 10: Processing the Probability 161 Introducing Counting Methods 161 Multiplication method of counting 162 Using permutations for counting 163 Counting with combinations 165 Determining the Probability of an Event 167 Binomial distributions 169 Using probability trees 171 Applying Probability Techniques 174 Games of chance 174 Probability of being chosen 177 Chapter 11: Counting on the Mathematics of Finance 181 Considering Simple Interest 181 Compounding Things with Compound Interest 182 Continuous compounding 184 Effective interest rate 185 Presenting present value 185 Analyzing Annuities 188 Future value of an annuity 188 Present value of an annuity 189 Sinking funds 190 Amortization 191 Creating an amortization schedule 191 Accelerating to payoff 193 Chapter 12: Telling the Truth with Statistics 195 Presenting Data Graphically 195 Barring none with a bar graph 196 Histograms 197 Baking up a pie chart 198 Stem-and-leaf graphs 199 Measures of Central Tendency 200 Meaning it with the mean 200 Riding down the middle with the median 202 Making the most of the mode 202 Recognizing the geometric mean 203 Comparing measures of central tendency 203 Box-and-whisker plots 207 Variance and Standard Deviation 208 Variance 208 Standard deviation 209 Investigating the Normal Distribution 210 Chapter 13: Logic 213 Logically Presenting the Vocabulary 213 Finding the Truth with Truth Tables 215 Considering the conjunction 215 Displaying the disjunction 216 Looking into negativity 217 Conditionally making statements 217 Analyzing compound statements 218 Equivalent Statements 219 Studying the Conditional 221 Analyzing Arguments 222 Applying Logic to Circuits 225 Part 4: Employing the Tools of Finite Math to Expand and Investigate 229 Chapter 14: Markov Chains 231 Recognizing a Markov Chain 231 Coming to Terms with Markov Chains 232 Working with Transition Matrices 233 Using charts and trees 233 Dealing with diagrams 236 Probability Vectors 239 Absorbing Chains 242 Making Long-Term Predictions 244 Avoiding ruin 244 Alternating even and odd 246 Chapter 15: Playing Games with Game Theory 249 Playing Fairly 249 Playing by the Rules 252 Matrix representation 252 Vocabulary 252 Vocabulary illustrated 253 Getting Strategic 255 Yielding to Domination 258 Determining the Moves 259 Finding no saddle point 259 Getting down to business 263 Chapter 16: Applications of Matrices and Game Theory 267 Traffic Flow 267 Battle of the Bismarck Sea 270 The Game of Chicken 271 The Prisoner’s Dilemma 272 The Traveler’s Dilemma 273 Blotto’s Rules 274 Jack Be Nimble 275 Nim with two heaps 275 Upping the Nim stacks to three 277 Part 5: the Part of Tens 279 Chapter 17: Ten Financial Formulas 281 The Rule of 72 281 Leverage Ratio 282 Gains and Losses 282 Determining Depreciation 283 Total Return on Investments 283 Expected Return 284 Inflation-Adjusted Return 284 Remaining Balance 285 Future Value of Annuity Due 286 Bond Pricing Formula 286 Chapter 18: Ten Important Graphing Calculator Functions 289 Graphing Lines for Intersections 289 Adjusting the Window 290 Entering Matrices 291 Adding, Subtracting, and Multiplying Matrices 292 Powering Up Matrices 293 Finding Matrix Inverses 294 Solving Systems of Equations Using Matrices 295 Decimals to Fractions 296 Counting with Permutations and Combinations 296 Making Statistical Statements 298 Glossary 301 Index 305

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Book SynopsisAlgebra I For Dummies, 2nd Edition (9781119293576) was previously published as Algebra I For Dummies, 2nd Edition (9780470559642). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Factor fearlessly, conquer the quadratic formula, and solve linear equations There''s no doubt that algebra can be easy to some while extremely challenging to others. If you''re vexed by variables,Algebra I For Dummies, 2nd Edition provides the plain-English, easy-to-follow guidance you need to get the right solution every time! Now with 25% new and revised content, this easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems with confidence. You''ll understand how to factor fearlessly, conquer the quadratic formula, and solve linear equations. Table of ContentsIntroduction 1 About This Book 1 Conventions Used in This Book 2 What You’re Not to Read 2 Foolish Assumptions 3 How This Book Is Organized 3 Part 1: Starting Off with the Basics 3 Part 2: Figuring Out Factoring 4 Part 3: Working Equations 4 Part 4: Applying Algebra 4 Part 5: The Part of Tens 5 Icons Used in This Book 5 Where to Go from Here 6 Part 1: Starting off with the Basics 7 Chapter 1: Assembling Your Tools 9 Beginning with the Basics: Numbers 10 Really real numbers 10 Counting on natural numbers 10 Wholly whole numbers 11 Integrating integers 12 Being reasonable: Rational numbers 12 Restraining irrational numbers 12 Picking out primes and composites 13 Speaking in Algebra 13 Taking Aim at Algebra Operations 14 Deciphering the symbols 14 Grouping 15 Defining relationships 16 Taking on algebraic tasks 16 Chapter 2: Assigning Signs: Positive and Negative Numbers 19 Showing Some Signs 20 Picking out positive numbers 20 Making the most of negative numbers 20 Comparing positives and negatives 21 Zeroing in on zero 22 Going In for Operations 22 Breaking into binary operations 22 Introducing non-binary operations 23 Operating with Signed Numbers 25 Adding like to like: Same-signed numbers 25 Adding different signs 26 Subtracting signed numbers 27 Multiplying and dividing signed numbers 29 Working with Nothing: Zero and Signed Numbers 31 Associating and Commuting with Expressions 31 Reordering operations: The commutative property 32 Associating expressions: The associative property 33 Chapter 3: Figuring Out Fractions and Dealing with Decimals 35 Pulling Numbers Apart and Piecing Them Back Together 36 Making your bow to proper fractions 36 Getting to know improper fractions 37 Mixing it up with mixed numbers 37 Following the Sterling Low-Fraction Diet 38 Inviting the loneliest number one 39 Figuring out equivalent fractions 40 Realizing why smaller or fewer is better 41 Preparing Fractions for Interactions 43 Finding common denominators 43 Working with improper fractions 45 Taking Fractions to Task 46 Adding and subtracting fractions 46 Multiplying fractions 47 Dividing fractions 50 Dealing with Decimals 51 Changing fractions to decimals 52 Changing decimals to fractions 53 Chapter 4: Exploring Exponents and Raising Radicals 55 Multiplying the Same Thing Over and Over and Over 55 Powering up exponential notation 56 Comparing with exponents 57 Taking notes on scientific notation 58 Exploring Exponential Expressions 60 Multiplying Exponents 65 Dividing and Conquering 66 Testing the Power of Zero 66 Working with Negative Exponents 67 Powers of Powers 68 Squaring Up to Square Roots 69 Chapter 5: Doing Operations in Order and Checking Your Answers 73 Ordering Operations 74 Gathering Terms with Grouping Symbols 76 Checking Your Answers 78 Making sense or cents or scents 79 Plugging in to get a charge of your answer 79 Curbing a Variable’s Versatility 80 Representing numbers with letters 81 Attaching factors and coefficients 82 Interpreting the operations 82 Doing the Math 83 Adding and subtracting variables 84 Adding and subtracting with powers 85 Multiplying and Dividing Variables 86 Multiplying variables 86 Dividing variables 87 Doing it all 88 Part 2: Figuring Out Factoring 91 Chapter 6: Working with Numbers in Their Prime 93 Beginning with the Basics 94 Composing Composite Numbers 95 Writing Prime Factorizations 96 Dividing while standing on your head 96 Getting to the root of primes with a tree 98 Wrapping your head around the rules of divisibility 99 Getting Down to the Prime Factor 100 Taking primes into account 100 Pulling out factors and leaving the rest 103 Chapter 7: Sharing the Fun: Distribution 107 Giving One to Each 108 Distributing first 109 Adding first 109 Distributing Signs 110 Distributing positives 110 Distributing negatives 111 Reversing the roles in distributing 112 Mixing It Up with Numbers and Variables 113 Negative exponents yielding fractional answers 115 Working with fractional powers 115 Distributing More Than One Term 117 Distributing binomials 117 Distributing trinomials 118 Multiplying a polynomial times another polynomial 119 Making Special Distributions 120 Recognizing the perfectly squared binomial 120 Spotting the sum and difference of the same two terms 121 Working out the difference and sum of two cubes 123 Chapter 8: Getting to First Base with Factoring 127 Factoring 127 Factoring out numbers 128 Factoring out variables 130 Unlocking combinations of numbers and variables 131 Changing factoring into a division problem 133 Grouping Terms 134 Chapter 9: Getting the Second Degree 139 The Standard Quadratic Expression 140 Reining in Big and Tiny Numbers 141 FOILing 142 FOILing basics 142 FOILed again, and again 143 Applying FOIL to a special product 146 UnFOILing 147 Unwrapping the FOILing package 148 Coming to the end of the FOIL roll 151 Making Factoring Choices 152 Combining unFOIL and the greatest common factor 153 Grouping and unFOILing in the same package 154 Chapter 10: Factoring Special Cases 157 Befitting Binomials 157 Factoring the difference of two perfect squares 158 Factoring the difference of perfect cubes 159 Factoring the sum of perfect cubes 162 Tinkering with Multiple Factoring Methods 163 Starting with binomials 163 Ending with binomials 164 Knowing When to Quit 165 Incorporating the Remainder Theorem 166 Synthesizing with synthetic division 166 Choosing numbers for synthetic division 167 Part 3: Working Equations 169 Chapter 11: Establishing Ground Rules for Solving Equations 171 Creating the Correct Setup for Solving Equations 172 Keeping Equations Balanced 172 Balancing with binary operations 173 Squaring both sides and suffering the consequences 174 Taking a root of both sides 175 Undoing an operation with its opposite 176 Solving with Reciprocals 176 Making a List and Checking It Twice 179 Doing a reality check 179 Thinking like a car mechanic when checking your work 180 Finding a Purpose 181 Chapter 12: Solving Linear Equations 183 Playing by the Rules 184 Solving Equations with Two Terms 184 Devising a method using division 185 Making the most of multiplication 186 Reciprocating the invitation 188 Extending the Number of Terms to Three 189 Eliminating the extra constant term 189 Vanquishing the extra variable term 190 Simplifying to Keep It Simple 191 Nesting isn’t for the birds 192 Distributing first 192 Multiplying or dividing before distributing 194 Featuring Fractions 196 Promoting practical proportions 196 Transforming fractional equations into proportions 198 Solving for Variables in Formulas 199 Chapter 13: Taking a Crack at Quadratic Equations 203 Squaring Up to Quadratics 204 Rooting Out Results from Quadratic Equations 206 Factoring for a Solution 208 Zeroing in on the multiplication property of zero 209 Assigning the greatest common factor and multiplication property of zero to solving quadratics 210 Solving Quadratics with Three Terms 211 Applying Quadratic Solutions 217 Figuring Out the Quadratic Formula 219 Imagining the Worst with Imaginary Numbers 221 Chapter 14: Distinguishing Equations with Distinctive Powers 223 Queuing Up to Cubic Equations 224 Solving perfectly cubed equations 224 Working with the not-so-perfectly cubed 225 Going for the greatest common factor 226 Grouping cubes 228 Solving cubics with integers 228 Working Quadratic-Like Equations 230 Rooting Out Radicals 234 Powering up both sides 235 Squaring both sides twice 237 Solving Synthetically 239 Chapter 15: Rectifying Inequalities 243 Translating between Inequality and Interval Notation 244 Intervening with interval notation 244 Grappling with graphing inequalities 246 Operating on Inequalities 247 Adding and subtracting inequalities 247 Multiplying and dividing inequalities 248 Solving Linear Inequalities 249 Working with More Than Two Expressions 250 Solving Quadratic and Rational Inequalities 252 Working without zeros 255 Dealing with more than two factors 255 Figuring out fractional inequalities 256 Working with Absolute-Value Inequalities 258 Working absolute-value equations 258 Working absolute-value inequalities 260 Part 4: Applying Algebra 263 Chapter 16: Taking Measure with Formulas 265 Measuring Up 265 Finding out how long: Units of length 266 Putting the Pythagorean theorem to work 267 Working around the perimeter 269 Spreading Out: Area Formulas 273 Laying out rectangles and squares 273 Tuning in triangles 274 Going around in circles 276 Pumping Up with Volume Formulas 276 Prying into prisms and boxes 277 Cycling cylinders 277 Scaling a pyramid 278 Pointing to cones 279 Rolling along with spheres 279 Chapter 17: Formulating for Profit and Pleasure 281 Going the Distance with Distance Formulas 282 Calculating Interest and Percent 283 Compounding interest formulas 284 Gauging taxes and discounts 286 Working Out the Combinations and Permutations 287 Counting down to factorials 288 Counting on combinations 288 Ordering up permutations 290 Chapter 18: Sorting Out Story Problems 291 Setting Up to Solve Story Problems 292 Working around Perimeter, Area, and Volume 294 Parading out perimeter and arranging area 294 Adjusting the area 295 Pumping up the volume 297 Making Up Mixtures 300 Mixing up solutions 301 Tossing in some solid mixtures 302 Investigating investments and interest 302 Going for the green: Money 304 Going the Distance 305 Figuring distance plus distance 306 Figuring distance and fuel 307 Going ’Round in Circles 307 Chapter 19: Going Visual: Graphing 311 Graphing Is Good 312 Grappling with Graphs 313 Making a point 314 Ordering pairs, or coordinating coordinates 315 Actually Graphing Points 316 Graphing Formulas and Equations 317 Lining up a linear equation 317 Going around in circles with a circular graph 318 Throwing an object into the air 319 Curling Up with Parabolas 321 Trying out the basic parabola 321 Putting the vertex on an axis 322 Sliding and multiplying 324 Chapter 20: Lining Up Graphs of Lines 327 Graphing a Line 327 Graphing the equation of a line 329 Investigating Intercepts 332 Sighting the Slope 333 Formulating slope 335 Combining slope and intercept 337 Getting to the slope-intercept form 337 Graphing with slope-intercept 338 Marking Parallel and Perpendicular Lines 339 Intersecting Lines 341 Graphing for intersections 341 Substituting to find intersections 342 Part 5: The Part of Tens 345 Chapter 21: The Ten Best Ways to Avoid Pitfalls 347 Keeping Track of the Middle Term 348 Distributing: One for You and One for Me 348 Breaking Up Fractions (Breaking Up Is Hard to Do) 348 Renovating Radicals 349 Order of Operations 349 Fractional Exponents 349 Multiplying Bases Together 350 A Power to a Power 350 Reducing for a Better Fit 351 Negative Exponents 351 Chapter 22: The Ten Most Famous Equations 353 Albert Einstein’s Theory of Relativity 353 The Pythagorean Theorem 354 The Value of e 354 Diameter and Circumference Related with Pi 354 Isaac Newton’s Formula for the Force of Gravity 355 Euler’s Identity 355 Fermat’s Last Theorem 356 Monthly Loan Payments 356 The Absolute-Value Inequality 356 The Quadratic Formula 357 Index 359

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Book SynopsisTable of ContentsIntroduction 1 Part 1: Getting Started with Trigonometry 5 Chapter 1: Taking On Trig Technicalities 7 Chapter 2: Cooperating with Cartesian Coordinates 31 Chapter 3: Finding Degrees in Triangles and Planes 51 Chapter 4: Dishing Out the Pi: Radians 63 Chapter 5: Tackling Right Triangles 77 Part 2: Trigonometric Functions 89 Chapter 6: Describing Trig Functions 91 Chapter 7: Relating Triangles to Circular Functions 107 Chapter 8: Taking Trig Functions Global 123 Chapter 9: Applying Yourself to Trig Functions 139 Part 3: Identities 159 Chapter 10: Introducing Basic Identities 161 Chapter 11: Operating on Identities 177 Chapter 12: Proving Identities: The Basics 197 Chapter 13: Sleuthing Out Identity Solutions 213 Part 4: Equations and Applications 231 Chapter 14: Investigating Inverse Trig Functions 233 Chapter 15: Making Inverse Trig Work for You 241 Chapter 16: Solving Trig Equations 253 Chapter 17: Obeying the Laws and Applying Them 277 Part 5: The Graphs of Trig Functions 301 Chapter 18: Graphing Sine and Cosine 303 Chapter 19: Graphing Tangent and Cotangent 319 Chapter 20: Graphing Two More Trig Functions 327 Chapter 21: Topping Off Trig Graphs 339 Part 6: The Part of Tens 353 Chapter 22: Ten Basic Identities Plus Some Bonuses 355 Chapter 23: Ten Not-So-Basic Identities 361 Appendix: Graphs and Function Values 367 Index 373

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Book Synopsis"Business Math" is a catch-all title for a collection of topics that are anything but calculus. Business Math For Dummies takes complex mathematical theories and formulas and applies them to practical business situations. It also includes practical practice problems to help readers hone their skills.Table of ContentsIntroduction 1 Part I: Reviewing Basic Math for Business and Real Estate Transactions 7 Chapter 1: Starting from the Beginning 9 Chapter 2: Fractions, Decimals, and Percents 15 Chapter 3: Determining Percent Increase and Decrease 31 Chapter 4: Dealing with Proportions and Basic Algebra 37 Part II: Taking Intriguing Math to Work 47 Chapter 5: Working with Formulas 49 Chapter 6: Reading Graphs and Charts 67 Chapter 7: Measuring the World around You 79 Chapter 8: Analyzing Data and Statistics 97 Part III: Discovering the Math of Finance and Investments 109 Chapter 9: Computing Simple and Compound Interest 111 Chapter 10: Investing in the Future 131 Chapter 11: Understanding and Managing Investments 149 Chapter 12: Using Loans and Credit to Make Purchases 165 Part IV: Putting Math to Use in Banking and Payroll 177 Chapter 13: Managing Simple Bank Accounts 179 Chapter 14: Protecting Against Risk with Insurance 193 Chapter 15: Planning for Success with Budgets 207 Chapter 16: Dealing with Payroll 223 Part V: Successfully Handling the Math Used in the World of Goods and Services 235 Chapter 17: Pricing with Markups and Discounts 237 Chapter 18: Calculating Profit, Revenue, and Cost 251 Chapter 19: Accounting for Overhead and Depreciation 273 Chapter 20: Keeping Track of Inventory 291 Part VI: Surviving the Math for Business Facilities and Operations 305 Chapter 21: Measuring Properties 307 Chapter 22: Taking Out Mortgages and Property-Related Loans 335 Part VII: The Part of Tens 359 Chapter 23: Ten Tips for Leasing and Managing Rental Property 361 Chapter 24: Ten Things to Watch Out for When Reading Financial Reports 369 Index 373

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