Pre-calculus Books

Book SynopsisEach step higher in math studies is crucial to doing well at the next level. Pre-Calc is the gateway to higher level mathematics of which the best degrees and careers are built upon. The core essentials in 6 laminated pages can be used along with your text and lectures, as a review before testing, or as a memory companion that keeps key answers always at your fingertips. The most answers for your money in what students have said is 'a must have' study tool. Suggested uses: Quick Reference -- instead of digging into the textbook to find a core answer you need while studying, use the guide to reinforce quickly and repeatedly; Memory -- refreshing your memory repeatedly is a foundation of studying, have the core answers handy so you can focus on understanding the concepts; Test Prep -- no student should be cramming, but if you are, there is no better tool for that final review.

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Book SynopsisAn open textbook covering pre-calculus including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisited more extensively in the third chapter. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.

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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 SynopsisFranklin D. Demana Frank Demana received his master's and Ph.D. degrees in mathematics from Michigan State University. Currently, he is Professor Emeritus of Mathematics at The Ohio State University. As an active supporter of the use of technology to teach and learn mathematics, he is cofounder of the international Teachers Teaching with Technology (T3) professional development program. He has been the director or codirector of more than $10 million of National Science Foundation (NSF) and foundational grant activities, including a $3 million grant from the U.S. Department of Education Mathematics and Science Educational Research program awarded to The Ohio State University. Along with frequent presentations at professional meetings, he has published a variety of articles in the areas of computer-and calculator-enhanced mathematics instruction. Dr. Demana is also cofounder (with Bert Waits) of the annual International Conference on Technology in Collegiate MaTable of Contents Functions and Graphs Polynomial, Power, and Rational Functions Exponential, Logistic, and Logarithmic Functions Trigonometric Functions Analytic Trigonometry Applications of Trigonometry Systems and Matrices Analytic Geometry in Two and Three Dimensions Discrete Mathematics Statistics and Probability An Introduction to Calculus: Limits, Derivatives, and Integrals Algebra Review Logic Key Formulas

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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 SynopsisTable of Contents1. Linear Functions, Equations, and Inequalities 1.1 Real Numbers and the Rectangular Coordinate System 1.2 Introduction to Relations and Functions Reviewing Basic Concepts (Sections 1.1 - 1.2) 1.3 Linear Functions 1.4 Equations of Lines and Linear Models Reviewing Basic Concepts (Sections 1.3 - 1.4) 1.5 Linear Equations and Inequalities Unifying Linear Functions 1.6 Applications of Linear Functions Reviewing Basic Concepts (Sections 1.5 - 1.6) Summary Review Exercises Test 2. Analysis of Graphs of Functions 2.1 Graphs of Basic Functions and Relations; Symmetry 2.2 Vertical and Horizontal Shifts of Graphs 2.3 Stretching, Shrinking, and Reflecting Graphs Reviewing Basic Concepts (Sections 2.1 - 2.3) 2.4 Absolute Value Functions Unifying Absolute Value Functions 2.5 Piecewise-Defined Functions 2.6 Operations and Composition Reviewing Basic Concepts (Sections 2.4 - 2.6) Summary Review Exercises Test 3. Quadratic Functions 3.1 Complex Numbers 3.2 Quadratic Functions and Graphs Reviewing Basic Concepts (Sections 3.1 - 3.2) 3.3 Quadratic Equations and Inequalities Unifying Quadratic Functions 3.4 Applications of Quadratic Functions and Models Reviewing Basic Concepts (Sections 3.3 - 3.4) Summary Review Exercises Test 4. Polynomial Functions of Higher Degree 4.1 Graphs of Polynomial Functions 4.2 Topics in the Theory of Polynomial Functions (I) Reviewing Basic Concepts (Sections 4.1 - 4.2) 4.3 Topics in the Theory of Polynomial Functions (II) 4.4 Polynomial Equations, Inequalities, Applications, and Models Reviewing Basic Concepts (Sections 4.3 - 4.4) Unifying Polynomial Functions Summary Review Exercises Test 5. Rational, Power, and Root Functions 5.1 Rational Functions and Graphs (I) 5.2 Rational Functions and Graphs (II) 5.3 Rational Equations, Inequalities, Models, and Applications Reviewing Basic Concepts (Sections 5.1 - 5.3) 5.4 Functions Defined by Powers and Roots 5.5 Equations, Inequalities, and Applications Involving Root Functions Reviewing Basic Concepts (Sections 5.4 - 5.5) Unifying Root Functions Summary Review Exercises Test 6. Inverse, Exponential, and Logarithmic Functions 6.1 Inverse Functions 6.2 Exponential Functions Unifying Exponential Functions 6.3 Logarithms and Their Properties Reviewing Basic Concepts (Sections 6.1 - 6.3) 6.4 Logarithmic Functions 6.5 Exponential and Logarithmic Equations and Inequalities Unifying Logarithmic Functions 6.6 Further Applications and Modeling with Exponential and Logarithmic Functions Reviewing Basic Concepts (Sections 6.4 - 6.6) Summary Exercises on Functions: Domains, Defining Equations, and Composition Summary Review Exercises Test 7. Systems and Matrices 7.1 Systems of Equations 7.2 Solution of Linear Systems in Three Variables 7.3 Solution of Linear Systems by Row Transformations Reviewing Basic Concepts (Sections 7.1 - 7.3) 7.4 Matrix Properties and Operations 7.5 Determinants and Cramer's Rule 7.6 Solution of Linear Systems by Matrix Inverses Reviewing Basic Concepts (Sections 7.4 - 7.6) 7.7 Systems of Inequalities and Linear Programming 7.8 Partial Fractions Reviewing Basic Concepts (Sections 7.7 - 7.8) Summary Review Exercises Test 8. Conic Sections, Nonlinear Systems, and Parametric Equations 8.1 Circles Revisited and Parabolas 8.2 Ellipses and Hyperbolas Reviewing Basic Concepts (Sections 8.1 - 8.2) 8.3 The Conic Sections and Nonlinear Systems 8.4 Introduction to Parametric Equations Reviewing Basic Concepts (Sections 8.3 - 8.4) Summary Review Exercises Test 9. Trigonometric Functions and Applications 9.1 Angles, Arcs, and Their Measures 9.2 Trigonometric Functions and Fundamental Identities 9.3 Right Triangles and Evaluating Trigonometric Functions 9.4 Applications of Right Triangles 9.5 The Circular Functions 9.6 Graphs of the Sine and Cosine Functions 9.7 Graphs of the Other Circular Functions 9.8 Harmonic Motion Summary Review Exercises Test 10. Trigonometric Identities and Equations 10.1 Trigonometric Identities 10.2 Sum and Difference Identities 10.3 Further Identities 10.4 The Inverse Circular Functions 10.5 Trigonometric Equations and Inequalities (I) 10.6 Trigonometric Equations and Inequalities (II) Unifying Trigonometric Functions Summary Review Exercises Test 11. Applications of Trigonometry and Vectors 11.1 The Law of Sines 11.2 The Law of Cosines and Area Formulas 11.3 Vectors and Their Applications 11.4 Trigonometric (Polar) Form of Complex Numbers 11.5 Powers and Roots of Complex Numbers 11.6 Polar Equations and Graphs 11.7 More Parametric Equations Summary Review Exercises Test 12. Further Topics in Algebra 12.1 Sequences and Series 12.2 Arithmetic Sequences and Series 12.3 Geometric Sequences and Series Reviewing Basic Concepts (Sections 12.1 - 12.3) 12.4 Counting Theory 12.5 The Binomial Theorem Reviewing Basic Concepts (Sections 12.4 -12.5) 12.6 Mathematical Induction 12.7 Probability Reviewing Basic Concepts (Sections 12.6 - 12.7) Summary Review Exercises Test R. Review: Basic Algebraic Concepts R.1 Review of Sets R.2 Review of Exponents and Polynomials R.3 Review of Factoring R.4 Review of Rational Expressions R.5 Review of Negative and Rational Exponents R.6 Review of Radicals Test Appendices A: Geometry Formulas B: Vectors in Space C: Polar Form of Conic Sections D: Rotation of Axes Instructor's Answers Answers to Selected Exercises (Note: In the AIE, Instructor's Answers replaces Answers to Selected Exercises.) Index

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Book SynopsisTrade Review"There are plenty of books about managing your wealth, but The Calculus of Happiness: How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love, by Oscar Fernandez of Princeton University Press, sounds intriguing."--Matthew Partridge, Money Week "[E]ngaging... Readers are sure to get a sense of how content from algebra and precalculus can help inform us about important decisions that are almost universally relevant."--Jason M. Graham, MAA Reviews "Brilliant... Where Fernandez's book scores highly is that it goes beyond being a typical self-help manual for the numerate, by presenting example after example of how mathematical topics such as probability, game theory and exponential functions really do make sense of a world that can sometimes seem so subjective. It's also an easy-going analysis of those areas in life that get brushed under the carpet, to be attended to another day. Once you realise it all boils down to maths, you will wake up happier, wealthier and healthier tomorrow morning, and we have Oscar E. Fernandez to thank for that."Nick Smith, Engineering & TechnologyTable of ContentsPreface ix Math Topics Covered by Chapter xiii I: A Healthier You Is Just a Few Equations Away 1 1 How Many Calories Should You Eat Each Day? 3 1.1 The Linear Functions Hidden in Your Diet 4 1.2 The Mathematics of Metabolism 8 1.3 Burn Those Calories! Work Those Quads! 11 1.4 The Calories Required to Digest Food 14 2 Live Longer (and Be Healthier) by Eating the Right Foods 20 2.1 A Game of Macronutrient Musical Chairs 20 2.2 How to Eat More and Be Healthier: Energy Density 29 2.3 Live Long(er) and Prosper with theWaist-Height Ratio 34 II: A Mathematician's Guide to Managing Your Money 41 3 Dissecting Your Monthly Budget 43 3.1 The Return of the King (the Linear Function) 44 3.2 To Expenses, and Beyond! 49 3.3 How Many YearsWill It Take You to Reach Financial Independence? 62 4 How to Beat Wall Street at Its Own Game 69 4.1 How to Make 15% a Year, Guaranteed 70 4.2 The Safest Investments 71 4.3 Quantifying Investment Risk and Return 73 4.4 Stocks, Bonds, and the "All-Weather" Portfolio 77 III: Looking for Love? There May Be an Equation for That 87 5 Finding "The 1" 89 5.1 What the Search for Aliens Can Teach You about FindingYour Soulmate 89 5.2 Why Hiring a Secretary Is Like Dating 92 5.3 The Stable Matching Problem 97 6 Living Happily Ever After with "The 1" 103 6.1 Your Relationship as a Dynamical System 104 6.2 Need Help Making a Joint Decision? There's an Equation for That 108 6.3 How Psychologists Use Math to Predict Divorce 113 Epilogue 118 Acknowledgments 120 Appendix A: Background Content 121 Appendix 1 123 Appendix 2 128 Appendix 3 130 Appendix 4 141 Appendix 5 143 Appendix 6 144 Bibliography 151 Index 157

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Book SynopsisTrade Review“Surveys a wide variety of ways that mathematics can be used to improve decision making and general well-being.”—Chris Wilson, TIME.com“Readers are sure to get a sense of how content from algebra and precalculus can help inform us about important decisions that are almost universally relevant.”—Jason M. Graham, MAA Reviews“Brilliant. . . . Once you realise it all boils down to maths, you will wake up happier, wealthier and healthier tomorrow morning, and we have Oscar E. Fernandez to thank for that.”—Nick Smith, Engineering and Technology“The Calculus of Happiness . . . demonstrate[s] how mathematics can yield powerful insights into everyday life."—Helen Thomson, New Scientist“Fernandez generates such enthusiasm [for studying math] by considering topics that people do want to learn more about—food, money, other people—and skillfully weaving solid mathematical concepts within these topics.”—Sandra L. Arlinghaus, Mathematical Reviews

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisIncludes: Print Student EditionTable of ContentsChapter 0 Preparing for Precalculus0-1 Sets0-2 Operations with Complex Numbers0-3 Quadratic Functions and Equations0-4 nth Roots and Real Exponents0-5 Systems of Linear Equations and Inequalities0-6 Matrix Operations0-7 Probability with Permutations and Combinations0-8 StatisticsChapter 1 Functions from a Calculus Perspective1-1 Functions1-2 Analyzing Graphs of Function and Relations1-3 Continuity, End Behavior, and Limits1-4 Extrema and Average Rates of Change1-5 Parent Functions and TransformationsExtend 1-5 Graphing Technology Lab: Nonlinear Inequalities1-6 Function Operations and Composition of Functions1-7 Inverse Relations and FunctionsExtend 1-7 Graphing Technology Lab: Graphing Inverses Using Parametric EquationsChapter 2 Power, Polynomials, and Rational Functions2-1 Power and Radical FunctionsExplore 2-2 Graphing Technology Lab: Behavior and Graphs2-2 Polynomial FunctionsExtend 2-2 Graphing Technology Lab: Hidden Behavior in Graphs2-3 The Remainder and Factor Theorems2-4 Zeros of Polynomial Functions2-5 Rational Functions2-6 Nonlinear InequalitiesChapter 3 Exponential and Logarithmic Functions3-1 Exponential FunctionsExtend 3-1 Graphing Technology Lab: Financial Literacy: Exponential Functions3-2 Logarithmic Functions3-3 Properties of Logarithms3-4 Exponential and Logarithmic EquationsExtend 3-4 Graphing Technology Lab: Exponential and Logarithmic Inequalities3-5 Modeling with Nonlinear RegressionChapter 4 Trigonometric Functions4-1 Right Triangle Trigonometry4-2 Degrees and Radians4-3 Trigonometric Functions on the Unit CircleExplore 4-4 Graphing Technology Lab: Graphing the Sine Function Parametrically4-4 Graphing Sine and Cosine FunctionsExtend 4-4 Graphing Technology Lab: Sums and Differences of Sinusoids4-5 Graphing Other Trigonometric Functions4-6 Inverse Trigonometric Functions4-7 The Law of Sines and the Law of CosinesChapter 5 Trigonometric Identities and Equations5-1 Trigonometric Identities5-2 Verifying Trigonometric Identities5-3 Solving Trigonometric EquationsExtend 5-3 Graphing Technology Lab: Solving Trigonometric Inequalities5-4 Sum and Difference IdentitiesExtend 5-4 Graphing Technology Lab: Reduction Identities5-5 Multiple-Angle and Product-to-Sum IdentitiesChapter 6 Systems of Equations and Matrices6-1 Multivariable Linear Systems and row Operations6-2 Matrix Multiplication, Inverses, and DeterminantsExtend 6-2 Graphing Technology Lab: Determinants and Areas of Polygons6-3 Solving Linear Systems Using Inverses and Cramer’s RuleExtend 6-3 Graphing Technology Lab: Matrices and Cryptography6-4 Partial Fractions6-5 Linear OptimizationChapter 7 Conic Sections and Parametric Equations7-1 Parabolas7-2 Ellipses and Circles7-3 Hyperbolas7-4 Rotations of Conic SectionsExtend 7-4 Graphing Technology Lab: Systems of Nonlinear Equations and Inequalities7-5 Parametric EquationsExtend 7-5 Graphing Technology Lab: Modeling with Parametric EquationsChapter 8 Vectors8-1 Introduction to Vectors8-2 Vectors in the Coordinate Plane8-3 Dot Products and Vector Projections8-4 Vectors in Three-Dimensional SpaceExtend 8-4 Graphing Technology Lab: Vector Transformations with Matrices8-5 Dot and Cross Products of Vectors in SpaceChapter 9 Polar Coordinates and Complex Numbers9-1 Polar CoordinatesExtend 9-1 Graphing Technology Lab: Investigate Graphs of Polar Equations9-2 Graphs of Polar Equations9-3 Polar and Rectangular Forms of Equations9-4 Polar Forms of Conic Sections9-5 Complex Numbers and De Moivre’s TheoremChapter 10 Sequences and Series10-1 Sequences, Series, and Sigma Notation10-2 Arithmetic Sequences and Series10-3 Geometric Sequences and SeriesExtend 10-3 Graphing Technology Lab: Continues Fractions10-4 Mathematical Induction10-5 The Binomial Theorem10-6 Functions as infinite SeriesExtend 10-6 Spreadsheet Lab: Detecting Patterns in DataChapter 11 Inferential Statistics11-1 Descriptive Statistics11-2 Probability Distributions11-3 The Normal DistributionExtend 11-3 Graphing Technology Lab: Transforming Skewed Data11-4 The Central Limit Theorem11-5 Confidence Intervals11-6 Hypothesis Testing11-7 Correlations and Linear RegressionExtend 11-7 Graphing Technology Lab: Median-Fit LinesChapter 12 Limits and Derivatives12-1 Estimating Limits Graphically12-2 Evaluating Limits AlgebraicallyExplore12-3 Graphing Technology Lab: The Slope of a Curve12-3 Tangent Lines and Velocity12-4 Derivatives12-5 Area Under a Curve and Integration12-6 The fundamental Theorem of Calculus

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Book SynopsisTable of Contents0 Review: Equations and Inequalities 1 0.1 Linear Equations 2 0.2 Quadratic Equations 17 0.3 Other Types of Equations 30 0.4 Inequalities 43 0.5 Graphing Equations 59 0.6 Lines 74 0.7 Modeling Variation 86 0.8* Linear Regression: Best Fit 0.8-1 1 Functions and Their Graphs 100 1.1 Functions 101 1.2 Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change 118 1.3 Graphing Techniques: Transformations 138 1.4 Operations on Functions and Composition of Functions 152 1.5 One-to-One Functions and Inverse Functions 163 2 Polynomial and Rational Functions 185 2.1 Quadratic Functions 186 2.2 Polynomial Functions of Higher Degree 203 2.3 Dividing Polynomials: Long Division and Synthetic Division 219 2.4 The Real Zeros of a Polynomial Function 227 2 .5 Complex Zeros: The Fundamental Theorem of Algebra 242 2.6 Rational Functions 251 3 Exponential and Logarithmic Functions 278 3.1 Exponential Functions and Their Graphs 279 3.2 Logarithmic Functions and Their Graphs 295 3.3 Properties of Logarithms 311 3.4 Exponential and Logarithmic Equations 320 3.5 Exponential and Logarithmic Models 331 4 Trigonometric Functions of Angles 350 4.1 Angle Measure 351 4.2 Right Triangle Trigonometry 369 4.3 Trigonometric Functions of Angles 387 4.4 The Law of Sines 405 4.5 The Law of Cosines 418 5 Trigonometric Functions of Real Numbers 440 5.1 Trigonometric Functions: The Unit Circle Approach 441 5.2 Graphs of Sine and Cosine Functions 451 5.3 Graphs of Other Trigonometric Functions 481 6 Analytic Trigonometry 507 6.1 Trigonometric Identities 508 6.2 Sum and Difference Identities 519 6.3 Double-Angle and Half-Angle Identities 531 6.4 Product-to-Sum and Sum-to-Product Identities 547 6.5 Inverse Trigonometric Functions 555 6.6 Trigonometric Equations 576 7 Vectors, the Complex Plane, and Polar Coordinates 602 7.1 Vectors 603 7.2 The Dot Product 619 7.3 Polar (Trigonometric) Form of Complex 7.4 Products, Quotients, Powers, and Roots of Complex Numbers 638 7.5 Polar Coordinates and Graphs of Polar Equations 649 8 Systems of Linear Equations and Inequalities 674 8.1 Systems of Linear Equations in Two Variables 675 8.2 Systems of Linear Equations in Three Variables 691 8.3 Systems of Linear Equations and Matrices 703 8.4 Matrix Algebra 726 8.5 The Determinant of a Square Matrix and Cramer's Rule 751 8.6 Partial Fractions 765 8.7 Systems of Linear Inequalities in Two Variables 776 9 Conics and Systems of Nonlinear Equations and Inequalities 800 9.1 Conic Basics 801 9.2 The Parabola 804 9.3 The Ellipse 818 9.4 The Hyperbola 832 9.5 Systems of Nonlinear Equations 844 9.6 Systems of Nonlinear Inequalities 854 9.7 Rotation of Axes 864 9.8 Polar Equations of Conics 872 9.9 Parametric Equations and Graphs 881 10 Sequences and Series 897 10.1 Sequences and Series 898 10.2 Arithmetic Sequences and Series 909 10.3 Geometric Sequences and Series 918 10.4 Mathematical Induction 929 10.5 The Binomial Theorem 933 11 Limits: A Preview to Calculus 948 11.1 Introduction to Limits: Estimating Limits Numerically and Graphically 949 11.2 Techniques for Finding Limits 961 11.3 Tangent Lines and Derivatives 975 11.4 Limits at Infinity; Limits of Sequences 986 11.5 Finding the Area Under a Curve 995 Review 1010 Review Exercises 1012 Practice Test 1014 Cumulative Test 1015 ANSWERS TO ODD-NUMBERED EXERCISES 1016 APPLICATION INDEX 1076 SUBJECT INDEX 1080 APPENDIX (ONLINE ONLY) *online only

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Book SynopsisHelps you focus on preparing students for calculus. This book includes a brief algebra review to the core precalculus topics along with coverage of analytic geometry in three dimensions and an introduction to concepts covered in calculus.Table of Contents1. FUNCTIONS AND THEIR GRAPHS. Rectangular Coordinates. Graphs of Equations. Linear Equations in Two Variables. Functions. Analyzing Graphs of Functions. A Library of Parent Functions. Transformations of Functions. Combinations of Functions: Composite Functions. Inverse Functions. Mathematical Modeling and Variation. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 2. POLYNOMIAL AND RATIONAL FUNCTIONS. Quadratic Functions and Models. Polynomial Functions of Higher Degree. Polynomial and Synthetic Division. Complex Numbers. Zeros of Polynomial Functions. Rational Functions. Nonlinear Inequalities. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions and Their Graphs. Logarithmic Functions and Their Graphs. Properties of Logarithms. Exponential and Logarithmic Equations. Exponential and Logarithmic Models. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters 1-3. Proofs in Mathematics. P.S. Problem Solving. 4. TRIGONOMETRY. Radian and Degree Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. Applications and Models. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 5. ANALYTIC TRIGONOMETRY. Using Fundamental Identities. Verifying Trigonometric Identities. Solving Trigonometric Equations. Sum and Difference Formulas. Multiple-Angle and Product-to-Sum Formulas. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 6. ADDITIONAL TOPICS IN TRIGONOMETRY. Law of Sines. Law of Cosines. Vectors in the Plane. Vectors and Dot Products. Trigonometric Form of a Complex Number. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters 4-6. Proofs in Mathematics. P.S. Problem Solving. 7. SYSTEMS OF EQUATIONS AND INEQUALITIES. Linear and Nonlinear Systems of Equations. Two-Variable Linear Systems. Multivariable Linear Systems. Partial Fractions. Systems of Inequalities. Linear Programming. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 8. MATRICES AND DETERMINANTS. Matrices and Systems of Equations. Operations with Matrices. The Inverse of a Square Matrix. The Determinant of a Square Matrix. Applications of Matrices and Determinants. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 9. SEQUENCES, SERIES, AND PROBABILITY. Sequences and Series. Arithmetic Sequences and Partial Sums. Geometric Sequences and Series. Mathematical Induction. The Binomial Theorem. Counting Principles. Probability. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters 7-9. Proofs in Mathematics. P.S. Problem Solving. 10. TOPICS IN ANALYTIC GEOMETRY. Lines. Introduction to Conics: Parabolas. Ellipses. Hyperbolas. Rotation of Conics. Parametric Equations. Polar Coordinates. Graphs of Polar Equations. Polar Equations of Conics. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 11. ANALYTIC GEOMETRY IN THREE DIMENSIONS. The Three-Dimensional Coordinate System. Vectors in Space. The Cross Product of Two Vectors. Lines and Planes in Space. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 12. LIMITS AND AN INTRODUCTION TO CALCULUS. Introduction to Limits. Techniques for Evaluating Limits. The Tangent Line Problem. Limits at Infinity and Limits of Sequences. The Area Problem. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters. Proofs in Mathematics. P.S. Problem Solving. APPENDIX A. Review of Fundamental Concepts of Algebra. A.1 Real Numbers and Their Properties. A.2 Exponents and Radicals. A.3 Polynomials and Factoring. A.4 Rational Expressions. A.5 Solving Equations. A.6 Linear Inequalities in One Variable. A.7 Errors and the Algebra of Calculus. APPENDIX B. Concepts in Statistics (web). B.1 Representing Data. B.2 Measures of Central Tendency and Dispersion. B.3 Least Squares Regression.

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