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No part of this book may be reproduced in any manner without the written permission of the publisher.  \nThis edition published by Greenhall Publishing  \nGreenhall Publishing Thousand Oaks, CA 91358 [http:// greenhallpublishing.com](http:// greenhallpublishing.com)  \nWritten by Thomas Hyun  \nCover design by Hespenheide Design  \nPrinted in the United States of America  \nISBN-13: 978-0-9754753-8-6  \nAP and Advanced Placement are registered trademarks ofthe College Entrance Examination Board, which does not affiliated this book.  \nContents  \nABOUT THE EXAMS v PART A: MATH REVIEW 1  \nChapter 1 Limits and Continuity 3  \n1.1 Rates of Change 3  \n1.2 The Limit of a Function and One Sided Limits 5  \n1.3 Calculating Limits Using the Limit Laws 11  \n1.4 Properties of Continuity and Intermediate Value Theorem 16  \n1.5 Limits and Asymptotes 20  \nChapter 2 Differentiation 25  \n2.1 Definition of Derivatives and the Power Rule 25  \n2.2 The Product and Quotient Rules and Higher Derivatives 32  \n2.3 The Chain Rule and the Composite Functions 37  \n2.4 Derivatives of Trigonometric Functions 41  \n2.5 Derivatives of Exponential and Logarithmic Functions 45  \n2.6 The Tangent Lines and the Normal Lines 50  \n2.7 Implicit Differentiation 54  \n2.8 Derivatives of an Inverse Function 59  \n2.9 Derivatives of Inverse Trigonometric Functions 62  \n2.10 Approximating a Derivative 65  \nChapter 3 Applications of Differentiation 67  \n3.1 Related Rates 67  \n3.2 Position, Velocity, and Acceleration 74  \n3.3 The Roll’s Theorem and The Mean Value Theorem 77  \n3.4 The First Derivative Test and the Extreme Values of Functions 82  \n3.5 The Second Derivative Test 91  \n3.6 Curves of f , f ′ , f ′′ and Curve Sketching 98  \n3.7 Optimization Problems 107  \n3.8 Tangent Line Approximation and Differentials 110  \nChapter 4 Integration 117  \n4.1 Antiderivatives and Indefinite Integrals 117  \n4.2 Riemann Sum and Area Approximation 121  \n4.3 Definite Integral, Area Under a Curve, and Application 126  \n4.4 Properties of Definite Integral 132  \n4.5 Trapezoidal Rule 135  \n4.6 The Fundamental Theorem of Calculus Part 1 139  \n4.7 The Fundamental Theorem of Calculus Part 2 143  \n4.8 Integration by Substitution 147  \n4.9 Integration of Exponential and Logarithmic Function 152  \nChapter 5 Applications of Integration 155  \n5.1 Area of a Region between Two Curves 155  \n5.2 Volumes by Disk and Washers 158  \n5.3 Volumes of Solids with Known Cross Sections 164  \n5.4 The Total Change Theorem (Application of FTC) 169  \n5.5 Motion of a Particle, Distance, and Displacement 174  \n5.6 Average Value of a Function 181  \n5.7 Length of a Curve (Distance Traveled Along a Curve) BC 187  \nChapter 6 Techniques of Integration 191  \n6.1 Basic Integration Rules 191  \n6.2 Trigonometric Integrals 196  \n6.3 Trigonometric Substitutions 201  \n6.4 L’Hospital’s Rule 205  \n6.5 Integration by Partial Fractions BC 209  \n6.6 Integration by Parts BC 213  \n6.7 Improper Integrals BC 219  \nChapter 7 Further Applications of Integration 223  \n7.1 Slope Field 223  \n7.2 Separable Differential Equations 227  \n7.3 Exponential Growth and Decay 232  \n7.4 Logistic Equations BC 235  \n7.5 Euler’s Method BC 240  \nChapter 8 Parametric Equations, Vectors, and Polar Coordinates BC 245  \n8.1 Slopes and Tangents to the Parametric Curves 245  \n8.2 Arc Length (Distance Traveled Along a Curve) in Parametric Form 251  \n8.3 Vector Valued Functions 254  \n8.4 Polar Coordinates and Slopes of Curves 260  \n8.5 Areas in Polar Coordinates 264  \nChapter 9 Infinite Sequences and Series BC 269  \n9.1 Sequenc","cbCaimvaq47ZDJJ1","https://ap.wps.com/l/cbCaimvaq47ZDJJ1","pdf",6702970,434,"English","# About the Exams\n## Using this Book\n# PART A: MATH REVIEW\n## Chapter 1 Limits and Continuity\n## Chapter 2 Differentiation\n## Chapter 3 Applications of Differentiation\n## Chapter 4 Integration\n## Chapter 5 Applications of Integration\n## Chapter 6 Techniques of Integration\n## Chapter 7 Further Applications of Integration\n## Chapter 8 Parametric Equations, Vectors, and Polar Coordinates\n## Chapter 9 Infinite Sequences and Series\n# PART B: PRACTICE TESTS\n## Calculus AB Practice Test 1\n## Calculus AB Practice Test 2\n## Calculus BC Practice Test 1\n## Calculus BC Practice Test 2\n## Answer Key","[{\"question\":\"What exams does this book prepare students for?\",\"answer\":\"It prepares students for the Calculus AB and Calculus BC AP exams and reviews both the core concepts and the BC extension topics.\"},{\"question\":\"How is each chapter organized in the math review section?\",\"answer\":\"Each concept is introduced with a definition, followed by example problems. Chapters then include exercise sets and step-by-step solutions.\"},{\"question\":\"What topics are emphasized beyond Calculus AB for the BC exam?\",\"answer\":\"The BC exam extends AB with more advanced material such as improper integrals, series, logistic curves, and parametric and polar functions.\"}]","Acing AP Calculus AB and BC - 4 Full-Length Practice Tests | PDF",1094]