The AP Calculus Problem Book - crunchy math

1 The AP Calculus Problem book Z. Chuck Garner, Dedicated to the students who used previous editions of this book ! BC Class of 2003 BC Class of 2004 BC Class of 2005 BC Class of 2006 BC Class of 2007 BC Class of 2008. Will Andersen Anita Amin Jonathan Andersen John Barnett Betsey Avery Layla Bouzoubaa Kenny Baskett Anushka Amin James Bascle Chelsea Britt Aaron Bullock Kevin Brawley Amanda Dugan Rachel Atkinson Eryn Bernardy Sam Brotherton Cecily Bullock Ashley Chackalayil Rochelle Dunlap Max Bernardy Joesph Bost Justin Carlin Daniel Chen Nate Coursey Daniel Eisenman Lindsey Broadnax William Brawley Ryan Ceciliani Raymond Clunie Michelle Dang Kylene Farmer Andy Brunton Alex Hamilton Nicole Fraute Jim Creager Kathryn Daniel Nathan Garcia Mitch Costley Sue Ann Hollowell Carin Godemann Katie Dugan Justin Easley Brandon Jackson Caitlin Dingle Vicky Johnson Megan Harris Mitchell Granade Samantha Girardot Drew Keenan Krista Firkus Kayla Koch Zack Higbie Allyse Keel Jessie Holmes Amin Makhani Justin Gilstrap Amy Lanchester Nayoon Kim Jacob Kovac Johnathan Johnson

2 Patrick McGahee Casey Haney Dana McKnight Amy Kovac Jan Lauritsen Kathryn Johnson Rachel Meador Kendra Heisner Kathryn Moore Julie Leber Ally Long Tyler Kelly Richard Moss Daniel Hendrix Ryan Moore Salman Makhani Chris Long Rochelle Lobo Trent Phillips Candace Hogan Candace Murphy Julie Matthews Nick Macie Monica Longoria John Powell Luke Hotchkiss Hannah Newman Chris Meador Will Martin April Lovering Blake Serra Shawn Hyde Bre'Ana Paige Sophia Newton Justin McKithen Kevin Masters Jon Skypek Whitney Irwin Lacy Reynolds Chris Randall Ruhy Momin David McCalley David Thompson Garett McLaurin Jacob Schiefer Nicole Richardson Steven Rouk Gary McCrear C. K. Newman Kevin Todd Britt Schneider Tyler Sigwald Patti Murphy Matt Robuck Amanda Wallace Michaela Simoes Lauren Troxler Sarah Pace AB Class of 2003 Melissa Sanders Jesse Smith Ryan Young Bijal Patel Jonathan Wysolovski Ryan Boyd Drew Sheffield Kunal Patel Keeli Zanders R.

3 T. Collins Carsten Singh Miriam Perfecto Holly Ellington Andrea Smith AB Class of 2006 AB Class of 2007 Thomas Polstra Stephen Gibbons Frankie Snavely AB Class of 2005 Shail Amin Melanie Allen James Rives Aly Mawji Elizabeth Thai Lacey Avery Lucky Baker Briana Brimidge Khaliliah Smith Chris McKnight Ray Turner Alicia Bellis Savannah Barrus Michelle Dang Andrew Stover Franklin Middlebrooks Timothy Van Heest Mollie Bogle Taylor Boggus Kyle Davis Aswad Walker Kelly Morrison Josh Williams Carin Godemann Justin Clemons Holly Dean Ashley Williams Julien Norton Ben Wu Shawn Kumar Kim Dang Shaunna Duggan Jurod Russell Jodie Wu Joe Madsen Will Gibson Chris Elder Michael Wysolovski Julie Matthews Latiria Hill Kevin Gorman AB Class of 2008. Drew Yaun Jazmine Reaves John-Lee Hughey Jessie Holmes Omair Akhtar Sarah Singh Michael Hyman Gary McCrear John Collins Andrew Vanstone Cassandra Lohmeyer Faith Middlebrooks Rachel Delevett AB Class of 2004 Jawaan Washington Chris Long D'Andra Myers Kelsey Hinely Brooke Atkinson Michael Westbury Jason Long Brandi Paige Sarah Kustick Kevin Dirth Jeremy Wilkerson Joseph Long Miriam Perfecto Bianca Manahu Jaimy Lee Cason Lowe Thomas Polstra Shonette McCalmon Robert Parr Cassie Lowury Torri Preston Ansley Mitcham Garion Reddick Victoria Nesmith Heather Quinn Tesia Olgetree Andre Russell Dion Roseberry Andrew Smith Lauren Powell Megan Villanueva Cassie Smith Nicole Thomas Xan Reynolds Aniya Watson Lauren Stewart Matt Wann Ryan Young The AP Calculus Problem book Z.

4 Chuck Garner, Rockdale Magnet School for Science and Technology Fourth Edition, Revised and Corrected, 2008. The AP Calculus Problem book Publication history: First edition, 2002. Second edition, 2003. Third edition, 2004. Third edition Revised and Corrected, 2005. Fourth edition, 2006, Edited by Amy Lanchester Fourth edition Revised and Corrected, 2007. Fourth edition, Corrected, 2008. This book was produced directly from the author's LATEX files. Figures were drawn by the author using the TEXdraw package. TI-Calculator screen-shots produced by a TI-83 Plus calculator using a TI-Graph Link. LATEX (pronounced Lay-Tek ) is a document typesetting program (not a word processor) that is available free from , which also includes TEXnicCenter, a free and easy-to-use user-interface. Contents 1 LIMITS 7. Graphs of Functions .. 8. The Slippery Slope of Lines.

5 9. The Power of Algebra .. 10. Functions Behaving Badly .. 11. Take It to the Limit .. 12. One-Sided Limits .. 13. One-Sided Limits (Again) .. 14. Limits Determined by Graphs .. 15. Limits Determined by Tables .. 16. The Possibilities Are .. 17. Average Rates of Change: Episode I .. 18. Exponential and Logarithmic Functions .. 18. Average Rates of Change: Episode II .. 19. Take It To the Limit One More Time .. 20. Solving Equations .. 21. Continuously Considering Continuity .. 22. Have You Reached the Limit? .. 23. Multiple Choice Questions on Limits .. 24. Sample Problems on Limits .. 26. Last Year's Limits Test .. 27. 2 DERIVATIVES 35. Negative and Fractional Exponents .. 36. Logically Thinking About Logic .. 37. The Derivative By Definition .. 38. Going Off on a Tangent .. 39. Six Derivative Problems .. 40. Trigonometry: a Refresher .. 41. 1. 2 The AP Calculus Problem book .

6 Continuity and Differentiability .. 42. The RULES: Power Product Quotient Chain .. 43. Trigonometric Derivatives .. 44. Tangents, Normals, and Continuity (Revisited) .. 45. Implicit Differentiation .. 46. The Return of Geometry .. 47. Meet the Rates (They're Related) .. 48. Rates Related to the Previous Page .. 49. Excitement with Derivatives! .. 50. Derivatives of Inverses .. 51. D eriv e, Derivado, Ableitung, Derivative .. 52. Sample Problems on Derivatives .. 54. Multiple-Choice Problems on Derivatives .. 56. Last Year's Derivatives Test .. 58. 3 APPLICATIONS of DERIVATIVES 67. The Extreme Value Theorem .. 68. Rolle to the Extreme with the Mean Value Theorem .. 69. The First and Second Derivative Tests .. 70. Derivatives and Their Graphs .. 71. Two Derivative Problems .. 73. Sketching Functions .. 74. Problems of Motion .. 76. Maximize or Minimize?

7 78. More Tangents and Derivatives .. 80. More Excitement with Derivatives! .. 81. Bodies, Particles, Rockets, Trucks, and Canals .. 82. Even More Excitement with Derivatives! .. 84. Sample Problems on Applications of Derivatives .. 86. Multiple-Choice Problems on Applications of Derivatives .. 89. Last Year's Applications of Derivatives Test .. 92. 4 INTEGRALS 101. The ANTI derivative! .. 102. Derivative Rules Backwards .. 103. The Method of Substitution .. 104. Using Geometry for Definite Integrals .. 105. Some Riemann Sums .. 106. The MVT and the FTC .. 107. The FTC, Graphically .. 108. Definite and Indefinite Integrals .. 109. Integrals Involving Logarithms and Exponentials .. 110. It Wouldn't Be Called the Fundamental Theorem If It Wasn't Fundamental .. 111. Definite and Indefinite Integrals Part 2 .. 113. Regarding Riemann Sums .. 114. Definitely Exciting Definite Integrals!

8 116. How Do I Find the Area Under Thy Curve? Let Me Count the .. 117. Three Integral Problems .. 118. CONTENTS 3. Trapezoid and Simpson .. 119. Properties of Integrals .. 120. Sample Problems on Integrals .. 121. Multiple Choice Problems on Integrals .. 124. Last Year's Integrals Test .. 127. 5 APPLICATIONS of INTEGRALS 135. Volumes of Solids with Defined Cross-Sections .. 136. Turn Up the Volume! .. 137. Volume and Arc Length .. 138. Differential Equations, Part One .. 139. The Logistic Curve .. 140. Differential Equations, Part Two .. 141. Slope Fields and Euler's Method .. 142. Differential Equations, Part Three .. 143. Sample Problems on Applications of Integrals .. 144. Multiple Choice Problems on Application of Integrals .. 147. Last Year's Applications of Integrals Test .. 150. 6 TECHNIQUES of INTEGRATION 159. A Part, And Yet, .. 160. Partial Fractions.

9 161. Trigonometric Substitution .. 162. Four Integral Problems .. 163. L'H opital's Rule .. 164. Improper Integrals! .. 165. The Art of Integration .. 166. Functions Defined By Integrals .. 168. Sample Problems on Techniques of Integration .. 170. Sample Multiple-Choice Problems on Techniques of Integration .. 173. Last Year's Techniques of Integration Test .. 175. 7 SERIES, VECTORS, PARAMETRICS and POLAR 183. Sequences: Bounded and Unbounded .. 184. It is a Question of .. 185. Infinite Sums .. 186. Tests for Convergence and Divergence .. 187. More Questions of .. 188. Power Series! .. 189. Maclaurin Series .. 190. Taylor Series .. 191. Vector Basics .. 192. Calculus with Vectors and Parametrics .. 193. Vector-Valued Functions .. 194. Motion Problems with Vectors .. 195. Polar Basics .. 196. Differentiation (Slope) and Integration (Area) in Polar.

10 197. Sample Problems on Series, Vectors, Parametrics, and Polar .. 198. 4 The AP Calculus Problem book . Sample Multiple-Choice Problems on Series, Vectors, Parametrics, and Polar .. 201. Last Year's Series, Vectors, Parametrics, and Polar Test .. 203. 8 AFTER THE EXAM 211. Hyperbolic Functions .. 212. Surface Area of a Solid of Revolution .. 213. Linear First Order Differential Equations .. 214. Curvature .. 215. Newton's Method .. 216. 9 PRACTICE and REVIEW 217. Algebra .. 218. Derivative Skills .. 219. Can You Stand All These Exciting Derivatives? .. 220. Different Differentiation Problems .. 222. Again! .. 224. Int egrale, Integrale, Integraal, Integral .. 225. Calculus Is an Integral Part of Your Life .. 226. Particles .. 227. Areas .. 228. The Deadly Dozen .. 229. Two Volumes and Two Differential Equations .. 230. Differential Equations, Part Four.