2 Editorial Rob Franek, Senior VP, Publisher Casey Cornelius, VP Content Development Mary Beth Garrick, Director of Production Selena Coppock, Managing Editor Meave Shelton, Senior Editor Colleen Day, Editor Sarah Litt, Editor Aaron Riccio, Editor Orion McBean, Editorial Assistant Random House Publishing Team Tom Russell, Publisher Alison Stoltzfus, Publishing Manager Melinda Ackell, Associate Managing Editor Ellen Reed, Production Manager Kristin Lindner, Production Supervisor Andrea Lau, Designer The Princeton Review 24 Prime Parkway, Suite 201 Natick, MA 01760 E-mail: [email protected] Copyright © 2015 by TPR Education IP Holdings, LLC. All rights reserved. Cover art © Image Source / Alamy Published in the United States by Penguin Random House LLC, New York, and in Canada by Random House of Canada, a division of Penguin Random House Ltd., Toronto. Terms of Service: The Princeton Review Online Companion Tools (“Student Tools”) for retail books are available for only the two most recent editions of that book. Student Tools may be activated only twice per eligible book purchased for two consecutive 12-month periods, for a total of 24 months of access. Activation of Student Tools more than twice per book is in direct violation of these Terms of Service and may result in discontinuation of access to Student Tools Services. eBook ISBN: 978-0-8041-2642-7 Trade Paperback ISBN: 978-0-8041-2612-0 AP and Advanced Placement Program are registered trademarks of the College Board, which does not sponsor or endorse this product. The Princeton Review is not affiliated with Princeton University. Editor: Meave Shelton Production Editor: Harmony Quiroz 3 Production Coordinator: Deborah A. Silvestrini v3.1 4 Acknowledgments First of all, I would like to thank Arnold Feingold and Peter B. Kahn for once again doing every problem, reading every word, and otherwise lending their invaluable assistance. I also want to thank Calvin Cato and Meave Shelton for being terrific editors, Gary King for his first-rate reading, analysis, and contributions, and the production team of Harmony Quiroz and Deborah Silvestrini. Thanks to Frank, without whose advice I never would have taken this path. Thanks to Jeffrey, Miriam, and Vicki for moral support. Thanks Mom. Finally, I would like to thank the people who really made all of this effort worthwhile—my students. I hope that I haven’t omitted anyone, but if I have, the fault is entirely mine. Aaron and Sasha, Aaron, Abby B., Abby F., Abby H., Abby L., Abbye, Abigail H., Addie, Aidan, Albert G., Albert G., Alan M., Alec M., Alec R., Alex and Claire, Alex A., Alex and Daniela B., Alex F., Alex D., Alex G., Alex H., Alex I., Alex S., Alex and Gabe, Alexa, Alexandra, Natalie and Jason, Alexes, Alexis and Brittany, Ali and Jon, Ali and Amy Z., Ali H., Alice, Alice C., Alicia, Alisha, Allegra, Allie and Lauren, Allison and Andrew, Allison and Matt S., Allison H., Allison R., Ally, Ally T., Aly and Lauren, Alyssa and Courtney, Amanda, Brittany, and Nick A., Amanda and Pamela B., Amanda C., Amanda H., Amanda M., Amanda R., Amanda S., Amanda Y., Amber and Teal, Amparo, Andrea T., Andrea V., Andrei, Andrew A., Andrew B., Andrew C., Andrew D., Andrew E., Andrew H., Andrew M., Andrew S., Andy and Sarah R., Andy and Allison, Angela, Angela F., Angela L., Anisha, Ann, Anna C-S., Anna D., Anna and Jon, Anna and Max, Anna L., Anna M., Anna W., Annabelle M., Annie, Annie W., Antigone, Antonio, Anu, April, Ares, Ariadne, Ariane, Ariel, Arielle and Gabrielle, Arthur and Annie, Arya, Asheley and Freddy, Ashley A., Ashley K., Ashley and Sarah, Ashley and Lauren, Avra, Becca A., Becky B., Becky S., Becky H., Ben S., Ben and Andrew Y., Ben D., Ben S., Benjamin D., Benjamin H., Benji, Beth and Sarah, Bethany and Lesley, Betsy and Jon, Blythe, Bianca and Isabella, Bonnie, Bonnie C., Braedan, Brendan, Brett, Brett A., Brette and Josh, Brian, Brian C., Brian N., Brian W., Brian Z., Brigid, Brin, Brittany E., Brooke, Devon, 5 and Megan, Brooke and Lindsay E., Butch, Caitlin, Caitlin F., Caitlin M., Caitlin and Anna S., Camilla and Eloise, Camryn, Caroline A., Caroline C., Caroline H., Caroline S., Caroline and Peter W., Carrie M., Catherine W., Chad, Channing, Charlie, Charlotte, Charlotte B., Charlotte M., Chelsea, Chloe, Chloe K., Chris B., Chris C., Chris K., Chrissie, Christian, Christian C., Christine, Christine W., Claire H., Clare, Claudia, Clio, Conor G., Corey, Corinne, Coryn, Courtney and Keith, Courtney B., Courtney F., Courtney S., Craig, Dan M., Dana J., Dani and Adam, Daniel, Daniel and Jen, Daniella, Daniella C., Danielle and Andreas, Danielle and Nikki D., Danielle G., Danielle H., Danny K., Dara and Stacey, Dara M., Darcy, David B., David C., David R., David S., Deborah and Matthew, Deniz and Destine, Deval, Devin, Devon and Jenna, Dilly, Dong Yi, Dora, Eairinn, Eddy, Elana, Eleanor K., Elexa and Nicky, Elisa, Eliza, Elizabeth, Elizabeth and Mary C., Elizabeth F., Ella, Ellie, Elly B., Emma, Emily A., Emily B., Emily and Allison, Emily and Catie A., Emily C., Emily G., Emily H., Emily K., Emily L., Emily and Pete M., Emily R., Emily R-H., Emily S., Emily T., Emma and Sophie, Eric N., Erica F., Erica H., Erica R., Erica S., Eric and Lauren, Erica and Annie, Erika, Erin, Erin I., Ernesto, Ethan, Eugenie, Eva, Evan, Eve H., Eve M., Frank, Gabby, Geoffrey, George and Julian., George M., Gloria, Grace M., Grace P., Gracie, Graham and Will, Greg, Greg F., Griffin, Gylianne, Gussie, Hallie, Hannah C., Hannah J., Hannah R., Hannah and Paige, Harrison, Annabel and Gillian, Halle R., Harry, Hayley and Tim D., Hazel, Heather D., Heather F., Heather and Gillian, Hernando and Vicki, Hilary and Lindsay, Hilary F., Holli, Holly G., Holly K., Honor, Ian, Ian P., Ingrid, Ira, Isa, Isabel, Isabella and Simone, Isabelle T., Ismini, Isobel, Ivy, Jacob and Kara, Jacob D., Jack, Jack B., Jackie and Vicky, Jackie, Jackie S., Jackson, Jaclyn and Adam, Jake T., James S., Jamie, Jarrod, Jason P., Jason L., Jason and Andrew, Jay, Jay K., Jae and Gideon, Jayne and Johnny, Jed D., Jed F., Jeffrey M., Jenna, Jen, Jenn N., Jennifer B., Jennifer W., Jenny K, Jenny and Missy, Jeremy C., Jeremy and Caleb, Jess, Jess P., Jesse, Jessica, Jessica and Eric H., Jessica L., Jessica T., Jessie, Jessie C., Jessie and Perry N., Jill, Jillian, Daniel and Olivia, Jillian S., Jimin, Jimmy C., Jimmy P., Joanna, Joanna C., Joanna G., Joanna M., Joanna and Julia M., Joanna W., Jocelyn, Jody and Kim, Joe B., Johanna, John, John and Dan, Jonah and Zoe, Jonathan G., Jonathan P., Jonathan W., Jongwoo, Jordan C., Jordan and Blair F., Jordan 6 G., Jordan P., Jordana, Jordyn, Josh and Jesse, Josh and Noah, Judie and Rob, Julia and Caroline, Julia, Julia G., Julia H., Julia and Charlotte P., Julia T., Julie H., Julie and Dana, Julie P., Juliet, Justin L., Kara B., Kara O., Kasia and Amy, Kat R., Kate D., Kate F., Kate G., Kate L., Kate P., Kate S., Kate W., Katie C., Katie F., Katherine C., Kathryn, Leslie, and Travis, Katie, Katie M., Katrina, Keith M., Kelly C., Ken D., Kimberly, Kirsten, Kitty and Alex, Krista, Erika, and Karoline, Kristen, Kristen and Magan F., Laila and Olivia R., Laura B., Laura F., Laura G., Laura R., Laura S., Laura T., Laura Z., Lauren and Eric, Lauren R., Lauren S., Lauren T., Lauren and Allie, Leah, Lee R., Leigh and Ruthie, Leigh, Lexi S., Lila, Lila M., Lilaj, Lili C., Lily, Lily M-R., LilyHayes, Lisbeth and Charlotte, Lina, Lindsay F., Lindsay K., Lindsay L., Lindsay N., Lindsay R, Lindsay and Jessie S., Lindsey and Kari, Lisa, Liz D., Liz H., Liz M., Lizzie A., Lizzi B., Lizzie M., Lizzie W., Lizzy, Lizzy C., Lizzy R., Lizzy T., Louis, Lucas, Luke C., Lucinda, Lucy, Lucy D., Mackenzie, Maddie and JD, Maddie P., Maddy H., Maddy W., Madeline, Magnolia, Mara and Steffie, Marcia, Margaret S., Mariel C., Mariel L., Mariel S., Marielle K., Marielle S., Marietta, Marisa C., Marissa, Marnie and Sam, Mary M., Matt, Matthew B., Matthew K., Matt F., Matt G., Matt and Caroline, Matt V., Matthew G., Mavis H, Max B., Max and Chloe K., Max M., Maxx, Ben, and Sam, Maya and Rohit, Maya N., Meesh, Megan G., Melissa, Melissa and Ashley I., Meredith, Meredith and Gordie B., Meredith and Katie D., Meredith R., Meredith S-K., Michael and Dan, Michael H., Michael R., Michaela, Michal, Mike R., Miles, Milton, Miranda, Moira, Molly L., Molly R., Molly and Annie, Morgan, Morgan C., Morgan, Zoe, and Lila, Morgan K., Nadia and Alexis, NaEun, Nancy, Nanette, Naomi, Natalie and Andrew B., Natasha and Mikaela B., Natasha L., Nathania, Nico, Nicolette, Nick, Nicky S., Nicole B., Nicole J., Nicole N., Nicole P., Nicole S., Nidhi, Nikki G., Nina R., Nina V., Nora, Nushien, Oli and Arni, Oliver, Oliver W., Olivia and Daphne, Olivia P., Omar, Oren, Pam, Paige, Pasan, Paul A., Peter, Philip and Peter, Phoebe, Pierce, Pooja, Priscilla, Quanquan, Quinn and Chris, Rachel A, Rachel B., Rachel and Adam, Rachel H., Rachel I., Rachel and Jake, Rachel K., Rachel L., Rachel and Mitchell M., Rachel S., Rachel and Eli, Rachel and Steven, Rachel T., Rachel W., Ramit, Randi and Samantha, Rayna, Rebecca A., Rebecca B., Rebecca G., Rebecca and Gaby K., Rebecca R., Rebecca W., Resala, Richard, Tina, and Alice, Richie D., Ricky, Rob L., 7 Robin P., Romanah, Rose, Ryan, Ryan B., Ryan S., Saahil, Sabrina and Arianna, Sally, Sam C., Sam L., Sam R., Sam S., Sam W., Samantha M., Samuel C., Samar, Sara H., Sara L., Sara R., Sara S., Sara W., Sarah, Patty, and Kat, Sarah and Beth, Sarah A., Sarah C., Sarah D., Sarah F., Sarah G., Sarah and Michelle K., Sarah L., Sarah M-D., Sarah and Michael, Sarah S., Sascha, Samara, Saya, Selena G., Sean, Seung Woo, Serena, Shadae, Shannon, Siegfried, Simon W., Simone, Sinead, Skye F., Skye L., Sofia G., Sofia M., Sonja, Sonja and Talya, Sophia A., Sophia J., Sophia S., Sophie and Tess, Sophie D., Sophie S., Sophie W., Stacey, Stacy, Stephanie, Stephanie K., Stephanie L., Stephen C., Sumair, Sunaina, Suzie, Sydney, Sydney S., Tammy and Hayley, Tara and Max, Taylor, Tenley and Galen, Terrence, Tess, Thomas B., Timothy H., Tita, Tom, Torri, Tracy, Tracy K., Tripp H., Tripp W., Tyler, Tyrik, Uma, Vana, Vanessa and John, Veda, Vicky B., Victor Z., Victoria, Victoria H., Vinny and Eric, Vivek, Vladimir, Waleed, Will A., Will, Teddy and Ellie, William M., William Z., Wyatt and Ryan, Wyna, Xianyuan, Yakir, Yesha, Yujin, Yuou, Zach, Zach B., Zach S., Zach Y., Zachary N., Zaria, Zoë, Zoe L., and Zoey and Rachel. 8 Contents Cover Title Page Copyright Acknowledgments Register Your Book Online! Part I: Using This Book to Improve Your AP Score Preview: Your Knowledge, Your Expectations Your Guide to Using This Book How to Begin Part II: Practice Test 1 Practice Test 1 Practice Test 1: Answers and Explanations Part III: About the AP Calculus AB Exam AB Calculus vs. BC Calculus The Structure of the Calculus Exam Overview of Content Topics General Overview of This Book How AP Exams Are Used Other Resources Designing Your Study Plan Part IV: Test-Taking Strategies for the AP Calculus AB Exam 1 How to Approach Multiple-Choice Questions 2 How to Approach Free-Response Questions Part V: Content Review for the AP Calculus AB 9 Exam Unit 1: Differential Calculus Essentials 3 Limits What is a Limit? Limits of Trigonometric Functions Practice Problem Set 1 4 Continuity The Definition of Continuity Types of Discontinuities Practice Problem Set 2 5 The Definition of the Derivative Deriving the Formula Differentiability Practice Problem Set 3 6 Basic Differentiation Notation The Power Rule The Addition Rule Higher Order Derivatives Practice Problem Set 4 The Product Rule The Quotient Rule The Chain Rule Practice Problem Set 5 Derivatives of Trig Functions Graphical Derivatives Practice Problem Set 6 7 Implicit Differentiation How to Do It Second Derivatives Practice Problem Set 7 Unit 1 Drill 10