Cracking the AP Calculus AB & BC Exams, 2014 Edition

1146 Pages·2013·27.63 MB·English

by  Princeton Review

Editorial
Rob Franek, Senior VP, Publisher
Mary Beth Garrick, Director of Production
Selena Coppock, Senior Editor
Calvin Cato, Editor
Kristen O’Toole, Editor
Meave Shelton, Editor
Alyssa Wolff, Editorial Assistant Random House Publishing Team
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Alison Stoltzfus, Managing Editor The Princeton Review, Inc.
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Copyright © 2013 by TPR Education IP Holdings, LLC
Cover photograph © Jonathan Pozniak
All rights reserved. Published in the United States by Random House LLC, New York, a Penguin Random House
Company, and in Canada by Random House of Canada Limited, Toronto, Penguin Random House Companies.
eBook ISBN: 978-0-30794619-5
ISBN: 978-0-307-94618-8
The Princeton Review is not affiliated with Princeton University.
AP and Advanced Placement Program are registered trademarks of the College Board, which does not sponsor or
endorse this product.
Editor: Calvin S. Cato
Production Editor: Jesse Newkirk
Production Coordinator: Deborah A. Silvestrini 2014 Edition
v3.1
About the Author
David S. Kahn studied applied mathematics and physics at the
University of Wisconsin and has taught courses in calculus, precalculus,
algebra, trigonometry, and geometry at the college and high school
levels. He has worked as an educational consultant for many years and
tutored more students in mathematics than he can count! He has worked
for The Princeton Review since 1989, and, in addition to AP calculus, he
has taught math and verbal courses for the SAT, SAT II, LSAT, GMAT,
and the GRE, trained other teachers, and written several other math
books as well.
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 for
being a terrific editor, Gary King for his first-rate reading, analysis, and
contributions, and the production team of Jesse Newkirk 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., Abbye, Abigail
H., Aidan, Alec G, Alan M., Alec M., Alec R., Alex and Claire, Alex A.,
Alex 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, Allie and
Lauren, Allison and Andrew, Allison and Matt S., 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., Amber and Teal, Amparo, Andrea T., Andrea V., 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.,
Anisha, Ann, Anna C-S., Anna D., Anna and Jon, Anna and Max, Anna
L., Anna M., Anna W., Annie, Annie W., 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,
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, and Megan, Brooke and Lindsay E., Butch, Caitlin,
Caitlin F., Caitlin M., Caitlin and Anna S., Camilla and Eloise, Caroline A.,
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., Chrissie, Christian, Christine,
Christine W., Claire H., Clare, Claudia, Clio, Corey, Corinne, Courtney
and Keith, Courtney B., Courtney F., Courtney S., Craig, Dan M., Dana
J., Dani and Adam, Daniel, Daniel and Jen, Daniella, Danielle and
Andreas, Danielle and Nikki D., Danielle G., Danielle H., Danny K., Dara
and Stacey, Dara M., Darcy, David B., 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., Ellie, Elly B., 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, Ethan, Eugenie, Eva,
Evan, Eve H., Eve M., Frank, Gabby, Geoffrey, George and Julian.,
George M., Gloria, Gracie, Graham and Will, Greg, Greg F., Gussie,
Hallie, Hannah C., Hannah J., Hannah and Paige, Harrison, Annabel and
Gillian, 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, Jack, Jack B.,
Jackie and Vicky, Jackie, Jackie S., Jackson, Jaclyn and Adam, James
S., Jamie, Jason P., 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,
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., Jordan C., Jordan and Blair F., Jordan 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, Kara B., Kara O., Kasia
and Amy, Kat R., Kate D., Kate F., Kate G., Kate L., Kate P., Kate S.,
Kate W., Katherine C., Kathryn, Leslie, and Travis, Katie, Katie M.,
Katrina, Keith M., Kelly C., Kimberly, Kirsten, Kitty and Alex, Krista, Erika,
and Karoline, Kristen, Laila, Laura F., Laura G., Laura R., Laura S., Laura
T., Laura Z., Lauren and Eric, Lauren R, Lauren T., Lauren and Allie,
Leah, Lee R., Leigh and Ruthie, Leigh, Lila, Lila M., Lilaj, Lili C., Lily, Lily
M-R., LilyHayes, Lisbeth. and Charlotte, 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, Lucinda, Lucy, Lucy D., Maddie and
JD, Maddie P., 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.,
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 and Annie,
Morgan, Morgan C., Morgan and Zoe H., Morgan K., Nadia and Alexis,
NaEun, Nancy, Nanette, Naomi, Natasha B., Natasha L., Nathania, Nico,
Nick, Nicky S., Nicole B., Nicole J., Nicole N., Nicole S., Nidhi, Nikki, Nina
R., Nina V., Nora, Nushien, Oli and Arni, Oliver, Olivia and Daphne,
Olivia P., Omar, Oren, Pam, Paige, Paul A., Peter, Philip and Peter,
Phoebe, Pierce, 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 W., Ramit, Randi and Samantha, Rayna, Rebecca B.,
Rebecca G., Rebecca and Gaby K., Rebecca R., Rebecca W., Resala,
Richard, Tina, and Alice, Richie D., Ricky, Rob L., Romanah, Rose,
Richard, Tina, and Alice, Richie D., Ricky, Rob L., Romanah, Rose,
Ryan, Ryan B., Ryan S., Saahil, Sabrina, 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 D., Sarah F., Sarah G., Sarah and Michelle K., Sarah L., Sarah
M-D., Sarah and Michael, Sarah S., Sascha, Samara, Saya, Selena G.,
Seung Woo, Shadae, Siegfried, Simon W., Simone, Sinead, Skye F.,
Skye L., Sofia G., Sofia M., Sonja, Sonja and Talya, Sophia J., Sophia S.,
Sophie and Tess, Sophie D., Sophie S., Sophie W., Stacey, Stacy,
Stephanie, Stephanie L., Stephen C., Sunaina, Suzie, Sydney, Tammy
and Hayley, Tara and Max, Taylor, Tenley and Galen, Terrence, Tess,
Timothy H., Tita, Tom, Torri, Tracy, Tracy K., Tripp H., Tripp W., Tyler,
Tyrik, 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., Wyatt and Ryan, Wyna, Xianyuan, Yakir, Yesha,
Zach, Zach S., Zachary N., Zoë, Zoe L., and Zoey and Rachel.
Contents
Cover
Title Page
Copyright
About the Author
Acknowledgments
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: About the AP Calculus Exam
AB Calculus vs BC Calculus
The Structure of the Calculus Exam
How the Calculus Exam Is Scored
Overview of Content Topics
General Overview of This Book
How AP Exams Are Used
Other Resources
Designing Your Study Plan
Part III: Test-Taking Strategies for the AP Calculus
Exam
1 How to Approach Multiple Choice Questions
2 How to Approach Free Response Questions
Part IV: Content Review for the AP Calculus Exam
3 Limits
4 Continuity
5 The Definition of the Derivative
6 Basic Differentiation
7 Implicit Differentiation
8 Basic Applications of the Derivative
9 Maxima and Minima
10 Motion
11 Exponential and Logarithmic Functions, Part One
12 Other Topics in Differential Calculus
13 The Integral
14 Definite Integrals
15 Exponential and Logarithmic Functions, Part Two
16 The Area Between Two Curves
17 The Volume of a Solid of Revolution
18 Integration by Parts
19 Trig Functions
20 Other Applications of the Integral
21 Differential Equations
22 Infinite Series
23 Answers to Practice Problem Sets
Part V: The Princeton Review AP Calculus Practice
Tests
24 AB Calculus Practice Test 1
25 AB Calculus Practice Test 1 Answers and Explanations
26 AB Calculus Practice Test 2
27 AB Calculus Practice Test 2 Answers and Explanations
28 AB Calculus Practice Test 3
29 AB Calculus Practice Test 3 Answers and Explanations
30 BC Calculus Practice Test 1
31 BC Calculus Practice Test 1 Answers and Explanations