David Bock - AP Calculus Premium, 2022-2023

Copyright 2022, 2019, 2017, 2015, 2013, 2012, 2010, 2008 by Kaplan, Inc., d/b/a Barrons Educational Series Prior editions Copyright 2005, 2002, 1998 by Kaplan, Inc., d/b/a Barrons Educational Series under the title How to Prepare for the AP Advanced Placement Examination in Calculus and 1995, 1992, 1987, 1983, 1971 under the title How to Prepare for the Advanced Placement Examination: Mathematics. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without the written permission of the copyright owner. Published by Kaplan, Inc., d/b/a Barrons Educational Series 1515 W Cypress Creek Road Fort Lauderdale, FL 33309 www.barronseduc.com ISBN: 978-1-5062-7959-6 10 9 8 7 6 5 4 3 2 1 Kaplan, Inc., d/b/a Barrons Educational Series print books are available at special quantity discounts to use for sales promotions, employee premiums, or educational purposes. For more information or to purchase books, please call the Simon & Schuster special sales department at 866-506-1949. Dennis Donovan has been a math teacher at Xaverian Brothers High School for more than 25 years, teaching AP Calculus, both AB and BC, for more than 20 years.

He has served as an AP Calculus Reader and as one of nine national Question Leaders for the AP Calculus exam. Dennis leads professional development workshops for math teachers as a consultant for the College Board and a T3 Regional Instructor for Texas Instruments. David Bock taught AP Calculus during his 35 years at Ithaca High School, and served for several years as an Exam Reader for the College Board. He also taught mathematics at Tompkins-Cortland Community College, Ithaca College, and Cornell University. A recipient of several local, state, and national teaching awards, Dave has coauthored five textbooks, and now leads workshops for AP teachers. IN MEMORIAMShirley O.

Hockett(19202013)Shirley Hockett taught mathematics for 45 years, first at Cornell University and later at Ithaca College, where she was named Professor Emerita in 1991. An outstanding teacher, she won numerous awards and authored six mathematics textbooks. Shirleys experiences as an Exam Reader and Table Leader for AP Calculus led her to write the first ever AP Calculus review book, published in 1971. Her knowledge of calculus, attention to detail, pedagogical creativity, and dedication to students continue to shine throughout this book. On behalf of the thousands of AP Calculus students who have benefited from her tireless efforts, we gratefully dedicate this review book to Shirley.

The diagnostic tests for both AB and BC Calculus are practice AP tests. The diagnostic tests for both AB and BC Calculus are practice AP tests.

They are followed by solutions keyed to the corresponding topical review chapter.

Topical Review and Practice includes 10 chapters with notes on the main topics of the Calculus AB and BC syllabi and numerous carefully worked-out examples. Each chapter concludes with a set of multiple-choice questions, usually divided into calculator and no-calculator sections, followed immediately by answers and solutions. This review is followed by further practice: (1) , a set of miscellaneous free-response problems that are intended to be similar to those in Section II of the AP examinations. They are followed by detailed solutions. The next part of this book, titled AB Practice Tests and BC Practice Tests, has three AB and three BC practice tests that simulate the actual AP examinations. The next part of this book, titled AB Practice Tests and BC Practice Tests, has three AB and three BC practice tests that simulate the actual AP examinations.

Each is followed by answers and explanations.

In addition to the two diagnostic tests and six practice tests within this book, there are also four full-length online practice tests. You may take these tests in practice (or untimed) mode or in timed mode. Two of these online tests mirror the AB test, and the other two mirror the BC test. Detailed answers and explanations are provided for every question. The teacher who uses this book with a class may profitably do so in any of several ways. The teacher who uses this book with a class may profitably do so in any of several ways.

If the book is used throughout a years course, the teacher can assign all or part of each set of multiple-choice questions and some miscellaneous exercises after the topic has been covered. These sets can also be used for review purposes shortly before examination time. The practice tests will also be very helpful when reviewing toward the end of the year. Teachers may also assemble examinations by choosing appropriate problems from the sample miscellaneous practice questions in .

Students who use this book independently will improve their performance by studying the illustrative examples carefully and trying to complete practice problems before referring to the solutions. As you review the content in this book to work toward earning that on your AP CALCULUS BCexam, here are five things that you MUST know above everything else:

	Understand that a derivative is an instantaneous rate of change, and be able to apply that concept to:
use LHospitals Rule to find limits of indeterminate forms (only and ) (); find equations of tangent lines (); determine where a function is increasing/decreasing (); analyze the speed, velocity, and acceleration of an object in motion (); solve related rates problems () when necessary.
	Understand that integrals represent accumulation functions based on antiderivatives, and be able to apply those concepts to:
the average value of a function (); area (); the position of objects in motion and distance traveled (); total amount when given the rate of accumulation (); differential equations, including solutions and slope fields ().
	Be able to apply any of the above calculus concepts to functions defined algebraically, graphically, or in tables.
	Be able to maximize your score on the exam by: answering all the multiple-choice questions; knowing how and when to use your calculator, and when not to; understanding what work you need to show; knowing how to explain, interpret, and justify answers when a question requires that. (The free-response solutions in this book model such answers.)

Master the Essential 5 listed for the AB Calculus Exam. (The free-response solutions in this book model such answers.)