Cracking the AP Calculus AB Exam by David Kahn

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 Subject Tests, LSAT, GMAT, and the GRE, trained other teachers, and written several other math books

AP Calculus AB Exam Contents

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

• How to Approach Multiple-Choice Questions
• How to Approach Free-Response Questions

Part V: Content Review for the AP Calculus AB Exam

Unit 1: Differential Calculus Essentials

• Limits
• What is a Limit?
• Limits of Trigonometric Functions
• Practice Problem Set 1
• Continuity
• The Definition of Continuity
• Types of Discontinuities
• Practice Problem Set 2
• The Definition of the Derivative
• Deriving the Formula
• Differentiability
• Practice Problem Set 3
• 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
• Implicit Differentiation
• How to Do It
• Second Derivatives
• Practice Problem Set 7

Unit 1 Drill

Unit 2: Differential Calculus Applications

• Basic Applications of the Derivative
• Equations of Tangent Lines and Normal Lines
• Practice Problem Set 8
• The Mean Value Theorem for Derivatives
• Rolle’s Theorem
• Practice Problem Set 9
• Maxima and Minima
• Applied Maxima and Minima Problems
• Practice Problem Set 10
• Curve Sketching
• Practice Problem Set 11
• Motion
• Related Rates
• Practice Problem Set 12
• Position, Velocity, and Acceleration
• Practice Problem Set 13
• Exponential and Logarithmic Functions, Part One
• The Derivative of ln x
• The Derivative of e
• The Derivative of logax
• The Derivative of a
• Practice Problem Set 14
• Other Topics in Differential Calculus
• The Derivative of an Inverse Function
• Practice Problem Set 15
• Differentials
• Practice Problem Set 16
• L’Hôopital’s Rule
• Practice Problem Set 17

Unit 3: Integral Calculus Essentials

• • The Integral
  • The Antiderivative
  • Integrals of Trig Functions
  • Addition and Subtraction
  • Practice Problem Set 18
  • u-Substitution
  • Practice Problem Set 19
  • Definite Integrals
  • Area Under a Curve
  • Tabular Riemann Sums
  • Practice Problem Set 20
  • The Mean Value Theorem for Integrals
  • Practice Problem Set 21
  • Exponential and Logarithmic Functions, Part Two
  • More Integrals of Trig Functions
  • Integrating e
  • x and a
  • x
  • Practice Problem Set 22

Unit 4: Integral Calculus Applications

• The Area Between Two Curves
• Vertical Slices
• Horizontal Slices
• Practice Problem Set 23
• The Volume of a Solid of Revolution
• Washers and Disks
• Cylindrical Shells
• Volumes of Solids with Known Cross-Sections
• Practice Problem Set 24
• Differential Equations
• Separation of Variables
• Slope Fields
• Practice Problem Set 25
• Solutions to Practice Problem Sets and Unit Drills

Part VI: Additional Practice Tests

• Practice Test 2
• Practice Test 2: Answers and Explanations
• Practice Test 3
• Practice Test 3: Answers and Explanations

Download Cracking the AP Calculus AB Exam 2020, Premium Edition Epub 

Author(s): David S  Kahn

Series: The Princeton Review

Publisher: Random House Children’s Books;Penguin Random House, Year: 2019

ISBN: 9780525568148,052556814X

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