AP calculus AB 2019

Cover
Title Page
Copyright Page
Contents
Preface
Acknowledgments
About the Author
Introduction: The Five-Step Program
STEP 1 Set Up Your Study Plan
	1 What You Need to Know About the AP Calculus AB Exam
		1.1 What Is Covered on the AP Calculus AB Exam?
		1.2 What Is the Format of the AP Calculus AB Exam?
		1.3 What Are the Advanced Placement Exam Grades?
			How Is the AP Calculus AB Exam Grade Calculated?
		1.4 Which Graphing Calculators Are Allowed for the Exam?
			Calculators and Other Devices Not Allowed for the AP Calculus AB Exam
			Other Restrictions on Calculators
	2 How to Plan Your Time
		2.1 Three Approaches to Preparing for the AP Calculus AB Exam
			Overview of the Three Plans
		2.2 Calendar for Each Plan
			Summary of the Three Study Plans
STEP 2 Determine Your Test Readiness
	3 Take a Diagnostic Exam
		3.1 Getting Started!
		3.2 Diagnostic Test
		3.3 Answers to Diagnostic Test
		3.4 Solutions to Diagnostic Test
		3.5 Calculate Your Score
			Short-Answer Questions
			AP Calculus AB Diagnostic Test
STEP 3 Develop Strategies for Success
	4 How to Approach Each Question Type
		4.1 The Multiple-Choice Questions
		4.2 The Free-Response Questions
		4.3 Using a Graphing Calculator
		4.4 Taking the Exam
			What Do I Need to Bring to the Exam?
			Tips for Taking the Exam
STEP 4 Review the Knowledge You Need to Score High
	5 Review of Precalculus
		5.1 Lines
			Slope of a Line
			Equations of a Line
			Parallel and Perpendicular Lines
		5.2 Absolute Values and Inequalities
			Absolute Values
			Inequalities and the Real Number Line
			Solving Absolute Value Inequalities
			Solving Polynomial Inequalities
			Solving Rational Inequalities
		5.3 Functions
			Definition of a Function
			Operations on Functions
			Inverse Functions
			Trigonometric and Inverse Trigonometric Functions
			Exponential and Logarithmic Functions
		5.4 Graphs of Functions
			Increasing and Decreasing Functions
			Intercepts and Zeros
			Odd and Even Functions
			Shifting, Reflecting, and Stretching Graphs
		5.5 Rapid Review
		5.6 Practice Problems
		5.7 Cumulative Review Problems
		5.8 Solutions to Practice Problems
		5.9 Solutions to Cumulative Review Problems
	Big Idea 1: Limits
		6 Limits and Continuity
			6.1 The Limit of a Function
				Definition and Properties of Limits
				Evaluating Limits
				One-Sided Limits
				Squeeze Theorem
			6.2 Limits Involving Infinities
				Infinite Limits (as → a)
				Limits at Infinity (as x → ± ∞)
				Horizontal and Vertical Asymptotes
			6.3 Continuity of a Function
				Continuity of a Function at a Number
				Continuity of a Function over an Interval
				Theorems on Continuity
			6.4 Rapid Review
			6.5 Practice Problems
			6.6 Cumulative Review Problems
			6.7 Solutions to Practice Problems
			6.8 Solutions to Cumulative Review Problems
	Big Idea 2: Derivatives
		7 Differentiation
			7.1 Derivatives of Algebraic Functions
				Definition of the Derivative of a Function
				Power Rule
				The Sum, Difference, Product, and Quotient Rules
				The Chain Rule
			7.2 Derivatives of Trigonometric, Inverse Trigonometric, Exponential, and Logarithmic Functions
				Derivatives of Trigonometric Functions
				Derivatives of Inverse Trigonometric Functions
				Derivatives of Exponential and Logarithmic Functions
			7.3 Implicit Differentiation
				Procedure for Implicit Differentiation
			7.4 Approximating a Derivative
			7.5 Derivatives of Inverse Functions
			7.6 Higher Order Derivatives
			7.7 L’Hôpital’s Rule for Indeterminate Forms
			7.8 Rapid Review
			7.9 Practice Problems
			7.10 Cumulative Review Problems
			7.11 Solutions to Practice Problems
			7.12 Solutions to Cumulative Review Problems
		8 Graphs of Functions and Derivatives
			8.1 Rolle's Theorem, Mean Value Theorem, and Extreme Value Theorem
				Rolle's Theorem
				Mean Value Theorem
				Extreme Value Theorem
			8.2 Determining the Behavior of Functions
				Test for Increasing and Decreasing Functions
				First Derivative Test and Second Derivative Test for Relative Extrema
				Test for Concavity and Points of Inflection
			8.3 Sketching the Graphs of Functions
				Graphing without Calculators
				Graphing with Calculators
			8.4 Graphs of Derivatives
			8.5 Rapid Review
			8.6 Practice Problems
			8.7 Cumulative Review Problems
			8.8 Solutions to Practice Problems
			8.9 Solutions to Cumulative Review Problems
		9 Applications of Derivatives
			9.1 Related Rate
				General Procedure for Solving Related Rate Problems
				Common Related Rate Problems
				Inverted Cone (Water Tank) Problem
				Shadow Problem
				Angle of Elevation Problem
			9.2 Applied Maximum and Minimum Problems
				General Procedure for Solving Applied Maximum and Minimum Problems
				Distance Problem
				Area and Volume Problems
				Business Problems
			9.3 Rapid Review
			9.4 Practice Problems
			9.5 Cumulative Review Problems
			9.6 Solutions to Practice Problems
			9.7 Solutions to Cumulative Review Problems
		10 More Applications of Derivatives
			10.1 Tangent and Normal Lines
				Tangent Lines
				Normal Lines
			10.2 Linear Approximations
				Tangent Line Approximation (or Linear Approximation)
				Estimating the nth Root of a Number
				Estimating the Value of a Trigonometric Function of an Angle
			10.3 Motion Along a Line
				Instantaneous Velocity and Acceleration
				Vertical Motion
				Horizontal Motion
			10.4 Rapid Review
			10.5 Practice Problems
			10.6 Cumulative Review Problems
			10.7 Solutions to Practice Problems
			10.8 Solutions to Cumulative Review Problems
	Big Idea 3: Integrals and the Fundamental Theorems of Calculus
		11 Integration
			11.1 Evaluating Basic Integrals
				Antiderivatives and Integration Formulas
				Evaluating Integrals
			11.2 Integration by U-Substitution
				The U-Substitution Method
				U-Substitution and Algebraic Functions
				U-Substitution and Trigonometric Functions
				U-Substitution and Inverse Trigonometric Functions
				U-Substitution and Logarithmic and Exponential Functions
			11.3 Rapid Review
			11.4 Practice Problems
			11.5 Cumulative Review Problems
			11.6 Solutions to Practice Problems
			11.7 Solutions to Cumulative Review Problems
		12 Definite Integrals
			12.1 Riemann Sums and Definite Integrals
				Sigma Notation or Summation Notation
				Definition of a Riemann Sum
				Definition of a Definite Integral
				Properties of Definite Integrals
			12.2 Fundamental Theorems of Calculus
				First Fundamental Theorem of Calculus
				Second Fundamental Theorem of Calculus
			12.3 Evaluating Definite Integrals
				Definite Integrals Involving Algebraic Functions
				Definite Integrals Involving Absolute Value
				Definite Integrals Involving Trigonometric, Logarithmic, and Exponential Functions
				Definite Integrals Involving Odd and Even Functions
			12.4 Rapid Review
			12.5 Practice Problems
			12.6 Cumulative Review Problems
			12.7 Solutions to Practice Problems
			12.8 Solutions to Cumulative Review Problems
		13 Areas and Volumes
			13.1 The Function F(x)= f(t)dt
			13.2 Approximating the Area Under a Curve
				Rectangular Approximations
				Trapezoidal Approximations
			13.3 Area and Definite Integrals
				Area Under a Curve
				Area Between Two Curves
			13.4 Volumes and Definite Integrals
				Solids with Known Cross Sections
				The Disc Method
				The Washer Method
			13.5 Rapid Review
			13.6 Practice Problems
			13.7 Cumulative Review Problems
			13.8 Solutions to Practice Problems
			13.9 Solutions to Cumulative Review Problems
		14 More Applications of Definite Integrals
			14.1 Average Value of a Function
				Mean Value Theorem for Integrals
				Average Value of a Function on [a, b]
			14.2 Distance Traveled Problems
			14.3 Definite Integral as Accumulated Change
				Business Problems
				Temperature Problem
				Leakage Problem
				Growth Problem
			14.4 Differential Equations
				Exponential Growth/Decay Problems
				Separable Differential Equations
			14.5 Slope Fields
			14.6 Rapid Review
			14.7 Practice Problems
			14.8 Cumulative Review Problems
			14.9 Solutions to Practice Problems
			14.10 Solutions to Cumulative Review Problems
STEP 5 Build Your Test-Taking Confidence
	AP Calculus AB Practice Exam 1
	AP Calculus AB Practice Exam 2
	Appendix
	Bibliography
	Websites