AP calculus BC 2019

Cover
Title Page
Copyright Page
Contents
Dedication and Acknowledgments
Preface
About the Authors
Introduction: The Five-Step Program
STEP 1 Set Up Your Study Plan
	1 What You Need to Know About the AP Calculus BC Exam
		1.1 What Is Covered on the AP Calculus BC Exam?
		1.2 What Is the Format of the AP Calculus BC Exam?
		1.3 What Are the Advanced Placement Exam Grades?
			How Is the AP Calculus BC Exam Grade Calculated?
		1.4 Which Graphing Calculators Are Allowed for the Exam?
			Calculators and Other Devices Not Allowed for the AP Calculus BC Exam
			Other Restrictions on Calculators
	2 How to Plan Your Time
		2.1 Three Approaches to Preparing for the AP Calculus BC 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 BC Diagnostic Exam
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
	Big Idea 1: Limits
		5 Limits and Continuity
			5.1 The Limit of a Function
				Definition and Properties of Limits
				Evaluating Limits
				One-Sided Limits
				Squeeze Theorem
			5.2 Limits Involving Infinities
				Infinite Limits (as x → a)
				Limits at Infinity (as x → ± ∞)
				Horizontal and Vertical Asymptotes
			5.3 Continuity of a Function
				Continuity of a Function at a Number
				Continuity of a Function over an Interval
				Theorems on Continuity
			5.4 Rapid Review
			5.5 Practice Problems
			5.6 Cumulative Review Problems
			5.7 Solutions to Practice Problems
			5.8 Solutions to Cumulative Review Problems
	Big Idea 2: Derivatives
		6 Differentiation
			6.1 Derivatives of Algebraic Functions
				Definition of the Derivative of a Function
				Power Rule
				The Sum, Difference, Product, and Quotient Rules
				The Chain Rule
			6.2 Derivatives of Trigonometric, Inverse Trigonometric, Exponential, and Logarithmic Functions
				Derivatives of Trigonometric Functions
				Derivatives of Inverse Trigonometric Functions
				Derivatives of Exponential and Logarithmic Functions
			6.3 Implicit Differentiation
				Procedure for Implicit Differentiation
			6.4 Approximating a Derivative
			6.5 Derivatives of Inverse Functions
			6.6 Higher Order Derivatives
				L'Hôpital's Rule for Indeterminate Forms
			6.7 Rapid Review
			6.8 Practice Problems
			6.9 Cumulative Review Problems
			6.10 Solutions to Practice Problems
			6.11 Solutions to Cumulative Review Problems
		7 Graphs of Functions and Derivatives
			7.1 Rolle's Theorem, Mean Value Theorem, and Extreme Value Theorem
				Rolle's Theorem
				Mean Value Theorem
				Extreme Value Theorem
			7.2 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
			7.3 Sketching the Graphs of Functions
				Graphing without Calculators
				Graphing with Calculators
			7.4 Graphs of Derivatives
			7.5 Parametric, Polar, and Vector Representations
				Parametric Curves
				Polar Equations
				Types of Polar Graphs
				Symmetry of Polar Graphs
				Vectors
				Vector Arithmetic
			7.6 Rapid Review
			7.7 Practice Problems
			7.8 Cumulative Review Problems
			7.9 Solutions to Practice Problems
			7.10 Solutions to Cumulative Review Problems
		8 Applications of Derivatives
			8.1 Related Rate
				General Procedure for Solving Related Rate Problems
				Common Related Rate Problems
				Inverted Cone (Water Tank) Problem
				Shadow Problem
				Angle of Elevation Problem
			8.2 Applied Maximum and Minimum Problems
				General Procedure for Solving Applied Maximum and Minimum Problems
				Distance Problem
				Area and Volume Problem
				Business Problems
			8.3 Rapid Review
			8.4 Practice Problems
			8.5 Cumulative Review Problems
			8.6 Solutions to Practice Problems
			8.7 Solutions to Cumulative Review Problems
		9 More Applications of Derivatives
			9.1 Tangent and Normal Lines
				Tangent Lines
				Normal Lines
			9.2 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
			9.3 Motion Along a Line
				Instantaneous Velocity and Acceleration
				Vertical Motion
				Horizontal Motion
			9.4 Parametric, Polar, and Vector Derivatives
				Derivatives of Parametric Equations
				Position, Speed, and Acceleration
				Derivatives of Polar Equations
				Velocity and Acceleration of Vector Functions
			9.5 Rapid Review
			9.6 Practice Problems
			9.7 Cumulative Review Problems
			9.8 Solutions to Practice Problems
			9.9 Solutions to Cumulative Review Problems
	Big Idea 3: Integrals and the Fundamental Theorems of Calculus
		10 Integration
			10.1 Evaluating Basic Integrals
				Antiderivatives and Integration Formulas
				Evaluating Integrals
			10.2 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
			10.3 Techniques of Integration
				Integration by Parts
				Integration by Partial Fractions
			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
		11 Definite Integrals
			11.1 Riemann Sums and Definite Integrals
				Sigma Notation or Summation Notation
				Definition of a Riemann Sum
				Definition of a Definite Integral
				Properties of Definite Integrals
			11.2 Fundamental Theorems of Calculus
				First Fundamental Theorem of Calculus
				Second Fundamental Theorem of Calculus
			11.3 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
			11.4 Improper Integrals
				Infinite Intervals of Integration
				Infinite Discontinuities
			11.5 Rapid Review
			11.6 Practice Problems
			11.7 Cumulative Review Problems
			11.8 Solutions to Practice Problems
			11.9 Solutions to Cumulative Review Problems
		12 Areas, Volumes, and Arc Lengths
			12.1 The Function F(x) = fxa f(t)dt
			12.2 Approximating the Area Under a Curve
				Rectangular Approximations
				Trapezoidal Approximations
			12.3 Area and Definite Integrals
				Area Under a Curve
				Area Between Two Curves
			12.4 Volumes and Definite Integrals
				Solids with Known Cross Sections
				The Disc Method
				The Washer Method
			12.5 Integration of Parametric, Polar, and Vector Curves
				Area, Arc Length, and Surface Area for Parametric Curves
				Area and Arc Length for Polar Curves
				Integration of a Vector-Valued Function
			12.6 Rapid Review
			12.7 Practice Problems
			12.8 Cumulative Review Problems
			12.9 Solutions to Practice Problems
			12.10 Solutions to Cumulative Review Problems
		13 More Applications of Definite Integrals
			13.1 Average Value of a Function
				Mean Value Theorem for Integrals
				Average Value of a Function on [a, b]
			13.2 Distance Traveled Problems
			13.3 Definite Integral as Accumulated Change
				Business Problems
				Temperature Problem
				Leakage Problem
				Growth Problem
			13.4 Differential Equations
				Exponential Growth/Decay Problems
				Separable Differential Equations
			13.5 Slope Fields
			13.6 Logistic Differential Equations
			13.7 Euler's Method
				Approximating Solutions of Differential Equations by Euler's Method
			13.8 Rapid Review
			13.9 Practice Problems
			13.10 Cumulative Review Problems
			13.11 Solutions to Practice Problems
			13.12 Solutions to Cumulative Review Problems
	Big Idea 4: Series
		14 Series
			14.1 Sequences and Series
				Convergence
			14.2 Types of Series
				p-Series
				Harmonic Series
				Geometric Series
				Decimal Expansion
			14.3 Convergence Tests
				Divergence Test
				Integral Test
				Ratio Test
				Comparison Test
				Limit Comparison Test
				Informal Principle
			14.4 Alternating Series
				Error Bound
				Absolute and Conditional Convergence
			14.5 Power Series
				Radius and Interval of Convergence
			14.6 Taylor Series
				Taylor Series and MacLaurin Series
				Common MacLaurin Series
			14.7 Operations on Series
				Substitution
				Differentiation and Integration
				Error Bounds
			14.8 Rapid Review
			14.9 Practice Problems
			14.10 Cumulative Review Problems
			14.11 Solutions to Practice Problems
			14.12 Solutions to Cumulative Review Problems
STEP 5 Build Your Test-Taking Confidence
	AP Calculus BC Practice Exam 1
	AP Calculus BC Practice Exam 2
	Formulas and Theorems
	Bibliography
	Websites