5 Steps to a 5: AP Calculus BC 2020

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) = 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