5 Steps to a 5 AP Calculus BC 2019

AP-Calculus-BC 2727-MA-Book May 11, 2018 14:

1 What You Need to Know About the AP Calculus BC Exam STEP 1 Set Up Your Study Plan
- 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

3 Take a Diagnostic Exam STEP 2 Determine Your Test Readiness
- 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

4 How to Approach Each Question Type STEP 3 Develop Strategies for Success
- 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

5 Limits and Continuity Big Idea 1: Limits
- 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 (asx→a)
  - Limits at Infinity (asx→±∞)
  - 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

6 Differentiation Big Idea 2: Derivatives
- 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
  - Exponential, and Logarithmic Functions 6.2 Derivatives of Trigonometric, Inverse Trigonometric,
    - 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'Ho√pital'sRule for Indeterminate Forms
- 6.7 Rapid Review

6.9 Cumulative Review Problems Contents vii

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

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
  - and Minimum Problems General Procedure for Solving Applied Maximum
  - Distance Problem
  - Area and Volume Problem
  - Business Problems
- 8.3 Rapid Review

8.4 Practice Problems viii Contents

8.5 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 thenth 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

10 Integration Big Idea 3: Integrals and the Fundamental Theorems of Calculus

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 Contents ix

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
  - and Exponential Functions Definite Integrals Involving Trigonometric, Logarithmic,
- 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

12 Areas, Volumes, and Arc Lengths

a f(t)dt ∫x

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 x Contents
- 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

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

14 Series Big Idea 4: Series

14.1 Sequences and Series
- Convergence

14.2 Types of Series
- p-Series
- Harmonic Series
- Geometric Series
- Decimal Expansion

14.3 Convergence Tests Contents xi
- 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

- AP Calculus BC Practice Exam STEP 5 Build Your Test-Taking Confidence
- AP Calculus BC Practice Exam
- Formulas and Theorems
- Bibliography
- Websites

5 Steps to a 5 AP Calculus BC 2019

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