AP calculus BC premium prep
Book - 2024
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Study guides
Examinations - Published
-
New York, NY :
Penguin Random House
2024-
- Language
- English
- Item Description
- "5 full-length practice tests" -- Cover, 11th edition.
- Physical Description
- volumes : illustrations ; 28 cm
- Publication Frequency
- Annual.
- ISBN
- 9780593517598
- ISSN
- 2690733X
- Get More (Free) Content
- 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: Diagnostic Answer Key and Explanations
- Practice Test 1: Free-Response Questions Grading Rubrics
- How to Score Practice Test 1
- Part III. About the AP Calculus BC Exam
- AB Calculus vs. BC Calculus
- Structure of the AP Calculus BC Exam
- How the AP Calculus BC Exam Is Scored
- Past AP Calculus BC Score Distributions
- 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 BC Exam
- 1. How to Approach Multiple-Choice Questions
- 2. How to Approach Free-Response Questions
- Part V. Content Review for the AP Calculus BC Exam
- 3. Limits and Continuity
- Introducing Calculus: Can Change Occur at an Instant?
- Defining Limits and Using Limit Notation
- Estimating Limit Values from Graphs
- Estimating Limit Values from Tables
- Determining Limits Using Algebraic Properties of Limits
- Determining Limits Using Algebraic Manipulation
- Selecting Procedures for Determining Limits
- Determining Limits Using the Squeeze Theorem
- Connecting Multiple Representations of Limits
- Exploring Types of Discontinuities
- Defining Continuity at a Point
- Confirming Continuity over an Interval
- Removing Discontinuities
- Connecting Infinite Limits and Vertical Asymptotes
- Connecting Limits at Infinity and Horizontal Asymptotes
- Working with the Intermediate Value Theorem (IVT)
- Chapter 3 Drill
- Answers to Practice Problem Sets
- Answers to Chapter 3 Drill
- 4. Differentiation: Definition and Basic Derivative Rules
- Defining Average and Instantaneous Rates of Change at a Point
- Defining the Derivative of a Function and Using Derivative Notation
- Estimating Derivatives of a Function at a Point
- Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
- Applying the Power Rule
- Derivative Rules: Constant, Sum, Difference, and Constant Multiple
- Derivatives of cos x, sin x, e x, and In x
- The Product Rule
- The Quotient Rule
- Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
- Chapter 4 Drill
- Answers to Practice Problem Sets
- Answers to Chapter 4 Drill
- 5. Differentiation: Composite, Implicit, and Inverse Functions
- The Chain Rule
- Implicit Differentiation
- Differentiating Inverse Functions
- Differentiating Inverse Trigonometric Functions
- Selecting Procedures for Calculating Derivatives
- Calculating Higher-Order Derivatives
- Chapter 5 Drill
- Answers to Practice Problem Sets
- Answers to Chapter 5 Drill
- 6. Contextual Applications of Differentiation
- Interpreting the Meaning of the Derivative in Context
- Straight-Line Motion: Connecting Position, Velocity, and Acceleration
- Rates of Change in Applied Contexts Other Than Motion
- Introduction to Related Rates
- Solving Related Rates Problems
- Approximating Values of a Function Using Local Linearity and Linearization
- Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
- Chapter 6 Drill
- Answers to Practice Problem Sets
- Answers to Chapter 6 Drill
- 7. Analytical Applications of Differentiation
- Using the Mean Value Theorem
- Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
- Determining Intervals on Which a Function Is Increasing or Decreasing
- Using the First Derivative Test to Determine Relative (Local) Extrema
- Using the Candidates Test to Determine Absolute (Global) Extrema
- Determining Concavity of Functions over Their Domains
- Using the Second Derivative Test to Determine Extrema
- Sketching Graphs of Function and Their Derivatives
- Connecting a Function, Its First Derivative, and Its Second Derivative
- Introduction to Optimization Problems
- Solving Optimization Problems
- Exploring Behaviors of Implicit Relations
- Chapter 7 Drill
- Answers to Practice Problem Sets
- Answers to Chapter 7 Drill
- 8. Integration and Accumulation of Change
- Exploring Accumulations of Change
- Approximating Areas with Riemann Sums
- Riemann Sums, Summation Notation, and Definite Integral Notation
- The Fundamental Theorem of Calculus and Accumulation Functions
- Interpreting the Behavior of Accumulation Functions Involving Area
- Applying Properties of Definite Integrals
- The Fundamental Theorem of Calculus and Definite Integrals
- Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
- Integrating Using Substitution
- Integrating Functions Using Long Division and Completing the Square
- Integration Using Integration by Parts
- Using Linear Partial Fractions
- Evaluating Improper Integrals
- Selecting Techniques for Antidifferentiation
- Chapter 8 Drill
- Answers to Practice Problem Sets
- Answers to Chapter 8 Drill
- 9. Differential Equations
- Modeling Situations with Differential Equations
- Verifying Solutions for Differential Equations
- Sketching Slope Fields
- Reasoning Using Slope Fields
- Approximating Solutions Using Euler's Method
- Finding General Solutions Using Separation of Variables
- Finding Particular Solutions Using Initial Conditions and Separation of Variables
- Exponential Models with Differential Equations
- Logistic Models with Differential Equations
- Chapter 9 Drill
- Answers to Practice Problem Sets
- Answers to Chapter 9 Drill
- 10. Applications of Integration
- Finding the Average Value of a Function on an Interval
- Connecting Position, Velocity, and Acceleration Functions Using Integrals
- Using Accumulation Functions and Definite Integrals in Applied Contexts
- Finding the Area Between Curves Expressed as Functions of x
- Finding the Area Between Curves Expressed as Functions of y
- Finding the Area Between Curves That Intersect at More Than Two Points
- Volumes with Cross-Sections: Squares and Rectangles
- Volumes with Cross-Sections: Triangles and Semicircles
- Volume with Disc Method: Revolving Around the x- or y-Axis
- Volume with Disc Method: Revolving Around Other Axes
- Volume with Washer Method: Revolving Around the x- or y-Axis
- Volume with Washer Method: Revolving Around Other Axes
- The Arc Length of a Smooth, Planar Curve and Distance Traveled
- Chapter 10 Drill
- Answers to Practice Problem Sets
- Answers to Chapter 10 Drill
- 11. Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- Defining and Differentiating Parametric Equations
- Second Derivatives of Parametric Equations
- Finding Arc Lengths of Curves Given by Parametric Equations
- Defining and Differentiating Vector-Valued Functions
- Integrating Vector-Valued Functions
- Solving Motion Problems Using Parametric and Vector-Valued Functions
- Defining Polar Coordinates and Differentiating in Polar Form
- Finding the Area of a Polar Region or the Area Bounded by a Single Polar Curve
- Finding the Area of the Region Bounded by Two Polar Curves
- Chapter 11 Drill
- Answers to Practice Problem Sets
- Answers to Chapter 11 Drill
- 12. Infinite Sequences and Series
- Defining Convergent and Divergent Infinite Series
- Working with Geometric Series
- The nth Term Test for Divergence
- Integral Test for Convergence
- Harmonic Series and p-Series
- Comparison Tests for Convergence
- Alternating Series Test for Convergence
- Ratio Test for Convergence
- Determining Absolute or Conditional Convergence
- Alternating Series Error Bound
- Finding Taylor Polynomial Approximations of Functions
- Lagrange Error Bound
- Radius and Interval of Convergence of Power Series
- Finding Taylor or Maclaurin Series for a Function
- Representing Functions as Power Series
- Chapter 12 Drill
- Answers to Practice Problem Sets
- Answers to Chapter 12 Drill
- Part VI. Practice Tests 2 and 3
- 13. Practice Test 2
- 14. Practice Test 2: Answers and Explanations
- Practice Test 2: Free-Response Questions Grading Rubrics
- How to Score Practice Test 2
- 15. Practice Test 3
- 16. Practice Test 3: Answers and Explanations
- Practice Test 3: Free-Response Questions Grading Rubrics
- How to Score Practice Test 3
- About the Author
- Practice Test 4
- Practice Test 4. Answers and Explanations
- Practice Test 5
- Practice Test 5. Answers and Explanations