Barron's 2025 AP calculus premium
Book - 2024
"This book provides comprehensive review and extensive practice for both of the AP exams in Calculus. It is based on the latest Course and Exam Description published by the College Board and covers the topics listed there for both AP Calculus AB and AP Calculus BC"--Page ix.
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- Subjects
- Genres
- examination study guides
Study guides
Examinations
Guides de l'étudiant - Published
-
Fort Lauderdale, FL :
Kaplan North America, LLC, d/b/a Barron's Educational Series
[2024]
- Language
- English
- Main Author
- Other Authors
- ,
- Item Description
- "12 full-length practice tests with detailed answer explanations; online practice with a timed test option and scoring; comprehensive review and practice for all topics on the exam; expert tips plus Barron's 'Essential 5' things you need to know"--Cover.
Includes index. - Physical Description
- ix, 553 pages : illustrations ; 28 cm
- ISBN
- 9781506291680
- How to Use This Book
- Barron's Essential 5
- Introduction
- Content Areas
- Exam Format
- Scoring of the Exams
- Using Your Graphing Calculator on the AP Exam
- Diagnostic Tests
- Diagnostic Test Calculus AB
- Answer Explanations
- Diagnostic Test Calculus BC
- Answer Explanations
- Topical Review and Practice
- 1. Functions
- A. Definitions
- B. Special Functions
- C. Polynomial and Other Rational Functions
- D. Trigonometric Functions
- E. Exponential and Logarithmic Functions
- F. Parametrically Defined Functions
- G. Polar Functions
- Practice Exercises
- Answer Explanations
- 2. Limits and Continuity
- A. Definitions and Examples
- B. Asymptotes
- C. Theorems on Limits
- D. Limit of a Quotient of Polynomials
- E. Other Basic Limits
- F. Continuity
- Practice Exercises
- Answer Explanations
- 3. Differentiation
- A. Definition of Derivative
- B. Formulas
- C. The Chain Rule: The Derivative of a Composite Function
- D. Differentiability and Continuity
- E. Estimating a Derivative
- E1. Numerically
- E2. Graphically
- F. Derivatives of Parametrically Defined Functions
- G. Implicit Differentiation
- H. Derivative of the Inverse of a Function
- I. The Mean Value Theorem
- J. Indeterminate Forms and L'Hospital's Rule
- K. Recognizing a Given Limit as a Derivative
- Practice Exercises
- Answer Explanations
- 4. Applications of Differential Calculus
- A. Slope; Critical Points
- B. Tangents to a Curve
- C. Increasing and Decreasing Functions
- Case I. Functions with Continuous Derivatives
- Case II. Functions Whose Derivatives Have Discontinuities
- D. Maximum, Minimum, Concavity, and Inflection Points: Definitions
- E. Maximum, Minimum, and Inflection Points: Curve Sketching
- Case I. Functions That Are Everywhere Differentiable
- Case II. Functions Whose Derivatives May Not Exist Everywhere
- F. Global Maximum or Minimum
- Case I. Differentiable Functions
- Case II. Functions That Are Not Everywhere Differentiable
- G. Further Aids in Sketching
- H. Optimization: Problems Involving Maxima and Minima
- I. Relating a Function and Its Derivatives Graphically
- J. Motion Along a Line
- K. Motion Along a Curve: Velocity and Acceleration Vectors
- L. Tangent-Line Approximations
- M. Related Rates
- N. Slope of a Polar Curve
- Practice Exercises
- Answer Explanations
- 5. Antidifferentiation
- A. Antiderivatives
- B. Basic Formulas
- C. Integration by Partial Fractions
- D. Integration by Parts
- E. Applications of Antiderivatives; Differential Equations
- Practice Exercises
- Answer Explanations
- 6. Definite Integrals
- A. Fundamental Theorem of Calculus (FTC); Evaluation of Definite integrals
- B. Properties of Definite Integrals
- C. Definition of Definite Integral as the Limit of a Riemann Sum
- D. The Fundamental Theorem Again
- E. Approximations of the Definite Integral; Riemann Sums
- E1. Using Rectangles
- E2. Using Trapezoids
- E3. Comparing Approximating Sums
- F. Graphing a Function from Its Derivative; Another Look
- G. Interpreting In x as an Area
- H. Average Value
- Practice Exercises
- Answer Explanations
- 7. Applications of Integration to Geometry
- A. Area
- A1. Area Between Curves
- A2. Using Symmetry
- A3. Region Bounded by Polar Curve
- B. Volume
- B1. Solids with Known Cross Sections
- B2. Solids of Revolution
- C. Length of Curve (Arc Length)
- D. Improper integrals
- Practice Exercises
- Answer Explanations
- 8. Further Applications of Integration
- A. Motion Along a Straight Line
- B. Motion Along a Plane Curve
- C. Other Applications of Riemann Sums
- D. FTC: Definite Integral of a Rate Is Net Change
- Practice Exercises
- Answer Explanations
- 9. Differential Equations
- A. Basic Definitions
- B. Slope Fields
- C. Euler's Method
- D. Solving First-Order Differential Equations Analytically
- E. Exponential Growth and Decay
- Case I. Exponential Growth
- Case II. Restricted Growth
- Case III. Logistic Growth
- Practice Exercises
- Answer Explanations
- 10. Sequences and Series
- A. Sequences of Real Numbers
- B. Infinite Series
- B1. Definitions
- B2. Theorems About Convergence or Divergence of Infinite Series
- B3. Tests for Convergence of Infinite Series
- B4. Tests for Convergence of Nonnegative Series
- B5. Alternating Series and Absolute Convergence
- C. Power Series
- C1. Definitions; Convergence
- C2. Functions Defined by Power Series
- C3. Finding a Power Series for a Function: Taylor and Maclaurin Series
- C4. Approximating Functions with Taylor and Maclaurin Polynomials
- C5. Taylor's Formula with Remainder; Lagrange Error Bound
- C6. Computations with Power Series
- C7. Power Series over Complex Numbers
- Practice Exercises
- Answer Explanations
- 11. Miscellaneous Multiple-Choice Practice Questions
- Answer Explanations
- 12. Miscellaneous Free-Response Practice Exercises
- Answer Explanations
- AB Practice Tests
- AB Practice Test 1
- Answer Explanations
- AB Practice Test 2
- Answer Explanations
- BC Practice Tests
- BC Practice Test 1
- Answer Explanations
- BC Practice Test 2
- Answer Explanations
- Appendix: Formulas and Theorems for Reference
- Index