AP Calculus Premium, 2025: Prep Book with 12 Practice Tests + Comprehensive Review + Online Practice

Be prepared for exam day with Barron's. Trusted content from AP experts! Barron's AP Calculus Premium, 2025 includes in‐depth content review and practice for the AB and BC exams. It's the only book you'll need to be prepared for exam day. Written by Experienced Educators Learn from Barron's‐‐all content is written and reviewed by AP experts Build your understanding with comprehensive review tailored to the most recent exams Get a leg up with tips, strategies, and study advice for exam day‐‐it's like having a trusted tutor by your side Be Confident on Exam Day Sharpen your test‐taking skills with 12 full‐length practice tests ‐‐3 AB practice tests and 3 BC practice tests in the book, including one diagnostic test each for AB and BC to target your studying‐‐and 3 more AB practice tests and 3 more BC practice tests... Cover Title Page Copyright About the Authors Table of Contents 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 ln 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 Be prepared for exam day with Barrons. Trusted content from AP experts!Barrons AP Calculus Premium, 2025 includes indepth content review and practice for the AB and BC exams. Its the only book youll need to be prepared for exam day. Written by Experienced Educators Learn from Barronsall content is written and reviewed by AP expertsBuild your understanding with comprehensive review tailored to the most recent examsGet a leg up with tips, strategies, and study advice for exam dayits like having a trusted tutor by your side Be Confident on Exam Day Sharpen your testtaking skills with 12 fulllength practice tests 3 AB practice tests and 3 BC practice tests in the book, including one diagnostic test each for AB and BC to target your studyingand 3 more AB practice tests and 3 more BC practice tests onlineplus detailed answer explanations for all questionsStrengthen your knowledge with indepth review covering all units on the AP Calculus AB and BC exams Reinforce your learning with dozens of examples and detailed solutions, plus a series of multiplechoice practice questions and answer explanations, within each chapterEnhance your problemsolving skills by working through a chapter filled with multiplechoice questions on a variety of tested topics and a chapter devoted to freeresponse practice exercises Robust Online Practice Continue your practice with 3 fulllength AB practice tests and 3 fulllength BC practice tests on Barrons Online Learning HubSimulate the exam experience with a timed test optionDeepen your understanding with detailed answer explanations and expert adviceGain confidence with scoring to check your learning progress