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AP Calculus Premium, 2022-2023: 12 Practice Tests + Comprehensive Review + Online Practice


Author: David Bock M.S.

Publisher: Barrons Educational Services


Publish Date: January 4, 2022

ISBN-10: 1506263941

Pages: 672

File Type: Epub

Language: English

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Book Preface

Diagnostic Tests

The diagnostic tests for both AB and BC Calculus are practice AP tests. They are followed by solutions keyed to the corresponding topical review chapter.

Review and Practice

“Topical Review and Practice” includes 10 chapters with notes on the main topics of the Calculus AB and BC syllabi and numerous carefully worked-out examples. Each chapter concludes with a set of multiple-choice questions, usually divided into calculator and no-calculator sections, followed immediately by answers and solutions.

This review is followed by further practice: (1) Chapter 11, which includes a set of multiple-choice questions on miscellaneous topics and an answer key and answer explanations; (2) Chapter 12, a set of miscellaneous free-response problems that are intended to be similar to those in Section II of the AP examinations. They are followed by detailed solutions.

In this ebook, review material on topics covered only in Calculus BC is indicated by an asterisk (*), as are both multiple-choice questions and free-response-type problems that are likely to occur only on a BC examination.

Practice Tests

The next part of this book, titled “AB Practice Tests” and “BC Practice Tests,” has three AB and three BC practice tests that simulate the actual AP examinations. Each is followed by answers and explanations.

Online Practice

In addition to the two diagnostic tests and six practice tests within this book, there are also four full-length online practice tests. You may take these tests in practice (or untimed) mode or in timed mode. Two of these online tests mirror the AB test, and the other two mirror the BC test. Detailed answers and explanations are provided for every question. Refer to the card at the beginning of this book, which provides instructions for accessing these online tests.

For Teachers

The teacher who uses this book with a class may profitably do so in any of several ways. If the book is used throughout a year’s course, the teacher can assign all or part of each set of multiple-choice questions and some miscellaneous exercises after the topic has been covered. These sets can also be used for review purposes shortly before examination time. The practice tests will also be very helpful when reviewing toward the end of the year. Teachers may also assemble examinations by choosing appropriate problems from the sample miscellaneous practice questions in Chapters 11 and 12.

For Students

Students who use this book independently will improve their performance by studying the illustrative examples carefully and trying to complete practice problems before referring to the solutions.

Table of Contents

Review material on topics covered only in Calculus BC is indicated by an asterisk (*).

How To Use This Book

Barron’s Essential 5


The Courses

Topic Outline for the AB and BC Calculus Exams

The Examinations

The Graphing Calculator: Using Your Graphing Calculator on the AP Exam

Grading the Examinations


Diagnostic Test Calculus AB

Diagnostic Test Calculus BC




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

2Limits and Continuity

A.Definitions and Examples


C.Theorems on Limits

D.Limit of a Quotient of Polynomials

E.Other Basic Limits


Practice Exercises


A.Definition of Derivative


C.The Chain Rule: The Derivative of a Composite Function

D.Differentiability and Continuity

E.Estimating a Derivative



*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

4Applications 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



B.Basic Formulas

*C.Integration by Partial Fractions

*D.Integration by Parts

E.Applications of Antiderivatives; Differential Equations

Practice Exercises

6Definite 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

7Applications of Integration to Geometry


A1.Area Between Curves

A2.Using Symmetry

*A3.Region Bounded by Polar Curve


B1.Solids with Known Cross Sections

B2.Solids of Revolution

*C.Length of Curve (Arc Length)

*D.Improper Integrals

Practice Exercises

8Further 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

9Differential 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

10*Sequences and Series

A.Sequences of Real Numbers

B.Infinite Series


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

11Miscellaneous Multiple-Choice Practice Questions

12Miscellaneous Free-Response Practice Exercises


AB Practice Test 1

AB Practice Test 2

AB Practice Test 3


BC Practice Test 1

BC Practice Test 2

BC Practice Test 3

Appendix: Formulas and Theorems for Reference


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