Barron's How to Prepare for the AP Calculus Advanced Placement Examination: Review of Calculus AB and Calculus BC,9780764177514

Barron's How to Prepare for the AP Calculus Advanced Placement Examination: Review of Calculus AB and Calculus BC

by ;
Edition: CD
ISBN13: 9780764177514
ISBN10: 0764177516
Format: Paperback
Pub. Date: 2004-08-01
Publisher(s): Barrons Educational Series Inc
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Summary

New with this currently available title is a CD-ROM which presents practice AP Calculus tests in a format that reflects actual test-taking conditions. The book presents four model exams in Calculus AB and four more in Calculus BC with all questions answered and explained. A general subject review covers functions and their graphs, derivatives and integrals, differential equations, sequences and series, and many applications.

Table of Contents

Preface vii
Introduction viii
The Courses viii
Comparison of Calculus AB and Calculus BC Courses viii
The ``New'' AP Calculus Courses viii
Topics That May Be Tested on the Calculus AB Exam ix
Topics That May Be Tested on the Calculus BC Exam x
The Examinations xi
The Graphing Calculator: Using Your Graphing Calculator on the AP Exam xi
Grading the Examinations xvi
The CLEP Calculus Examination xvii
This Review Book xvii
TOPICAL REVIEW AND PRACTICE
Functions
1(21)
Definitions
1(3)
Special Functions
4(3)
Polynomial and Other Rational Functions
7(1)
Trigonometric Functions
7(3)
Exponential and Logarithmic Functions
10(1)
Parametrically Defined Functions
11(11)
Limits and Continuity
22(23)
Definitions and Examples
22(5)
Asymptotes
27(1)
Theorems on Limits
28(2)
Limit of a Quotient of Polynomials
30(1)
Other Basic Limits
31(1)
Continuity
32(13)
Differentiation
45(48)
Definition of Derivative
45(2)
Formulas
47(1)
The Chain Rule; The Derivative of a Composite Function
48(4)
Differentiability and Continuity
52(1)
Estimating a Derivative
53(3)
Numerically
53(2)
Graphically
55(1)
Derivatives of Parametrically Defined Functions
56(2)
Implicit Differentiation
58(1)
Derivative of the Inverse of a Function
59(3)
The Mean Value Theorem
62(1)
Indeterminate Forms and L'Hopital's Rule
63(2)
Recognizing a Given Limit as a Derivative
65(28)
Applications of Differential Calculus
93(59)
Slope; Critical Points
93(2)
Tangents and Normals
95(1)
Increasing and Decreasing Functions
96(1)
Case I. Functions with Continuous Derivatives
96(1)
Case II. Functions Whose Derivatives Have Discontinuities
97(1)
Maximum, Minimum, and Inflection Points: Definitions
97(1)
Maximum, Minimum, and Inflection Points: Curve Sketching
98(5)
Case I. Functions That Are Everywhere Differentiable
98(4)
Case II. Functions Whose Derivatives May Not Exist Everywhere
102(1)
Global Maximum or Minimum
103(1)
Case I. Differentiable Functions
103(1)
Case II. Functions That Are Not Everywhere Differentiable
104(1)
Further Aids in Sketching
104(2)
Optimization: Problems Involving Maxima and Minima
106(4)
Relating a Function and Its Derivatives Graphically
110(3)
Motion along a Line
113(2)
Motion along a Curve: Velocity and Acceleration Vectors
115(6)
Derivative of Arc Length
115(1)
Vector Functions: Velocity and Acceleration
116(5)
Local Linear Approximations
121(2)
Related Rates
123(2)
Slope of a Polar Curve
125(27)
Integration
152(32)
Antiderivatives
152(1)
Basic Formulas
152(6)
Trigonometric Substitutions
158(2)
Integration by Partial Fractions
160(2)
Integration by Parts
162(1)
Applications of Antiderivatives; Differential Equations
163(21)
Definite Integrals
184(41)
Fundamental Theorem of Calculus (FTC); Definition of Definite Integral
184(1)
Properties of Definite Integrals
184(4)
Integrals Involving Parametrically Defined Functions
188(1)
Definition of Definite Integral as the Limit of a Sum: The Fundamental Theorem Again
189(2)
Approximations to the Definite Integral; Riemann Sums
191(12)
Comparing Approximating Sums
194(2)
Graphing a Function from its Derivative; Another Look
196(7)
Interpreting In x as an Area
203(1)
Average Value
204(21)
Applications of Integration to Geometry
225(49)
Area
225(6)
Volume
231(4)
Arc Length
235(2)
Improper Integrals
237(37)
Further Applications of Integration
274(23)
Motion along a Straight Line
274(2)
Motion along a Plane Curve
276(3)
Other Applications of Riemann Sums
279(4)
FTC: Definite Integral of a Rate Is Net Change
283(14)
Differential Equations
297(42)
Basic Definitions
297(2)
Slope Fields
299(5)
Euler's Method
304(6)
Solving First-Order Differential Equations Analytically
310(1)
Exponential Growth and Decay
311(28)
Case I: y = cekt
311(5)
Case II: y = A ± ce-kt
316(3)
Case III: Logistic Growth; y = A/1 + ce-akt
319(20)
Sequences and Series
339(54)
Sequences of Real Numbers
339(3)
Definitions
339(1)
Theorems
340(2)
Series of Constants
342(13)
Definitions
342(4)
Theorems about Convergence or Divergence of Series of Constants
346(1)
Tests for Convergence of Positive Series
346(5)
Alternating Series and Absolute Convergence
351(2)
Computations with Series of Constants
353(2)
Power Series
355(38)
Definitions; Convergence
355(2)
Functions Defined by Power Series
357(3)
Taylor Polynomials
360(4)
Finding a Power Series for a Function; Taylor Series
364(4)
Taylor's Formula with Remainder; Lagrange Error Bound
368(3)
Computation with Power Series
371(5)
Power Series over Complex Numbers
376(17)
Miscellaneous Multiple-Choice Practice Questions
393(37)
Miscellaneous Free-Response Practice Questions
430(193)
PRACTICE EXAMINATIONS: SECTIONS I AND II
AB One
455(22)
AB Two
477(21)
AB Three
498(25)
AB Four
523(28)
BC One
551(17)
BC Two
568(18)
BC Three
586(17)
BC Four
603(20)
Appendix: Formulas and Theorems For Reference 623(9)
Index 632

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