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

by Hockett, Shirley O.; Bock, David

• ISBN13: 9780764177514
• ISBN10: 0764177516
• Edition: CD
• Format: Paperback
• Copyright: 2004-08-01
• Publisher: Barrons Educational Series Inc

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