Be Prepared for the Ap Calculus Exam

by Howell, Mark; Montgomery, Martha

• ISBN13: 9780972705554
• ISBN10: 0972705554
• Format: Paperback
• Copyright: 2004-12-15
• Publisher: Skylight Pub

Table of Contents

How to Use This Book	xiv
Introduction	1	(2)
Exam Format, Grading, and Tips	3	(10)
Exam Format	3	(2)
Grading	5	(2)
AB or BC?	7	(1)
The Use of Graphing Calculators	8	(3)
Exam-Taking Tips	11	(2)
Limits and Continuity	13	(38)
The Concept of Limit	13	(8)
Properties of Limits	21	(2)
Techniques for Finding Limits	23	(14)
Finding Limits Using Continuity	24	(2)
Finding Limits of Rational Functions	26	(3)
Finding Limits Using Algebraic Techniques	29	(2)
Finding Limits Using the Squeeze Theorem	31	(2)
Finding Limits that are Derivatives in Disguise	33	(1)
L'Hopital's Rule	34	(3)
Continuity	37	(7)
Relative Rates of Growth	44	(7)
Limits and Continuity Worksheet	47	(4)
Derivatives	51	(28)
Concepts and Notation	51	(4)
Differentiation Methods	55	(8)
Derivatives of Algebraic Functions	55	(3)
Derivatives of Trig, Exponential, and Logarithmic Functions	58	(2)
The Chain Rule	60	(3)
Higher Order Derivatives	63	(2)
Implicit Differentiation	65	(3)
The Derivative of the Inverse Function	68	(2)
Differentiability and Continuity	70	(3)
Finding Derivatives with a Calculator	73	(6)
Derivatives Worksheet	75	(4)
Applications of Derivatives	79	(30)
Tangent and Normal Lines and Linear Approximation	79	(3)
The Mean Value Theorem	82	(3)
Analysis of Function Graphs	85	(13)
Increasing and Decreasing Functions	87	(2)
Extreme Values (Relative and Absolute)	89	(4)
Concavity and Points of Inflection	93	(3)
Using the Graphs of f, f', and f'' in Combination	96	(2)
Modeling and Optimization	98	(2)
Related Rates Problems	100	(4)
Distance, Velocity, Acceleration	104	(3)
Data-Driven Problems	107	(2)
Integration	109	(50)
The Fundamental Theorem of Calculus	109	(2)
Definite and Indefinite Integrals	111	(2)
Approximating Definite Integrals with Sums	113	(10)
Finding Limits of Sums Using Definite Integrals	123	(2)
Properties of Definite Integrals	125	(2)
Calculating Definite Integrals Using Geometry	127	(2)
Calculating Definite Integrals Using the FTC	129	(2)
Calculating Integrals with a Calculator	131	(3)
Finding Antiderivatives	134	(14)
General Antidifferentiation Rules	135	(1)
Antiderivatives from Known Derivatives	136	(4)
u-Substitution (a.k.a. ``Change of Variable'')	140	(3)
Antidifferentiation by Parts (BC Only)	143	(3)
Antidifferentiation by Partial Fractions (BC Only)	146	(2)
Improper Integrals (BC Only)	148	(11)
Integration Worksheet	155	(4)
Applications of Integrals	159	(22)
Overview	159	(1)
Finding the Area of a Region	159	(5)
Calculating Volumes	164	(5)
Volumes of Solids of Revolution	165	(3)
Volumes of Solids with Specified Cross Sections	168	(1)
Average Value of a Function	169	(2)
Net Change of a Function	171	(3)
Motion of a Particle	174	(2)
Accumulation Functions	176	(3)
Arc Length (BC Only)	179	(2)
Differential Equations	181	(20)
What is a Differential Equation?	181	(1)
Slope Fields	182	(5)
Separation of Variables	187	(3)
The Exponential Model	190	(1)
The Logistic Model (BC Only)	191	(4)
Euler's Method (BC Only)	195	(6)
Parametric, Vector, and Polar Functions (BC Only)	201	(18)
Parametric Functions	201	(7)
Vector Functions	208	(5)
Polar Functions	213	(6)
Series (BC Only)	219	(26)
The Concept of a Series	219	(1)
Geometric Series	220	(1)
Tests for Convergence	221	(10)
n-th Term Test	223	(1)
Integral Test	224	(2)
p-Series	226	(1)
Comparison Test	226	(1)
Ratio Test	227	(1)
Alternating Series Test	227	(1)
Applying Convergence Tests	228	(3)
Taylor and Maclaurin Polynomials	231	(4)
Taylor and Maclaurin Series	235	(4)
Taylor's Theorem and Lagrange Remainder	239	(6)
Annotated Solutions to Past Free-Response Questions	245	(2)
http://www.skylit.com/calculus/fr.html
Appendix: Calculator Skills	247	(12)
Practice Exams	259	(134)
AB-1	259	(16)
AB-2	275	(18)
AB-3	293	(20)
BC-1	313	(18)
BC-2	331	(22)
Answers and Solutions	353	(8)
Answers and Solutions	361	(6)
Answers and Solutions	367	(8)
Answers and Solutions	375	(8)
Answers and Solutions	383	(10)
Index	393