CliffsAP calculus AB and BC 3rd Edition by Kerry King, Dale W Johnson ISBN 0764586831 978-0764586835

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Product details: 

ISBN 10: 0764586831

ISBN 13:  978-0764586835

Author: Kerry J. King, Dale W Johnson

CliffsAP study guides help you gain an edge on Advanced Placement* exams. Review exercises, realistic practice exams, and effective test-taking strategies are the key to calmer nerves and higher AP* scores.
CliffsAP Calculus AB and BC is for students who are enrolled in AP Calculus AB and/or BC or who are preparing for the Advanced Placement Examination in these areas. The Calculus BC exam includes all of the material in the Calculus AB exam plus additional selected topics, notably on sequences and series. Inside, you’ll find test-taking strategies, a clear explanation of the exam format, a look at how exams are graded, and more:

A topic-by-topic look at what’s on the exam
Tips for test preparation
Suggested approaches to free-response and multiple-choice questions
Two full-length practice tests
Answers to frequently asked questions about the exam
Sample questions (and answers!) and practice tests reinforce what you’ve learned in areas such as limits and continuity, antiderivatives and definite integrals, and polynomial approximations. CliffsAP Calculus AB and BC also includes information on the following:

Trigonometric functions
Algebraic techniques for finding limits
Derivatives of exponential functions
Differential equations and slope fields
Radius and interval of convergence of power series
Numerical solutions to differential equations: Euler’s Method
This comprehensive guide offers a thorough review of key concepts and detailed answer explanations. It’s all you need to do your best — and get the college credits you deserve.

*Advanced Placement Program and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse this product.

Table of contents: 

PART I: INTRODUCTION

Introduction
Questions Commonly Asked About the AP Calculus AB and BC Exams
Strategies for the Exam
Multiple-Choice Questions
Free-Response Questions
Calculator Questions
Topics Covered on a Recent AP Calculus AB or BC Exam

Precalculus
Calculus
PART II: SPECIFIC TOPICS

Precalculus Topics
Functions and Function Notation

Definition of a Function
Vocabulary
Notation
Zeros or Roots
Symmetry
Definition of Even and Odd Functions
Graphing a Function
Shifts and Distortions of Graphs
Absolute-Value Distortions
Inverse Functions

Definition of Inverse Functions
Notation
Polynomial Functions

Degree Test
Leading Coefficient Test
Trigonometric Functions

Graphs, Domain and Range, Periods
Shifts and Distortions for Trig Functions
Trig Identities
Solving Trig Equations
Inverse Trig Functions
Exponential and Logarithmic Functions

Exponential Functions
Logarithmic Functions
Special Log Functions
Properties of Logarithms
Relationship Between Logs and Exponentials
Rational Functions

Definition of a Rational Function
Graphing a Rational Function

Conic Sections

Completing the Square
Algebra

Interval Notation
Lines
Interval Testing
Absolute Value
Parametric Equations (BC Only)

Domain of t
Eliminating the Parameter

Particle Problems
Polar Coordinates and Graphs (BC Only)

Notation
Conversion
Calculators
Polar Graphs
Symmetry
Intersections
Converting Equations from Rectangular to Polar Form
Converting Equations from Polar to Rectangular Form
Special Polar Graphs
Vectors and Vector-Valued Functions (BC Only)

Component Form of a Vector
Magnitude and Direction of a Vector in Standard Position
Vectors Operations
Alternate Component Form
Magnitude/Direction to Component Form
Vector-Valued Functions
Sample Multiple Choice Questions: Precalculus
Answers to Multiple-Choice Questions
Sample Free-Response Question: Precalculus
Answer to Free-Response Question

Limits and Continuity
Intuitive Definition of a Limit
Algebraic Techniques for Finding Limits
One-Sided Limits
Infinite Limits
Theorem for Infinite Limits
Limits at Infinity
Theorem for Limits at Infinity
Special Trig Limits

Continuity

Definition of Continuity at a Point
Definition of Continuity on an Open Interval
Definition of Continuity on a Closed Interval
Sample Multiple-Choice Questions: Limits and Continuity
Answers to Multiple-Choice Questions
Sample Free-Response Questions: Limits and Continuity
Answers to Free-Response Questions

Derivatives
Definition of the Derivative
Differentiation Rules
Constant Rule
Power Rule

Sum and Difference Rule
Power Rule
Trigonometric Rules
Product Rule
Quotient Rule
The Chain Rule

Chain Rule
Alternative Form of the Chain Rule
Power Rule with Chain
Trig Rules with Chain
Higher-Order Derivatives

Derivatives of Exponential Functions

Exponential Rule
Base e Exponential Rule
Derivatives of Logarithmic Functions

Natural Log Rule
Base b Logarithms Rule
Derivatives of Inverse Trigonometric Functions

Inverse Trig Rules
Derivatives of Inverses

Implicit Differentiation

Logarithmic Differentiation

Parametric Derivatives (BC Only)

Parametric Form of the Derivative
Parametric Form of the Second Derivative
Differentiation with Polar Curves (BC Only)

Slope in Polar
Limits and Continuity of Vector-Valued Functions

Limit and Continuity of a Vector-Valued Function
Differentiation of Vector-Valued Functions (BC Only)

Derivative of a Vector-Valued Function
Differentiability and Continuity

Differentiability Implies Continuity
Sample Multiple-Choice Questions: Derivatives
Answers to Multiple-Choice Questions
Sample Free-Response Question: Derivatives
Answer to Free-Response Question

Applications of the Derivative
Tangent and Normal Lines
Position, Velocity, and Acceleration
Theorem for PVA
Related Rates

Sample Problem
Relate Extrema and the First Derivative Test

Theorem on Increasing and Decreasing
First Derivative Test for Extrema
Concavity and the Second Derivative Test

Definition of Concavity
Theorem Test for Concavity
Definition of an Inflection
Second Derivative Test for Extrema
Absolute Extrema and Optimization

Extreme Value Theorem

Sample Problem

Rolle’s Theorem and the Mean Value Theorem
Rolle’s Theorem
Mean Value Theorem
Differentiation with Limits

L’Hôpital’s Rule (BC Only)
Theorem: L’Hôpital’s Rule
Summary of Forms Requiring L’Hôpital’s Rule
Sample Multiple-Choice Questions: Applications of the Derivative
Answers to Multiple-Choice Questions
Sample Free-Response Questions: Applications of the Derivative
Answers to Free-Response Questions

Antiderivatives and Definite Integrals
Antiderivatives

Definition of an Antiderivative
Theorem on Antiderivatives
Notation
Vocabulary
Constant Multiple Rule
Sum and Difference Rule
Trig Rules
Power Rule
The Chain Rule for Antiderivatives

Chain Rule for Antiderivatives
Exponential Antiderivatives

Exponential Antiderivative
Antiderivative of Other Exponentials
Antiderivatives and the Natural Log

Antiderivative Rule for the Natural Log
Trig Integrals

Antiderivatives of Inverse Trig Functions

Inverse Trig Antiderivatives
Integration by Parts (BC Only)

Theorem: Integration by Parts
Integration by Partial Fractions (BC Only)

Improper Integrals (BC Only)

Examples of Improper Integrals
Improper Integrals with Infinite Bounds of Integration
Improper Integrals with Infinite Discontinuities
Sample Multiple-Choice Questions: Antiderivatives
Answers to Multiple-Choice Questions

Applications of Antiderivatives and Definite Integrals
The Fundamental Theorem of Calculus

Fundamental Theorem of Calculus
Notation

Definition of the Definite Integral

Definition of the Definite Integral
Theorem: Properties of the Definite Integral
Theorem: Area Between Curves
Four Properties of the Definite Integral

Property for Even and Odd Functions
Variable Mean Value

Average-Value Property

Volume
Vertical Axis of Revolution
Horizontal Axis of Revolution
Known Cross Sectional Area
Solids of Revolution
Solids with Known Cross Sections
Differential Equations
Numerical Solutions to Differential Equations: Euler’s Method
Euler’s Method as a Recursion Formula
Differential Equations and Slope Fields
PVA with Antiderivatives
Theorem for PVA
Exponential Decay and Newton’s Law of Cooling
Bounded Growth
Logistic Growth (BC Only)
Spread of a Rumor
Spread of a Disease
Population Growth
Work (BC Only)
Work Along a Straight Line
Liquid Work
Length of an Arc (BC Only)
Length of an Arc
Arc Length for Parametric Curves (BC Only)
Arc Length in Parametric
Area and Arc Length for Polar Curves (BC Only)
Area in Polar
Arc Length in Polar
Integration of Vector-Valued Functions (BC Only)
Sample Multiple-Choice Questions: Applications of Antiderivatives and Definite Integrals
Answers to Multiple-Choice Questions
Sample Free-Response Question: Applications of Antiderivatives and Definite Integrals
Answer to Free-Response Question

Sequences, Infinite Series, and Polynomial Approximations (BC Only)
Sequences
Using Current Technology
Series
Tests of Convergence or Divergence of an Infinite Series
Other Useful Information Regarding Infinite Series
Summary of Tests for Convergence or Divergence of Infinite Series
Alternating Series Error Bound
Radius and Interval of Convergence of Power Series
Sample Multiple-Choice Questions: Sequences and Infinite Series
Answers to Multiple-Choice Questions
Sample Free-Response Question: Sequences and Series
Answer to Free-Response Question

Polynomial Approximations and Functions (Taylor and Maclaurin Polynomials)
Differentiation and Integration of Power Series
Lagrange Form of the Remainder of a Taylor Polynomial
Taylor’s Theorem
Power Series for Some Common Functions
Sample Multiple-Choice Questions: Polynomial Approximations of Functions (Taylor and Maclaurin Polynomials)

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