Preparing for the Calculus AP Exam with Calculus: Graphical, Numerical Algebraic / Edition 2

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Overview

This preparation manual, directly linked to Calcululus: Graphical, Numerical, Algebraic byFinney, Demana, Waits, and Kennedy, will help to reinforce the important connections between what you will learn in class and what you will be tested on in the AP* Calculus Exam. Or, if you simply need a refresher for the exam, this guide has everything that you need to help pave your way to success.
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Product Details

  • ISBN-13: 9780321335746
  • Publisher: Pearson
  • Publication date: 2/3/2006
  • Series: AP Test Prep Series
  • Edition description: REV
  • Edition number: 2
  • Pages: 336
  • Product dimensions: 8.40 (w) x 10.80 (h) x 1.10 (d)

Meet the Author

Ray Barton teaches AP* Calculus BC at Olympus High School in Salt Lake City, Utah. He has been an Advanced Placement Calculus exam reader and is an active instructor for Teachers Teaching with Technology. He has coauthored Advanced Placement Calculus with the TI-89 and Differential Equations with the TI-86. Ray received the Presidential Award for Excellence in Mathematics and Science Teaching in 1995. He is a strong proponent of using technology to teach mathematics.

John R. Brunsting taught AP* Calculus at Hinsdale Central High School in Hinsdale, Illinois. He has been an Advanced Placement Calculus exam reader and table leader, as well as an AP* Calculus Test Development Committee member. He was a consultant for the Midwest Region of the College Board. Now retired, John is a director of Illinois Advanced Placement Institutes and Mathematics & Technology Institutes, providing summer training for AP* teachers.

John J. Diehl has taught AP* Calculus and AP* Statistics at Hinsdale Central High School in Hinsdale, Illinois. He has been an Advanced Placement Statistics exam reader and table leader, as well as an AP* Statistics Test Development Committee member. John is a consultant for the Midwest Region of the College Board and a Teachers Teaching with Technology Institute instructor. John is coauthor of Advanced Placement Calculus with the TI-89.

Greg Hill teaches AP* Calculus BC at Hinsdale Central High School in Hinsdale, Illinois. A nearly twenty-year veteran, he has been an Advanced Placement Calculus exam reader for the last five years. As a consultant for the College Board, Greg has presented numerous AP* Calculus workshops across the Midwest. An active Teachers Teaching with Technology instructor, Greg guides teachers in the appropriate uses of technology in algebra, precalculus, and calculus.

Karyl Tyler teaches AP* Calculus AB at Hinsdale Central High School in Hinsdale, Illinois. Her twenty-eight years of teaching experience include eleven years of teaching calculus. Beyond her classroom, Karyl assists with instruction at Teachers Teaching with Technology Institutes, sharing her passion for using technology in the mathematics classroom.

Steven L. Wilson teaches AP* Calculus AB at Hinsdale Central High School in Hinsdale, Illinois. His twelve years of teaching experience include eight years of teaching calculus. A versatile mathematician, Steve shares his deep understandings with students training for rigorous mathematics oral competitions.

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Table of Contents

Part I Introduction to the AP* AB and BC Calculus Exams

Part II Precalculus Review of Calculus Prerequisites

Calculus Prerequisites

Precalculus — A Preparation for Calculus

Functions

Transformations

Polynomial Functions

Rational Functions

Exponential Functions

Sinusoidal Functions

More Trigonometric Functions

Inverse Trigonometric Functions

Parametric Relations

Numerical Derivatives and Integrals

Part III Calculus Review of AB and BC Topics

Functions, Graphs, and Limits

Analysis of Graphs

Limits of Functions

Asymptotic and Unbounded Behavior

Function Magnitudes and Their Rates of Change

Continuity

Intermediate and Extreme Value Theorems

Parametric, Polar, and Vector Functions

Derivatives

Concept of the Derivative

Differentiability and Continuity

Slope of a Curve at a Point

Local Linearity

Instantaneous Rate of Change

Relationships Between the Graphs of f and f’

The Mean Value Theorem

Equations Involving Derivatives

Correspondences Between the Graphs of f, f’ and f”

Points of Inflection

Concavity of Functions

Extreme Value of Functions

Analysis of Parametric, Polar, and Vector Curves

Optimization

Related Rates

Implicit Differentiation

Derivative as a Rate of Change

Slopefields

Euler's Method

L’Hopital’s Rule

Derivatives of Basic Functions

Derivative Rules

Chain Rule Explorations

Chain Rule

Derivatives of Parametric, Polar, and Vector Functions

Integrals

Riemann Sums

Definite Integral of a Rate of Change

Basic Properties of Definite Integrals

Applications of Integrals

Fundamental Theorem of Calculus

Antiderivative Basics

Integration by Substitution

Integration by Parts

Integration by SimplePartial Fractions

Improper Integrals

Initial Value Problems

Separable Differential Equations

Numerical Approximations to Definite Integrals

Polynomial Approximations and Series

Concept of Series

Geometric, Harmonic and Alternating Series

Integral Test, Ratio Test, Comparison Test

Taylor Polynomials

Maclaurin and Taylor Series

Manipulating Taylor Series

Power Series

Radius and Interval of Convergence

Lagrange Error Bound

Part IV Practice Examinations

AB Exam 1

AB Exam 2

BC Exam 1

BC Exam 2

Part V Answers and Solutions

Solutions for Part 2: Precalculus Review of Calculus Prerequisites

Solutions for Part 3: Calculus Review of AB and BC Topics

AB Exam 1 Solutions

AB Exam 2 Solutions

BC Exam 1 Solutions

BC Exam 2 Solutions

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