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Chapter One: Inside the AP Calculus Exam
Advanced Placement exams have been around for half a century. While the format and content have changed over the years, the basic goal of the AP Program remains the same: to give high school students a chance to earn college credit or advanced placement. To do this, a student needs to do two things:
The first part is easy, since the majority of colleges accept AP scores in some form or another. The second part requires a little more effort. If you have worked diligently all year in your coursework, you've laid the groundwork. The next step is familiarizing yourself with the test.
There are actually two AP Calculus tests offered to students, a Calculus AB exam and a Calculus BC exam. The BC exam covers some more advanced topics; it's not necessarily a harder test, but its scope is broader. Most students opt to take the AB exam because they find it somewhat easier, but the BC exam is worth more credit at many universities.
Your decision to take the AP Calculus exam involves many factors, but in essence it boils down to a question of choosing between three hours of time spent on the AP Calculus exam and several hours of time spent in a college classroom. Depending on the college, a score of 3, 4, or 5 on the AP Calculus exam can allow you to leap over the introductory courses and jump right into more advanced classes. These advanced classes are usually smaller, more specifically focused, more intellectually stimulating, and simply more interesting than a basic course. If you are concerned solely about fulfilling your mathematics requirement so you can get on with your study of pre-Columbian art, Elizabethan music, or some other area apart from Calculus, the AP exam can help you there, too. If you do well on the AP Calculus exam, you may never have to take a math class again, depending on the requirements of the college you choose.
Introduction to the AP Calculus exam
If you're holding this book, chances are you are already gearing up for the AP Calculus exam. Your teacher has spent the year cramming your head full of the math know-how you will need to have at your disposal. But there is more to the AP Calculus exam than math know-how. You have to be able to work around the challenges and pitfalls of the test -- and there are many -- if you want your score to reflect your abilities. Studying math and preparing for the AP Calculus exam are not the same thing. Rereading your textbook is helpful, but it's not enough.
That's where this book comes in. We'll show you how to marshal your knowledge of calculus and put it to brilliant use on test day. We'll explain the ins and outs of the test structure and question format so you won't experience any nasty surprises. We'll even give you test strategies designed specifically for the AP Calculus exam.
Preparing for the AP Calculus exam means doing some extra work. You need to review your text and master the material in this book. Is the extra push worth it? If you have any doubts, think of all the interesting things you could be doing in college instead of taking an introductory course that covers only material that you already know.
Overview Of The Test Structure
The AP Calculus exam consists of two sections. In Section I, you have 105 minutes to answer 45 multiple-choice questions with five answer choices each. This section is worth half of your total score. This is the portion of the test in which the right answer is provided to you as one of five choices. Section II of the exam consists of six "free-response" questions that are worth the other half of your score. The term "free-response" means roughly the same thing as "large, multi-step, and involved"; you will use most -- probably all -- of the 90 minutes allotted for Section II answering these six problems. Although these free-response problems are long and made up of multiple parts, they don't usually cover an obscure topic. Instead, they take a fairly basic calculus concept and ask you a bunch of questions about it. It's a lot of calculus work, but it's fundamental calculus work.
Both the AB and BC exams have the same format. Everything that is presented on the AB exam is fair game for the BC exam. However, the BC exam also includes a variety of additional information that is not covered on the AB exam. This book divides a large body of calculus material into multiple chapters, outlined below. Topics that are unique to the BC exam are marked with an asterisk (*) in this list.
Chapter 3: Calculator Basics
Chapter 4: Graphing with a Calculator
Chapter 5: Equation Solving with a Calculator
Chapter 6: Operations with Functions on a Calculator
NOTE: The AP Calculus exam does not directly test whether you know how to use your calculator properly -- it assumes that you do. The information in Chapter 3 is included in this book because it is an important part of doing well on the exam.
Chapter 7: Limits
Chapter 8: Asymptotes
Chapter 9: Continuous Functions
Chapter 10: Functions, Graphs, and Limits
Chapter 11: The Concept of the Derivative
Chapter 12: Computation of Derivatives
Chapter 13: The Derivative at a Point
Chapter 14: The Derivative as a Function
Chapter 15: Second Derivatives
Chapter 16: Applications of Derivatives (including BC content: numerical solution of differential equations using Euler's method, and L'Hôpital's Rule)
Chapter 17: Interpretation of Integrals
Chapter 18: Applications of Integrals
Chapter 19: Antiderivatives -- The Indefinite Integral
Chapter 20: The Fundamental Theorem of Calculus
Chapter 21: Techniques of Antidifferentiation (including BC content: antiderivatives by substitution of variables (including change of limits for definite integrals), parts, and simple partial fractions (nonrepeating linear factors only), improper integrals (as limits of definite integrals)
Chapter 22: Applications of Antidifferentiation (including BC content: solving logistic differential equations and using them in modeling)
Chapter 23: Numerical Approximations
Chapter 24: The Concept of Series
Chapter 25: The Properties of Series
Chapter 26: Taylor Series
How The Exam Is Scored
When your three-plus hours of testing are up, your exam is sent away for grading. The multiple-choice part is handled by a machine, while qualified readers -- current and former calculus teachers and professors -- grade your responses to Section II. After an interminable wait, your composite score will arrive. Your results will be placed into one of the following categories, reported on a five-point scale:
5 Extremely well-qualified (to receive college credit or advanced placement)
2 Possibly qualified
1 No recommendation
Some colleges will give you college credit for a score of 3 or higher, but it's much better to get a 4 or a 5. If you have an idea about which colleges you want to go to, check out their Web sites or call the admissions office to find their particular rules regarding AP scores.
Registration and Fees
You can register for the exam by contacting your guidance counselor or AP Coordinator. If your school doesn't administer the exam, contact AP Services for a listing of schools in your area that do. The fee for each AP exam is $82. For students with financial need, a $22 reduction is available. To learn about other sources of financial aid, contact your AP Coordinator.
For more information on all things AP, visit collegeboard.com or contact AP Services:
P.O. Box 6671
Princeton, NJ 08541-6671
Phone: (609) 771-7300 or (888) 225-5427 (toll-free in the U.S. and Canada)
Copyright © 2006 by Anaxos, Inc.
Excerpted from Kaplan AP Calculus AB & BC 2006 by Kaplan Copyright © 2005 by Kaplan. Excerpted by permission.
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