EXCERPT
About Research & Education Association
Research & Education Association (REA) is an organization of educators, scientists, and engineers specializing in various academic fields. Founded in 1959 with the purpose of disseminating the most recently developed scientific information to groups in industry, government, high schools, and universities, REA has since become a successful and highly respected publisher of study aids, test preps, handbooks, and reference works.
REA's Test Preparation series includes study guides for all academic levels in almost all disciplines. Research & Education Association publishes test preps for students who have not yet completed high school, as well as high school students preparing to enter college. Students from countries around the world seeking to attend college in the United States will find the assistance they need in REA's publications. For college students seeking advanced degrees, REA publishes test preps for many major graduate school admission examinations in a wide variety of disciplines, including engineering, law, and medicine. Students at every level, in every field, with every ambition can find what they are looking for among REA's publications.
While most test preparation books present practice tests that bear little resemblance to the actual exams, REA's series presents tests that accurately depict the official exams in both degree of difficulty and types of questions. REA's practice tests are always based upon the most recently administered exams, and include every type of question that can be expected on the actual exams.
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Preface
This book gives you the tools to prepare effectively for the Advanced Placement Examination in Mathematics: Calculus BC. These tools include a concise topical review and six full-length practice tests.
Our review succinctly covers areas considered most relevant to this exam. Each REA practice test contains every type of question you can expect to encounter when you sit for the AP exam. (Readers should note, however, that the number and types of questions, as well as the length of time allotted for the actual AP exam can vary slightly from one test administrator to another.) Following each of our tests is an answer key complete with detailed explanations designed to clarify the material for you. By completing all six tests and studying our explanatory material, you will put yourself in a position to master the AP Calculus BC exam.
ABOUT THE TEST
The Advanced Placement Calculus BC Examination is offered each May at participating schools and multi-school centers throughout the world.
The Advanced Placement Program is designed to allow high school students to pursue college-level studies while attending high school. The participating colleges, in turn, grant credit and/or advanced placement to students who do well on the examinations.
The Advanced Placement Calculus BC course is designed to represent college-level mathematics, and is considerably more extensive than Calculus AB. The full year course covers the calculus of functions, including such topics as sequences, series, and differential equations, in addition to the topics covered in Calculus AB. The course is intended for students who have a thorough knowledge of analytic geometry and elementary functions as well as college-preparatory algebra, geometry, and trigonometry. The exam is divided into two sections:
I. Multiple-choice: Composed of 45 multiple-choice questions, designed to measure the student's abilities in a wide range of mathematical topics. These questions vary in difficulty and complexity. This section consists of two parts. Part A comprises 28 questions, for which a calculator cannot be used. Part B contains 17 questions, some of which may require the use of a graphing calculator. One hour and forty-five minutes is allotted for Section I.
II: Free-response: Designed to demonstrate the student's reasoning aptitude, Section II is composed of six questions - three in Part A (portions of which require a graphing calculator) and three in Part B (in which calculator use is not permitted). This section involves a more extensive application of calculus and other mathematical principles as compared to the Section I questions. Forty-five minutes is allotted for each part of this section.
The sample tests in this book provide calculator questions with explanations that include the steps necessary with the calculator. These steps are illustrated after the word calculator, where the keystrokes that should be used are listed.
ABOUT THE REVIEW SECTION
This book contains review material that students will find useful as a study aid while preparing for the AP Calculus BC Examination. This review provides information that will most likely appear on the actual test. Included in this section are the following topics:
Elementary Functions - This chapter describes the Properties of Functions, the Properties of Particular Functions, and Limits.
Differential Calculus - This chapter deals with Derivatives and Application of the Derivative.
Integral Calculus - This chapter explains Anti-Derivatives, Applications of Anti-Derivatives, the Law of Exponential Change, Techniques of Integration, the Definite Integral, and Applications of the Integral.
Sequences and Series - This chapter describes the Sequences of Real Numbers and Functions; Convergence, Series of Real Numbers, Series of Functions, and Power Series
Elementary Differential Equations - This chapter deals with First Order, Variable Separable Equations
SCORING THE TEST
SCORING THE MULTIPLE-CHOICE SECTION
For the multiple choice section, use this formula to calculate your raw score:
Number Right - (Number Wrong x 1/4) = Raw Score (round to nearest whole number)
DO NOT INCLUDE UNANSWERED QUESTIONS
SCORING THE FREE-RESPONSE SECTION
For the free-response section, use this formula to calculate your raw score:
Problem 1 + Problem 2 + Problem 3 + Problem 4 + Problem 5 + Problem 6 = Raw ScoreThe score for each problem should reflect how completely the question was answered, that is, the solution that was produced and the steps taken. You should gauge at what point a mistake was made, and determine whether any use of calculus or mathematics was incorrect. Each problem is given a score of between 0 and 9 points. More points should be given for correct answers that include all work in the answer explanation, and fewer points should be given for incorrect answers and necessary work that was not written down. It might help to have a teacher or an impartial person knowledgeable in calculus decide on how points should be awarded.
THE COMPOSITE SCORE
To obtain your composite score, use the following method:
1.200 x Multiple-Choice Raw Score = Weighted Multiple-Choice Raw Score
(round to the nearest whole number)
NOW ADD:
(Weighted Multiple-Choice Raw Score) + (Free-Response Raw Score) = Composite Score
Compare your score with this table to approximate your grade:
AP GRADE / COMPOSITE SCORE
5 / 78-102
4 / 64-77
3 / 45-63
2 / 30-44
1 / 0-29
The overall scores are interpreted as follows: 5-extremely well qualified; 4-well qualified; 3-qualified; 2-possibly qualified; and 1-no recommendation. Most colleges will grant students who earn a 3 or above either college credit or advanced placement. Check with your school guidance office about specific school requirements.
