AP® Calculus AB & BC Crash Course, 2nd Ed., Book + Online: Get a Higher Score in Less Time

PART I

INTRODUCTION

Chapter 1

Keys for Success on the AP Calculus AB & BC Exams

Let’s face it. The AP Calculus exams are not easy. The course itself is filled with hundreds of formulas, diagrams, and nuances that can be confusing, and by the time you take the actual AP exam, you may be overwhelmed by what you think you need to know to get a good score. But don’t worry, this Crash Course focuses on the key information you really need to know for both calculus exams. However, this is not a traditional review book. During the course of the school year, you should learn most of the material that will appear on the AP Calculus exam you’re taking. As you go through this book, if you discover that there is something you don’t understand, consult your textbook or ask your teacher for clarification.

This Crash Course will help you become more pragmatic in your approach to studying for the AP Calculus exams. It’s like taking notes on 3 × 5 cards, except we’ve already done it for you in a streamlined outline format.

Both the AP Calculus AB and BC exams have the same format.

Each section of the test is worth 50% of your grade. You will have 3¼ hours to complete your exam. According to the College Board, in Section II of Calculus AB and BC, if you complete Part A before your time is up, you cannot move on to Part B. So if you finish that section early, you will have time to check your answers. However, if you complete Part B before your 60 minutes are up, you can return to Part A, without the use of the calculator. You will have enough space to work out your problems in the exam booklet.

The multiple-choice answers are scored electronically, and you are not penalized for incorrect answers. Therefore, it makes sense to guess on a question if you don’t know the answer.

In the free-response section of the exams, it is important to show your work so the AP readers can evaluate your method of achieving your answers. You will receive partial credit as long as your methods, reasoning, and conclusions are presented in a clear way. You should use complete sentences when answering the questions in this portion of the exam.

For those questions requiring the use of a graphing calculator, the scorers will want to see your mathematical setup that led to the solution provided by the calculator. You should demonstrate the equation being solved, derivatives being evaluated, and so on. Your answers should be in standard mathematical notation.

If a calculation is given as a decimal approximation, it should be correct to three places following the decimal point, unless you are asked for something different in the question.

Changes to the AP Calculus Exams

Starting with the administration of the 2017 AP Calculus exams, there will be several changes to the curriculum: L’Hôspital’s rule will now be a part of the AB exam. It is unknown to what extent L’Hôspital’s rule will be covered in the AB exam. It is likely that the simpler use of L’Hôspital’s rule using the and forms will be covered in the AB exam, while the more complicated indeterminate forms (∞ – ∞, 0 · ∞, 1∞, 0⁰, ∞⁰) will be part of the BC exam. Absolute and conditional convergence of infinite series has been added to the BC exam topics, as well as the limit comparison test and the alternating series error. All of these topics are covered in this book.

Also, please note that although Newton’s method, cylindrical shells, and powers of trig functions are no longer tested on the AP Calculus exams, we have included the information in this book because of its overall usefulness.

The biggest change is that the multiple-choice questions in the AB exam will have four choices rather than five. All multiple-choice sample problems in this book and in the online practice tests incorporate this change.

The scores from Section I and Section II are combined to create a composite score.

AP SCORE SCALE

To be qualified is to receive college credit or advanced placement. However, the acceptance of these scores for credit is at the discretion of the individual college. You should check with the colleges to which you are applying to see what AP scores they accept for college credit or advanced placement.

According to the statistics reported by the College Board, 57.7% of all the students who took the AP Calculus AB exam in 2013 scored a 3 or higher and 22.6% received a 5. Almost 46% scored a 5 on the AP Calculus BC exam.

Remember, if you’re taking the AP Calculus BC exam, you will also receive a Calculus AB subscore for that part of the Calculus BC exam that covers AB topics.

What does this all mean? Why do so many more students who take the AP Calculus BC exam score a 5? It has to do with the level of the student taking the BC exam. It doesn’t mean they’re smarter, but rather that they’ve already been through the Calculus AB course, which represents about 40% of the BC-level exam. Thus, it stands to reason that the BC exam would, in effect, be much easier. After all, almost 85% who took the BC exam scored a 3 or higher on the AB portion of the BC test.

Most of this shouldn’t have too much impact on how you do on the exam. If you study for the test using this Crash Course book and pay attention during the school year, you will likely be pleasantly surprised when you receive your scores.

Keep in mind that one of the best ways to prepare for your exam is to research past exams. Although the AP Calculus exams have changed slightly for 2017, it still makes sense to go back to previous tests and answer the questions. The single most important aspect of scoring high on any standardized test is to have complete familiarity with the questions that will be asked on the test. You may not find the exact questions, but you will find those that are similar in content to questions you will encounter on your exam. On the College Board website you will find past free-response questions posted. The more questions you answer in preparation for the test, the better you will do on the actual exam.

On the actual exam, make sure you write clearly. This sounds like a very simple thing, but if the AP Reader scoring your exam cannot read your answer, you will lose credit. We suggest that you cross out your incorrect work rather than erase it.

Along those lines, keep in mind that because you will be graded on your method of calculations, make sure you show all of your work. Clearly identify functions, graphs, tables, or any other items that you’ve included in order to reach your conclusions.

Read the graphs carefully, as well as the questions. Make sure they correspond and that you are dealing with like terms.

You do not need to simplify numeric or algebraic answers. Decimal approximations should be correct to three places—unless stated otherwise.

This Crash Course contains everything you need to know in order to score well on either the AP Calculus AB or BC exams. The AP Calculus Course Description Booklet published by the College Board can also be a very useful tool in your studies (www.collegeboard.org).

In addition, REA’s AP Calculus AB & BC All Access® Book + Web + Mobile study system further enhances your exam preparation by offering a comprehensive review book plus a suite of online assessments (topic-level quizzes, mini-tests, full-length practice tests, and e-flashcards), all designed to pinpoint your strengths and weaknesses and help focus your study for the exam.

Good luck on your AP Calculus exams!

PART II

FUNCTIONS, GRAPHS, AND LIMITS

Chapter 2

Analysis of Graphs

A.Basic Functions—you need to know how to graph the following functions and any of their transformations by hand.

1.Polynomials, absolute value, square root functions

2.Trigonometric functions

3.Inverse trigonometric functions and their domain and range

4.Exponential and Natural Logarithmic functions