- Integrals and the Fundamental Theorem of Calculus
- Reasoning with definitions and theorems
- Connecting concepts
- Implementing algebraic/computational processes
- Connecting multiple representations
- Building notational fluency
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Ultimate Guide to the AP Calculus AB Exam
As you probably already know by this point in your high school career, Advanced Placement (AP) courses and exams are administered each year under the oversight of the College Board. AP Calculus courses are among the most popular choices.
In 2016, over 300,000 of the 2.6 million students taking AP exams took the Calculus AB exam. This places it among the top 4 most popular AP exams. If you are interested in taking the AP Calculus AB exam, whether you have taken the class or are planning to self-study, read on for a breakdown of the test and CollegeVine’s advice for how you can prepare for it.
About the Course
The AP Calculus AB course focuses on the unifying themes of calculus, including derivatives, integrals, limits, approximation, and applications and modeling, all the while providing general experience with appropriate methods and applications. Though computational competence is important, the primary emphasis of the course is on a multidimensional approach to calculus, with concepts, results, and problems expressed in numerous ways including graphically, numerically, analytically, and verbally. The course also emphasizes the importance of the connections and relationships between these various representations of functions. The course relies heavily on technology to reinforce relationships among functions, confirm written work, implement experimentation, and assist in interpreting results.
The AP Calculus AB course requires a good deal of foundational knowledge in order to be successful, whether you enroll in the course or self-study. Before beginning your Calculus AB studies, you will need four years of secondary mathematics covering algebra, geometry, trigonometry, analytic geometry, and elementary functions. Your knowledge should cover linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions. You will need to be familiar with the properties of functions, the algebra of functions, the graphs of functions, and the language of functions. You will need access to a graphing calculator for the duration of the course and you should know that you cannot take both AP Calculus AB and AP Calculus BC within the same year.
The AP Calculus AB course is newly redesigned for the 2016-2017 school year. Its content remains the same, with a single addition (L’Hôpital’s Rule), but the format of the course outline has changed significantly in order to make essential mathematical practices explicit and to directly align course content with demonstrable learning objectives. For a complete description of the revisions, see AP Calculus Updates: Key Changes.
About the Exam
While taking the AP Calculus AB exam, you may use a scientific calculator on one part of the multiple-choice section and on one part of the free-response section. Your calculator should be able to plot the graph of a function within an arbitrary viewing window, find the zeros of functions, numerically calculate the derivative of a function, and numerically calculate the value of a definite integral. More information and a list of acceptable calculator models can be found in the official Calculator Policy.
The AP Calculus AB exam is one of the longest AP exams, clocking in at three hours and 15 minutes. It is comprised of two sections. The first section contains 45 multiple-choice questions, spans one hour and 45 minutes, and accounts for 50% of your total score. This section is divided into two parts. Part A contains 30 questions and lasts for 60 minutes. You will not be allowed to use your calculator on this part. Part B contains 15 questions, lasts for 45 minutes, and allows the use of a calculator.
The second section is the free-response section, which lasts for one hour and 30 minutes and accounts for the remaining 50% of your score. This section is divided into six questions and, like the multiple-choice section, is split into two parts. Part A contains two problems, which you will have 30 minutes to complete with the use of your calculator. Part B has four problems, which you will have 60 minutes to complete without the use of your calculator.
The AP Calculus AB exam seems to be one that students either grasp well or not at all. In 2016, over 55% of students taking the exam scored either at the highest end with a top score of 5 or at the lowest end with a bottom score of 1. Specifically, nearly a quarter of all test-takers scored a 5 while a third of all test-takers scored a 1. Overall, 59.5% of students who took the exam received a 3 or higher (typically considered passing).
Keep in mind, credit and advanced standing based on AP scores varies widely from school to school. Though a score of 3 is typically considered passing, it is not always enough to receive credit. Regulations regarding which APs qualify for course credits or advanced placement at specific colleges and universities can be found here.
A full course description that can help to guide your studying and understanding of the knowledge required for the exam can be found in the College Board course description.
Read on for tips for preparing for the exam.
Step 1: Assess Your Skills
Take a practice test to assess your initial knowledge of the material. This is an integral step to shaping your personalized study path. To learn more about the importance of formative assessments and how you can use one to get your studying off on the right foot, check out the CollegeVine article What Is a Formative Assessment and Why Should I Use One to Study?
Although the AP Calculus AB course was recently redesigned, its content has remained almost entirely the same. For this reason, previous exams are still valuable for assessment purposes. You can find the 2012 exam, 1998 exam, and 1988 exams all available from the College Board. Alternatively, you could also use a practice or diagnostic test provided in one of the many up-to-date commercial study guides.
Once you have taken some kind of formative assessment, score it to identify the areas you already understand and those in need of improvement. From an accurate formative assessment, you will get a better idea of where to focus your studying efforts.
Step 2: Study the material
The AP Calculus AB course focuses on differential and integral calculus while relying heavily on a strong foundation in algebra, geometry, trigonometry, and elementary functions. To be successful on the exam you will need to learn the concepts and skills of limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus. You should have knowledge about how to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and you should be able to use technology to help solve problems, experiment, interpret results, and support conclusions.
In order to understand the material in the AP Calculus AB course, you’ll need to understand the structure of the course outline, which is available in the course description. The outline organizes key concepts into three “big ideas” that you will need to understand completely. This comprehension should include each of the “enduring understandings” (falling under each big idea,) and examples of essential knowledge to support them. The big ideas encompass core mathematical principles and theories, along with their application. The three big ideas of the AP Calculus AB course are:
To apply your knowledge, you will also need to master the following six mathematical practices for AP Calculus AB:
To get a better idea of the course content and structure, you should review the sample course syllabi available here and here. You might also choose to review the College Board’s video overview of curriculum, assessment, and instructional approaches.
For a more specific idea of where to focus your studying, you may consider using a commercial study guide. The Princeton Review’s Cracking the AP Calculus AB Exam, 2017 Edition: Proven Techniques to Help You Score a 5 provides a comprehensive and updated guide to the exam, with reviews of each unit, practice problems, and three complete practice tests. Another solid choice is Barron’s AP Calculus, 13th Edition which covers both AB and BC calculus content in a concise and accurate way.
There are also a number of free study resources available online. Many AP teachers have posted complete study guides, review sheets, and test questions. One can be found here and another here, but these are just a few of the many that are out there.
Another new, fun way to study is to use one of the recently developed apps for AP exams. These range in price from $0.99 to $4.99, but they provide a fun and easy way to quiz yourself. Make sure you read reviews before choosing one – their quality varies widely.
Step 3: Practice Multiple-Choice Questions
Once you have your theory down, give a try by practicing multiple-choice questions. You can find these in most study guides or through online searches. You could also try taking the multiple-choice section of another practice exam. The College Board even provides a set of sample questions with scoring explanations. Additionally, there are several study books available that consist of just multiple-choice questions with answers. The most highly rated of those is available here.
The College Board Course Description includes many practice multiple choice questions along with explanations of their answers. As you go through these, try to keep track of which areas are still tripping you up, and go back over this theory again. Focus on understanding what each question is asking and keep a running list of any vocabulary that is still unfamiliar.
Step 4: Practice Free Response Questions
The free-response portion of the AP Calculus AB exam will test your ability to solve problems using an extended chain of reasoning. It will challenge you to demonstrate your knowledge of correct mathematical reasoning and thinking while articulating the reasoning and methods that support your answer. In most cases, an answer without supporting work will receive no credit. Some questions will ask you to justify an answer or determine whether a theorem can be applied. Each part of the free-response section is timed, and you may use a graphing calculator only for Part A. During Part B, you may not use a calculator and though you are allowed to return to working on Part A questions during Part B, you must do so without a calculator.
When completing the free-response section, be very careful to show all of your work, even when you’re using a calculator. This means that every step you took to arrive at a solution should be clearly notated for the exam reader, who will be assessing your knowledge through not only your final answer, but also your methods that led to it. If you use your calculator to solve an equation, compute a numerical derivative, or find a definite integral, then be sure to write the equation, derivative, or integral first. Even a correct answer will not receive full credit if your work is not readily apparent.
To ensure success on this section, make sure to the review the scoring rubric located on page 72 of the course description. You can also get a better understanding of the scoring by reading scoring commentary from the Development Team and authentic examples of student responses and their scoring explanations from previous exam administrations.
Step 5: Take another practice test
As you did at the very beginning of your studying, take a practice test to evaluate your progress. You should see a steady progression of knowledge, and it’s likely that you will see patterns identifying which areas have improved the most and which areas still need improvement.
If you have time, repeat each of the steps above to incrementally increase your score.
Step 6: Exam day specifics
In 2017, the AP Calculus AB Exam will be administered on Tuesday, May 9 at 8 AM.
For complete registration instructions, check out CollegeVine’s How to Register for AP Exams (Even If You Didn’t Take the Class).
For information about what to bring to the exam, see CollegeVine’s What Should I Bring to My AP Exam (And What Should I Definitely Leave at Home)?
If you feel like you still need more help or you are not sure that you can do it on your own, look no further. For personalized AP tutoring, check out the CollegeVine Academic Tutoring Program, where students who are intimately familiar with the exam can help you ace it too, just like they did.
For more about APs, check out these CollegeVine posts