Cracking Guideline for AP Calculus AB Exam

AP Calculus AB is an Advanced Placement calculus course. It is traditionally taken after precalculus and is the first calculus course offered at most schools except for possibly a regular calculus class. The Pre-Advanced Placement pathway for math helps prepare students for further Advanced Placement classes and exams.

Why this Exam?

  • An AP course in calculus consists of a full high school academic year of work that is comparable to calculus courses in colleges and universities. It is expected that students who take an AP course in calculus will seek college credit, college placement, or both, from institutions of higher learning.
  • The AP Program includes specifications for two calculus courses and the exam for each course. The two courses and the two corresponding exams are designated as Calculus AB and Calculus BC. Calculus AB can be offered as an AP course by any school that can organize a curriculum for students with advanced mathematical ability.

About the Exam

The AP Calculus AB Exam is 3 hours and 15 minutes. The 105-minute, 45-question multiple-choice section tests your proficiency on a wide variety of topics. The 90-minute, six-problem free-response section gives you the chance to demonstrate your ability to solve problems using an extended chain of reasoning.

Section - I: Multiple Choice

The multiple-choice section of the exam has two parts. For Part A, you'll have 55 minutes to complete 28 questions without a calculator. For Part B, you'll have 50 minutes to answer 17 questions using a graphing calculator. 

Unlike other multiple-choice tests, random guessing can hurt your final score. While you don't lose anything for leaving a question blank, one-quarter of a point is subtracted for each incorrect answer on the test. But if you have some knowledge of the question and can eliminate one or more answers, it's usually to your advantage to choose what you believe is the best answer from the remaining choices.

Section - II: Free Response

The free-response section tests your ability to solve problems using an extended chain of reasoning. You'll have 45 minutes for each of the two parts of the free-response section. In Part A, you'll answer three questions using a graphing calculator. In Part B, you'll answer three questions without a calculator. During the second timed portion of the free-response section (Part B), you are permitted to continue work on problems in Part A, but you are not permitted to use a calculator during this time.

Included Topics

The material includes the study and application of differentiation and integration, and graphical analysis including limits, asymptotes, and continuity. An AP Calculus AB course is typically equivalent to one semester of college calculus.

  • Analysis of Graphs (Predicting and Explaining Behavior).
  • Limits of Functions (One and Two Sided).
  • Asymptotic and Unbounded Behavior.
  • Continuity.
  • Derivatives. (Concept, At a Point, As a Function, Applications, Higher Order Derivatives, Techniques).
  • Integrals (Interpretations, Properties, Applications, Techniques, Numerical Approximations).
  • Fundamental Theorem of Calculus.
  • Anti differentiation.
  • L'Hospitals Rule, starting in the 2016-17 school year. 

Sample Questions

Looking at sample questions is one of the best ways to get a feel for any kind of test or exam. Here are four sample questions, one from each part of the AP exam. Each of these questions was taken from the official AP Calculus AB Course Description, which you can look at for more complete answer explanations and additional sample problems.

Multiple Choice (NO Calculator)

This question tests your ability to calculate derivatives. You'll need to use the chain rule to differentiate composite functions. The correct answer to this problem is B.

Multiple Choice (With Calculator)

This question tests your ability to solve problems with rapid rates of change. You'll have to find the derivative in order to find the rate of change of the temperature of the water. The correct answer is B.

Free Response (With Calculator)

This question tests your knowledge of integrals.‚ Parts A, B, and C are each worth 3 points.

Free Response (NO Calculator)

This question tests your knowledge of multiple topics, including derivatives and integrals. You can receive up to 1 point for part A, 2 points for part B, and 3 points each for parts C and D.

Tips and Tricks for AP Calculus AB Exam

  • Memorize Important Formulas.

There are certain formulas for AP Calculus AB that you should have down pat. There's no formula sheet given on the AP exam, so you'll have to memorize the formulas you'll need. Many teachers give out formula sheets for students to memorize.

There are also various formula cheat sheets you can use to review before the exam. To find these, simply Google AP Calculus AB formula sheet and look at your options. 

In general, any formula you use regularly in class is a good one to memorize. Major formulas you should have memorized include those for limits, differentiation, and integration, as well as the fundamental theorems.

  • Know How to Use Your Calculator

You're allowed to use your calculator for two of the four exam parts and most of the questions in these two sections will be difficult, if not impossible, to solve without a graphing calculator.

While it might seem obvious that you should know how to work your calculator, knowing exactly how and when to use its different functions can save you a lot of time on the exam and increase your chances of getting the correct answer.

The four calculator capabilities you'll use the most during the AP Calculus AB exam and should easily be able to do with your calculator are as follows:

  • Plot the graph of a function within an arbitrary viewing window.
  • Find the zeros of functions.
  • Numerically calculate the derivative of a function.
  • Numerically calculate the value of a definite integral.

  • Get Used to Showing All Your Work

For most free-response questions on the AP Calculus AB test, the final answer to a problem is only worth 1-2 points out of a possible 9. This means that the majority of points are earned through intermediate steps of the problem and if you don't show how you reached those intermediate steps, you won't get a high score on this section.

Even if you get a correct answer by using your calculator, you have to write the setup (such as the equation being solved or the derivative being evaluated) as well as the answer in order to get credit for your work. 

You might be used to not writing down certain work that seems particularly obvious on homework and class tests. However, even if your teacher doesn't mind, AP graders will.

Remember that AP graders are more interested in how you reached your final answer than they are in what that final answer is, so get yourself in the habit of showing each step of your work well before exam time.

If you want to know more about AP Calculus AB Exam, you may take a look at: ''Best AP Calculus AB Books''.

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