The AP Calculus AB test is a standardized test in calculus that could earn you actual college credits. In fact, a high enough score on the exam may entitle you to 3-5 credits before even walking onto campus! With college tuition soaring, getting AP credits is like having money in the bank.
What is the Format of the Exam?
The AP Calculus AB test consists of two main sections, multiple choice and free response. In turn, each section has two parts, one that permits a graphing calculator and one that does not.
|Section / Part||Type of questions||Number of questions||Time Limit||Calculator permitted?|
|IA||Multiple Choice||30||60 minutes||No|
|IB||Multiple Choice||15||45 minutes||Yes|
|IIA||Free Response||2||30 minutes||Yes|
|IIB||Free Response||4||60 minutes||No|
Multiple Choice Questions
All multiple choice questions show a problem or ask a question and then give four choices to pick from. There is no “None of the Above,” so you know that the correct choice must be in the list somewhere. Often you can use this fact to your advantage, especially if you only have to work out part of an answer in order to pick the right one.
Free Response Questions
The free response questions are more substantial, requiring significant time to work out. Write all of your work in the space provided on the test booklet. And try not to skip steps in your work, since that is exactly what they are grading on. You may use calculator features to speed your work, but if you do, then indicate what you did. Simply writing a correct final answer may not receive credit.
A typical free response question describes a scenario or problem and then asks 3-4 questions about it. Although the parts may build upon one another, don’t automatically assume that the answer to one part affects the remaining parts.
Should I Bring a Calculator?
Yes! Be sure to bring a graphing calculator that you are familiar with. The instructions for the calculator sections state specifically:
“A graphing calculator is required for some problems or parts of problems on this section of the examination.”
So if the test-makers are telling you that some problems require a calculator, then you better have one! For more information about calculators on the AP Calculus AB test, check out: Can I use a Calculator on the AP Calculus Exam?
Topics on the AP Calculus AB Exam
The material on the exam falls into three main categories:
- Limits and Continuity
- Differential Calculus
- Integral Calculus
Limits and Continuity
You’ll need to know how to work out limits using algebra and estimate their values from graphs and other data. Know about infinite limits and their role in determining the asymptotes of a graph. Understand continuity and how to use the Intermediate Value Theorem and Extreme Value Theorem.
Definitely know your derivative rules, including the product, quotient, and chain rules. Know how to use derivatives to find slope, tangent lines, linear approximations, differentials, and rates of change of functions.
Furthermore, you’ll need to be able to do implicit and logarithmic differentiation. Understand how to apply the Mean Value Theorem. You will also see slope fields and basic differential equations on the test.
Finally, be familiar with applications of the derivative, including optimization, related rates, and the analysis of graphs. Understand the relationships among position, velocity, and acceleration functions.
Integral calculus covers a lot of ground, starting with the concept of a Riemann sum and estimating definite integrals. Know the differences between definite and indefinite integrals and how to compute them using antidifferentiation and the Fundamental Theorem of Calculus.
Last but not least, be able to set up and evaluate integrals that compute average value, areas between curves, and volumes of solids of revolution.
More Information about the Exam
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About Shaun Ault
Shaun earned his Ph. D. in mathematics from The Ohio State University in 2008 (Go Bucks!!). He received his BA in Mathematics with a minor in computer science from Oberlin College in 2002. In addition, Shaun earned a B. Mus. from the Oberlin Conservatory in the same year, with a major in music composition. Shaun still loves music -- almost as much as math! -- and he (thinks he) can play piano, guitar, and bass. Shaun has taught and tutored students in mathematics for about a decade, and hopes his experience can help you to succeed!
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