AP Calculus AB and BC · Exam guide
Using Your Graphing Calculator on the AP Calculus Exam: Four Skills and the Rules
The exam names four things you are expected to do with a graphing calculator. Learn them well and learn how to write them down, because on a free-response question the calculator's answer earns no credit unless the setup is on the page.
The four calculator skills
| Skill | Example |
|---|---|
| Plot the graph of a function in a viewing window | Graph a rate function to see where it is positive. |
| Find the zeros of a function | Solve a rate equation like \(R(t) = 0\) or find where two curves meet. |
| Numerically calculate the derivative of a function at a point | Find \(f'(2)\) for a function that is hard to differentiate by hand. |
| Numerically calculate the value of a definite integral | Find the total change from a rate that has no simple antiderivative. |
Anything else a calculator can do, such as symbolic algebra or finding an antiderivative, is not what the exam expects. If your calculator offers it, you may use it, but you must still show the work the question asks for.
How to write it down
- Write the integral or equation you are solving, with limits, before the answer. For example: \(\int_0^2 \sin(x^2)\,dx\).
- A graph is a method, but say what you read from it (for example, the zero of \(R(t)\) is at \(t = 3.126\)).
- Store a value you will reuse, and do not round it until the end.
- Give final answers to three places after the decimal point unless the question says otherwise.
A worked example
A particle's velocity is \(v(t) = \sin(t^2)\) for \(0 \le t \le 2\). Find the particle's total change in position on this interval.
The total change in position is \(\int_0^2 \sin(t^2)\,dt\). There is no simple antiderivative, so evaluate the integral numerically on the calculator. The result is 0.805, to three decimal places.
The answer is right, but no integral or reasoning is shown, so the setup point is lost.
It shows the integral with its limits, then the value.
Rounding and truncating
Three decimal places means either rounding or truncating is accepted. An answer that is wrong in the third decimal place, because you rounded part-way through, can lose the answer point, so keep the full value in the calculator until the last step.
Common mistakes
- Writing only the number from the calculator.
- Working in degree mode on a question that uses radians.
- Reading a graph to estimate a zero and then reporting the estimate as exact.
- Using the calculator on a Part B free-response question, where none is allowed.
Frequently asked questions
Which calculator should I use?
Use a graphing calculator that is approved by the College Board, and practice with the exact one you will take to the exam.
Can I use the calculator on every free-response question?
No. A graphing calculator is required on Part A, the first two questions, and not allowed on Part B.
Do I lose points if I use the calculator for something I could do by hand?
No, as long as the setup and reasoning are on the page.
Should I keep a calculator in radian mode?
Yes, unless the problem uses degrees.
Where can I find the official calculator policy?
Exam formats change a little from year to year, so check the current course and exam description on the College Board site before test day.
Keep practicing
Every lesson in the AP Calculus courses ends with practice problems and an Exam focus box that shows how the topic is tested, and every unit has a 10-problem practice set with worked answers. These free lessons also build the skills the free-response section tests:
See the AP Calculus AB and BC course Free lessons and lesson list See the AP Calculus BC course
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Multiple choice
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