# AP Calculus: Use of Graphing Calculators

The use of a graphing calculator in AP Calculus is an integral part of the course. Teachers should use this technology on a regular basis with students so that students become adept at using their graphing calculators.

## The Development Committee Perspective

The AP Calculus Development Committee considers two main concerns when deciding what level of technology should be required for the exams: equity issues and teacher development. The committee can develop exams that are appropriate for any given level of technology, but it cannot develop exams that are fair to all students if the spread in the capabilities of the technology is too wide.

The range of capabilities of graphing calculators has increased significantly. Some calculators are much more powerful than first-generation graphing calculators and may include symbolic algebra features. Other graphing calculators are intended for students studying mathematics at lower levels than calculus. Therefore, the committee has found it necessary to make certain requirements of the technology that will help ensure that all students have sufficient computational tools for the AP Calculus Exams. Exam restrictions should not be interpreted as restrictions on classroom activities. The committee continues to monitor the developments of technology and reassess the testing policy regularly.

## Showing Work on the Free-Response Sections of the Exams

Students must show all of their work. They may also be asked to use complete sentences to explain their methods or the reasonableness of their answers, or to interpret their results.

For results obtained using one of the four required calculator capabilities listed below, students are required to write the setup (e.g., the equation being solved, or the derivative or definite integral being evaluated) that leads to the solution, along with the calculator result. For example, if the student is asked to find the area of a region, they are expected to show a definite integral (i.e., the setup) and the answer. The student does not need to compute the antiderivative; the calculator may be used to calculate the value of the definite integral without further explanation. For solutions obtained using a calculator capability other than one of the four required ones, students must also show the mathematical steps that lead to the answer: a calculator result is not sufficient. For example, if the student is asked to find a relative minimum value of a function, the student is expected to use calculus and show the mathematical steps that lead to the answer. It is not sufficient to graph the function or use a built-in minimum folder.

When a student is asked to justify an answer, the justification must include mathematical reasons, not merely calculator results. Functions, graphs, tables, or other objects that are used in a justification should be clearly identified.

## Exploration Versus Mathematical Solution

A graphing calculator is a powerful tool for exploration, but students should know that exploration is not a mathematical solution. Exploration with a graphing calculator can lead a student toward an analytical solution, and after a solution is found, a graphing calculator can often be used to check the reasonableness of the solution.

Note: As on previous AP Calculus Exams, a decimal answer must be correct to three decimal places unless otherwise indicated. Students should be cautioned against rounding values in intermediate steps before a final calculation is made. Students should also be aware that there are limitations inherent in graphing calculator technology; for example, answers obtained by tracing along a graph to find roots or points of intersection might not produce the required accuracy.

## Graphing Calculator Capabilities for the Exams

A graphing calculator appropriate for use on the exams is expected to have the built-in capability to:

- plot the graph of a function within an arbitrary viewing window
- find the zeros of functions (solve equations numerically)
- numerically calculate the derivative of a function
- numerically calculate the value of a definite integral

One or more of these capabilities should provide the sufficient computational tools to solve any exam question that requires the use of a calculator. We take care to ensure that the exam questions do not favor students who use graphing calculators with more extensive built-in features.

For a list of approved calculators and technology restrictions on the exams, please refer to the AP Calculator Policy page.

If a student wishes to use a calculator not on the list, then the AP teacher must contact ETS (609-771-7300) prior to April 1 of the testing year to receive written permission for the student to use the calculator on the AP Exams.