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AP^®

The use of a graphing calculator is considered an integral part of the AP Calculus course, and is permissible on parts of the AP Calculus Exams. Students should use this technology on a regular basis so that they become adept at using their graphing calculators. Students should also have experience with the basic paper-and-pencil techniques of calculus and be able to apply them when technological tools are unavailable or inappropriate.

The Development Committee Perspective
Graphing Calculator Capabilities for the Exams
2007-08 List of Graphing Calculators
Technology Restrictions on the Exams
Showing Work on the Free-Response Sections of the Exams
Exploration Versus Mathematical Solution

The Development Committee Perspective

The AP Calculus Development Committee understands that new calculators and computers, capable of enhancing the teaching of calculus, continue to be developed. There are two main concerns that the Committee considers 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 use of graphing calculators was introduced in 1994-95, and the course description was revised in 1997-98 to reflect significant changes in calculus instruction. The AP Calculus Development Committee recognizes the large burden placed on AP teachers to incorporate these changes into their courses.

Over time, 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, by design, 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 will continue to monitor the developments of technology and will reassess the testing policy regularly.

Graphing Calculator Capabilities for the Exams

The committee develops exams based on the assumption that all students have access to four basic calculator capabilities used extensively in calculus. 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 for successful development of a solution to any exam question that requires the use of a calculator. Care is taken to ensure that the exam questions do not favor students who use graphing calculators with more extensive built-in features.

2007-08 List of Graphing Calculators

Graphing calculators having the expected built-in capabilities listed above are indicated with an asterisk (*). However, students may bring any calculator on the list to the exam.

Note: This list is current as of August 2007; other allowable machines will be added as necessary.

Technology Restrictions on the Exams

Nongraphing scientific calculators, powerbooks and portable/handheld computers, pocket organizers, electronic writing pads or pen-input/stylus-driven devices (e.g., Palm, PDAs, Casio ClassPad 300), devices with QWERTY keyboards (e.g., TI-92 Plus, Voyage 200), and cell phone calculators are not permitted for use on the AP Calculus Exams.

Proctors are required to check calculators before the exam. Therefore, it is important for each student to have an approved calculator. Students should be thoroughly familiar with the operation of the calculators they plan to use on the exam. Calculators may not be shared, and communication between calculators is prohibited during the exam. Students may bring to the exam one or two (but no more than two) graphing calculators from the current List of Graphing Calculators.

Calculator memories will not be cleared. Students are allowed to bring to the exam calculators containing whatever programs they want.

Students must not use calculator memories to take test materials out of the room. Students that attempt to remove test materials from the room by any method will have their exam grades invalidated.

Showing Work on the Free-Response Sections of the Exams

Students are expected to show enough of their work for Readers to follow their line of reasoning. To obtain full credit for the solution to a free-response problem, students must communicate their methods and conclusions clearly. Answers should show enough work so that the reasoning process can be followed throughout the solution. This is particularly important for assessing partial credit. Students 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 above, 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 result produced by the calculator. For example, if the student is asked to find the area of a region, the student is expected to show a definite integral (i.e., the setup) and the answer. The student need not 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 must be cautioned 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.

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