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AP Calculus: Use of Graphing Calculators


Professional mathematics organizations, such as the National Council of Teachers of Mathematics, the Mathematical Association of America, and the Mathematical Sciences Education Board of the National Academy of Sciences, have strongly endorsed the use of calculators in mathematics instruction and testing.

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

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

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.

Technology Restrictions on the Exams
Unacceptable machines, models and features include the following: Non-graphing scientific calculators, portable/handheld computers, laptops, electronic writing pads, pocket organizers; models with QWERTY (i.e., typewriter) keypads as part of hardware or software (e.g., TI-92 Plus, Voyage 200); models with pen-input/stylus/touch-screen capability (e.g., Palm, PDAs, Casio ClassPad); models with wireless or Bluetooth capability; models with paper tapes; models that "talk" or make noise; models that require an electrical outlet; models that can access the Internet; models that have cell phone capability or audio/video recording capability; models that have a digital audio/video player; models that have a camera or scanning capability. In addition, the use of hardware peripherals with an approved calculator is not permitted.

Test administrators 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 should be warned that their scores will be invalidated if they attempt to remove test materials from the room by any method.

Showing Work on the Free-Response Sections of the Exams
Students are expected to 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 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.

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.

List of Graphing Calculators
Review the list of accepted graphing calculators for the AP Calculus AB and Calculus BC exams.

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.

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