Calculator Features Permitted
On AP Calculus Examinations

[rev. 9/26/2002, 10/7/2002, 2/14/2007]

This is Mr. Hansen’s annotated version of the list found on page 14 of the AP Course Description.

1. Graph a function within an arbitrary viewing window. Implicit within this is the ability to compute a function value at a point without showing any work, since you could always use TRACE to find the value of a function at a point. Other ways to find the value of a function at a point must therefore be allowed: using the Y₁(X) notation in the 8-line mode of your calculator, constructing a TI-83 table, using STAT EDIT to define a computed column, etc. Use whichever method is best for the task at hand. However, use standard math notation, never calculator notation, for writing your results.

2. Find zeros of functions (MATH 0 or 2nd CALC zero). Implicit within this is the ability to find intersection points of any two functions f and g, since f and g intersect precisely at the zeros of the function (f – g).

3. Find numeric derivative at a point (nDeriv, or MATH 8, or 2nd CALC 6 ENTER). However, remember that you cannot use this notation in your written work; use dy/dx or “prime” notation instead.

4. Find numeric value of a definite integral (fnInt, or MATH 9, or 2nd CALC 7). Again, remember that you must use standard integral notation, not calculator notation.

What else must we remember?

• Final answers must be accurate to at least 3 places after the decimal point.
• Be careful not to write an equal sign (=) if the more appropriate symbol is the “approximately equal” sign (»), especially in problems involving linear approximation or Taylor series expansion.
• Do not round any intermediate results. Maintain the full accuracy of your calculator (14 significant digits, though normally only 10 are displayed) until you round once at the very end. You can certainly use the » sign or the ellipsis ( . . . ) to avoid wasting time writing down all those digits. The STO key on your calculator is also useful as a time-saver.

What is prohibited?

• You cannot use a maximum or minimum finder such as the one provided on the TI-83. In other words, you must use traditional methods of the calculus to find maxima and minima: set derivative to 0 or DNE, check second derivative (or behavior of first derivative in a neighborhood), check endpoints, and make sure there are no other critical points.

• You cannot use a graph to prove continuity, the existence of a cusp, the existence of local maxima or minima, or almost anything else that you might be tempted to see on a graph. Reason for this seemingly arbitrary rule: There are many examples of functions that can fool calculators. Graphs are for illustration and exploration only. For example, if you are supposed to locate a point of inflection, you must use traditional methods of the calculus; you cannot “eyeball” the point of inflection, nor can you use nDeriv of nDeriv to plot the second derivative as a function and then run the root finder on that. Of course, before you start writing up your solution, you could use any technique you wish to help you understand the problem, even awkward techniques such as taking the nDeriv of nDeriv. The bottom line is that your writeup cannot be based solely on the calculator; you have to interpret and present what the calculator says, and you have to show all the algebraic steps in standard notation. Don’t try to use a calculator-produced graph as a proof of anything.

Side note: Interestingly enough, you can reason from a sketch accompanied with a sentence of explanation—provided the sketch is based on an analysis of the signs of the function and its derivatives. For example, a sketch showing that f '' is continuous, positive for all x > 3, and negative for all x < 3 is ironclad proof that f has a point of inflection at x = 3, provided that you show clear algebraic support for those inequalities and explain what it is about the sign change that leads you to draw your conclusion. For example, your explanation would be adequate if you wrote, “There is a point of inflection at x = 3 because f '' changes sign there.” However, as noted above, a calculator-produced plot of f '' showing an apparent x-axis crossing at 3 proves nothing. Similarly, “sign charts” unaccompanied by words of explanation are no longer accepted by the AP graders. See this article from the AP site if you desire the full details.

• You cannot use a computer algebra system (such as the TI-89) to perform polynomial division for you or to remove all the intermediate steps in the simplification of an algebraic expression. Except for features 1-4 listed above, you must show all algebraic steps in your solutions. You can use the TI-89 to check your work, of course, but you still have to write out the work manually.

• You cannot use any computer or calculator that has a QWERTY keyboard, nor can you use a stylus- or pen-based computer (Palm Pilot, etc.). The College Board publishes a list of approved electronic devices (including, fortunately, both the TI-83 and the TI-89), but most other devices are prohibited. Even “el cheapo” non-graphing scientific calculators are prohibited! Obviously, cell phones are prohibited.

• Although you can bring to the examination anything you like in your calculator’s memory, including programs and text comments stored as programs, you cannot take away any secrets when you leave. In other words, you must not store any problems or portions of problems into your calculator’s memory, since the entire examination is treated as privileged information. Not even your teacher is allowed to know the problems. (Free-response problems are publicly released a few days later, but multiple-choice problems are released only once every several years.)