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 (fg).

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?


What is prohibited?


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.