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A Review of AP Calculus Graphing Calculator Skills

Witch of Agnesi animation

       AP question

       AP question 2

       AP question 3

       AP question 4

       AP question 5

       AP question 6

       AP question 7

       AP question 8

       AP question 9

       AP question 10


*AP® Course Descriptions and various test items.  Copyright© 2005 by the College Board.  Reproduced with permission.  All rights reserved.  < >.

This material has been reprinted with permission by the College Board, the copyright owner, and may not be mass distributed or resold, electronically or otherwise.  Unauthorized use, reproduction, duplication, editing, or dissemination of this material, in part or in whole, is forbidden by law.

These problems were selected with permission from the CollegeBoard AP® Calculus Course Description.  Thus, these skills and the multiple choice answers have been carefully tested by thousands of students.  Problems #5 and #7 have been on the BC level exam.  All others are from the AB level.

Please make sure you can to do the following on a graphing calculator:
      (i.)     Produce a graph of a function within an arbitrary viewing window;
      (ii.)    Find the zeros of a function;
      (iii.)   Compute the derivative of a function numerically;
      (iv.)   Compute definite integrals numerically.

Of course there is far more to be learned.  But knowing these four skills and being confident about what is appearing on your calculator screen should enhance your mathematics education.
Tangent to a parabola

Closing Words from a Very Wise Woman on Learning Calculus . . . .

Maria Gaetana Agnesi, the eldest of 21 children, assumed the care of her father's household after the deaths of not only her mother, but also her two subsequent stepmothers.  She also assumed the responsibility of teaching her younger brothers the new calculus.  For them she wrote two volumes of mathematics. 

She wrote a wonderfully clear book.  She even had the printing press installed in the family living room so that she could check each page as it first appeared.  The volumes are large, easy to read, and nearly perfect.  Her work soon received widespread acclaim.  Today we recognize her Institutzioni Analytiche (1748) as the first surviving mathematics publication written by a woman.

At the end of the second volume she penned a closing message.  Her advice remains good to this very day.

"I will finish the Instituzioni with a warning.  The expert analyst should be industrious in trying to search for solutions to these problems and will be much more advanced by means of the techniques that are "born" during this process.

These techniques are used by illustrious mathematicians.  Thus, now it may be possible for you to read problems in other works, and find solutions in other books, that utilize the skills and techniques learned here."
Milan, Italy
For a detailed translation please see
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Agnesi's Institutzioni is opened to her famous curve,

The Witch of Agnesi.

Courtesy of the Huntington Library
San Marino, CA.

Graphing calculator on Agnesi's calculus