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AP Calculus – MANDATORY Summer Packet

Welcome to AP Calculus. This is a rigorous, yet rewarding, math course. Most of the students who have taken Calculus in the past are amazed at how much they have to rely on prior knowledge from Algebra I and II to complete a problem. Many times they find that it is not the Calculus steps that trip them up, but the embedded Algebra that needs to be done. To help you prepare for this course and make it through the “tedious algebra”, I feel that it would be beneficial to show you some of the skills you will come across and have you practice them. If you struggle with any topics and want to review, a good web site is by Paul Dawkins of Lamar University, Dr. Dawkins has many notes, sample problems and tutorials that you may find helpful as you review and prepare for AP Calculus. Another website that will be useful is .

You will also have to develop your critical thinking skills in this class. For some of you, this is a natural skill, for others, not so natural. There are many problems in this packet that don’t “look” like something you know how to do, but are not that bad once you figure out what it’s asking. This is typical of the type of problems that you will see in Calculus next year and I want to give you a chance to start practicing your problem solving skills early. In addition to reviewing some of the past material learned, we need to get a jump start on the new material. In order to get everything taught in time, I would like to have you begin to learn the first topic in Calculus – Limits. I have shown you examples and given you a few to try on your own. If you need further assistance, there are many web sites that have tutorials over Calculus material. One that I recommend is It has animated pictures of what is happening as you take a limit. You were also introduced to the topic in PreAP PreCal, although it may not have been called “limits”.

You should do this packet without a calculator unless indicated and, of course, show all of your work. The answers are given so that you may check you work. Also, round everything to three decimal places.

In order to ensure that you complete the packet, we will be testing over this material sometime during the first week of school. You will have a chance to get your questions answered the first day or so of school.

Have fun this summer, but do a little bit of studying. Believe me, a little studying now will save a lot of time this coming school year. I look forward to seeing all of you in the fall.

Mrs. Cyphert