After reading my post on “The First and Second Day of School” Paul A. Foerster, was nice enough to share these problems from a recent presentation. They give a taste of derivatives and integrals in the first week of school and get the kids into calculus right off the bat.
Paul who recently retired after 50 (!) years of teaching, is Teacher Emeritus of Mathematics of Alamo High Heights School in San Antonio, Texas. He is the author of several textbooks including Calculus: Concepts and Applications, Second Edition, 2005, published by Kendall Hunt Publishing Company, www.kendallhunt.com (Formerly published by Key Curriculum Press).
Many years ago (almost 50) I remember teaching from his fine Trigonometry book .
Thank you, Paul!
Teaching Calculus 
Great information and a handy tool. I’m a newbie AP Calculus teacher and I need all the help I can get. Question though…do you have the solutions somewhere?
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Hi Yvette
Welcome to AP Calculus. You can find exams and solutions here:
AB https://apcentral.collegeboard.org/courses/ap-calculus-ab/exam/past-exam-questions
BC https://apcentral.collegeboard.org/courses/ap-calculus-bc/exam/past-exam-questions
Free-response questions, solution, and scoring guidelines for the last three years are at the links above (2025 will be fully posted soon). There will be a full exam with multiple-choice posted in January (they say).
Previous exams are no longer available (#$&@!) The questions are in the Classroom section but by topic and not a full exam.
I hope you’ve had a chance to attend a summer institute, if not, try to schedule one for next year. They are a big help especially for new teachers.
There is lots more information here for AB
and here for BC
Especially, download the Course and Exam Description on these pages (same for AB and BC). Study it and even have your students download their own copy so they can check off the topics as they learn them.
If I can be of any more help, please contact me at LinMcMullin2@gmail.com I especially like helping new teachers.
Have a good year
Lin
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