One thing we love about the AP Calc exam is that it challenges students to have deep, conceptual understanding that allows them to flexibly apply what they know to familiar and unfamiliar problems. Because this takes a lot of working memory, we need to find ways to decrease the cognitive load in other areas so students can focus their attention on those more challenging questions. How do we do this? By making sure they have the basics down pat! This means being very familiar with all derivative and integral rules, as well as important area, volume, and average value formulas.
Here we present a list of things your students should know like the back of their hand.
Download the handout for students to complete while watching the video.
Flashcards are a great way for students to practice these when they're studying on their own, but we also enjoy coming up with fun, interactive ways to reinforce these skills during class. To review derivative and antiderivative rules, we like to play "I have, Who has?". Cut up the cards in the pdf below and give each student a card (or 2 or 3, depending on how many students you have.) All cards must be distributed. Have your students stand in a circle. The person with the "Start" card reads their card out loud, ending with the question "Who has...?" The person who has that derivative or antiderivative will read their card next by saying "I have...". This then continues in a loop until all cards have been read and the final student says "End." Time your students and see if they can get faster. We sometimes have our different AP Calc periods compete against each other to see who can get the fastest time.