Building a Better Review for the AP Calc Exam

Both years I have taught AP Calculus AB, I have kind of dreaded the couple weeks of review. They are hard to plan for and probably really boring for students. On top of that, last year, I felt like I squandered the review time. I mostly gave them free time in class to do whatever they needed to do, and I am not sure how effective this was. 45 minutes straight of studying really dragged and I felt like students didn’t really even know what they needed to work on. In addition, the lack of structure I think prompted some students just to look at answer keys instead of struggling through problems themselves.

This year, I was dreading review again, but it really went much better and I think was much more engaging and effective. A few things I changed this year:

1. We started reviewing in class earlier, even before we finished all the material.
2. Review was more structured by me at first and slowly led to more independence, with opportunities for students to see which topics they needed most work on.
3. I spent literally 1% of the time explaining at the front of the classroom and 99% of the time having them to do the work.

The learning structures I used for review:



For about 3 weeks before we started review (i.e. while we were still doing DiffEQs, volume etc), we started class with 5 to 6 quick skill based questions. I tried to put a range of topics, from evaluating limits to writing a tangent line to finding the average value of a function. Students pulled out their notebooks and worked on the questions silently (or as silently as I could get my 85%-chatty-bro class to work). They did the ones they could do and tried the rest. After the timer ran out, I would scroll down and show the answers and show what Standard that the question corresponded with. Then, after explaining anything that needed explaining, we would vote as a class on whether to retire a topic if they felt confident or keep it on for the next day. This took about 10 minutes at the beginning of class.
I loved
this because even though it ate up class time during the end of the year and forced the actual material to take longer, by the time we were ready to review, students had already brushed up on the skills and could focus on big ideas.
Next time, I will try to be more organized about it and have a booklet printed, or sheets for them to glue – I was improvising with this and I felt like it took students too much time to copy things down from the projector.

(this is sort of what it looked like below, but this is for integrals earlier in the year – I’m between computers right now and don’t have all my old files!)


At the end of  many units towards the end of the year, we would do a 12 minute timed Free Response Question, and this is something that we did almost daily during our review time. I would hand out a free response question on a little slip of paper, they would glue it into their notebooks and work on it for 12 minutes silently. If they didn’t know how to do it, they would just try as hard as they could, struggle through it and write down what they know. Then, after 12 minutes, I would hand out the answer key and they would grade themselves, AP style.
I loved that this forced them to struggle through a question and see what they actually know, and I loved that this got them used to AP grading (I had a much lower incidence of unit-forgetting and less-than-3-decimal precision). The trick for both of these benefits is in really holding out on the answer keys until the end of the time!
Next time, I will try to coordinate the 5 minute skill drill with this so that students can recall the topic before a tricky free response question, as I had some students who were so stuck that they didn’t really write anything down and got nothing out of the exercise.


I find multiple choice harder to integrate into class than free response, but one learning structure I liked for multiple choice was Jigsaw. For those that don’t know this (I assume it is fairly common), there would be a set at 12 questions and groups of 3-4 would all work on a third of the questions together (1-4, 5-8, 9-12). Once every group got through theirs, I would rearrange the classroom so that each new group had one person who had worked on each of the sections. Then, they would either work on the rest of the questions individually and then check with each other when they got stuck, or they would just take turns and teach the other members of the group their questions. Some students reported to me that the process of explaining a question out loud really helped them understand what was going on.
I loved the interactions that this activity prompted and I loved how efficient it was for getting through many multiple choice questions (students could do this much faster than working on them on their own).
Next time, I will try to deal with the awkwardness of groups finishing at separate times and weak students incapable of explaining questions to their classmates, though I am not sure how.


I didn’t trust my students to do free response questions at home. They would just look up the answers and get NOTHING out of the process! But we did do a lot of multiple choice questions at home, through Moodle. It is super easy to set up quizzes, so I would just upload images of the questions from a multiple choice collection I had and set the correct answer. I would do 15 questions in a quiz, and it would take my students about 40 minutes to do. We started this about a month and a half before the exam, and then all the homework during the review time become these online multiple choice questions. Before the test, every single student did about 130 multiple choice questions, which amounts to about 3 full tests, and then many did more questions on their own outside of that.
I loved that the work was immediately self checked and automatically graded, as I think this did a lot for their learning from these questions.
Next time, I don’t think I would do so many of these as I think they got a bored with them. Also, I felt like some students were just clicking through the questions, so I would try to think of ways to get them to take these learning opportunities a bit more seriously.



This is, of course, nothing original, but if you have the luxury of stealing a few hours from your students on a weekend for a Mock Exam, do it! Correct it for them, but don’t put a grade on it so that it can be a truly diagnostic tool. This was the most helpful thing for my students in prepping for the exam, because, on top of everything else, the Mock really helped them figure out their weaknesses so that they could really be productive when finally I gave them…


By the time I was giving them large chunks of time to work in class on their own, most students knew what their weaknesses were (from the Mock, timed Free Response, Moodle Multiple Choice etc). Whether they needed to improve their multiple choice or their free response, or they needed to work on specific topics (and could with a packet I gave them with AP Free Response questions split up by type), I felt like most students REALLY used the time well, to the point where a lot of students didn’t even bother studying the night before the exam. All the structure and diagnosing we did at the beginning, and all the work that THEY were doing instead of me talking helped them become far more independent and effective in the review process. I hope it worked – I will find out in a few weeks!

Any review structures you used that worked well?

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Posted on June 23, 2013, in Calculus and tagged , . Bookmark the permalink. 6 Comments.

  1. For my BC class this year I was using Lin McMullin’s list of AP FR questions and he has them divided into 9 categories. I chose 8 examples of each category and gave them to my students. We worked four of them together over two days with them doing the other four outside of class, then on the third day I gave a timed quiz graded by the AP rubric. It took 27 total days, but my kids all felt thoroughly prepared and reviewed by the time their AP test rolled around.

    • Yeah, that sounds great, mostly because you planned well enough to have so much time!! I had about 12 days left. I avoided doing anything in front of the class for review.

      • Well, I have the advantage of being in a school where our BC class is a second year class for our Calc students. All BC kids come in having had AB so we have a great deal of time to play and dig (and review). I did work hard to protect that space at the end of the year, but I am thinking hard about your plan to incorporate it more regularly – especially since they’ve had the AB year first. This would also give us more time for MC questions near the end of the year.

  2. Soooo…any chance I could get your 5-minute skill drills…?

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