This appeared as a reply to a question on the AP Calculus Community bulletin board on August 1, 2015. It has been revised for the blog.
AP Calculus teachers find it helpful to use actual AP free-response (FR) and multiple-choice (MC) questions on their exams and for homework throughout the year. Early in the year, it is difficult to find or write a free-response style question that can be used for this purpose. This is because FR questions typically cover topics from the entire year – differentiation and integration topics in the same question. This is done to make “the course a cohesive whole rather than a collection of unrelated topics” (to quote the AP Calculus Philosophy statement). Using actual questions helps students will see how disparate topics can be included in one question, but in the beginning of the year you cannot really do that.
Experienced teachers recommend using AP questions throughout the year. They do so by adapting them. This can be done by using only the parts of FR questions that students have studied. They either omit the other parts and adjust the points accordingly, or they add new parts on the topics students have studied that can be answered from the same stem, thus going deeper into the topic. At the beginning of the year through mid-year do not be too concerned about copying the style and format of actual AP questions. There will be plenty of time later in the year and during review for that. All year long concentrate on the content and topics in the questions. Add questions to explore the topics in more depth. This is easy to do, since AP questions, by including topics from the entire year, must omit some obvious questions that could be asked using the same stem. My occasional series on “Good Questions” has suggestions and examples on how to do this.
Multiple-choice questions are a little easier to use, since they typically test only one topic. Even here adjustments can be made. Try giving a MC question without the choices – make it a constructed response question and check their work; or leave the choices, require students show their work, and grade it. Often MC questions can be expanded as well. For an example, see my post Good Question 4.
The person who wrote the original post on the AP Calculus Community was trying to write a question on limits for her first test. I suggested:
As for a limit based FR question see my blog post Good Question 5. This question concerns an AP question from 1998 AB 2. Students were asked in part (a) to find the limits of a function at plus and minus infinity (end behavior). In part (b) they were asked to find the minimum value of the function. At the beginning of the year students won’t know how to do the calculus involved, but you could just give them the minimum or have them graph the function and find the minimum using their graphing calculator. (Yes, I know that’s not allowed on the AP exam, but the point is to use the result in the next two parts of the question). Knowing the minimum, in part (c) students were asked for the range of the function (combining the results of (a) and (b). Then in part (d) students were asked about the minimum of the similar family of functions of the form . This can be answered without using calculus (although using calculus was intended); the blog post will explain how – and some students actually did this on the exam.