Super Free-Response Calculus Questions


While multiple-choice calculus questions tend to focus on one concept, free-response questions can test multiple concepts. It is not unusual for such a question to test both use of derivatives and integrals.


Typical free-response questions on the AP® exam give a problem situation (called the stem) and then usually 3 or 4 subparts. And while the subparts are usually diverse, they are limited by time. In general, at most 15 minutes should be allocated to any free-response question and there are limited number of concepts that can be adequately tested in that time period.


Introducing MasterMathMentor's

Super Free-Response Questions!


These problems are inspired by past AP® exams but instead of the usual 4 subparts, these have 10 or more subparts. They allow a thorough investigation of the stem, possibly in areas that students hadn't considered.  In short, everything but the kitchen sink has been thrown into these questions.


Because of COVID, none of this is for sale.

IT IS ALL FREE, questions and solutions.


For each Super FRQ, there are 3 offerings:


  • A Student PDF. This is the entire question with all its subparts. Students will print this out. Space is given in which students write their solutions. Space is also given for a student to write in how many points their answer would be awarded when it is actually graded.


  • A Solution PDF. This is the entire question with all its subparts. But for each subpart, the solution is given.  Not just the answer, but the thought that goes into the answer is explained.  And, there is a rubric on how to award points for each subpart.  Based on the comprehensive nature of these problems, students are shown how to get a feel for how they will perform on the AP exam. However, directions are also given for student to pool their results on all the Super FRQ's to get a much better idea of their strengths and weaknesses.


  • A Solution YouTube.  This contains the solutions contained in the solution PDF as well as the grading rubric. But because they are narrated (by me), it allows much greater depth into the solution process and what students should be thinking when they read the subpart. It focuses on how to use the calculator, when allowed, and what those screens and keystrokes should look like. It also addresses the type of errors that are common to student work.  It is highly recommended that students who struggle with AP® Calculus grade their work using the YouTube video rather than the PDF, as it has more flexibility in terms of guiding student thought.


AB Super FRQ's (double-click to download)


Topic (* Calculator based) Student Solution YouTube Solution URL
1.  Application of Integration * Stud AB 1 Soln AB 1
2.  Particle Motion * Stud AB 2 Soln AB 2
3.  Volume/Related Rates Stud AB 3 Soln AB 3
4.  Graph of f Stud AB 4 Soln AB 4
5.  Slope Fields and DEQ's Stud AB 5 Soln AB 5
6.  Riemann Sums and Volume * Stud AB 6 Soln AB 6



BC Super FRQ's (double-click to download)


Topic (* Calculator based) Student Solution YouTube Solution URL
1.  Polar Equations * Stud BC 1 Soln BC 1
2  Parametric Equations & Vectors Stud BC 2 Soln BC 2
3. DEQ's signifying growth/decay Stud BC 3 Soln BC 3
4. Taylor Series/Polynomials Stud BC 4 Soln BC 4



There are 10 Super FRQ's, 6 in AB and 4 in BC. Some are calculators based and others are not.


The nice thing about these super free-response questions is that you can just give the students the link to this page and they are off on their own. It does not need you as the teacher to monitor.  However, feel free to use these as teaching guides when you start reviewing.


If you or your students find any errors in these questions and their solutions, please email me at


Hope you and your students are and remain safe.