My AP Calc Bonus FRQ Bin
One of my favorite ways of helping students practice for the GAME DAY AP exam is with my Free Response Question (FRQ) bin, which is my filing bin full of FRQs from the 1970’s until the current year. In mid-October, I begin giving my students lots of exposure to FRQ questions during classwork time, either as general practice at their seats, vertical whiteboard practice in pairs, or timed group quizzes. But there is just not enough time during class for all of the FRQ practice I want, so I created this bin my first year teaching AP Calculus and have been updating it every year since then.
I organize the bin alphabetically by topic, using the following commonly seen topics on the exam. Each topic gets a green hanging file with a label:
Average Value
Accumulation
Convergence testing
Derivative rules
Differential equations and slope fields
Euler’s method
Extrema testing
Graphs f, f’, f’’ (two hanging files are dedicated to this frequently seen topic)
Implicit differentiation
Linear approximation
Optimization (relatively small section, mainly older questions)
Parametric equations
Particle Motion
Polar
Related Rates (relatively small section, mainly older questions)
Tables (two hanging files are dedicated to this frequently seen topic)
Taylor series
Unknown constants (very small section)
Volume/Area (two hanging files are dedicated to this frequently seen topic)
For the past couple of months, it has been difficult for my students to choose FRQs that they can do, since most questions cover material throughout the entire course, and they had never seen an integral before. I was mainly leading them to the Implicit Differentiation and Related Rated hanging file topics.
We are now at a point in the curriculum (end of Unit 6) where students can finally choose from a large variety of questions.
So the AP CollegeBoard website only lists FRQs dating back to 1998, but this PDF file has older questions from 1969 to 1978 and this PDF file has questions from 1979 to 1988.
Although I used to teach AP Calculus AB and BC, now I only teach BC. I still include AB and BC FRQs since half of the FRQs on the BC exam are also on the AB exam. I do not separate the AB from BC FRQs; they are all mixed in together.
Within each hanging file are numerous folders, with the year and “AB” or “BC” written on the tab. Inside each folder is at least one copy of the question (some of my favorite questions have multiple copies in case I have many students staying after school working on these and they each want their own copy) and one copy of the scoring guideline.
I used to require each student to complete at least two FRQs from the bin each month, but now it is strictly by student choice and I offer 1 bonus point added to the quarter grade for each FRQ completed according to the following guidelines:
WORD DOCUMENT version of the above bin label.
I record all of the FRQs done by each student in a printed out Excel sheet for my own personal reference, but my students were looking for a way to keep better track themselves of which problems they had done already. This year I started having them record and keep track of the problems they’ve done in a binder next to the bin. I printed out 28 copies of the log sheet; one for each student. So far they’re done a great job with this!
BLANK GOOGLE DOC of the log sheet.
In past years, I used to keep this bin on my desk during after-school extra helps days and I would watch it like a hawk to make sure students were filing the papers correctly and keeping things neat. This year, I let the reins loose a little but found I had some folders that were missing questions or scoring guidelines, or had written-on papers. I spent a couple hours over Holiday Break going through every folder and reprinting things as needed.
I have found that my students generally struggle a bit to use a hanging file system. One issue is that when students see a folder tab and want to know which green hanging file it is a part of, they look for the hanging file label IN FRONT of the folder rather than BEHIND the folder. For example, in the photo below, I circled in red the “AB 2022” yellow folder tab. Although this question is actually part of the “Differential Equation/Slope field” hanging file, many would mistakenly think it was part of the “Derivative Rules” hanging file section. This leads to mistakes when they have to put papers back and find their folder. I encourage them to use sticky notes to mark their place so they know where to go again, and this does help.
I’ve been using hanging files my entire adult life to organize credit card statements, mortgage statements, doctor paperwork for me and my kids, school/work documents, bank paperwork, Vanguard stocks/ETF statements, insurance paperwork, etc, but I don’t think students today have much experience with them since they’re used to organizing computer files in a virtual folder. Actually, I think even among my age group I am in the minority since most adults don’t use paper anymore, and instead use automatic payments with electronic statements.
Anyways, a couple of my students asked if anyone had ever done every FRQ in the bin. No one has EVER come even close to doing this before! They were going to challenge themselves to do every FRQ, but they realized today there are about 250 questions in the bin (I had actually never counted them before, so I was shocked when they told me this today!). With about 15 weeks left until the AP Calculus exam, and with my after school schedule of 2-3 days per week, from 1:45 - 3:30, they would have to do about 8 questions per day!
If you teach any AP class and don’t have a bin organized with past questions organized by topic, I would highly recommend making one! It is a big time investment the first year, but once this is done, it’s quick to add the handful of new questions after each school year. It also gives you great insight as to what kinds of questions are on the exam and helps you see trends and changes over the years (AP Calculus FRQs have changed a lot over the past 60 years).