We're excited to once again share with you our early solutions to this year's AP Calc Free Response Questions. This year's solutions feature both the AB and BC questions! Note that questions 1, 3, and 4 were identical on both exams. We've listed all 6 AB questions first, and then the three BC only questions.

Some of of our __exam predictions__ turned out to be spot on (finding a second derivative on the differential equation problem!), but who would have thought there would be no rate-in, rate-out question?

You can see this year’s AB questions __here__ and BC questions __here__. Although the official scoring guidelines don’t release until the summer, here’s a first attempt at solutions. (Please be gentle if we have any errors!).

### Reflections:

Overall, we thought this year's exam was...easy? Or at least not surprising in any way. Most questions felt familiar and perhaps even less computation heavy than in some other years. We were surprised that question 1 was not a rate-in rate-out question!

We think students will do very well on questions 1 and 2. Question 3 is more difficult but differential equations of this type have been on the exam for several years now. Let's hope they remember that negative sign from the u-substitution when solving the differential equation! Question 4 also felt very accessible and did not require all that much geometry to find the values of f in the Candidate's Test. Question 5 was that fun function mash-up that we thought would be on LAST year's exam. It's never a bad day to know the chain rule, product rule and FTC! Question 6 was perhaps the most challenging but still not too bad. Will students be able to generate a strategy for solving 6d? We love how this question on the AB exam previews some Calc BC topics!

Note that for the sake of these solutions we have simplified our answers a bit more than we might recommend to students. Remember that all equivalent answers are accepted!

What did you think about this year's questions? How might they inform our teaching practice moving forward?

#1 is asking the average rate of flow, not the average value of the function right?

Advanced students are expected to understand concepts.

So #3 is extremely similar to 2011 AB problem 5, and in that problem the scoring guidelines for the over/underestimate part state that the second derivative is negative on the whole interval between the point of tangency and the point of estimation. I don't know if that's a requirement, but it seems like it might be? Especially since [0,2] is a fairly wide interval for approximation.

Thank you so much for posting this!! I believe 4c ends up being 3/-1 rather than -3/-1 (although I could definitely be wrong).

My wife thought I was crazy because I couldn't wait to sit down to do the problems after dinner last night! Just as I finished up my solutions, I received Sarah's email.