Reviewing 7 multiple choice questions from the 2012 BC Calculus exam

I’ve been teaching my son calculus this school year with the goal of having him take the BC Calculus exam in May of 2019. We’ve finished most of the course material (the main gap is techniques of integration which I’ve put off a bit) and I had him take the publicly available 2012 BC Calculus exam this past weekend.

He missed 7 questions on the multiple choice part of the exam, and we went over those questions this morning.

The test itself is here on the AP website:

The 2012 Public BC Calculus Exam

Our discussion of the 7 multiple choice problems he missed is below . . . and, dang, the actual questions are a little out of focus in the videos. I’ll upload pics before each question to clear up that little technical glitch:

Question #4:

Question4

Here’s our talk through this problem – I think the error here was simply being a little careless during the exam:

Question #14:

Question14

Again, I think the error was a little careless during the exam.

Question #20

Quesiton20

This question is asking about integration using the technique of partial fractions, so a topic we have not yet covered. I showed him the basic idea of partial fractions and also how he could have estimated the value of this definite integral.

Question #24

Question24

I like this question. It touches on integration by parts and also the fundamental theorem of calculus. Even though he left it blank on the exam, he was able to find the solution here:

Question #85

Question85.jpg

This question is a “related rates” question. It still gave him a little trouble today.

Question #90

Question90

I like this question – it hits on several important properties of convergent / non-convergent series. Although he got this problem wrong on the exam, he does a nice job talking through the ideas in the problem here:

Question #92

Question92

This question might be my personal favorite on the exam. The underlying concepts are basically even / odd functions and the definition of the derivative.

My son is able to recognize why two of the properties listed in the question do not have to be true, but recognizing why the 2nd property has to be true was still a little out of reach for him. Definitely a fun problem to talk through, though (and listening to my explanation for the solution as I publish this blog post . . . I definitely wish my explanation was a little less careless):

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