I have learned a LOT about teaching Calculus in the last year and my kids did a dynamite job. Optimistically, my passing rate is going to a) exist and b) be significant. Now for a more thorough breakdown with an approximation of how many points my kids were capable of getting on each.

### Question 1: Data Table Analysis

A prominent feature of the exam and one my kids found easy. It is an incredibly straight forward data table question and as one girl described it "I was dancing in my seat." Part c and d required some justifications and I'm not totally sure what kind of reasoning would've earned credit.

7-9 points

### Question 2: Particle Motion

Also straightforward, and super bonus for it being a calculator question. While part c and d asked some simple questions (find the position at a point, find the total distance traveled), the setup may have caused some of my kids to goof. The problem gave an *end* condition, not an initial one, requiring a reverse integral in there somewhere I'm pretty sure. And while all of mine should've triggered on "total distance" as a phrase for integral, I'm not sure they would've set it up right. The given function changes direction.

4-6 points

### Question 3: Function Behavior of a Piecewise Graph

Straightforward again, and many kids calling it the "easy" one. Part c asks about justifying the location of an absolute minimum and maximum. Lucky for the kids, the local min/max shown just so happen to be the absolute min/max. Whether or not more than a couple could justify it is another story.

7-9 points

### Question 4: Differential Equations

Praise Calculus Davidson on this one. All your low hanging fruit here: sketching a slope field, finding the equation of a tangent line, and finding a particular solution. The dy/dx given is a little goofy to integrate, but not impossible. Lots of cheers when I drew the slope field, though a bit of a mood killer when I said this sort of thing might be worth 1 pt max. To which I got "yay! I got at least 1 point!"

7-9 points

### Question 5: Volume/Related Rates

AKA The Funnelβ’. There were complaints about this one far and wide. No traditional volume question this year, instead the concept of rotational volume was wrapped in a related rates context. A couple made a go at things they recognized, such as a request for average value in part a, but for the most part this question was a wash. In my planning, the time/reward scale for related rates just wasn't there this year.

0-2 points

### Question 6: Differentiation/Integration of Abstract Functions

A very interesting question that exposed some flaws in my curriculum. I invested a lot of time in discussing integrals and derivatives in very abstract ways. Questions like, what does an integral represent if you know nothing about f(x)? What I failed to do was extend that idea further. Here students were asked to apply the chain rule, quotient rule, and integration to functions labeled f(x) and g(x). Select values of f(x), g(x), and their derivatives were given in a table. In a tear to my eye moment, I had two students admit they caught on to it and applied the rules correctly. Most saw it as an easy question but went about it wrong.

0-3 points

### Conclusion

The goal was to give them a fighting chance. From what I saw here, they all had a fighting chance. My approximations add up to 25 points on the low end and 38 points on the high end. Assuming I successfully did something about the dreadful multiple choice situation, that gives me some actual optimism (A 3 generally requires about 40 points). I was optimistic last year, but I was naΓ―ve. When I applied a critical eye to the 2015 questions like I did here, the absolute MAX the 2015 group could've gotten was 20 points. There was just no way to really succeed with a low FRQ score like that.

Other than The Funnelβ’, the kids felt adequately prepared for the free response. One even said "we were over prepared. We needed more multiple choice practice." To that, I was happy, but rolled my eyes a tad (through the year they ONLY had 161 items to practice with....). Others admitted defeat, but that was to be expected. They recognized it was due to limited preparation on their part.

All in all, great news. 2015 averaged 12 pts on the MC and 9.3 pts on the FRQ, a mid-range 1. I could easily see the 2016 group move the average composite score from a 1 to a 2. That is some serious progress.

Did I mention all of this happened with no textbook, minimal homework, and laser tag?