I would LOVE to be wrong about that particular question, but I know at an AP training that I attended, the trainer (who was one of the readers of last year's exam) actually graded that question and was told that the question leaders at the College Board thought this part of calculus was
underemphasized. I know that the vast majority of my students missed the derivative of the inverse function in part (d) of that question; it's something that we talked about in class once or twice, and then everybody forgot about it come test time.
As far as the size of the curve, I'm not sure anybody outside the Chief Reader knows what it actually was. I
do know that my students were claiming that the multiple choice was actually easier than the practice tests we had gone through, so maybe the curve didn't need to be so generous? I also know that there were very few genuine surprises on the scores.
As far as this year's test goes, it could also be a good sign that it was made before they saw the 2007 test; they might not have gotten any ideas off of it. I'm not sure that the 2007 test making team and the 2008 test making team talk to each other.
Another thing that I
do know is that the 2008 exam is scheduled to be released to the public sometime after the 2009 group takes their exam. They usually take advantage of these opportunities to strongly hint at the direction of the AP Calculus test in the future.
Let's be honest, a lot of folks takes a look at the 2003 test (the last released test) and says, "Man, that test isn't so bad." (Especially if they've taken some of the earlier ones.) The cut scores for that particular test were surprisingly low to a lot of folks. But the students at the time in 2003 didn't do so well on this particular test: only 18.5% of the nation ended up getting 5's, and that number has been at least 20% in every year since.
I guess the point that I'm trying to make is that there are many years where the test seems difficult, because there are elements that haven't been emphasized as often in the past. Then they throw it on the AP Test, and every single teacher who looks at last year's test is going to be sure to mention the IVT and MVT problems as something to watch out for.
But in the year they actually release an exam, my guess is that they're going to be very careful about what exactly is on it. And if they're going to put something on the AP Calculus exam this year, it's going to be because they think those items are valuable for the next five to ten years. So if there are any "surprises" this year, it will be because the College Board thinks these topics need major work on the part of teachers.
Or at least that's my take on it.
And in answer to the math teacher question, I
do teach AP Calculus at a high school.
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