Dear 100 Hour Board,
I was reading a high school course offerings book and it said a prerequisite for AP Calculus BC is having taken AP Calculus AB. According to what I've read about the differences between the two, it appears that BC is AB plus some additional topics, which would seem to imply that one takes either AB or BC, depending on one's level of skill up to that point.
But if one had taken AB in, say, the eleventh grade, wouldn't it be a whole lot of "I already know this!" coming back at the beginning of twelfth grade and hearing what a limit is, and only getting to new material near the end of the year?
So in most districts is it either-or (making the school I read about uncommon), or is it common for students to take both?
In my district, it was either/or. You didn't have to take AB before BC because - like you said - they're almost entirely the same class.
From what I could see on some random forums on the Interwebs, it seems like most people don't have to take one before the other, though I don't think there is a rule that says you have to do it one way or the other.
When I was in high school, I had the same debate. I ended up taking both AB and BC because the pre-calc class I took was taught by a permanent substitute teacher who was the absolute worst.
There are many similarities between BC and AB, but I'll put in this plug for taking both: repetition helps you to cement and understand concepts on a deeper level. Calculus is pretty basic, but being adept at basics is very useful later on (assuming you pursue something math related). Besides, there's always a new perspective to take on things. For instance, a derivative can be approached as an approximation to something instead of the rate of change (you can often represent derivatives as linear transformations, which I think is pretty cool). Or the concept of limits can be used to understand limit points. Traditional calculus can be exchanged for other kinds of calculus, like Ito calculus.
Whatever you decide, I don't think there's a wrong choice to make here.
My high school only allowed you to take both. How does that work? They made you take a class called Calc AB/BC that was 2 class periods and lasted a whole year. By teaching both classes together, it allowed the class to be more efficient and reinforce the material of both classes. So I don't know which stuff was AB and which was BC because they were all mixed together. It seemed to work however because about 50% of the class scored 5s on the AP test which is considerably better than average.