Saturday, April 19, 2008

The Return of the Lost Scribe... whoops

So now we are well into exam review and for good reason. (There are only 6 classes left until the exam).

On Thursday our class consisted of five accumulation problems from the AP exams of five different years.

We completed them in groups and then Mr. K. went over them in class. The questions were not extremely hard, but there were a few tricky parts. I believe after Mr. K. discussed them in full, we understood where we had made our mistakes.

The more important part of the exercise was to notice how the same type of problem changed over the different years. Looking at them, you can see that the graphs are the most noticeable things that change. They become less familiar in behaviour and less points are actually drawn and labeled. The graphs also begin to have a lot of corners which are discrepancies in the second derivative as the are undefined. It then asks if these points are points of inflection, which are usually calculated via the second derivative. That is probably the trickiest part of these questions, but with a little understanding of how the derivatives and their graphs relate to each other, it is easy to get around.
The questions also change fairly drastically, as they go from just understanding how to use the graph and the given functions, to looking past the given graph and fuctions and using it to find characteristics of the parent/derivative functions and their graphs. In the later examples, they begin to ask questions about behaviour of the functions over certain intervals and even ask to draw the graph of the parent function on the axes.
The final example (from 2007) is quite different from the others as there is no graph given, but a table of values is. The table includes two functions (ƒ and g) and their derivatives. It then asks questions about the function h(x) = ƒ(g(x)) - 6 and how it behaves over certain intervals. It also asks a new question that we have not seen yet.
It asks us to find the derivative of the inverse of a function ( g^-1 ). It is a rule that Mr. K. has not yet taught us, but it was explained to me as "the derivative of an inverse of a function is equal to the inverse of its derivative" basically, ∂/∂x(g^-1) = 1/g'. From there just apply it as you would any derivative and solve the question.

Finally, Mr. K. said that this last example is probably the closest example of how it will be presented on our exam, so it would be a good idea to go over this some time in the next two weeks to make sure you have this under your belt, it should be easy marks now.

That is all for my scribe post, remember to start studying "fiendishly" (if you haven't already) there are only 18 days left. O_O

The next scribe is Van I guess...

Enjoy the rest of your weekends!

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