- Best score: 76/80
- Median score: 55.5/80
- Was long: some of you didn't get a chance to finish it.
- You can resubmit your exam with the problems corrected --
on separate pages,
cleanly done. Do not make changes to your exam,
and include the original exam with the
corrections. You have until Friday.
You can receive up to half of the missing points (provided your
corrections are indeed correct)!
- First of all, I want to emphasize that a great deal of
this exam could be done with a ruler and an aptitude
for computing (or estimating) slopes of lines:
remember well that
The derivative of \(f\) at a point \(x=a\), \(f'(a)\), is the
slope of the tangent line at \(x=a\); and it is approximated by
the slope of a secant line around \(x=a\).
- I want to spend a little time on some of the most profound errors
I saw, which I would like to never see again....
These are things that I expected to see, but which I hoped I
would not see. I saw them anyway, unfortunately.
- Suppose that \(f(x+h) = f(x) + h\) (serious
composition errors)
- Suppose that terms canceled (serious algebra errors)
- Suppose that linear equations weren't linear....
- Reminder: that slopes are negative when the
function is decreasing, and that slopes are
positive when the function is increasing.
- Finally, here's a
key that will assist you in fixing up your errors.
Let's check out a few highlights (and maybe even a few dark
places!:). But these are solutions that I like.