[tags]Calculus, teaching, grading[/tags]
A problem in the most recent homework set for calculus gives a formula for the height of an arrow after t seconds: h = 58t – 0.83t2. The problem then asks for the average velocity of the arrow over several different time intervals.
The student in question calculated the average velocity over the time interval from t=1 to t=2 correctly:
(He didn’t actually type it up, but this is exactly as it appears in its written form on the homework. Including the units, which is nice to see.) Again, this calculation is correct. The student then sets up the similar expression to find the average velocity from t=1 to t=1.5 seconds:
The fraction on the left is correct (although the 85.13 should technically be 85.1325). But the result should be 55.92 m/s, not -29.21 m/s. And again, the above is typed in exactly as it appears on the student’s paper.
Question: What did the student do wrong?
Good question. Took me a couple looks, but it appears your student simply didn’t know how to use his calculator. For the second question, he got -29.21 by typing in “85.13 – 57.17 / 0.5,” which, thanks to the calculator doing the operations in the correct order, yielded 85.13 – 114.34 = -29.21.
Thanks for the teaser!
Oops—I should have noted that he probably did the same thing in the first problem, but it didn’t matter there, because
112.68 – 57.17 / 1 = (112.68 – 57.17) / 1.
We have a winner! Looks like he did the subtraction in the denominator in his head, and then literally typed in 85.13 – 57.17 / 0.5. At least, this is the best theory I can come up with. I’m going to check with him this morning to see if that’s right.
[...] Barsidius figured out what my calculus student did to get an incorrect result from a correctly set-up fraction. What I didn’t mention was that the two calculations I posted were only half of the velocity calculations for that problem. (Reread the post for a description of the problem.) The second half of the problem has incorrect answers — but for different reasons. [...]
This is another example of why it’s better to use an RPN calculator. With an RPN calculator, typing the obvious “85.13 57.17 – 0.5 /” does give you the correct answer.