I’ve just emerged from the cave of slightly grubby paper that I inhabit during the marking season. As ever, most of the idiocies with which I’ve been vexing my spirit are sad rather than amusing — or even vaguely sweet, like the student who admitted that “these answers don’t agree because I made up my own maths to do the question”. There’s a small crop, though, of specimens for any future researcher on the subject of what our students do instead of learning.
Let’s start with a simple one: an intricate calculation to determine , defined as the area of a particular finite region, concluded that
This was accompanied by a perfectly acceptable sketch of the cos and sin functions: why the alarm bells didn’t ring is a mystery to me.
Sometimes, of course, the alarm bells ring a little too readily:
Sometimes you can see what’s going on… roughly, at least. Two examples:
. The velocity is -2 in the x-direction.
Our imaginary friend featured in a more mystifying specimen as well, which concluded
So is defined when , for all values of .
This year’s champion, however, is in a class of its own when it comes to getting from one line to the next by vague association.
Q: Given the function defined on the interval , find the inverse function and explain why an inverse function cannot be found if is defined on its natural domain.
The answer, in its entirety:
This is already an inverse function and you can’t have the inverse of an inverse.
I’d ask “who taught you this stuff?”, but sadly I already know the answer.