Just a guess...

IS more BE. Not sure about AE. A make up exam (AE) is commonly one given within a week or so of the orginal exam for those who missed it due to illness or some other reason.

I don't know about AE, but for BE, I would almost agree with Roger, but I think it is more natural to hyphenate the word "re-sit" and omit the "exam", which is generally understood implicitly without the dreaded word being mentioned!

Joe: I had the same impression as you (about the hyphen and using the word itself, not adding exam) but then looked it up. City university (in London) and Cardiff at least use resit exam.

@ Joe W: I'd agree it sounds a bit more natural without the 'exam' but 're-sit' with hyphen looks pretty dated. Didn't hyphens like that (see also 'cooperate', etc.) go out in BE about 20 years ago? The Oxford English Reference Dictionary gives it as one word without the hyphen.

This is the AE version, at least in high school. A make-up exam (or test) was for people who either failed the first time and had to take the test again, or who were absent for the first test.
Sorry, I didn't go to college in the US, only in Germany. :)

re-take

might be another option.