I wouldn't use take when talking about a tuition payment. Instead, I would use collect:
The bursar collected Mary's tuition.
I wouldn't use give, either, I would use pay:
Mary paid her tuition at the bursar's office.
Although it's worth noting that give and take can indeed be used with regards to money:
Paula gave $3000 to various charities last year.
Sam took $50 out of his checking account before he went to the movies.
For exams, though, give and take are often used:
The professor gave her exam on Monday. Joe was absent, though, so he will take the exam on Friday.
but this is just one meaning of the word take, out of several dozen. OneLook lists, among its many definition's of the word take, this one:
to do an examination in a particular subject
When dealing with flexible words like give and take, it's best to study all the definitions of the word, which is a task that might require you to look in more than one dictionary to complete. OneLook and Wordnik are two great places to start, because they provide links to, or take definitions from, more than one online dictionary.