Yes, we often say do an exercise. But cannot "make an exercise" describe that the exercise is formed by someone? ( I'm also not sure whether i can use form here ) For example, "In order that we can pass the examination, the teacher is making an exercise, which include the main point of our book.
I do not know why I have a feeling that there has to be a phrasal verb with the particle "up" to refer to "make/produce exercise" in the sence you mentioned! I think it is because of the English speakers' obsession with the phrasal verbs, or may be I'm right!
The verb "do" is correct in that context, but the word "exercise" should be pluralized. The other reason in sounds a little funny is that the answer to "What do the pupils do?" reads like a command and not an answer. More appropriate answers would be...
I found a grammar book that gave me some clarifications
The verb make is used to talk about all of the following
-creating and building : make a cake, make a meal, make the breakfast, make plans, make a model aeroplane -things that can't been seen or touched : make a suggestion, make a decision, make an excuse, make an attempt at something, make a noise, make an offer, make p