At University,say the lecturers hand out past papers with solutions for the students to revise from for an upcoming exam.
Is it common practise for the exam to contain a couple of the exact same questions which are in the previous past exams?
Is it common for the exam to contain questions which the lecturer has put in the assessed worksheets throughout the semester but has already handed out the solutions to?
If you hadn't included the "graduate school" tag, I would say this is both common and appropriate. My exams for undergrads are about half familiar material, that I've specifically indicated to them could appear on the exam. That way, most everyone who studies can at least pass.
But ideally, grad school should be more challenging than that.
In the U.S., in mathematics, by 2016 (as opposed to decades back, perhaps), I think it's by far most often the case that the only real "filter/gatekeeping" for grad school is admission in the first place. There are "qualifying exams" and/or equivalent "require courses", but these are rarely used as filters; rather, they are devices to induce students to study more broadly than they might have otherwise. Yes, at some point there is the entirely-different enterprise of thesis-writing, and skills relevant to timed exams have very little to do with thesis-writing skills.
Since the qualifying exams and/or required courses are meant to encourage a bit of breadth, and to make a case for the utility and sense of that, it is reasonable to be coooperative with students in such situations, rather than be their adversary or skeptic. In particular, giving many good sample-solutions, illustrating the virtues of the ideas being discussed, is surely a good thing. Give archetypes for "expert" solutions.
Further, one might argue that in basic graduate mathematics the list of key ideas is really not so large, and part of what we should convey/sell is indeed the simplicity of things when seen from a slightly more sophisticated vantage. Therefore, I do not want to contrive clever problems that obscure the simplicity I'm trying to claim/show.
For general theoretical papers, it is customary to have a few questions repeated over the past years. Taken in a proper sense this will compel students to learn certain important concepts of the course. Also having the paper entirely different each time might make some to rule out questions as improbable questions hence not capturing the rationale behind the learning aspect of the exam.
For courses with mathematical concepts, it would be ideal to add a more intuition in the selection of questions. You may utilize the same concepts with different data for calculation for each exam.
Concretely, the question paper should encompass important concepts covered in the course. A student who has learned entirely what was taught should be able to score higher marks, and with intelligent application, score complete marks. A student who has learned a satisfactory amount of the portions should be able to at least pass.
