As the title mentions: what is generic term for any work to be marked by teacher (exam, test, assignment, report) ?
Classwork or homework were the two categories used when I was at school. You could also add exercise to your list of more general words.
Exams and Tests tend to be under set conditions, usually timed and invigilated in some way. Assignments and reports are usually homework, because you are assigned to go away and report back on what you have learned.
edit: as @Geobits pointed out, a good general word for assessed work working towards a particular qualification is coursework.