“Doubtful he went through the trouble of copywriting the test.”
Copyright is automatic. No filing required.
Do I have to register with your office to be protected?
No. In general, registration is voluntary. Copyright exists from the moment the work is created. You will have to register, however, if you wish to bring a lawsuit for infringement of a U.S. work. See Circular 1, Copyright Basics, section “Copyright Registration.”
There’s also “fair use” of limited portions of copyrighted materials, especially in an “educational” context.
Prof just needs to mix up his exam questions.