I’ve had those dreams too (I usually end up getting to the exam without having taken any classes), and so does my dad, who’s a good three-four decades older than me. If I had to guess, I would say that the life-or-death importance many of us attach to our education, combined with being in such a state for several years, is so intense that it seeps into our subconscious and stays there long after we graduate. I’ve heard stories of personal assistants having dreams about their bosses calling for them, so it isn’t just limited to people in uni.
I keep having this recurring nightmare that I’m in college, but somehow have either forgotten or otherwise blown off all my classes. And it’s getting near the end of the term when I suddenly realize I haven’t gone to class at all, and have missed all of the tests and assignments and I’m going to fail everything.
It’s been ten years (!) since I graduated college, and back then I think I skipped class no more than one or two times total, so I have no idea why my subconscious is so fixated on something that never happened. Brains are weird.