A shadowy figure randomly decides to stop at a small college campus and stalk the student body.
Final Exam is an anomaly of the early 80s slasher craze. It eschews blood, gore, and sex, in favor of characters and atmosphere. For me this film succeeds for all the reasons that most viewers consider it a failure. The character development actually works.
The characters are all stereotypes. The virgin, the tramp, the airhead, the nerd, the jock, and the preppy. But three of those characters are really memorable. Courtney the virgin, (Cecile Bagdadi), is so likeable and believable. Radish the nerd, (Joel S. Rice) is annoying yet endearing. Wildman the jock, (Ralph Brown) is a total goofball. I really enjoyed watching these people interact.
The killing doesn't commence until the last third of the film, but it's really atmospheric with the killer stalking his victims on the dark, deserted campus. Limestone College in Gaffney, SC where this was filmed was the perfect location and really adds to the atmosphere.
The killer having no motive actually works much better than having some convoluted motive. The killer not wearing a mask, but mostly being in the shadows is very effective. Roaming the campus wearing a mask when it's not even Halloween would've been kind of conspicuous.
If you want to time travel back to 1981 at the peak of the slasher craze, watch Final Exam. Then watch The Burning and The Prowler.