terminal exam

I've never heard anyone say terminal exam.

End-of-term exam is okay, but the more common term is final exam or final.

For example, a student might say, "I have two finals next week." Or, "I have two final exams next week."

Pretty much what Roberta said. 'Terminal exam' sounda kind of scary, like you will die at the end of it. We speak of deadly illnesses as 'terminal diseases.'

There used to be a barber shop in Kendall Square (Cambridge) near the
subway station. It was called "Terminal Barber Shop". I never got a haircut
there.