"next exam" is correct and usable in written English.
It refers to a specific upcoming exam that is going to take place. Example: "I need to study for my next exam, it's for my biology class next week."
The next exam session will be only the next year.
The next exam is scheduled for Feb. 27.
The next exam is scheduled for late next year.
Kaplan offered to help her, and she scored a ninety-five on her next exam.
Often learning at school is focused on progressing past the next exam hurdle.
For his next exam, he is considering a $20 bill as a reward to whoever gets the highest score.
He said he would have to study again for the next exam and meet with his tutor.
Professor Wright then moves on to discuss the final form that will be taught before the students' next exam: ostinato.
Any student who will retake the general examination should expect to retake the exam during the next exam period.
When the bell rang, out shuffled the audience, a dozen teenagers who might or might not remember any of this material beyond the next exam.
Overstuffed envelopes, conveniently containing an application for the next exam, became as much a part of his Thanksgivings as overstuffed turkeys.
