Note: Teachers give (not run) exams. Students take exams. I think "hurry up" is good and more common but "speed up" also works. But they don't have exactly the same meaning. If I'm at home and getting ready to go to the airport, I'd say We better hurry up, or we are going to miss our plane. (There's urgency. We have to do our tasks faster, or even decide not to do certain tasks to get ready. "speed up" doesn't work) Driving to the airport. You better speed up. We're still running late. (Do a specific thing (drive) at a higher rate. "hurry up" could also work.) You test takers need to speed up. (you need to solve your problems faster)

Hurry up , speed up ? When taking exams, what to tell students? Hurry up! Speed up ( in a vehicle )

hurry up everyone