Exam's used in American English, plenty. It tends to connote something a bit more serious or formal than a test, but I don't think you'd get much of a difference in reaction just using the two interchangeably, in most contexts. At worst, you'd come off a bit pretentious, using "exam" to describe lesser tests.

"Test" dominates in primary and secondary school, "exam" becoming more common in post-secondary education and for professional certifications et c., but both occur in both contexts.