We can say "maths exam or test"
but we cannot say driving exam, blood exam.
we can say driving test, blood test. Exam is written or spoken test of knowledge. Test is a number of questions, exercises, jobs, etc. for measuring
someone's skill, cleverness, or knowledge of a particular subject. an intelligence test, eye test and so on..... Test has got more general meaning than exam.
Also test is used for an occasion of using something.
Ex: a nuclear weapon test.
In US schools, a "test" is a type of quiz that is given periodically throughout the year to review particular subjects covered in a recent period of time. For example, a teacher might say "study chapters five through eight this weekend, because we're going to have a test on them next week." An exam is a much longer, more involved type of test that covers topics covered in the previous three or four months. An exam grade usually counts for a large percentage of your overall grade in that subject. That is, you can get a bad grade on one or two tests, and still get a good final grade in the subject if you do well on all the other tests. But if you get a poor grade on an exam, that will affect your overall average and make it difficult to end up with a good final grade.