It is a normal occurrence to take a "make-up" test. If someone is absent when the test is given , the teachers give a make up test. As far as a retake test, in 35 years of public school teaching, I have never heard of a "retake" test. There may be some teachers who give them but I think it would be very rare. If you fail the test the first time, we don't give you another test to try to do better the second time. I am talking about tests in school, not a driver's test or something like that. Sometimes if a student is failing or has a very low grade, we may give him an extra-credit project to do to help his grade. I taught high school. It would be very inconvenient for a teacher to give retakes. He would have to grade the 1st test, then make up a second different test and find a way for the student to take it where he could not be alone and have a chance to cheat and then regrade it. There could be many students who would want a retake. If I had a lot of students fail a test, I would curve the grades but not do a retake. It would be twice as much work for the teacher because the student didn't study the first time. If a student felt sick before a test was given, I would not make him take the test, but the student would have to take the test before I gave the test papers back and I might change a few questions. However, giving re-takes is not often done here as far as I know. I know I wouldn't do it. The meaning of the term in English is correct as people have explained it. I am just adding a cultural note.