During my Russian classes and later, I never felt comfortable with the expressions "to take an exam" and "to pass an exam" as сдавать экзамен and сдать экзамен. It doesn't seem to me like taking an exam and passing it are honest aspectual pairs, but two very different ideas. The act of taking an exam has no definite implications that you will pass it, so why should taking the exam and passing be an aspectual pair? Do сдавать/сдать экзамен really refer to something that is not quite the same as taking or passing an exam, so the usual translations of these into English is missing some small point?
Some related questions on this theme:
1) If my exam ended a minute ago and I want to tell someone "I just took my exam", how is that expressed if I can't say я только что сдал экзамен, which apparently should mean "I just passed the exam", and that is not what I intended to say. Maybe the context is always supposed to make it clear whether сдавал экзамен refers to the past tense while the exam was happening or the past tense after the exam was over.
2) How can I say "I failed the exam" in a colloquial way other than with the phrase не сдать экзамен?
Is there a standard way to talk about taking an exam, in both aspects, without giving an indication one way or the other that you passed it or not?
If someone can indicate why taking and passing an exam really do seem like natural aspectual concepts, I'd be interested to hear about that too.