That's at least possible with the text, not the audio. For example, maybe the speaker assumes that students generally have one or more exams to study for simply because they're students and that's what students do! In that context, it would then make sense to ask, "Why aren't you studying for an exam?"
In short, by using "the exam", the speaker would assume that there is a specific, identifiable exam—one that can be (mentally) accessed and identified by both the speaker and the listener from the (communicative) context/situation. By using "an exam", the speaker would not be specifying a specific, identifiable exam.
As for the audio, I hear "la-mivkhan".
Edit: The second syllable in לומד might be interfering with how you hear the first syllable in למבחן. I've encountered such interference many, many times—especially for words and constructions that I haven't internalized sufficiently. That's one possibility, anyway!