Final answer:
The sentence in question uses a hypothetical conditional structure in the subjunctive mood, which is an English grammar topic typically taught in high school.
Step-by-step explanation:
The statement "If she was/were a professor, she wouldn't give any exams" is an example of a hypothetical conditional sentence, which falls under the subject of English grammar. The sentence is using the subjunctive mood, specifically the past subjunctive 'were' to talk about a situation that is contrary to reality - that is, she is not a professor and thus is not in a position to decide on giving exams. In English, the subjunctive mood is used to express wishes, hypotheses, or conditions that are not real.
In this case, the sentence suggests a hypothetical situation regarding what the subject's actions would be if her status were different. This topic often appears in high school curricula because understanding the nuances of mood and tense is a key component of mastering English grammar and composition. It's important to note that while both "was" and "were" can be heard in everyday speech, "were" is considered more formally correct in this hypothetical context.