Midterm is the exact middle of a semester or of a politician's time in office. A midterm exam is given near the halfway point of the academic term.
A school year is typically divided into semesters, trimesters, or quarters, and each of these can be called a term. Likewise, a president, governor, or representative serves a specific length of time that is called a term, whether it lasts one year, two years, or six years. The middle of a term, therefore, is a midterm, from mid-, from a Proto-Indo-European root meaning "middle," and term, from the Old French terme, "duration."