Well, since the entrance exam would likely be geared toward people graduating high school, wouldn't the entrance questions have to be at that level of educational experience?
Considering construction finished just 3 years before this exam was published, and the charter was formalized just 10 years before, I would say that MIT (known as Boston Tech from 1866-1916) was not among the foremost technical institutions. At the time.
From the wiki page, it seems like it was actually one of the first technical unis around: "a new form of higher education to address the challenges posed by rapid advances in science and technology in the mid-19th century that classic institutions were ill-prepared to deal with." (http://en.wikipedia.org/wiki/History_of_the_Massachusetts_In...)