The first appearance of the word is from 1784 and means an odd person. This sense survives today in the word "quizzical". It was also used in the term quizzing glass, a common accoutrement of English Regency dandies. It later acquired a meaning of to make fun of, or to mock. How it acquired its current meaning of a test is unknown, but that sense did not appear until 1867 and then it was in the United States.

The OED2 has a cite from 1847 where the word appears: "She com back and quiesed us", which could be a clue to its origin. Quiz as a test could be a corruption of the Latin Qui es, meaning "Who are you?" American Heritage says it may be from the English dialect verb quiset, meaning to question. In any case it is probably from the same root as question and inquisitive.