Word History:

The origins of the word quiz are as difficult to pin down as the answers to some quizzes.

We can say that its first recorded sense has to do with people, not tests.

The term, first recorded in 1782, meant “an odd or eccentric person.”

From the noun in this sense came a verb meaning “to make sport or fun of” and “to regard mockingly.”

In English dialects and probably in American English the verb quiz acquired senses relating to interrogation and questioning.

This presumably occurred because quiz was associated with question, inquisitive, or perhaps the English dialect verb quiset, “to question” (probably itself short for obsolete inquisite, “to investigate”).

From this new area of meaning came the noun and verb senses all too familiar to students.

The second recorded instance of the noun sense occurs in the writings of no less an educator than William James, who in a December 26, 1867, letter proffers the hope that “perhaps giving ‘quizzes’ in anatomy and physiology . . . may help along.”

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Online Etymology Dictionary –

quiz

1847, quies, perhaps from L. qui es? “who are you?,” first question in oral exams in L. in old-time grammar schools. Spelling quiz first recorded 1886, though it was in use as a noun from 1867, perhaps from apparently unrelated slang word quiz meaning “odd person” (1782, source of quizzical). The anecdote that credits this word to a bet by the Dublin theater-manager Daly that he could coin a word is regarded by authorities as “doubtful” and the first record of it appears to be in 1836 (in Smart’s “Walker Remodelled”; the story is omitted in the edition of 1840).

As a verb, 1794 – but at that point it meant to mock a person.

I do not know when our current usage came into being.

This from Merriam Webster’s 10th edition.