1825, "the use of a coach as a public conveyance;" 1849 as "special instruction or training for an exam or an athletic contest;" verbal noun from coach (v.).
Old English crammian "press something into something else," from Proto-Germanic *kramm- (source also of Old High German krimman "to press, pinch," Old Norse kremja "to squeeze, pinch"), from extended form of PIE root *ger- "to gather."
From early 14c. as "fill with more than can be conveniently contained." Meaning "study intensely for an exam in a short time" (with a view to passing the test, not real learning) is attested by 1803, transitive as well as reflexive, originally British student slang. Related: Crammed; cramming; crammer.
c. 1300, "put (someone) to question in regard to knowledge, competence, or skill, inquire into qualifications or capabilities;" mid-14c., "inspect or survey (something) carefully, scrutinize, view or observe in all aspects with the purpose of forming a correct opinion or judgment," from Old French examiner "interrogate, question, torture," from Latin examinare "to test or try; consider, ponder," literally "to weigh," from examen "a means of weighing or testing," probably ultimately from exigere "demand, require, enforce," literally "to drive or force out," also "to finish, measure," from ex "out" (see ex-) + agere "to set in motion, drive, drive forward; to do, perform" (from PIE root *ag- "to drive, draw out or forth, move"). Legal sense of "question or hear (a witness in court)" is from early 15c. Related: Examined; examining.
late 14c., "an instance typical of a class; a model, either good or bad, action or conduct as an object of imitation; an example to be avoided; punishment as a warning," partial re-Latinization of earlier essample, asaumple (mid-13c.), from Old French essemple "sample, model, example, precedent, cautionary tale," from Latin exemplum "a sample, specimen; image, portrait; pattern, model, precedent; a warning example, one that serves as a warning," literally "that which is taken out," from eximere "remove, take out, take away; free, release, deliver, make an exception of," from ex "out" (see ex-) + emere "buy," originally "take," from PIE root *em- "to take, distribute."
late 14c., "action of testing or judging; judicial inquiry," from Old French examinacion, from Latin examinationem (nominative examinatio), noun of action from past-participle stem of examinare "to weigh; to ponder, consider" (see examine). Sense of "test of knowledge" is attested from 1610s.