"a course, especially a fixed course of study at a college, university, or school," 1824, from a Modern Latin transferred use of classical Latin curriculum "a running, course, career" (also "a fast chariot, racing car"), from currere "to run" (from PIE root *kers- "to run"). Used in English as a Latin word since 1630s at Scottish universities.
Proto-Indo-European root meaning "to run."
It forms all or part of: car; career; cargo; caricature; cark; carpenter; carriage; carrier; carry; charabanc; charette; charge; chariot; concourse; concur; concurrent; corral; corridor; corsair; courant; courier; course; currency; current; curriculum; cursive; cursor; cursory; discharge; discourse; encharge; excursion; hussar; incur; intercourse; kraal; miscarry; occur; precursor; recourse; recur; succor.
It is the hypothetical source of/evidence for its existence is provided by: Greek -khouros "running;" Latin currere "to run, move quickly;" Lithuanian karšiu, karšti "go quickly;"Old Irish and Middle Welsh carr "cart, wagon," Breton karr "chariot," Welsh carrog "torrent;" Old Norse horskr "swift."
1510s, "degree of measurement," from French grade "grade, degree" (16c.), from Latin gradus "a step, a pace, gait; a step climbed (on a ladder or stair);" figuratively "a step toward something, a degree of something rising by stages," from gradi (past participle gressus) "to walk, step, go," from PIE root *ghredh- "to walk, go." It replaced Middle English gree "a step, degree in a series," from Old French grei "step," from Latin gradus.
Meaning "inclination of a road or railroad" is from 1811. Meaning "class of things having the same quality or value" is from 1807; meaning "division of a school curriculum equivalent to one year" is from 1835; that of "letter-mark indicating assessment of a student's work" is from 1886 (earlier used of numerical grades). Grade A "top quality, fit for human consumption" (originally of milk) is from a U.S. system instituted in 1912. To figuratively make the grade "be successful" is from 1912; early examples do not make clear whether the literal grade in mind was one of elevation, quality, or scholarship.