remake v.

word-forming element meaning "back, back from, back to the original place;" also "again, anew, once more," also conveying the notion of "undoing" or "backward," etc. (see sense evolution below), c. 1200, from Old French re- and directly from Latin re- an inseparable prefix meaning "again; back; anew, against."

Watkins (2000) describes this as a Latin combining form conceivably from Indo-European *wret-, metathetical variant of *wert- "to turn." De Vaan says the "only acceptable etymology" for it is a 2004 explanation which reconstructs a root in PIE *ure "back."

In earliest Latin the prefix became red- before vowels and h-, a form preserved in redact, redeem, redolent, redundant, redintegrate, and, in disguise, render (v.). In some English words from French and Italian re- appears as ra- and the  following consonant is often doubled (see rally (v.1)).

The many meanings in the notion of "back" give re- its broad sense-range: "a turning back; opposition; restoration to a former state;" "transition to an opposite state." From the extended senses in "again," re- becomes "repetition of an action," and in this sense it is extremely common as a formative element in English, applicable to any verb. OED writes that it is "impossible to attempt a complete record of all the forms resulting from its use," and adds that "The number of these is practically infinite ...."   

Often merely intensive, and in many of the older borrowings from French and Latin the precise sense of re- is forgotten, lost in secondary senses, or weakened beyond recognition, so that it has no apparent semantic content (receive, recommend, recover, reduce, recreate, refer, religion, remain, request, require). There seem to have been more such words in Middle English than after, e.g. recomfort (v.) "to comfort, console; encourage;" recourse (n.) "a process, way, course." Recover in Middle English also could mean "obtain, win" (happiness, a kingdom, etc.) with no notion of getting something back, also "gain the upper hand, overcome; arrive at;" also consider the legal sense of recovery as "obtain (property) by judgment or legal proceedings." 

And, due to sound changes and accent shifts, re- sometimes entirely loses its identity as a prefix (rebel, relic, remnant, restive, rest (n.2) "remainder," rally (v.1) "bring together"). In a few words it is reduced to r-, as in ransom (a doublet of redemption), rampart, etc.

It was used from Middle English in forming words from Germanic as well as Latin elements (rebuild, refill, reset, rewrite), and was used so even in Old French (regret, regard, reward, etc.).

Prefixed to a word beginning with e, re- is separated by a hyphen, as re-establish, re-estate, re-edify, etc. ; or else the second e has a dieresis over it: as, reëstablish, reëmbark, etc. The hyphen is also sometimes used to bring out emphatically the sense of repetition or iteration : as, sung and re-sung. The dieresis is not used over other vowels than e when re is prefixed : thus, reinforce, reunite, reabolish. [Century Dictionary, 1895]

Old English macian "to give being to, give form or character to, bring into existence; construct, do, be the author of, produce; prepare, arrange, cause; behave, fare, transform," from West Germanic *makōjanan "to fashion, fit" (source also of Old Saxon makon, Old Frisian makia "to build, make," Middle Dutch and Dutch maken, Old High German mahhon "to construct, make," German machen "to make"), from PIE root *mag- "to knead, fashion, fit." If so, sense evolution perhaps is via prehistoric houses built of mud. It gradually replaced the main Old English word, gewyrcan (see work (v.)).

Meaning "to arrive at" (a place), first attested 1620s, originally was nautical. Formerly used in many places where specific verbs now are used, such as to make Latin (c. 1500) "to write Latin compositions." This broader usage survives in some phrases, such as make water "to urinate" (c. 1400), make a book "arrange a series of bets" (1828), make hay "to turn over mown grass to expose it to sun." Make the grade is 1912, perhaps from the notion of railway engines going up an incline.

Read the valuable suggestions in Dr. C.V. Mosby's book — be prepared to surmount obstacles before you encounter them — equipped with the power to "make the grade" in life's climb. [advertisement for "Making the Grade," December 1916]

But the phrase also was in use in a schoolwork context at the time.

To make friends is from late 14c.; to make good "make right" is from early 15c.  To make do "manage with what is available" is attested by 1867; to make for "direct one's course to, proceed toward" is from 1580s, but "Not frequent before the 19th c." [OED]. To make of  "think, judge" is from c. 1300. To make off  "run away, depart suddenly" is from 1709; to make off with "run away with (something) in one's possession" is by 1820. To make way is from c. 1200 as "cut a path," early 14c. as "proceed, go."

Make time "go fast" is 1849; make tracks in this sense is from 1834. To make a federal case out of  (something) was popularized in 1959 movie "Anatomy of a Murder;" to make an offer (one) can't refuse is from Mario Puzo's 1969 novel "The Godfather." To make (one's) day is by 1909; menacing make my day is from 1971, popularized by Clint Eastwood in film "Sudden Impact" (1983). Related: Made; making.

also re-made, past-participle adjective from remake (v.).