According to the Oxford Companion to the English Language (1992), "A large part of the lexicon of Latin has entered English in two major waves: mainly religious vocabulary from the time of Old English until the Reformation, and mainly scientific, scholarly, and legal vocabulary . . . from the Middle Ages onwards." The influence of classical Greek on English has been largely indirect, through Latin and French.
In general, the further a person progresses educationally the more likely he or she is to have a need for English words derived from Greek or Latin roots.