"Exceed," "surpass," "excel," and "outdo" all mean to go beyond a certain limit, measure, or degree. "Exceed" suggests going beyond a limit set by authority, custom, or earlier achievement (as in, "she exceeded the speed limit" or "he exceeded his authority"). "Surpass" suggests being greater in worth, merit, or skill (as in, "the book surpassed our hopes" or "profits from the bake sale surpassed our goal"). "Excel" suggests supremacy in achievement or value, (as in, "she excels in science" or "he excelled at writing"). "Outdo" suggests bettering one's previous work (as in, "the chef really outdid herself this time").