He didn't conquer China-not much of it, at least.
Quote from Wikipedia "While Genghis Khan never conquered all of China, his grandson Kublai Khan completed that conquest,"
It was on or more of his decendants who conquered China. Kublia Khan is the best known one.
See:
http://en.wikipedia.org/wiki/Genghis_Khan
http://en.wikipedia.org/wiki/Kublai_Khan
And, for extra marks at school, read and memorize this poen:
http://en.wikipedia.org/wiki/Kubla_Khan
Cheers,
StrawCat.