Pre-med per se does not generally require math beyond single variable calculus and (sometimes calculus-based) statistics.
Note, however, that some medical schools do not accept AP credit for some or all pre-med courses, so if you complete single variable calculus with a high enough AP calculus BC score, then you may want to take a more advanced college math course like multivariable calculus.
Of course, if your major requires more math than pre-med does (e.g. math, statistics, physics), or if you are just interested in math, then you may want to take more math anyway.