I have an A.A. from NYC Technical College and a B.A. from Lehman College in the Bronx. Do I have to take a department test to enter as a math major? Do I have to take a school exam to graduate?
You would probably have to do a math placement test, but other than that, i don't think so. your best option is to
talk to an adviser. Prof. Joseph Bak is the guy you want to ask
if you haven't done advanced calculs 1,2, and 3, (or the equivalents of MAT 323 and MAT 318 at CCNY) you can forget about attempting any graduate study in math, and even several undergraduate courses. they won't allow you to graduate unless you have these courses under your belt, even if you enter with credits in other graduate math courses.
you say you have degrees in non-math subjects. this hardly matters (as far as becoming a math major is concerned, it should save you from the general core requirements though), what level is your math at?