Math Is Fun Forum

I am an eleventh grade student taking HL1 Math for the IB diploma.  For the uninitiated, HL Math is essentially AP calculus, but covering more topics.  Anyways, students have to do an Internal assessment, which in Math, takes the form of an investigation of the student's creation.  I was wondering if anyone in this marvelous forum could hook me up with some investigation ideas, maybe centering on calculus, infinity, e, or 0.  Really though, I'll take any ideas.  I know the equivelent of College Freshman differential Calculus and Integral calculus, along with implicit differentiation.