<p>Good to have diversity and depth. Being President of two diverse things like Math club and Student Gov. and Football team Captain with being a part-time computer programmer and lab intern would certainly raise eyebrows (in a mildly good way) in my opinion, and you're going in that direction.</p>
<p>Passion is important, make sure you demonstrate that you are passionate for one to 3 activities.</p>
<p>They all seem academically related, so no, not "nothing to do with each other." You're fine, maybe the diversity/depth will help out more.</p>
<p>This passion thing is overrated imo, anytime someone doesn't have a host of activities/tests/etc toward one area, it's auto-regarded as "passion-lacking"...which isn't true.</p>