My Nexus 4 has a Battery Problem

Using my Nexus 4 for 10 minutes often equates to a 10 percent drop in battery life. Taking it to school on a full charge and not unlocking it once until I'm back home usually finds the battery down to almost 50 percent.

I got my device in January and this didn't become a problem until recently. I have to assume I downloaded an app that's constantly draining my battery somehow in the background, or Chrome or Currents won't stop syncing or something.

Advice from anyone who can help me get to the bottom of this would be much, much appreciated. Thank you.