Q: Using iTunes Match, I have managed to fill my iPad mini to capacity with music. I would like to remove some songs to free up space. The problem is that the iPad lists ALL music, whether on the iPad or not. Is there a way, without weeding through the entire library album by album, to determine what is actually downloaded to the iPad?

A: Definitely. In the iOS Settings app, under the Music section, you’ll see a “Show All Music” option. Simply toggle this OFF and anything that hasn’t been downloaded to your device will vanish from the Music app.
Once you’ve done this, you can go into the Music app and remove individual tracks, or even entire albums or artists, simply by swiping right-to-left and tapping the “Delete” button that appears.
Note that if you simply want to remove everything that’s been downloaded to your device and start from scratch, this is an option as well. See Deleting your on-device iOS music library with one swipe for more information.
Once you’ve removed whatever you want, simply go back into the Settings app and toggle the “Show All Music” option back on, and you’re good to go. Note that this same basic process can also be used for Videos; a “Show All Videos” option found in the Videos settings works in much the same manner.