I figured it out. First UbuntuGIS appears to only support LTS releases. I ended up not using or needing UbuntuGIS.
To install the newest version of QGIS I added the QGIS repositories to my /etc/apt/sources.list file:
sudo nano /etc/apt/sources.list
and inserted these lines:
deb http://qgis.org/debian vivid main
deb-src http://qgis.org/debian vivid main
Remember to add the GPG keys as follows:
gpg --keyserver keyserver.ubuntu.com --recv 3FF5FFCAD71472C4
gpg --export --armor 3FF5FFCAD71472C4 | sudo apt-key add -
Then run:
sudo apt-get update
sudo apt-get install qgis python-qgis qgis-plugin-grass
This installed qgis 2.10.1