It's very easy to wirelessly display the screen from your Apple iPad Air 2 to a TV using the Apple TV box. Just swipe your finger from the bottom and press Apple TV.
You can choose to just mirror your iPad screen onto the TV using AirPlay.
If you want to play a movie or song from your iPad onto the TV, you don't need to use mirroring.
All you just need to do is use AirPlay to select the Apple TV as the destination for where you want to have the movie or song played
Here I was able to watch Wallace and Gromit from my iPad to a Panasonic TH-L42U20W TV connected to the Apple TV (2013) using HDMI.