With older iPads (notably the iPad 2) and iOS 8.2, use this trick if Airplay is not available.
Airplay may not show on your iPad after upgrading to iOS 8.2 or later:
Use these steps to get it going:
Touch “Airplane mode” (which turns off wireless and Bluetooth)
Touch “Airplane mode” again to switch wireless and Bluetooth back on. After a few seconds, the Airplay icon should appear.
Scroll through the list of available devices to find your Apple TV
Move the mirroring switch to the right to start using your Apple TV