Your iPad shouldn't have a problem doing this.
When displaying the content you wish to mirror on the iPad 2 (or better), iPad Mini, iPhone 4S (or better), double tap the home button (quickly) and swipe the bottom row of apps to the right to reveal the playback controls, tap the AirPlay icon and select your Apple TV from the list of available devices.
Your Mac can only do it if it is capable of mirroring.
AirPlay Mirroring requires a second-generation Apple TV or later, OS X 10.8 or better and is supported on the following Mac models: iMac (Mid 2011 or newer), Mac mini (Mid 2011 or newer), MacBook Air (Mid 2011 or newer), and MacBook Pro (Early 2011 or newer).