I wish I could help you but all I know is you can record the screen with QuickTime if you click one of the tabs on the top. Not sure which one if it's file or something but you can use that to record your ipad screen. Perhaps you can leave it like that displayed and just don't press record but I can't think of another way to do it. Especially if you are not jailbroken. Are you jailbroken?
Edit: Got it! You got to Quicktime, File, than Movie Record. Than you will see a red record button, next to it will be a downward pointing arrow.Click the arrow and select the name of your ipad and you will be good.
Another possible option for you: I don't know anything about iMacs, but if the monitors are like any standard monitors, then you can get a cable that hooks up to your iPad (or possibly iPhone, I've never tried that), and connects to a monitor. I've got one.. mine is the old 30-pin iOS cable on one side (for my iPad 2), to a VGA on the other side. It works pretty good, although you still need to hold the iPad since there's no way to use a mouse without jailbreaking.
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Edit: Got it! You got to Quicktime, File, than Movie Record. Than you will see a red record button, next to it will be a downward pointing arrow.Click the arrow and select the name of your ipad and you will be good.