Almost all classrooms now have some form of smart board (we have Promethean Boards in my school). I knew that the iPad 2 had AirPlay Mirroring, and I thought it might be useful to show how I connect my iPad to the smart board without using an Apple TV (I am still investigating the potential of an Apple TV, but wanted to try a cheaper alternative first).
I tend to have lots of PPTs and Keynote presentations for my lesson, but because my pupils tend to be in the workshop working I don't use a smart board for its intended purpose as often as I would like. So for those non interactive lessons, it's faster to connect my iPad to the projector than it is to boot up the desktop that is attached already.
So to connect your iPad to a projector you will need the following
I connected the HDMI cable to the back of the projector and then fed it down through the trunking,so it would always be available.
When you are ready to show your presentation you need to connect the iPad through the HDMI connector and select the correct source on the projector (mine has a source button which you press, then select HDMI).
Because I was using Keynote and I also have an iPhone, I was able to use Keynote Remote which allows me to move through the presentation without having to go near the iPad. You have to be on the same wifi network for it to work.
Keynote remote was very easy to setup, you can see the opening screen and controlling screen here.
If your projector doesn't have an HDMI input, then you can also get a VGA connector. In my department teaching space we have 4 different classrooms. Frustratingly, 2 of them use HDMI and the other 2 use VGA. So I have both types of connectors, but as yet I haven't managed to purchase a VGA cable so I've not been able to test the VGA connectivity.