Sync iPad 2 before upgrade iOS
Prior to upgrading, attempt the "transfer purchases" option in iTunes. With your iPad plugged in, go to "File" --> "Transfer Purchases from iPad". See if that transfers over your free applications as well. (I've had to do this sometimes to get all mine to transfer.) Note that this may take awhile to do.

Also note that this only transfers free applications from the app store, not built-in apps like the calendar, camera, etc.

And finally note that I've had occasions where even after I've transfered purchases multiple times, and can verify that everything did transfer correctly, that the upgrade process still insists that there are purchases that haven't been transferred. At that point, knowing I've done everything I can do, I ignore the warning and proceed with the upgrade. Probably won't happen to you, but something I've experienced in the past, so thought I'd pass it along.