Q: why cant the apps installed on my ipad be determined

Hello Rachael,

Thank you for the details of the issue you are experiencing when trying to sync your iPad.  I recommend signing out of the iTunes & App Store setting, resetting your iPad, and trying to sync again. 

Follow these steps to sign out of the iTunes & App Store:

Changing your Apple ID account

Tap Settings > iTunes & App Stores, then tap the Apple ID signed in.

Sign out of the current Apple ID account and then sign in with another account or create a new Apple ID.

iOS: Changing the signed-in iTunes Store Apple ID account

http://support.apple.com/kb/ht1311

Next reset your iPad:

Resetting your device

You can reset it by pressing and holding both the Sleep/Wake and Home buttons for at least ten seconds, until the Apple logo appears.

iOS: Turning off and on (restarting) and resetting

http://support.apple.com/kb/ht1430

Finally, try syncing your iPad again. 

Thank you for using Apple Support Communities.

Best,

Sheila M.