iOS 7 Apps on iPad show up as installed but are not actually installed
If they are installed, then the App Store should now say OPEN instead of buy, or re-download etc.

You can try to find the apps with Spotlight to see if they are just hidden icons (various bugs can hide your apps on occasion) or genuinely not installed; just swipe down from the center of the screen and search for the apps name.  if it finds it, then:

Settings &gt; General &gt; Reset &gt; Reset Home Screen will bring back all your missing icons, at the expense of removing all your folders and putting the pre-installed apps back to their original positions.