Can I adjust iPad display size to make it fit the screen better? I have an iPad mini (original model) running iOS 8.4
Recently I have noticed many apps seem to be too large for the screen; usually the top or bottom is partly off screen.

When I press the button, the home screen displays normally for a few seconds, then seems to "grow" e.g. the iPad in the top left now shows "Pad" wth the "i" off the screen.

This may have been since a software upgrade, but I can't be sure.
Perhaps you have somehow turned on the Zoom feature of Accessibility? 


Open the settings app
tap general
tap accessibility
turn off zoom


If you need more details, the following article might help

https://www.apple.com/ios/accessibility-tips/