Is Apex in use?

Application Express (APEX) is installed by default with the 11.1 and higher database. This document describes a couple of methods that can be used to determine whether APEX is in use, or if it can be deleted.

Solution

Determine the number of workspaces in the instance by logging in to SQLPLUS as either SYS or SYSTEM and run the following query:

select workspace, workspace_id from apex_workspaces;

This should return a single workspace: INTERNAL / 10 for a brand new installation. If only this workspace is returned, then you can be reasonably certain that this installation is not actively being used, since there are no applications defined. If the query returns more than one workspace, then that indicates that this installation has been active at some point in time.
Then run next query as SYS

select workspace, view_date, seconds_ago from apex_workspace_activity_log;

This will show if anyone has used APEX in the past. For non active Apex, no rows should be returned.
If both queries return mentioned results you might suppose that Apex is not in used. But to be sure, you have to make another check.
Check dba_source (and all other sources that you have) that they do not reference something like %WWV_FLOW% or %APEX% in int's content.

The End

Assuming that there are no indications that the installation is active, you can remove APEX by following the instructions Application Express Installation Guide > Cleaning Up After a Failed Installation > Removing Oracle Application Express from the Database.

Hope this helps someone.

Cheers!