Should I change "index" to "indexes", and thus "was" to "were", and "that of" to "those of"?
That doesn't really get rid of the ambiguity, it just changes it to a different ambiguity.
A reduplication of the preposition can help here to make explicit how many there really are.
In urban areas, the graduation index of (or for) general high school
and [of ...
The part of the backboard that connects to the rim is know as the 'break-away' or the 'break-away rim'. It is designed to release the force from the jump and to prevent damage to the backboard and rim.
See the Wikipedia entry