1)Taken for granted by most of us, paper is an esseantial part of our lives
participle:essential modifies:part
2)The papeer used today has developed over many centuries
participle:used mod.:paper
3)Ancient Egyptians wrote on a sheet formed from stalks of a reed
Part.:formed mod.:sheet
5)Cut down, the reed stalkswere sliced into thin strips
part.:cut down mod.:reed stalks
6)can you imagine the laborers working in the hot sun
part.:working mod.:laborers
8)Modern paper, however, started with a chines inventor serving emperos he di
part.:serving mod.:emperor
9)The inventor's was Cail Lun, also spelled Ts'ai Lun.
part.:inventors mod.:name
10)Arabs fighting near chinas borders captured chinese papermakers and brought their art to the west
part.:captured mod.:chinese
Your correct answers are 2, 3, 5, 6. The participal in 8 is also correct.
Remember what Writeacher explained: participles are forms of verbs.
In # 1, "essential" is not a form of a verb; it is not a participle.