Participial phrases generally occur after nouns. They are actually reduced (shortened) relative clauses. Present participles (which always end in -ing) are used to reduce adjective clauses that contain active verbs.
Minnesota, which joined the Union in 1858, became the thirty-second state.
(adjective clause with active verb)
Minnesota, joining the Union in 1858, became the thirty-second state.
(participial phrase with a present participle)
Most past participles end in -ed, but there are also many irregular forms. Past participles are used to reduce adjective clauses with passive verbs.
William and Mary College, which was founded in 1693, is the second oldest university in the United States.
(adjective clause with a passive verb)
William and Mary College, founded in 1693, is the second oldest university in the United States.
(participial phrase with a past participle)
Participial phrases can also come before the subject of a sentence.
Joining the Union in 1858, Minnesota became the thirty-second state.
Founded in 1693, William and Mary College is the second oldest university in the United States.
Usually, the participle itself is missing from this type of Structure item, but any part of a participial phrase as well as parts of a main clause may be missing.
∇ Sample Item
Natural resources provide the raw materials ________________ to produce finished goods.
(A) needed
(B) are needed
(C) which need
(D) needing
Option (B) is a passive verb; the sentence cannot contain two main verbs (are needed and provide) in the same clause. Choice (C) creates an adjective clause, but the verb in the clause is active and a passive verb is required. (However, a relative clause with a passive verb (which are needed) would be a correct answer.) Choice (D) is a present participle and has an active meaning; a past participle is needed. Therefore, the answer is (A).