Answer: An example for the first one
Explanation:
Part of speech: The student's work is progressing
Meaning: The student's work is increasing in skill and level, it is getting closer to the leveled difficulty assigned
The word FOR in the sentence is used as both C. a preposition and a conjunction.
A is incorrect because a gerund ends in -ing. The word for is neither a noun or adjective or an article (there are only three articles: a, an, the) or a verb, so only C is correct.