Randy's class is studying world history. *

Is that base, past, past particle, or present particle?

Randy's class is studying world history, is a present participle.

Explanation:

In English, present participle is a kind of verb which usually ends in 'ing.' For example: She is thinking. Here, 'thinking' is a verb form and a present participle. Similarly crying, laughing, playing, doing are all examples of present participle. The sentence, 'Randy's class is studying world history' is a present tense where the verb 'studying' acts as a present participle.