Answer: present participle: beginning. Past participle: begun.
Explanation: a participle is a word formed from a verb and used as an adjective or a noun. In English participles are also used to make compound verb forms. To form a present participle, we need to add "-ing" to the root of the verb, and to form a past participle (on a regular verb) we add "-ed" to the root of the verb. In the case of the verb "to begin" the present participle is "beginning" and the past participle is "begun" (it is irregular).