Can a Bechor make a Siyum on a Masechta of Mishnayos to absolve your obligation to fast.

Thank you for your question. There is a disagreement amongst the poskim about this. Some say that a siyum masechet Mishna is considered the equivalent of a siyum masechet Gemara which is what is required to exempt first born males of the fast on Erev Pesach. Others say that a siyum over a book of Mishna is not suitable. Since there is a disagreement about this it is preferable to finish a masechet of Gemara. However, if it is too difficult for one to finish a masechet of Gemara or if it is very important for someone to do a siyum on a masechet of Mishna that he learned seriously with commentaries (especially if he learned an entire seder/order of Mishna), then he may do so. Sources: see Chazon Ovadia Pesach (Taanit Bechorim, 10, comment 45), who says that 'be'shaat hadchak' (meaning if there is a special or urgent need to do so), if one learned an entire masechet of Mishna with the interpretation of Rabbi Ovadia of Bartanura and some of the Kitzur Tosafot Yom Tov he may do a siyum over that-- but he adds that if someone does do a siyum on Mishna he recommends that it should only be for himself and not to break the fast of other people who listened to the siyum. See Mikraei Kodesh by Harav Harari, Pesach (1:31) who lists the poskim who said that one masechet Mishna isn't enough for a siyum but a whole seder of Mishna is considered so. See also Peninei Halacha Pesach (13:5). Hagaon Harav Shlomo Zalman's opinion is brought in 'Halichot Shlomo' (erev pesach, comment 6) that a Mishna is not considered to be suitable for a siyum. However, once a soldier asked him about fasting on Erev Pesach and no one there was doing a sium. Harav Shlomo Zalman told the soldier to read Masechet Avot from the siddur and that will be considered as a siyum for him (The reason is that Harav Shlomo Zalman held that the soldier was actually exempt from the fast). See also Kol Mishalotecha (page 338) where Harav chain Kanievsky was asked if a siyum masechet Mishna or a siyum seder Mishna is considered a siyum masechet. Harav Kanievsky answered: "some say yes and some say no". If someone is intent on doing a quick siyum, I will mention that I heard Hagaon Harav Asher Weiss say that the shortest masechet in the entire shas is masechet Makot Yerushalmi. There are only 9 dapim in the masechta, and two of them are Mishnayot without Gemara. I therefore recommend learning this masechta if time is of the essence and knowing it well. This way one can do a siyum masechet 'lemehadrin' in a very short time. All the best!