B. Ten end-of-course exams were failed by ninth graders this year, a first for Lollapalooza High.
The most accurate way to describe the excerpt is to choose the option - it is a dependent clause. This means that something needs to be added - you need to finish the sentence so that it becomes an independent clause, and not a subordinate one.
The second sentence, because "sometimes anything" goes with the verb form "beats". "Sometimes anything beats" is more correct than "sometimes anything beat"