The broad topic for this question is: The Relationship(s) of Second Temple Judaism(s) and Early Christianity.
Part 1: Briefly explain the difference between "Second Temple Judaism(s)" the "the Jesus Community" that arises as a result of the Jesus' life, ministry, and death. Briefly explain how "the Jesus Community" at its earliest stages (during the lifetime of Jesus and just afterwards) related to Second Temple Judaism(s). (Hints: Look at the Cambridge Companion for help here. Historically and theologically, what did Jesus and the first generation of his disciples have in common with Second Temple Judaism(s)? Around what issues might they have diverged from Second Temple Judaism(s)?)
Part 2: Briefly explain the development of early Christianity relative to Second Temple Judaism(s). That is, in the years following the death of Jesus (roughly the last 60 years of the first century), in what ways did the ongoing communities of followers of Jesus relate to Second Temple Judaism(s) and in what way did they distance themselves from Second Temple Judaism(s)? What issues and events seem to sharpen the distinction between these generations of believers and Second Temple Judaism(s)? (Hints: You may wish to consider portrayals of the relationship found in the Letters of Paul, the Gospels, and the Acts of the Apostles. You should also consider the ways in which these Christian texts use and reinterpret Hebrew Scriptures.)
Part 3: (Thinking question): Given your comments in the preceding sections, how does this study of the origination of Christianity help us understand the Christian religion/ faith today? In what way is Christianity related to Judaism(s) and in what way is it a separate religion or faith. (hint: in this section you should give some broader reasons based on reflection about the overall importance of this course for understanding yourself as a thinking person in western society. An "A" answer will need to devote more than just a passing reference to this larger, "thinking" part of the question.
Final hint: If you choose to only write the longer essay, make sure that Part 2 of this essay includes a significant discussion of how the OT is used in the NT. You want to show me that you are able to tie together these two parts of the course. This is helpful for those that write this essay as part of the final, but those students will also be able to demonstrate an understanding of the OT from questions that discusses OT prophecy in the NT.