Hey!
Hopefully this reply might still be useful!
There isn't any particular method your exegesis must follow. Have a look at past assessor's reports - that should give you a good idea of what to incorporate.
These are my notes from last year, which worked well for me;
General notes:
- Read passage at least twice
- Porcupine the passage for points such as literary forms and literary techniques
- Take note of ALL the highlighted words/phrases
- Underline aspects that can be annotated as a theme central to the passage
YOUR WRITTEN EXEGESIS:
1) State the context of the passage
- What happened just before the passage? What occurs just after it?
- Give the setting. Where it is occuring? Who is involved?
2) Literary forms & literary techniques
- state the overall literary form of the passage
-include any literary techniques
- comment if appropriate on the structure especially if it aids understanding of the text e.g. chiasm, dialogue
e.g. is it a narrative, miracle, pronouncement story? Parable? Combination?
- Does it employ discourse, dialogue, proverbs, hymn, apposition, chiasm etc? Does this add to our understanding of the passage?
3) What is the general thrust of the passage; the theme or themes?
4) How do the theme/themes have relevance to Luke's community.
Note that there may well be a message for Jesus' original audience and this could be extended to include the Lukan audience
Consider need for inclusivity, problems of apostacy, mission and discipleship etc.
5) Conclusion - give a brief summary of your exegesis explaining the overall importance of this passage and its significance to Luke's community.
Best of luck