Hopefully someone will come along with a fresh answer! In the meantime, you might enjoy this related response (a follow-up) from /u/Vox_Imperatoris to:
There are also some sample questions elsewhere in the same thread.
Some relevant past discussion on the topic:
u/Tiako on the general structure in https://www.reddit.com/r/AskHistorians/comments/ydtya/what_were_the_questions_on_ancient_chinese_civil/
u/Vox_Imperatoris with more details on the types of questions and required answers in https://www.reddit.com/r/AskHistorians/comments/2nrv12/what_was_the_actual_content_of_chinese_civil/ and u/xingfenzhen providing the questions on the last exam administered (of course, this was Qing rather than Ming).
[deleted] providing a useful reference in https://www.reddit.com/r/AskHistorians/comments/1br6t2/chinese_imperial_civil_service_exam_ming_dynasty/ - Benjamin A. Elman, A Cultural History of Civil Examinations in Late Imperial China, University of California Press, 2000.
Elman's book is a great resource for learning more about the Ming-Qing examination system. Comprehensive, and lots of stuff that is difficult to find elsewhere, e.g., pp 388-399: A close look at the eight-legged essay, with two examples by Wang Ao (1450-1524), a first-ranked examinee twice (running into a jealous examiner for the 3rd (palace) examination, who was the only Ming three-times first-ranker and wanted to preserve that status). Despite his difficulty with his third exam, Wang Ao's 3rd essay was regarded as great, and his writing influence future essays greatly.
If the first two past answers don't satisfy, try Elman's book for 800 pages of juicy examination goodness.