Dear Wentao,

 Please consult

https://sites.math.rutgers.edu/~zeilberg/Hist21/mt1S.pdf

for the full solutions.

You got  62  points (out of 120).

Here is what you got wrong:


#1: -4 points (P does not have to be prime, it may be composite, but it does a prime factor different than p1,p2,..., pk)

#2: -10 points (see answer key)

#5: -5 points (you did not explain how you constructed it, it is not the one we get using the usual method)

#6: -3 points (you did not have dates to many of them)

#8: -6 points (Greek math was proof based, and Thales was the father)

#9: -10 points (see answer key)

#11: -10 points (see answer key)

#12: -10 points (see answer key)








 Best wishes,

   Dr. Z.