Dear Ben

 Please consult

https://sites.math.rutgers.edu/~zeilberg/Hist21/q2S.pdf

for the full solutions.

#1: 1 point
#2: 0 points
#3: 1 point
#4: 2 points (you had to explain, but this time I did not take points off)
#5: 1 point (right formula, but no proof.  I am curious where you was it before. It is not one of the famous ones)



So You got 5 points (out of 10). Good job!

 Best wishes,

   Dr. Z.