The Final Exam Theorem (or Postulate)

Wow!  It has been a while since I have written anything new.  I debated shutting down the blog but I really like writing on here.  I wish I could say I was extremely busy, but it actuality that's not the whole story.  Between this semester being nothing more than taking classes and reading literature, and a personal life which has been anything but smooth, finding the time and desire to write interesting stuff has been tough as of late.  However, I have been getting my ducks in a row and I really want to keep this thing going.  (Also, a couple friends of mine have rejuvenated their blogs and I felt inclined to follow suit.  Check them out; Mildly Competent and The Pit.)

Here at Purdue, finals are almost upon us again.  The air is warm, the trees are in bloom, I want to play golf instead of spending hours studying.  This leads me to my first theorem of my graduate career.  I present to you the "Final Exam Grade Theorem."  Now before I get to the carefully derived equation let me explain to you the inspiration behind it.  I felt that the amount of time spent studying can be correlated to your exam score but that as the more you study the less of an increase in you score (not a decrease in your score but a decrease in the amount you can improve your score).  With that in mind here is the equation...

Where EG=Final Exam Grade (out of 100), GPA=Your Cumulative GPA (or what kind of student are you; A student=4.0, B student=3.0, etc), A=attendance rate where 1 is attend all classes and 0 is attend no classes, and t=time spent studying for the final in hours.  Below is a graph of various degrees of GPA and Attendance rates.  It is quite interesting considering a 4.0 student who attends every class needs to study for about 4-5 hours to get a perfect score, compared to the 3.0 student who went to class with him/her who needs to study for 17-18 hours, and their poor 2.0 friend who went to every class with them but still needs to study for 37 hours.  

Now for my assumptions.  I am assuming that a 4.0 student who attends every class can get an 80 percent on the final if they study 0 hours.  And I honestly believe that if you go to every class and pay attention, do the homework and assignments, you can study nothing at all and get at least a C on the final (a genius 4.0 student should be able to do better than that, so I set that at 80).  Next, the attendance rate.  I used the 1/e^(1-A) because it if you attend every class (A=1.0) then it is directly related to how well you have done in school before (GPA).  But as you stop going to class it decreases in an exponential fashion.  At A=0 however, I did not want it to completely eliminate the GPA term, thus the e term to only fractionly decrease your base score. 

Lastly, the time spent studying term. I used my own experiences, GPA, and attendance rates to come up with the constant of 98.7.  And the square root comes from the idea that the more you study, the less of a change in your grade it will make. Overall, I have realized through explaining my theorem, that it is anything but a theorem and more of a postulate at this point.  Meaning it needs to be proven.  I would love to collect data from people and try and formulate a better equation that includes difficulty of the class, pre-requisites taken, and year in school (freshman, soph, etc).

Since I have either throughly confused you, annoyed you, or intrigued you, I ask for you to stew it over and plug in your own numbers to see where you stand.  If it is reasonable, great.  If not, sorry about luck. After I formulated the equation I tried it on my sophomore Physics class as it was my first all-nighter for an exam.  I had a GPA of 3.7 at the time, I went to almost all the classes (A=0.9).  With that, I remember having a 12 hour turn around between finals before my physics final.  I stayed up all night and got a 95% on the exam (I needed that score to get an A in the class, hence the motivation).  If you plug in the numbers to the EG equation it gives about 8 hours of studying to reach the grade of 95%.  If you assume that I ate two meals, and took breaks with my all-nighter that's about 8-9 hours.  Not too bad!