Mr. Nguyen scores his test in a unique way. A student’s score on the exam is directly proportional to the number of problems on the exam and inversely proportional to the square root of the number of problems a student misses. Let $S=$ the student’s score, $p=$ the number of problems on the exam and $m=$ the number of problems missed. 

1. Write an equation that calculates a student’s score. Do not forget the constant of proportionality.

   Answer (a):

   $S(q)=\frac{kp}{\sqrt{m}}$

2. On the last exam, there were $25$ questions and Saadia missed $4$. Her score for the exam was $90$. On the same exam, Alex missed $9$ questions. What was Alex’s score?

   Hint (b):

   1. Substitute Saadia’s information into the equation in part (a) and solve for $k$.
   2. Rewrite the equation with the known $k\text{-value}$.
   3. Determine Alex's score.

3. Mr. Nguyen’s exams are REALLY hard! No one has ever gotten all of the problems correct. Based on his scoring method, what will happen if a student gets every problem correct?

   Hint (c):

   What happens when the denominator is $0$?