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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 ,  and .

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

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

    1. Substitute Saadia's information into the equation in part (a) and solve for .
    2. Rewrite the equation with the known .
    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?

    What happens when the denominator is ?