Check if a student will pass an MCQ exam with negative marking Here is a scenario:
We have an MCQ exam with 100 questions.
Every 3 wrong answers will remove 1 correct answer.
The Minimum needed score to pass this exam is 50
I'm using the following formula :
score = ( (correct * 3) - wrong) / (3 * total)) * 100;
now, I will calculate the student's score on each question, at what point should I decided that this student will not pass the exam no matter what he would do on the remaining questions?
I have not slept for almost 96 hours and I can't think clearly at this point
 A: If the student answers all the questions, and the number of questions answered correctly is $r$ and the number answered incorrectly is $w$ we have $$r+w=100$$ and in order to pass, the student needs $$r-\frac w3\geq50$$  Eliminating $w$ gives $r\geq 62.5$ and since $r$ must be an integer, we have $r\geq63$, which implies $w\leq37$.  When the student has answered $38$ questions incorrectly, there is no possibility that he will pass.
The foregoing only applies if the student answers all the questions, but a student may skip some questions.  I think the easiest thing to do is to keep a running score.  If the student has answered $r$ questions correctly, $w$ incorrectly, and skipped $s$ questions, his score up to this point is $$r-\frac w3$$ and there are $100-r-w-s$ questions remaining, so the highest score he can possibly achieve is $$r-\frac w3+100-r-w-s=100-s-\frac{4w}{3}$$ If this is less than $50$, the student has no chance.  Furthermore, the minimum number of questions he must answer correctly in order to pass is $50$ minus his current score, round up to the next integer, if necessary.
For example, suppose the student has seen $60$ questions, answered $40$ correctly, skipped $15$, and answered $5$ wrong.  The student's score to this point is $$40-\frac53=38.333$$ so the student needs to answer at least $12$ more questions correctly.
If it were me, I would be reluctant to tell a student, "You must answer at least $12$ more questions correctly in order to pass," for fear he would interpret it, or at least say he interpreted it, as "If you answer at least $12$ more questions correctly, you will pass," which isn't true, since he might answer $12$ right and $28$ wrong.  I would rather show the current score and the number of questions remaining.  Then if a student sees that his current score is $40$ and there are only $9$ questions remaining, he will easily understand that he has no possibility of reaching $50$ and passing.
