Transmutation of scores

Question

Can you please help me to come up with a formula for transmuting raw scores into percentages the conditions are : The passing score is 40% which is the equivalent is 75, the lowest possible score has the equivalent of 70 and the highest possible score has the equivalent of 99.

Lets say 50 items. if the student get a score of 50 the equivalent is 99, if the student get a 0 the equivalent is 70 and if the student get the 40% of the total items for example 20 the equivalent is 75 because the 40% of 100 is 20.

my formula for base 50 is 50 * (RawScore/TotalItems) + 50. I want to come up with the formula for passing score for 40% which is equivalent to 75. I need the formula that i will input a raw score and the total items.

Thanks for the help, please help me.

Answer 1

$\frac{11x^2}{4000}+\frac{3x}{200}+70$ is the equivalent.

Where $x$ is the percentage.

If you put $x=40$ you get output as $75$

If you put $x=100$ you get output as $99$

Answer 2

As a general comment, decisions on the meaning of grading (and fixing grades) after the fact is a terrible idea.

What you should do is to fix some abilities your students are supposed to master in your class, define your exams to check that. A "pass" means they fullfill expectations, and goes up from there.