Formula to generate a grade I hope this question is appropriate for this site, if not sorry in advanced.
I'm trying to come up with a formula to generate a grade, which will take into consideration
the diffculty level of the questions.
The person taking this quiz can determine the diffculty of the questions so I want the result to give more credit to the harder questions, because if someone answered 8/8 questions correctly in level 8, it's much harder than answering 8/8 correctly in level 1.
Each one is asked X questions in 1-8 levels, but not necessarily all of them.
For example lets say X was 60 and these are the results:
5/9 - level1
4/9 - level2
3/8 - level3
3/7 - level4
4/8 - level5
0/0 - level6
2/10 - level7
1/9 - level8
Does anyone have an idea for such a formula?
 A: Try giving different number of points for different level correct answers: a correct answer for level 1 is worth 1 point, for level 2 is worth 2 points, and so on. Then one would need more correct answers on a low level to get a high score than if they attempted high level questions.
A: There are many functions that will work for what you want. I'll describe one group of such functions.

You could use increasing "weights" $w_1, w_2, \dots, w_8$ with $0 < w_8 < 1$ and, for all $n$ between $1$ and $7$ $$0 < w_n < 1 \qquad \text{and}\qquad w_n<w_{n+1}$$
$$\text{and} \qquad \sum\limits_{k=1}^8 w_k=1$$
If the fraction (number answered correctly over the number of questions for that level - not the number that they answered otherwise you could get $0/0$) that a person gets right on a level $n$ is $f_n$, then their total score will be $$\sum\limits_{k=1}^{8} w_kf_k$$
This score will have a maximum of $1$ and a minimum of $0$. 

Depending on how you assign the weights, this score could change quite a bit, but because the weights satisfy the restrictions I've stated in the first part above, the higher levels are more important. 
