To create a new scale for a maximum of 82 points, where 82 points correspond to 100 final points, you can use the concept of proportionality.

First, calculate the ratio of final points to initial points for the given scale: - For the initial scale, the ratio of final points to initial points is (8-7)/(12-7) = 1/5. - For the final scale, the ratio of final points to initial points is (100-1)/(82-1) = 99/81.

Now, apply this ratio to each initial point from 1 to 81 to determine the corresponding final point:

For 1 initial point: (1/5) * (99/81) = 99/405 ≈ 0.2444 So, for 1 initial point, the student would get approximately 0.2444 final points.

For 2 initial points: (2/5) * (99/81) = 198/405 ≈ 0.4889 So, for 2 initial points, the student would get approximately 0.4889 final points.

Continue this process for each initial point up to 81, using the ratio (99/81) to determine the corresponding final points.