B2. Students Gregor, Matej, and Miran were retaking a math test. The results of the first and the retake test are shown in the table below.

|  | First Test |  | Retake Test |  |
| :--- | :---: | :---: | :---: | :---: |
| Student | points achieved | possible points | points achieved | possible points |
| Gregor | 24 | 60 | 32 | 40 |
| Matej | 35 | 70 | 54 | 60 |
| Miran | 27 | 90 | 45 | 50 |

A For each student, calculate the percentage of points achieved in the first and the retake test. For which student is the difference in the percentages of points achieved the greatest?

B The final result is equal to the sum of $\frac{1}{4}$ of the percentage of points achieved in the first test and $\frac{3}{4}$ of the percentage of points achieved in the retake test.

What grades did the students achieve (see the criteria on the right)?

| Final Result | Grade |
| :---: | :---: |
| $0-50$ | 1 |
| $51-60$ | 2 |
| $61-75$ | 3 |
| $76-90$ | 4 |
| $91-100$ | 5 |
B2. The percentages of points achieved are:

| Student | first test | repeat test |
| :--- | :---: | :---: |
| Gregor | $\frac{24}{60}=0.4=40 \%$ | $\frac{32}{40}=0.8=80 \%$ |
| Matej | $\frac{35}{70}=0.5=50 \%$ | $\frac{54}{60}=0.9=90 \%$ |
| Miran | $\frac{27}{90}=0.3=30 \%$ | $\frac{45}{50}=0.9=90 \%$ |

The greatest difference is for Miran. . 1 point

B The grades of the students are:

| Student | Grade |  |
| :--- | :--- | :--- |
| Gregor | $0.25 \cdot 0.4 + 0.75 \cdot 0.8 = 0.70 = 70 \%$ | 3 |
| Matej | $0.25 \cdot 0.5 + 0.75 \cdot 0.9 = 0.80 = 80 \%$ | 4 |
| Miran | $0.25 \cdot 0.3 + 0.75 \cdot 0.9 = 0.75 = 75 \%$ | 3 |

The grades of the students are Gregor - 3, Matej - 4, Miran - 3. 3 points (1 point for each correctly determined grade, if the correct solution path is evident.)