Questions: In some 4.0 grading systems, a student's grade point average (GPA) is calculated by assigning letter grades the following numerical values. A=4.00, B-=2.67, D+=1.33, A-=3.67, C+=2.33, D=1.00, B+=3.33, C=2.00, D-=0.067, B=3.00, C-=1.67, F=0.00 Use this grading system to find this student's GPA. Round to the nearest hundredth. Tessa's cumulative GPA for 3 semesters was 3.18 for 46 course units. Tessa's fourth semester GPA was 3.74 for 12 course units. What is Tessa's cumulative GPA for all 4 semesters?

Solution Steps

To find the total grade points for Tessa's first three semesters, we use the formula:

\[ \text{Total Grade Points} = \text{Cumulative GPA} \times \text{Course Units} \]

Substituting the given values:

\[ \text{Total Grade Points for 3 Semesters} = 3.18 \times 46 = 146.28 \]

For the fourth semester, we calculate the total grade points similarly:

\[ \text{Total Grade Points for 4th Semester} = \text{GPA} \times \text{Course Units} \]

Substituting the values:

\[ \text{Total Grade Points for 4th Semester} = 3.74 \times 12 = 44.88 \]

Now, we sum the total grade points from all semesters:

\[ \text{Total Grade Points for All Semesters} = \text{Total Grade Points for 3 Semesters} + \text{Total Grade Points for 4th Semester} \]

Calculating this gives:

\[ \text{Total Grade Points for All Semesters} = 146.28 + 44.88 = 191.16 \]

Next, we find the total course units:

\[ \text{Total Course Units for All Semesters} = \text{Course Units for 3 Semesters} + \text{Course Units for 4th Semester} \]

Substituting the values:

\[ \text{Total Course Units for All Semesters} = 46 + 12 = 58 \]

Finally, we calculate the cumulative GPA using the formula:

\[ \text{Cumulative GPA} = \frac{\text{Total Grade Points for All Semesters}}{\text{Total Course Units for All Semesters}} \]

Substituting the values:

\[ \text{Cumulative GPA} = \frac{191.16}{58} \approx 3.295862068965517 \]

Rounding this to the nearest hundredth gives:

\[ \text{Cumulative GPA (rounded)} = 3.30 \]

Final Answer