Semester Grade worksheet

1. Grade needed on the final for 78%: 44.17%

1. Average the two quarters, because they count equally

   $\frac{\left(90+95\right)}{2}$$=92.5$

2. The quarters carry the 70% of the grade that the final doesn't, so take that share of the average

   $92.5\times \mathrm{70\%}$$=64.75$

3. Subtract that from your goal to see what the final must add

   $78-64.75$$=13.25$

4. Here's what that means for you

   $\text{This is within reach on a normal 100-point exam.}$

5. Divide by the final's 30% share to turn those points into an exam score

   $\frac{13.25}{\mathrm{30\%}}$$=\mathrm{44.166667\%}$

2. Semester grade: 77.2%

1. Average the two quarters, because they count equally

   $\frac{\left(64+84\right)}{2}$$=74$

2. The quarters carry the 80% of the grade that the final doesn't, so take that share of the average

   $74\times \mathrm{80\%}$$=59.2$

3. The final is worth 20% of the grade, so take that share of your exam score

   $90\times \mathrm{20\%}$$=18$

4. Add the two parts to get your semester grade

   $59.2+18$$=\mathrm{77.2\%}$

3. Grade needed on the final for 72%: -27%

1. Average the two quarters, because they count equally

   $\frac{\left(90+120\right)}{2}$$=105$

2. The quarters carry the 75% of the grade that the final doesn't, so take that share of the average

   $105\times \mathrm{75\%}$$=78.75$

3. Subtract that from your goal to see what the final must add

   $72-78.75$$=\mathrm{-6.75}$

4. Here's what that means for you

   $\text{You'll reach this goal even with a 0 on the final.}$

5. Divide by the final's 25% share to turn those points into an exam score

   $\frac{\mathrm{-6.75}}{\mathrm{25\%}}$$=\mathrm{-27\%}$

4. Semester grade: 87%

1. Average the two quarters, because they count equally

   $\frac{\left(85+95\right)}{2}$$=90$

2. The quarters carry the 70% of the grade that the final doesn't, so take that share of the average

   $90\times \mathrm{70\%}$$=63$

3. The final is worth 30% of the grade, so take that share of your exam score

   $80\times \mathrm{30\%}$$=24$

4. Add the two parts to get your semester grade

   $63+24$$=\mathrm{87\%}$

5. Grade needed on the final for 120%: 233.33%

1. Average the two quarters, because they count equally

   $\frac{\left(120+80\right)}{2}$$=100$

2. The quarters carry the 85% of the grade that the final doesn't, so take that share of the average

   $100\times \mathrm{85\%}$$=85$

3. Subtract that from your goal to see what the final must add

   $120-85$$=35$

4. Here's what that means for you

   $\text{This is above 100\%, so you'd need extra credit.}$

5. Divide by the final's 15% share to turn those points into an exam score

   $\frac{35}{\mathrm{15\%}}$$=\mathrm{233.333333\%}$

6. Semester grade: 84.35%

1. Average the two quarters, because they count equally

   $\frac{\left(100+66\right)}{2}$$=83$

2. The quarters carry the 85% of the grade that the final doesn't, so take that share of the average

   $83\times \mathrm{85\%}$$=70.55$

3. The final is worth 15% of the grade, so take that share of your exam score

   $92\times \mathrm{15\%}$$=13.8$

4. Add the two parts to get your semester grade

   $70.55+13.8$$=\mathrm{84.35\%}$

7. Grade needed on the final for 63%: -25%

1. Average the two quarters, because they count equally

   $\frac{\left(80+90\right)}{2}$$=85$

2. The quarters carry the 80% of the grade that the final doesn't, so take that share of the average

   $85\times \mathrm{80\%}$$=68$

3. Subtract that from your goal to see what the final must add

   $63-68$$=\mathrm{-5}$

4. Here's what that means for you

   $\text{You'll reach this goal even with a 0 on the final.}$

5. Divide by the final's 20% share to turn those points into an exam score

   $\frac{\mathrm{-5}}{\mathrm{20\%}}$$=\mathrm{-25\%}$

8. Semester grade: 93.25%

1. Average the two quarters, because they count equally

   $\frac{\left(90+95\right)}{2}$$=92.5$

2. The quarters carry the 70% of the grade that the final doesn't, so take that share of the average

   $92.5\times \mathrm{70\%}$$=64.75$

3. The final is worth 30% of the grade, so take that share of your exam score

   $95\times \mathrm{30\%}$$=28.5$

4. Add the two parts to get your semester grade

   $64.75+28.5$$=\mathrm{93.25\%}$

9. Semester grade: 85.25%

1. Average the two quarters, because they count equally

   $\frac{\left(110+80\right)}{2}$$=95$

2. The quarters carry the 75% of the grade that the final doesn't, so take that share of the average

   $95\times \mathrm{75\%}$$=71.25$

3. The final is worth 25% of the grade, so take that share of your exam score

   $56\times \mathrm{25\%}$$=14$

4. Add the two parts to get your semester grade

   $71.25+14$$=\mathrm{85.25\%}$

10. Grade needed on the final for 70%: -114.17%

1. Average the two quarters, because they count equally

   $\frac{\left(90+115\right)}{2}$$=102.5$

2. The quarters carry the 85% of the grade that the final doesn't, so take that share of the average

   $102.5\times \mathrm{85\%}$$=87.125$

3. Subtract that from your goal to see what the final must add

   $70-87.125$$=\mathrm{-17.125}$

4. Here's what that means for you

   $\text{You'll reach this goal even with a 0 on the final.}$

5. Divide by the final's 15% share to turn those points into an exam score

   $\frac{\mathrm{-17.125}}{\mathrm{15\%}}$$=\mathrm{-114.166667\%}$