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Apologies in advance if the question is wordy.

Let's say that I have $75\text{%}$ in a class.The grade is calculated with category weights. Here are the categories and their weights:

Homework: $0.1 (10\text{%})$

Projects: $0.2 (20\text{%})$

Exams: $0.7 (70\text{%})$

Here are the assignments with their scores, percentages, and categories.

Homework Assignment: $10/10 (100\text{%})$

Project: $8/10 (80\text{%})$

Exam: $7/10 (70\text{%})$

The grade for this class is $70\text{%}$. Now, what if I wanted to get it up to $80\text{%}$? I know that if I get $9/10$ on a test or $90\text{%}$, the grade goes up to $82\text{%}$. How could I represent this using a mathematical formula or function?

Insight on how the grades are calculated:

Each category has a certain number of points possible and points earned. Each time that a new assignment is added, the category's points possible go up by the denominator of the new assignment's score, and the category's points earned go up by the numerator of the new assignment's score.

Aiden Chow
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ca1c
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1 Answers1

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I'm not sure I understand exactly what you're trying to do. Let $g$ be the course grade, $h$ the homework score, $p$ the project score, and $t$ the test score. We are given $$g = .1h+.2p+.7t$$

As you say, if $h=1, p=.8,t=.7$ then $$g=.10+.16+.49=.75$$ If you get $90\%$ on the next exam, raising your exam average to $.8$ then your grade becomes $$g=.10+.16+.56=.82$$

Are you trying to solve $$.8=.10+.16+.7t?$$ This gives $$t=\frac{54}{70}\approx.7714$$ so to get a grade of at least $80\%$ you need to raise your test average to $78\%$ and assuming that the second exam has the same number of points as the first, you need to score $86\%$, because $$\frac{70+86}2 = 78$$

If this doesn't exactly answer your question, I hope it at least shows how you can answer it yourself.

saulspatz
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  • Thank you so much! This did answer my question. – ca1c Feb 12 '20 at 21:33
  • This is a reply to the last part of the answer: You said, "assuming that the second exam has the same number of points as the first". I found that it doesn't matter how many points each assignment has as long as the percentage stays the same: 7/10 = .7 and 70/100 = .7, add the numerators and the denominators to get: 77/110 = .7. The points are different but the percentage is conserved. – ca1c Feb 26 '20 at 19:17
  • Yes, if you score the same percentage on all the exams, that will remain your percentage score on the exams, but it doesn't answer the question of how to raise your grade. Presumably, if the second exam had twice as many points as the first, it would count twice as much in computing the grade. That was the rule in every course I ever took, and every course I ever taught. – saulspatz Feb 26 '20 at 19:25