Grade calculation

Question

My teacher said that $\frac{1}{3}$rd of the final grade will be based on Exam 1, $\frac{1}{12}$th each based on Exam 2-5, and $\frac{1}{3}$rd again based on Exam 6, how will my teacher calculate my final grade?

Answer 1

If $x_1, x_2, \dots, x_6$ are your scores on Exams $1,2,\dots,6$, then your final grade will be $$ \frac{x_1}{3} + \frac{x_2}{12} + \frac{x_3}{12} + \frac{x_4}{12} + \frac{x_5}{12} + \frac{x_6}{3}. $$

Answer 2

She will multiply your grade on each by the fractional equivalent of each weight: 1/3*Exam1+1/12(Exam2+Exam3+Exam4+Exam5)+1/3*Exam6

Answer 3

Let $p_1,p_2,p_3,p_4,p_5$, and $p_6$ be your percentage scores on Exams $1$-$6$, respectively. Your teacher will calculate a final percentage

$$\begin{align*} p&=\frac{p_1}3+\frac{p_2}{12}+\frac{p_3}{12}+\frac{p_4}{12}+\frac{p_5}{12}+\frac{p_6}3\\\\ &=\frac{p_1}3+\frac{p_2+p_3+p_4+p_5}{12}+\frac{p_6}3\\\\ &=\frac{p_1+p_6}3+\frac{p_2+p_3+p_4+p_5}{12}\\\\ &=\frac{4p_1+p_2+p_3+p_4+p_5+4p_6}{12}\;; \end{align*}$$

use whichever form seems most convenient.