Question

I have a 95 grade point average. I have submitted an assignment that is 31 % of my grade. What would be the maximum amount of points that could be deducted from my grade point average?

Answer 1

New GPA (g):
$$
\large{
g_{new}=\Sigma \cfrac{g_i+0.31}{n+1}\\
g_{old}=\Sigma \cfrac{g_i}{n}\\
g_{new}-g_{old}=\Sigma \cfrac{g_i+0.31}{n+1}-\Sigma \cfrac{g_i}{n}\\
=\Sigma \cfrac{(g_i+0.31)n-g_i(n+1)}{(n+1)n}\\
=\Sigma\cfrac{-g_i+0.31n}{n^2+n}\\
=\Sigma\cfrac{-g_i}{n^2+n}+\cfrac{0.31n}{n^2+n}\\
g_{old}-g_{new}=\cfrac{-0.31n}{n^2+n}+\Sigma\cfrac{g_i}{n^2+n}\\
=\cfrac{-0.31}{n+1}+\Sigma\cfrac{g_i}{n^2+n}\\
=\cfrac{-0.31}{n+1}+\cfrac{0.95}{n+1}\\
=\cfrac{0.95-0.31}{n+1}\\
=\cfrac{0.64}{n+1}
}
$$
Where \(g_i\) are the grades for each prior assignment and n are the number of prior assignments.
Now, \(g_{old}-g_{new}\) is maximum n=1, since n=0 is not possible.
$$
\large{
max(g_{old}-g_{new})=\cfrac{64}{2}=32
}
$$
This is also the maximum number of points tat could be deducted from your GPA.