Teacher will drop lowest test score beside final. Test 2 is 29 and test 4 is 22. Wondering why it would be advantageous to fail test 4.

Question

My teacher will drop the lowest test score beside the final. Test 2 is worth 29 points and test 4 is worth 22 points. I'm just wondering why it seems like it would be advantageous to fail test 4.

My earned points so far: 120.5

Total possible points so far: 123

Current percentage: 97.97%

Total maximum score before dropping any test: 194

Dropping Test 2

Total maximum score after dropping test 2: 194 - 29 = 165

     Points needed to earn an A after dropping test 2: 165 * .9 = 148.5

     Points earned so far after dropping test 2 but before considering ungraded assignments **(Hash Table = 1 point, Program 4 = 10 points, exam 4 = 22 points, and final = 38 points). I earned 26 points on test 2 so that makes: 120.5 - 26 = 94.5 points earned so far

    Remaining points possible if I drop test 2: ** 1 + 10 + 22 + 38 = 71

    Remaining points needed from remaining points possible to receive an A: 148.5 - 94.5 = 54. This means that I need to earn 54 out of 71 remaining points, aka, 76.056338% of remaining points

Dropping Test 4

Total maximum score after dropping test 4: 194 - 22 = 171

    Points needed to earn an A after dropping test 4: 171 * .9 = 153.9

    Points earned so far after dropping test 4 but before considering ungraded assignments **(HashTable = 1 point, Program 4 = 10 points, and final = 38 points. We are excluding test 4 because it will be dropped): 120.5

    Remaining points possible if I drop test 4: ** 1 + 10 + 38 = 49

    Remaining points needed from remaining points possible to receive an A: 153.9 - 120.5 = 33.4. This means that I need to earn 33.4 out of 49 remaining points, aka, 68.163265% of remaining points

Question

IF my math is correct, then that would mean I would need a higher percentage on the final if my percentage on test 4 is higher then 89%, my percentage on test 2. How could earning a higher percentage on test 4 actually put me at a disadvantage in getting an A in the class when compared to earning an F on test 4?

Answer 1

I may have judged this question too harshly, but to be fair, the question as written seemed to me to be hard to follow.

This hypothetical--with a different set of numbers, may make clear what I think the OP was getting at. Suppose, for a class, you first were given 3 tests, each worth 50 each, that you already took, and then a Final worth 300 points, that you have not yet taken. Suppose that your teacher agrees to drop the lowest (by percentage) test score from consideration of your grade (even if this lowest score happens to be the Final). Next, suppose that you got a 50/50 on Test 1, a 40/50 on Test 2, and a 50/50 on Test 3.

1. Yes, given your test performance so far, getting a 300/300 on the Final would be the best outcome when it comes to your total grade. In fact, let $x$ be the smallest score on the Final satisfying $\frac{50+50+x}{50+50+300}$ $\ge \frac{50+40+50}{50+50+50}$, you'd be improving your grade getting a score of $x$ or better on the Final and dropping Test 2. And of course assuming you get at least $x$ the higher the score the better.

2. HOWEVER, as OP may have been alluding to, you indeed actually would be worse off getting (say) 241/300 (80.3% > $\frac{40}{50}$) on the Final than you would totally bombing the Final, or more precisely, getting less than 80% on the Final. If you got 241/300 (or more precisely, a score less than $x$) you'd be replacing a score that was bringing your average down before, by a slightly higher score that still brings your average down, but the additional weighting (now 300 vs only 50 before) would be a millstone around your grade! So if you get 241/300 on the Final your grade will have gotten WORSE, whereas if you had bombed the Final so that it didn't count for you, you grade wouldn't have changed.

3. MEanwhile, in the other direction, if your Final (or last exam) were worth only 10 points instead of 300, then even if you got 5 out of 10 on your last exam, you'd really prefer that your teacher drop Test 2 that you got a better score and keep your 5/10 on the last exam. Yes 5/10 is a worse score than 40/50, but the 5 out of 10 would weigh so much less on your grade than the 40/50 would, that replacing 40/50 with 5/10 would actually help you. Your score would go from 140/150 to 105/110. That said, getting better than 8/10 on the last exam would be a big win for your grade. Not only are you replacing your minimum grade by a higher grade but you'd be replacing it with something that weighs less on your average--and may even bring your average up.

So to answer the OP, as test 4 is worth only 22 points and test 2 was worth 29 > 22 points, you would be better off doing as well as you can on Test 4 so that you get Test 2 dropped. If you do better on test 4 than you did on Test 2, then at the very least you'd be dropping a score that lowers your average by a slightly better score that is weighted less. If instead test 4 were worth 100 points then you either would want to get a great score on test 4 or a score worse than that of test 2. Getting a slightly better score on test 4 may actually bring your average down more as test 4 would be weighted more than test 2.

Answer 2

So if you drop test $4$ there are $194-22 = 172$ total points possible. To get an $A$ you need to get $.9*172 = 154.8$ points. You have to earn $154.8- 120.5 =34.3$ of the remaining $49$ points.

You earned $26/29 = 89.7\%$.

So you will NOT drop test 2 *unless you earn at least $.897*22 = 19.734$ on test $4$. So you will have earned at least $120.5 - 26 + 19.734=114.24$

So if you drop test $2$ there will be $194-29 = 165$ points and to get an $A$ you will need to get $165*.9 = 148.5$. So of the remaining points you will need to earn $34.26$ of the remaining $49$ points.

That's not a significant difference.

I think you were figuring if you drop 2, you'd still have to earn 89% of test 4. But you wouldn't drop 2 unless you already had earned those. So those are not points you will have to earn. Those are point you will have already have earned if the situation were to come up at all.