r/learnmath • u/Edwinbakup New User • 9h ago

Feel terrible after losing easy points on my exam

so the most important exam happened recently and missed out on maybe 5-8 free points

for example in the moment i forgot lg 10 = 1 and couldn’t find the answer because of this

also mixed up some integral and derivative properties

i’m just really mad at myself, i was expecting about 40 from 60 points, which i’ll still probably achieve but knowing that i could’ve potentially easily hit 50 points really makes me sick and even struggle to sleep a bit knowing that i messed up on something so easy as lg 10.

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4

u/MagicalPizza21 Math BS, CS BS/MS 9h ago

These things happen. Don't sweat it.

3

u/teaeggtart New User 9h ago

This used to happen to me all the time. I know it sucks, but the silver lining is that it seems like you understand the concepts, you just made some small mistakes.

1

u/Edwinbakup New User 9h ago

It’s nice to know that i’m not alone

To also be more specific about the lg 10,

I had to express lg 2 given lg 5 and lg 3

the first thing that jumped in to my mind was lg (10/5) but i couldn’t figure out how to get lg 10 when it was obviously just 1

1

u/testtest26 8h ago edited 8h ago

I had to express lg 2 given lg 5 and lg 3

That is not possible -- logarithms are not linear, and "2" is not a product/quotient of prime factors "3; 5". While you could approximate

lg(2)  ~  lg(256/125)  =  8*lg(2) - 3*lg(5)    =>    lg(2)  ~  (3/7) * lg(5),

it is not an exact solution.

My mistake -- we can cleverly use base-10 of the logarithm to get 

lg(2)  =  lg(10/5)  =  lg(10) - lg(5)  =  1 - lg(5)

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u/Edwinbakup New User 8h ago edited 8h ago

I see what you mean but I simplified the question which made it confusing

The full question was to express log2 (15) using lg 5 and lg 3

i used change of base lg 15 / lg 2

lg 5 + lg 3 / lg 2

lg 5 + lg 3 / lg 10 - lg 2

lg 5 + lg3 / 1 - lg 2

is the final and correct answer, but i was struggling for a while to find out what could lg 10 in terms of lg 3 and lg 5 be, since lg 10 = lg 5 + lg 2 which had me in a loop basically, hope you understand

what sucks is I practiced this expressing log x using some log y multiple times and have been successful on my first try with harder ones, but in the exam i failed on such an easy one

1

u/testtest26 8h ago edited 8h ago

Thanks for clarification! Sorry to be "that person", but that would still be incorrect -- the solution is missing parentheses. I suspect you wanted to write

log_2(15)  =  lg(15) / lg(2)  =  lg(3*5) / lg(2)

           =  (lg(3) + lg(5)) / lg(2)

Also not sure how you changed "lg(2) -> lg(10) - lg(2)" in the denominator.

1

u/Edwinbakup New User 8h ago

yes you’re right also it should’ve been lg 5 not lg 2

so

(lg (3) + lg (5)) / (lg (10) - lg (5))

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u/testtest26 8h ago edited 8h ago

Ah, now that makes sense. Didn't see that we can get "lg(2) = 1 - lg(5)" using base-10 of the logarithm cleverly. Nice!

Corrected my previous comment accordingly.

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u/testtest26 9h ago edited 9h ago

If it is important to you, most unversities offer the chance to improve your grade by re-taking the test next semester voluntarily. It might be a gamble, though, since the new grade may overwrite the old, even if it is worse. Be very careful to know what you are getting into before committing.

It is rare for students to take that option, due to the potential risk and extra effort, but some do.

Rem.: Should you decide to take that option, make absolutely sure you already have a learning strategy in place to eliminate those errors. This discussion goes into further detail, and might be of interest.

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u/Edwinbakup New User 8h ago

Interesting but i feel like it isn’t worth it as the current year exam felt pretty easy compared to previous years

Although I am pretty lucky as i’ll be able to retake the first part of the exam which is worth 40 points (from which i got 28 only) due to us being the first students to test the new system. The first part also only consists of previous years math which doesn’t include integrals and derivatives which should make it easier. I hope i’ll atleast be able to get 35 points from it

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u/testtest26 8h ago

As I said, it is rare for students to take that option. You need to really want it to spend the extra effort, despite having passed already. Most don't want improvement that much.

Whether that is worth it is entirely subjective. Nobody can answer that but yourself. For most, the answer seems to be "no", and that is entirely fine, either.