#competition-math
1 messages · Page 66 of 1
I’m buns at comp math tho
Oop. I find the problems interesting. I love proof-based problems that take you time to think on
its not there dawg
Also, are your lassmates also still "learning" how to measure angles with protractors?
thats excellent hobby
We did that but some still struggle
lmao
Ikr, and before that they were learning addition. im being serious
Bruh
Mhm. I took that one this year. Didn’t win any medals (wasn’t aiming to, anyway) but I really liked it)) I then brought the problems home and worked though them all
last year i kinda came up with the idea of using integration before knowing it existed to solve geometry
but
i didnt know how to execute it
lol
Bruh autocorrect
just solve normally bro
An excellent hobby
Also, do you guys ever get too lazy to do normal inequalities, and js use derivatives instead?
almost forgot that almost got me executed last time
yess
guys idk how to find MAA AMC test centres
it always annoys my teacher so much (non school)
bro asked ts twenty times already
yeah
Lmao my teacher marked me down on a frq once for “not showing my work”
someone help bro out
o wow
Have you asked in person
oh
nvm then 😭
oh damn
yeah thats real lwk
i mean i wanted to be challenge dat school,i was challenged, and then i got so frustrated of being challenged that i learned all the material and now im bored again... so. it doesn't always work out..
I suppose
a certain someone really hates combinatorics
Fair I guess….
ye
tbh, self studying is difficult without proper guidance
unless you follow strictly by textbook
at least theres online resources now than before
I js use multiple sources
thats effective too
Maybe. I personally find that I learn way better by self-studying and without someone hovering over me
Can somebody help me in
Int. 1+sin(logx)/1+cos(logx) dx
This is not competitive level
$\begin{aligned}
&\text{Calculus channel would be better but anyways} \
I &= \int \frac{1+\sin(\log x)}{1+\cos(\log x)},dx \
&\text{Let } u = \log x,\qquad dx = e^u,du \
\Rightarrow\quad
I &= \int e^u \left( \frac{1}{1+\cos u} + \frac{\sin u}{1+\cos u} \right),du \
&= \int e^u \left( \frac{1}{2}\sec^2\frac{u}{2} + \tan\frac{u}{2} \right),du \
&\text{Use } \int e^x(f(x)+f'(x)),dx = e^x f(x) + C
\end{aligned}$
| caesar |
What about this
b?
-1 and 1
did u do Pn=i^(n(n+1)/2)
i^2 and 1^ 4 will give only distinct real numbers
yeah
That’s what I thought of
no i just used that i²=-1 and i⁴=1
and so on
Ik the cycle
so whats the confusion..?
i^0 = 1, i^1= i, i^2=-1, and i^3=-i
None
👍🏼
That’s when x^2-x+2 is (x+1)(x+2)
It said sum of possible
then qp=2
q+p=a and qp=2
They said a is also an integer
exatcly
So it’s pq=2p+2q
Yep
oh ya
-1 and -2 ...
hmm wait lemme see soln
oh its 2 a my bad
i saw it as 2 only
thats super my bad i apologise
Yea
Do they get the 4 from completing the square
Metagaming it: assuming that there's actually sufficient information for a definite answer in the problem, that answer has to stay the same even in the limit where the diameter of the upper white circles go to 0.
In that limiting case, the diameter of the big circle is 20, and the lower white circles each have diameter 8 (namely, the lower chord and the radii towards the center form 3-4-5 triangles), so the answer is 10²pi - 2·4²pi.
is anyone doing bmmt
hmmm
How hard is it to learn synthetic geometry from scratch
There's barely any prerequisites, and the subject has been around for thousands of years ... I'd say easier than many other things, but it has fallen somewhat out of favor in professional mathematics, so it might be difficult to find really good textbook material. On the other hand, if you're self starting enough to learn from problems instead of a predigested textbooks, it's a topic where Wikipedia is an excellent reference source.
u cant divide both sides by A-B-C if you know that its 0
Ik it’s not true but it’s for fun
But is that look right
that means u can prove anything amirite
Yes
am i dumb or is x 5?
Think
it is
50/100 x 50
isn't it
,w (50/100)(50)
mhm
but you're dividing by 100, not multiplying by it
50/2 I mean
5
yes
Sure
This is five no
50% of 50 is 25
sqrrt of 25 is 5
ts is so easy
just dont confuse the 50% with other stuff
Wait
so you substitute:
i was thinking you could just make it sinxcosx = 1/2 sin2x, and solve for x
how would you solve that, make cos in terms of tan and make it a quadratic?
Isn’t this uh smrh with 45 deg
Prolly uh
135
Yeah
I think that works
Yeah
Wait am I geeked
yea i think it is
yeah
i mean, 315 might work too
But it don’t change the answer
yea
mhm
hmm
use double angle identity
Is it it 1/2 sin x
or 2npi depends
yea but you're not solving for x, you're solving for tanx so it doesnt matter
ook
real
the amount of sillies i had for not reading is yummy
i guess this could work
$\frac{t}{1+t^2} = \frac{-1}{2}$
stuffed
i saw 1/(1+t^2) and immediately thought arctan 
xD yea i would too
Rhis was my first idea too
hmmm
More generally without all of this machinery,
$$\tan x+\frac{1}{\tan x}=\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}=\frac{\sin^2 x +\cos^2 x}{\sin x \cos x}=\frac{1}{\sin x \cos x}.$$
Civil Service Pigeon
orz
orz
Wow
sinxcosx = -1/2
= sinxcosx/sin^2x+cos^2x
then divide both numerator and denom by cos^2x
get
tanx/tan^2x+1 = -1/2 and factor this would be what i do
hmmmm
how tf do bonus
Where do I practice a bunch of comp math other than past amcs
wait u could find ED and js bash from there
u could do alcumus or aime
Not good enough for aime but yea ill try alcumus ig
Can u just cross multiply
Tan x = u
This is an equation right
yes
inequalities comes in my syallbus
we are finding what tanx is
Multiply by 2 to get sin (2x) = -1, if 0 <= x < 2pi we just get 2x = 3pi/2 and tan(x) follows simply from here
what’s alcumus
Neither but we will be one day
nah donr do alcumus
yea assuming ur younger side just starting off contests without much foundation u should read thru aopsv2 imo should have all the theory u need
doing prohlems will take a lot of time obv but thats the point is to make u start to think creatively
never search up answers unless u are stuck after making progress in somew way or another (not drawing blank = u still gain something)
ehhhh
it might be a bit basic for aime
but it never hurts to have practice
have practice
ook
Or js do alcumus interm alg and precalc.
estrogenuinely
how do u find that
oh wait
yea that might be good catually
maybe i should do some to make sure my sklls are still not bad
is this something to be celebrated
shore
67
i think he really hates combinatorics
No
i just solved it if you want my explanation
gpt did get a different answer but i think im right and gpt is wrong
dont quote me on that though
Hm ok
ye
hi orz
ok
Its rough but i think it explains it
Sorry i had to flip it sideways
i'd say if that was your homework, that was quite diabolical but if i was it in a math competition it wouldn't be too bad, probably near the start
ye that'd probably be my first idea too
ye
i made that question myself
just as challenge
orz
sure
here
the first one
i made it for my friend to do but theres some trig needed
and he dont know how to do trig
why is hank on a leash 
lol do yk hank
rememberhim
idk
i'm doing language rn
yaey
here is a short solution
Oh lol
Guys just asking but I placed first in 3 events and 3rd in one event at WKU (West Kentucky University) math competition. Is that worth putting on the college app?
i haven't heard abt that but after a google search, ye, this seems like something u should put on ur college application
don't js take my word for it though
Alr!
...Chinese exams?
"integrate my dih" 💀
tbf some of the harder amc problems are fun to solve with calc
i mean depends on how many people u beat
and what else u have
There were 143 as far as I know
tf is this
ye
heres a question from my state's math olympiad if anyone wants to try.
James is trying to catch his dog, Brutus in his yard, which is an NxN grid of lattice points. James Starts in the top left corner, Brutus starts at a lattice point different from James, chosen at random. In each round, brutus moves first, moving to a neighboring lattice point in a horizontal or vertical direction. Then James moves, moving to a neighboring lattice point in a horizontal, vertical, or diagonal direction. Both must remain within the yard.
If at any point, James and Brutus are on the same lattice point, James catches Brutus. What is the expected number of moves it will take james to catch Brutus is brutus plays optimally to remain free as long as possible, and James plays optimally so as to catch Brutus as soon as possible?
huh
It's a trick question: ||No matter where Brutus starts, he can always stay free until exactly James's (N-1)th move.||
Namely: ||Brutus's strategy is to move straight towards the closest point on the bottom or right edge and then stay on that edge until he is caught.||
Meanwhile, ||James moves diagonally for as long as he's both above and to the left of Brutus. After that, his strategy is to keep on the same row/column as Brutus, moving towards the bottom/right edge at each turn.||
Interestingly, optimal strategies for both James and Brutus can be described very simply: Brutus always moves to the square he can reach that is farthest from James by the Euclidean norm. James always moves to the square he can reach that is closest to Brutus. But when described that way, is is not particularly obvious that the strategies are optimal, and especially not that they lead to the numerical result I claim.
7th grade romanian math olympiad
most of us cant read romanian
Most of us have a translator
There's nothing to solve anyway since those are the solutions
…
hmm
uhhh
just leave
i cant its literally the mathcounts nats server
bro what 😭
lock in
yaey i got to use lte lemma
Oh my, thank you.. I might forget it if you didn't say 🙂
but i forgot my password
ook
i js have google password manager 👍
fah
Perfect. Although I wrote a lot more for my solution, but the ideas are generally the same
orz
How do I prepare for IOQM?
I scored 20 in the previous exam
And could score 27 when I actually looked at the questions at home
I wanna score like 30-40+ this yr
I’m in 9th so anything to help me prepare?
I already have the Prashant Jain book and the challenges and thrills of pre college maths
Got 7 in RMO
welcome to the light side of the internet 
ook
lmao
I found some very in apropriate stuff on discord before
not what i was referring to but yes the stuff there is still weird
not as extreme though
and dont ask me to go into detail cuz omnipotententity is on my ass already
is this more of a server-only issue or an issue for discord as a whole
just the mods server really
they dont take teenage boys talking about gooning seriously
heck the mods can call people slurs and get away with it, some of them are in this server
more ignorance than anything ig
nah just moderators dont care about it
they literally have a channel called gooning
not even nsfw marked
wtf
maybe not talk abt this anymore
yea that was their "fix" for people talking about it too much
and they only did things bc active ppl started leaving iirc
otherwise they wouldnt have done anything
real
Its a thread created by a user, and its an ersatz memes channel
oh hi
all discord servers
bro what
i was in my own server and someone sent porn serv link
there were 5+ invites sent on one server today alone
i went on a mass report with my friends
lmao
but i don't think we should be talking abt this
true
I dont wanna get beheaded by the few corrupt mods that close their eyes to gooners and ban me for sending two gifs in a row
wtf
birdy wat servers r u in bud
bro 2 more were just fucking sent in another server
is discord on the fritz today or sum
why r u counting 😭
my current server tag is the server
hmm war thunder
...
Can we do grouping
multiply both sides by x-1
or divide by x^2 and complete whole square
or we could use summation of gp to find sum, that will be z^6=1 and then use complex no. to find roots
Can someone tell me😭
bro im stupid isn’t it just x=-1
im guessing no one here knows
It’s ok I asked about amc and didn’t get a good answer
Cant x + 1 be a factor of this
Issok man
Ig I’ll ask my teachers
amc like in australia?
u can solve (z^6-1), z not equal to 1 if you've done complex numbers
Nope there r five solutions I’m pretty sure
2 of the solutions would be 0 and x = -1
x = cis(2pi/6 + k2pi/6) for k = 0, ..., 5
then remove x=1
i think
wait no you're solving for -1 not 1 so
wait nvm
yea should be this
i think
I don’t understand a single word here lowk
uh sorry
This server humbles the hell out of me
conclusion is that the only real root would be x=-1
Sure, but 10 second solutions are nicer imo
Nah it’s probably jst that I don’t know this
i think i messed up
Nah isn’t it a property?
Like if the power of a and b are odd then a+1 is a factor of them?(I meant smth like a^3 + b^3)
(I might’ve used it incorrectly here)
Multiplying by $(x-1)$ gives you $x^6-1=0 \implies x=e^{2\pi i k/6}$ for $k=0,1,2,3,4,5$. We introduced $x=1$ as an extra solution, so the answer is
$$x=e^{\pi i/3}, \dots, e^{5\pi i/3}$$
and we are done.
Civil Service Pigeon
Oh wow
I didn’t know any of this
but i havent watched it
Which grade math is this??
year 12
topic is complex numbers
roots of unity
idk when in other countries though
its not difficult, u learn it at the start of the topic
Anyone got a good topic wise question bank online?
Even better if it’s divided into different levels
God, I would so recommend Skanavi, but it is in Russian. Not sure if there are English versions. Those problems are very good—ranging from combinatorics to stereometry and vectors. They are separated into three levels, A, Б, and B. B has some really interesting problems
What is your level? I might recommend some other books
Uh 9-11th grad rn
what topic
Check out “The USSR Olympiad Problem Book” by Shklarsky. Amazing book of problems. All really interesting and require you to think and write out intricate proofs
I am guessing you want olympiad-like problems? Since this is the competition maths channel
And ofc “Problem-Solving Strategies” by Engel is good. Recommended by a lot of people
Has very good problems and solutions, but more on the national and international level, I’d say
But past papers are always your best option for olympiads
Tell me if these are not what you’re looking for lol
Wait imma ss all of this
They’re good imo
I scrolled a little and the question are great
angelo my num 1 opp
That one is also really good
eed books to prepare for imo
like good ones
can be russian
preferably - i like the problems there
ANYBODY TRYING TO GO OVER THIS AOPS PRECALC TRIG IDENTITIES EXCERCISES WITH ME I READ THE WHOLE CHAPTER ALMOST TWICE AND STILL DIDNT UNDERSTAND SOME OF THE HARDER QUESTIONS
First one use graphing techniques or addition/subtraction angle, second one use subtraction angle for sin and cos and divide, third one is subtraction angle using common angles, fourth one expand using addition and subtraction angle (I think) and that’s all I could get to for now
yea but i alr got those ones i rlly need help starting 3.25 i totally frogot to mention this sorry and thnkd anyways
Oh lol
Ok 3.2.5 convert to tan(2x) = cot(3x) and convert cot to tan by translation and take arctan of both sides
Alr I gtg now I might be back tmrw these are interesting problems
peak book 🥹
lift exponent
i'm not elon musk boy 💔
was focusing on field theory
clipped for later 💔
ts is not tuff
why we flexing touching gass
Touching grass is not tuff if you didnt realise already plens
Ook
i hate how this has become a flex nowadays
damn
its hard to tell with your case
is it rly that hard
your uhhhh
mind you a lot of people are kinda weird with their expressions nowadays
including me
yo what other discord do yall hangout in?
why exactly
i wanna get in as many as i can for best advice
huh
idk
I sent two gifs in a row and got timed out for three days
”gif spam”
hmmm
i feel like there was
@versed dagger why did you ban me again
I deleted it from my memory
i meant timeout
ah this
consider the quadrilateral
||3 angles are 180-140=40, and the 3rd angles is 180+x, which should all sum to 360||
So x=60⁰
Right
Thank you guys
Can i make more questions every time? It's my first time talking in this server
And sorry for my english, i speak spanish
yeah
we love to help
sure, as long as it's mostly comp math related
Its so fun
yes
Just ask q to whichever topic it correlates to
or if u have like a harder q js ask in help channels
yes
I'm studying for math olympiad, but i don't suscribed for any competition
like international math olympiad?
I'm not*
fr
what taf
i have nothing to do so seeing other problems is fun
national level is so tuff
No no
<<<
You know
Minor
Department
But
I just want to solve IMO problems
hehehehehehe
those r very time consuming
but first you gotta master the basics
for example the q u needed help on was basic
i find math comp very draining
once u master those find harder q each time while simultaneously summarazing problem solving strats
Yes
yea that’s what i’ve been doing
prep for my placement test
it’s like easy precalc stuff
its way funner than regular math
"start" calc iii bfore the end of the school yr
your english is very good
and my teacher is letting me do trig instead of boring alg on so that’s fun
better than a lot of ppl ik
me??
Hahaha
mhm
Are you a professor?
i’m taking calc I
idk if ur asking about me or him
or the other guy
@silver forge
Both
no bro im freshman
me?
Oooh
i'm way too young
patrick’s in 7, i’m 8, other dudes 9
I'm 16 years old
me and patrick r both 13 tho
Professors are orz
ah ok
no revealing my name
no
actually u don't even have it
🤙
i think
wen prolly gave it to u
lmao u liar
💔
plens u need to build muscle
nope
i do both
hmm
ts orz asf
we bike 26 miles then run 8
holy orz
orz
holy spelling 💔
we travel the us for comps
nice
orz
go to olympics
no gifs
Where are you from guys?
o canada
I'm from Honduras
Center
my geography is buns
ooo cool
o so tropical
i’m in the ewst coast
hmmm
i've been to china
i’m slavic born and raised tho
but never lived there
sad
Wait
imagine not being born in europe
i was born in us
xian pen
ts not tuff
or whatever it is
is russia in asia
🇨🇿🇨🇿
Ts racist
Here
or europe
aha predicted
mostly asia
ook
both my parents are czech hur i have slovakian heritage my grandma has a slovak passport
alr what am i doing i have math to do
pirated egmo is calling to me
What's your level?
uhhh
comp math wise not very good
maybe i could get into aime
but i would make a fool of myself at jmo 💔
Ok
You stayed in USAMO?
Train hard
Calculate the sum of the interior angles at vertices A, B, C, D, and E.
wasn't the answer liek 180
What
Why
because the sum of the angles inside the pentagon is 540 so sum of the other angles of the triangles are 720 so A+B+C+D+E=180
orz
Or js assume that the pentagon is regular
nouuuuu
mitte
Im pretty sure this was an alcumus problem that i saw liek 3 yrs ago 😭
wait i got it by adding the angles of the 5 big triangles, then subtracting the pentagons angle sum, then dividing by 2 (since each tip angles is counted twice)
Explain more
so let the pentagon be A'B'C'D'E'
Yes
A'AB'+AA'B+AB'B=180, then the sum of angles of all of the 5 small triangles is 900
900-360-360=180
Yes
Do you understand or shall I explain again?
maybe i’m dumb (#18) but don’t four and six have an equal amount of ways?
umm
i got 3 pairs with 4
and 4 pairs with 6
(cus, one of the pairs with 4 is 2x2)
I'm pretty sure you're accounting for all possible combinations, and 6 has the most likely to appear on any number
ngl i lwk js drew a multiplication chart from 1 to 6 and brute forced it
Etc, so n(1,2,3... 6)
Where n = {1,2,3...6}
All answers would be
1 2 3 4 5 6
2 4 6 8 10 12
3 6 9 12 15 18
4 8 12 16 20 24
5 10 15 20 25 30
6 12 18 24 30 36
So 1 of 1
2 of 2
2 of 3
3 of 4
2 of 5
4 of 6
6 is the most likely to appear!
yay that’s what i guessed!!
i’m counting that as points
so does 3.1 and 1.3 count as two?
for example
Wdym like 1×3?
thats what i counted
cus like... statistically they're two distinct outcomes
here my brute fore method js highlighting as i went
oh wait i think i misunderstood the problem
i was doing like to become that number
like six has 2 and 3 and 6 and 1
oh no i didn’t
lol and each of those pairs can be reversed to 3 and 2, 1 and 6... so 4 6s... right?
ts looks like pascal
Or gauss
not sure tho
i know i did it before
draw diagram yay
real
gauss looks EASY NOW
beg ur teacher to sign u guys up
hi zelix
its one year chill
also i did good on gauss so i can be talking
R u doing it ts yr
Hi.
because ur like 7th or smth
fuh naw bruh
hi!!
why
i did gauss 8 in g5
hello
i forgot
your too young
physically
not intellectually
so u shud still do it
what did u score
yo can someone help me to prepare for the uni of waterloo competition for grade 10 next yr
i can check one sec
be careful
for galois
be careful
and like
do it super fast
i barely had time ts year
i used to be good at dis shit but i switched schools and this easy math rotting my brain
isnt all school math easy
i used to go to private skl
bro what school were u from be4 😭
it has to be uts or somethn to be hard enough to not rot ur brain
like polynomials
u go to uts?
na
o
bro these polynomials are genuinely brainrotting material and people find dis shit hard bruh
anyways
how do i
prepare
grade 10 thingy
is the old tests good start
no
dang
do like 1 or 2 mocks
thats it
right be4 the tests
like
a few days be4
and rest
just
idk
its not hard
dude i got a year i genuinely forgot almost all the important shit
i gotta relearn
like everything basically
how do i know what to relearn
is it jus like everything
a year is enough to learn what i forgot, i didnt forget any like concepts
for geo do EGMO for num theory well its not hard u can do it, maybe try aops, for algebra uhhh cant be taht hard on galois, for combo be careful
what is diff in galois and combo
huh
did u do both
or u jus do 1
im so confused bruh
ok so cayley is multiple choice and galois is like an actual test
138 smth
ye
r u like some sorta prodigy or sumn
nd more importantly how u on dc in grade 7
r u in any programs like ib or ibt or sumn
my school doesnt have ib
idk
ah nice
that’s what i’m aiming for
in practice i’ve been getting 135- low 140’s so i think im on target for now
consider yourself lucky
uh huh
it’s like 12 am i have nothin to do i’ve resorted to the sat
the math part ofc
orc
i do not have the patience to do the english
bro im stupid ash im only like 1 yr older than u guys nd u guys practicing for the sat in grade 8
optional too btw
but atleast sat isnt too hard
i’m not practicing really i’m just bored asf
it’s really easy too
at least mod 1
so far i’ve been able to do it with zero scratch work (i’m on problem 24)
dawg
I’m 35
do ur thing ig
Nah I’m just kidding I’m in 8th
r u also one of these prodigy dudes
mb
hello
Oh
Texas
i’m in east coast of us rn but i’ve lived all over europe
11:00
Yeah
AMC
so like comp math?
yeah i started prepping in 8th and im taking the sat at the end of 9th (well like june sat i think) i dont blame them-