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AMC and other contests, summer programs, etc.
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Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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k a AMC 10/12 A&B Coming up Soon!
jlacosta   0
Nov 1, 2024
There is still time to train for the November 6th and November 12th AMC 10A/12A and AMC 10B/12B, respectively! Enroll in our weekend seminars to be held on November 2nd and 3rd (listed below) and you will learn problem strategies, test taking techniques, and be able to take a full practice test! Note that the “B” seminars will have different material from the “A” seminars which were held in October.

[list][*]Special AMC 10 Problem Seminar B
[*]Special AMC 12 Problem Seminar B[/list]
For those who want to take a free practice test before the AMC 10/12 competitions, you can simulate a real competition experience by following this link. As you assess your performance on these exams, be sure to gather data!

[list][*]Which problems did you get right?
[list][*]Was the topic a strength (e.g. number theory, geometry, counting/probability, algebra)?
[*]How did you prepare?
[*]What was your confidence level?[/list]
[*]Which problems did you get wrong?
[list][list][*]Did you make an arithmetic error?
[*]Did you misread the problem?
[*]Did you have the foundational knowledge for the problem?
[*]Which topics require more fluency through practice (e.g. number theory, geometry, counting/probability, algebra)?
[*]Did you run out of time?[/list][/list]
Once you have analyzed the results with the above questions, you will have a plan of attack for future contests! BEST OF LUCK to all competitors at this year’s AMC 10 and AMC 12!

Did you know that the day after both the AMC 10A/12A and AMC 10B/12B you can join a free math jam where our AoPS team will go over the most interesting problems? Find the schedule below under “Mark your calendars”.

Mark your calendars for these upcoming free math jams!
[list][*]November 20th: Amherst College Info Session, 7:30 pm ET: Matt McGann, Dean of Admission and Financial Aid at Amherst College, and Nathan Pflueger, math professor at Amherst College, will host an info session exploring both Amherst College specifically and liberal arts colleges generally. Topics include opportunities in math, the admission process, and financial aid for both US and international students.
[*]November 7th: 2024 AMC 10/12 A Discussion, Thursday, 7:30 pm ET:
[*]AoPS instructors will discuss problems from the AMC 10/12 A, administered November 6. We will discuss some of the most interesting problems from each test!
[*]November 13th: 2024 AMC 10/12 B Discussion, Wednesday, 7:30 pm ET:
[*]AoPS instructors will discuss problems from the AMC 10/12 B, administered November 12. We will discuss some of the most interesting problems from each test![/list]
AoPS Spring classes are open for enrollment. Get a jump on the New Year and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!

Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile!

Whether you've taken our classes at AoPS Online or AoPS Academies or reached the top echelons of our competition training with our Worldwide Online Olympiad Training (WOOT) program, you can now add your AoPS experience to the education section on your LinkedIn profile.

Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!

Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
Nov 1, 2024
0 replies
Logical guessing game!
Mathdreams   22
N an hour ago by JH_K2IMO
Source: 2021 Fall AMC10B P10
Fourty slips of paper numbered $1$ to $40$ are placed in a hat. Alice and Bob each draw one number from the hat without replacement, keeping their numbers hidden from each other. Alice says, "I can't tell who has the larger number." Then Bob says, "I know who has the larger number." Alice says, "You do? Is your number prime?" Bob replies, "Yes." Alice says, "In that case, if I multiply your number by $100$ and add my number, the result is a perfect square. " What is the sum of the two numbers drawn from the hat?

$\textbf{(A) }27\qquad\textbf{(B) }37\qquad\textbf{(C) }47\qquad\textbf{(D) }57\qquad\textbf{(E) }67$
22 replies
Mathdreams
Nov 17, 2021
JH_K2IMO
an hour ago
Possibility of USAMO?
MathXplorer10   4
N an hour ago by MathXplorer10
Hi guys!


I got a 118.5 on the 12B test this year. I am wondering if it is possible to make USAMO (what do you think the cutoffs would be this year?)

For some background, I got 121.5/127.5 on the 10s last year, and got a 7 on AIME with no extra prep. Is it possible to go from a 7 to a 10 (or whatever I need to get on AIME)?

Thank you!
4 replies
MathXplorer10
4 hours ago
MathXplorer10
an hour ago
10a vs 10b
golden_star_123   111
N an hour ago by happyfish0922
Post the difference between your 10a and 10b score!
111 replies
golden_star_123
Wednesday at 6:24 PM
happyfish0922
an hour ago
What do next?
FuturePanda   2
N an hour ago by Tem8
Hi everyone,

I think I got an 81 and 102 for 12A and 10B, sillying way too much on both. I read all of the AOPS books, and I know most of the theorems for the AMC’s I just don’t know which ones to apply to solve the problems. Additionally, I suck at trig, complex, and logarithms. What should I do to improve?

For example, should I be grinding past AIME’s?
I plan on reading most of the Awesomemath books for L3
2 replies
FuturePanda
3 hours ago
Tem8
an hour ago
No more topics!
bull sigh
ostriches88   31
N 2 hours ago by nsking_1209
Source: 2024 AMC 10B p14, 12B p9
A dartboard is the region B in the coordinate plane consisting of points $(x, y)$ such that $|x| + |y| \le 8$. A target T is the region where $(x^2 + y^2 - 25)^2 \le 49$. A dart is thrown at a random point in B. The probability that the dart lands in T can be expressed as $\frac{m}{n} \pi$, where $m$ and $n$ are relatively prime positive integers. What is $m + n$?

$
\textbf{(A) }39 \qquad
\textbf{(B) }71 \qquad
\textbf{(C) }73 \qquad
\textbf{(D) }75 \qquad
\textbf{(E) }135 \qquad
$
31 replies
ostriches88
Wednesday at 5:32 PM
nsking_1209
2 hours ago
Source: 2024 AMC 10B p14, 12B p9
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ostriches88
1441 posts
#1 • 1 Y
Y by clarkculus
A dartboard is the region B in the coordinate plane consisting of points $(x, y)$ such that $|x| + |y| \le 8$. A target T is the region where $(x^2 + y^2 - 25)^2 \le 49$. A dart is thrown at a random point in B. The probability that the dart lands in T can be expressed as $\frac{m}{n} \pi$, where $m$ and $n$ are relatively prime positive integers. What is $m + n$?

$
\textbf{(A) }39 \qquad
\textbf{(B) }71 \qquad
\textbf{(C) }73 \qquad
\textbf{(D) }75 \qquad
\textbf{(E) }135 \qquad
$
This post has been edited 4 times. Last edited by jlacosta, Wednesday at 5:35 PM
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exp-ipi-1
965 posts
#2 • 1 Y
Y by kosarsi
Pretty sure it's b
Good problem imo
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ostriches88
1441 posts
#3
Y by
can confirm b

sillied this in fifteen different ways and wound up getting it right
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mathboy282
2966 posts
#4
Y by
concentric circles over a square. 14/(8sqrt2)^2=7/64
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osunm
355 posts
#5
Y by
the first equation is a tilted square and the second is a ring of thickness sqrt(2) iirc
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TiguhBabeHwo
208 posts
#6
Y by
my favorite problem
basically circle with radius rt32 and one of rt18 so you get 14pi/128, B
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Orthogonal.
563 posts
#7
Y by
sillied this one :sob:
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elizhang101412
1060 posts
#8
Y by
i got 7/128pi :sob: only problem I got wrong that I attempted in first 15
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UnearthedCyclone
102 posts
#9
Y by
Did anyone else think the square had side length 4sqrt2 and then proceed to never answer it or was that just me
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axusus
783 posts
#10
Y by
Orthogonal. wrote:
sillied this one :sob:

bro wHAT this is the only one you sillied
I sillied the equilateral rotation one because I forgot to do it after putting a random guess while looking through the problems
and I sillied the inradius problem (I made the observation that only equilateral triangles work, but I finished the problem wrong :wallbash_red: )
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pingpongmerrily
2394 posts
#11
Y by
$\frac{7}{64}$ hopefully i didn't miss bubble
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cosinesine
42 posts
#12
Y by
By difference of squares the equation is $(x^2 + y^2 - 32)(x^2 + y^2 - 18) \le 0$, so the point must lie in within exactly one of the circles, which is a region with area $32\pi - 18\pi = 14\pi$. The outer dartboard is a square with side length $8\sqrt{2}$ and area $128$, so the answer is $\frac{7\pi}{64} \implies \boxed{B}$
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MathRook7817
233 posts
#13
Y by
yeah, 7/64 through geometric probability
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andrewcheng
482 posts
#14
Y by
BRUH I ADDED 64+7 as 73
This post has been edited 1 time. Last edited by andrewcheng, Wednesday at 6:03 PM
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pingpongmerrily
2394 posts
#15
Y by
andrewcheng wrote:
BRUH I ADDED 64+7 as 73

i feel like a mighta done that too, i hope not tho
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LostDreams
124 posts
#17
Y by
cosinesine wrote:
By difference of squares the equation is $(x^2 + y^2 - 32)(x^2 + y^2 - 18) \le 0$, so the point must lie in within exactly one of the circles, which is a region with area $32\pi - 18\pi = 14\pi$. The outer dartboard is a square with side length $8\sqrt{2}$ and area $128$, so the answer is $\frac{7\pi}{64} \implies \boxed{B}$

yea this is exactly what I did
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successfulspark
10 posts
#18
Y by
lol I sillied this one cause I thought the side length of the square was 8 and not 8sqrt(2) :(
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akliu
1705 posts
#19 • 3 Y
Y by Firebreather14, Sedro, Alex-131
thank goodness $5$ isn't an answer choice
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Mr.Sharkman
386 posts
#20
Y by
Notice that $18 \le x^{2}+y^{2} \le 32.$ Now, the region $B$ has area $128.$ Then, target $T$ has area $32\pi-18\pi = 14\pi,$ giving $\frac{7}{64},$ or $71$ as our answer.
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mathenrichmentaops
503 posts
#21
Y by
UnearthedCyclone wrote:
Did anyone else think the square had side length 4sqrt2 and then proceed to never answer it or was that just me

same bruh
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puffypundo
18 posts
#22
Y by
andrewcheng wrote:
BRUH I ADDED 64+7 as 73

nooo :( i also did that the first time through but fortunately i caught the error while double checking
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axusus
783 posts
#23
Y by
yall if you did a quick sketch of the square yall would not have this issue :skull: sad
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Happy2Bee
6 posts
#24
Y by
the name of the question bulls "sigh" instead of "eye"
this thing got me :rotfl:
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giratina3
242 posts
#25
Y by
if you had a general idea how absolute graphs and circles worked on the coordinate plane, this problem was just absolutely free
This post has been edited 1 time. Last edited by giratina3, Yesterday at 2:42 AM
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elizhang101412
1060 posts
#26
Y by
alright i finally realized what i did wrong
i calculated the area of the square based on its diagonal oops
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Einstein394
646 posts
#27
Y by
Sillied cuz I thought (8sqrt2)^2 = 64 not 128 so I put 39
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Andrew2019
2216 posts
#28
Y by
first i thought 25+7 = 34

then i realized and corrected it
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FuturePanda
92 posts
#29
Y by
Beautiful problem though, my favorite!
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pog
4903 posts
#30
Y by
$~~~~~~~$
Attachments:
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SpeedCuber7
1392 posts
#31
Y by
i can't geometry
skipped
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SomeRandomGuyOnline
33 posts
#32
Y by
how do you get better as these graphing problems bcuz I suck at them?
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nsking_1209
81 posts
#33
Y by
SomeRandomGuyOnline wrote:
how do you get better as these graphing problems bcuz I suck at them?

I just experimented with a bunch of graphs on desmos and saw what happened. It becomes intuitive after you see different scenarios of equations and their graphs
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