2024 AMC 8 Problems
2024 AMC 8 (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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Contents
Problem 1
What is 2^34930490493049(N0 CALCULAT0RS ALL0WED!!!!!!!!!!!!!!) (A) 1 (B) 2 (C) idk (D) why are you cheating for amc8 (E) PLEASE LET ME USE A CALCULUSER!
Problem 2
What is the last 3 digits of "pi"?
-Multpi12
Problem 3
If Bartholomew's pet cat's favourite number in the alphabet is purple, then what is the square root of the combined time in years Bartholomew's father went to get the milk and the time it takes for you to count to 1 million out loud.
Problem 4
Bob has friends that go to school, only on Tuesday and Wednesday. The chance of rain on Tuesday and Wednesday is
. Assuming Bob and his friends are all humans, what is the street number of Bob's house?
Problem 5
Count from 1 to 278968797890807 for \text{freerobux_and_vbucks_not_scam.com}$.
==Problem 6==
4 random points are chosen on a sphere. What is the probability that the tetrahedron with vertices of the 4 points contains the center of the sphere?
(A) 1/2 (B) 1/4 (C) 3/8 (D) 1/8 (E) 3/10 (Source: Putnam) lmao
[[2024 AMC 8 Problems/Problem 6|Solution]]
==Problem 8== Bob has a magical nuclear button that will explode one out of the 12,500 nukes on our planet. One nuke is called the "Tsar Bomb". At random, what is the chance that Bob will explode the Tsar Bomba after detonating another special nuke called "OPO"?
(A) 1/12500 (B) People will die (C) The FBI will come (D) you don't know (E) you want to cheat for the AMC8
==Problem 9== Compute$ (Error compiling LaTeX. Unknown error_msg)\frac{1}{0}$.
(A) 1 (C) 5 (B) 2 (D) 6 (E)3
==Problem 10== What is the sum of the roots of$ (Error compiling LaTeX. Unknown error_msg)\frac{1}{x}$$ (Error compiling LaTeX. Unknown error_msg)+1=x$?
A)0 B)-1 C)1 D)-2 E)2
[[2024 AMC 8 Problems/Problem 10|Solution]]
==Problem 11== The equation (2^(333x-2))+(2^(111x+2))=(2^(222x+1))+1 has three real roots. Find their sum. (Source: AIME)
(A) 4/113 (B) 2/111 (C) 6/11 (D) 5/111 (E) 14/113
You thought we could let you cheat?
==Problem 12==
Assuming that$ (Error compiling LaTeX. Unknown error_msg)1+1=3\sqrt{235479^{\sqrt{9472853.23462}\times4912}} + \frac{1}{0}
\textbf{(A)}\ -1 \qquad \textbf{(B)}\ 0 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ 256246\qquad \textbf{(E)}\ 10000$==Problem 13==
A finite set$ (Error compiling LaTeX. Unknown error_msg)Ss\in S
d
s
t \in S
\gcd(s,t)=d
s
t$could be equal).
Given this information, find all possible values for the number of elements of$ (Error compiling LaTeX. Unknown error_msg)S$. (source: 2021 USAMO)
now that you read this problem you have to do it without looking at the solution or else... let's just say bad things will happen
==Problem 14== Let k >/ 2 be an integer. Find the smallest integer$ (Error compiling LaTeX. Unknown error_msg)n$>/ k + 1 with the property that there exists a set of n distinct real numbers such that each of its elements can be written as a sum of k other distinct elements of the set. (Source: IMO Shortlist Slovakia)
(A)$ (Error compiling LaTeX. Unknown error_msg)n=kn=k
n=k
n=k
n=k$+ 5
==Problem 15==
Let$ (Error compiling LaTeX. Unknown error_msg)DABC
AB > AC
\angle DAB= \angle CAD
E
AC
\angle ADE= \angle BCD
F
AB
\angle FDA= \angle DBC
X
AC
CX=BX
O_1
O_2
ADC
EXD
BC
EF
O_1 O_2$are concurrent. (source: 2021 IMO)
now go do this problem as a punishment for trying to cheat
[[2024 AMC 8 Problems/Problem 15|Solution]]
What is the value of 1, assuming that 1=1, but 1= 3(4x^2-7x+5) - 2(5x^2-9x-3)=6x
==Problem 17==
Let$ (Error compiling LaTeX. Unknown error_msg)\text{x=2024}((x^3-(x-8)^3)^4-(x-69)^2)^5$?
NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED. NO CALCULATORS ARE ALLOWED.
==Problem 18==
hi guys. trying to cheat? im ashamed of you code: nsb
==Problem 19== Write your AoPS name here if you took the AMC 8.
Probablity NapoleonicAviator Multpi12
==Problem 20== Find the sum of the square root of -2 and the last digit of pi.
==Problem 21== this question = 9+10, bc 9+10 = 21
==Problem 22== What is the sum of the cubes of the solutions cubed of$ (Error compiling LaTeX. Unknown error_msg)x^5+2x^4+3x^3+3x^2+2x+1=0$?
Problem 23
lol we are the defenders against the cheaters... get outta here and study
SubText: and im here writing soulutions for these joke problems. (Multpi12)
Problem 24
wait when are the questions coming tho I think it's 1/25 for official answers since all tests end at 1/24
Problem 25
Did you think you could cheat the AMC ;)
and why did you scroll all the way here lol
See Also
2024 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by 2023 AMC 8 |
Followed by 2025 AMC 8 | |
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All AJHSME/AMC 8 Problems and Solutions |