2024 AMC 8 Problems
2024 AMC 8 (Answer Key) Printable versions: • AoPS Resources • PDF | ||
Instructions
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==Problem 1== You can do it!
==Problem 1== You can do it!
Contents
- 1 Problem 2
- 2 Problem 3
- 3 Problem 4
- 4 Problem 5
- 5 Problem 6
- 6 Problem 8
- 7 Problem 9
- 8 Problem 42568
- 9 Problem 11
- 10 Problem 12
- 11 Problem 13
- 12 Problem 14
- 13 Problem 15
- 14 Problem 17
- 15 Problem 18
- 16 Problem 19
- 17 Problem 20
- 18 Problem 21
- 19 Problem 22
- 20 Problem 23
- 21 Problem 24
- 22 Problem 25
- 23 See Also
Problem 2
What is the last 3 digits of "pi"?
-Multpi12
Problem 3
If Bartholomew's second cousin's neighbor's doctor's teacher's pet cat's favourite number in the Egyptian 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 divided by the last digit of pi.
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 multiplied by the amount of force Bob exerted when calculating the last digit of pi assuming Bob went to sleep at
PM yesterday?
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
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 (F) you want to know how many problems you got correct on the AMC 8 (G) you think problem 15 would be really fun to solve (I) you looked at problem 15 (J) you didn't realize I skipped option H
Problem 9
If you are canoeing down a road, and a tire falls off, how many pancakes do you need to build a doghouse?
(A) 34 (C) purple (B) teaspoon (D) penguin (E)
Problem 42568
What is the sum of the roots of
?
A)0 B)-1 C)1 D)-2 E)2
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 , then what does
equal?
Problem 13
A finite set of positive integers has the property that, for each
, and each positive integer divisor
of
, there exists a unique element
satisfying
(the elements
and
could be equal).
Given this information, find all possible values for the number of elements of . (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 >/ 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) + 3 (B)
- 3 (C)
+ 4 (D)
(E)
+ 5
Problem 15
Let be an interior point of the acute triangle
with
so that
. The point
on the segment
satisfies
, the point
on the segment
satisfies
, and the point
on the line
satisfies
. Let
and
be the circumcentres of the triangles
and
respectively. Prove that the lines
,
, and
are concurrent. (source: 2021 IMO)
now go do this problem WITHOUT THE SOLUTION as a punishment for trying to cheat
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. Compute the last three digits of
.
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 funbeast mathkindacool_ Rainier2020
Problem 20
Find the sum of the square root of -2 and the last digit of pi.
Problem 21
what is 9+10?
(A) 21 (B) 69 (C) 19 (D) nothing (E) something
Problem 22
What is the sum of the cubes of the solutions cubed of ?
(A) 1 (B) 8 (C) 27 (D) -1 (E) -27
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)
And so am I ;)
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |