2024 AMC 8 Problems

2024 AMC 8 (Answer Key) Printable versions: Wiki • AoPS Resources • PDF
Instructions This is a 25-question, multiple choice test. Each question is followed by answers marked A, B, C, D and E. Only one of these is correct. You will receive 1 point for each correct answer. There is no penalty for wrong answers. No aids are permitted other than plain scratch paper, writing utensils, ruler, and erasers. In particular, graph paper, compass, protractor, calculators, computers, smartwatches, and smartphones are not permitted. Rules Figures are not necessarily drawn to scale. You will have 40 minutes working time to complete the test.
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==Problem 1== One behalf of the AoPS team we have came to notice that these questions are editable as our dev team in on break at the moment this bug will not be fixed. Everyone who has written something no matter what the reason has broken the code of conduct witch was signed in the creation of your account. By writing something here your account will be banned(In the next 48 hours) and you will be banned from taking any future AoPS competitions. Our team here at AoPS has also came to notice that the AMC-8 2024 answers have been leaked as this is changing the results all over the country we will not be counting this test and will be creating another one to take its place. We have also noticed that there is one individual trying to stop the cheating of AMC-8 and thank you for including some light hearted jokes to help lighten the mood. On the behalf of the AoPS team we thank you for reading this message.

Problem 2

One behalf of the AoPS team we have came to notice that these questions are editable as our dev team in on break at the moment this bug will not be fixed. Everyone who has written something no matter what the reason has broken the code of conduct witch was signed in the creation of your account. By writing something here your account will be banned(In the next 48 hours) and you will be banned from taking any future AoPS competitions. Our team here at AoPS has also came to notice that the AMC-8 2024 answers have been leaked as this is changing the results all over the country we will not be counting this test and will be creating another one to take its place. We have also noticed that there is one individual trying to stop the cheating of AMC-8 and thank you for including some light hearted jokes to help lighten the mood. On the behalf of the AoPS team we thank you for reading this message.

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 $5$ friends that go to school, only on Tuesday and Wednesday. The chance of rain on Tuesday and Wednesday is $50\%$ . 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 $9:00$ PM yesterday?

$\textbf{(A)}\ 75423 \qquad \textbf{(B)}\ 5987 \qquad \textbf{(C)}\ 491 \qquad \textbf{(D)}\ 653\qquad \textbf{(E)}\ 21574$

Problem 5

Count from 1 to 278968797890807 for $1000000 by going to$ \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

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 (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) $\infty$

Problem 4

What is the sum of the roots of $\frac{1}{x}$ $+1=x$ ?

A)0 B)-1 C)1 D)-2 E)2

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 $1+1=3$ , then what does $\sqrt{235479^{\sqrt{9472853.23462}\times4912}} + \frac{1}{0}$ equal?

$\textbf{(A)}\ -1 \qquad \textbf{(B)}\ 0 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ 256246\qquad \textbf{(E)}\ 10000$

Problem 13

A finite set $S$ of positive integers has the property that, for each $s\in S$ , and each positive integer divisor $d$ of $s$ , there exists a unique element $t \in S$ satisfying $\gcd(s,t)=d$ (the elements $s$ and $t$ could be equal).

Given this information, find all possible values for the number of elements of $S$ . (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 $n$ >/ 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) $n=k$ + 3 (B) $n=k$ - 3 (C) $n=k$ + 4 (D) $n=k$ (E) $n=k$ + 5

Problem 15

Let $D$ be an interior point of the acute triangle $ABC$ with $AB > AC$ so that $\angle DAB= \angle CAD$ . The point $E$ on the segment $AC$ satisfies $\angle ADE= \angle BCD$ , the point $F$ on the segment $AB$ satisfies $\angle FDA= \angle DBC$ , and the point $X$ on the line $AC$ satisfies $CX=BX$ . Let $O_1$ and $O_2$ be the circumcentres of the triangles $ADC$ and $EXD$ respectively. Prove that the lines $BC$ , $EF$ , and $O_1 O_2$ 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.

Try this.

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.

$(A) 2+\sqrt2i (B)3+\sqrt2i (C) 4+\sqrt2i (D) 5+\sqrt2i (E) 7+\sqrt2i$

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 $x^5+2x^4+3x^3+3x^2+2x+1=0$ ?

(A) 1 (B) 8 (C) 27 (D) -1 (E) -27

Solution

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

If Bob is travelling at the speed of 3 George Washington, how long will it take for him to finish his chutney.

A) 13 Hours B) 7 minute C) NA D) 12 Neptunes E) IDK

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

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2024 AMC 8 Problems

Contents

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 8

Problem 9

Problem 4

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

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