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Difference between revisions of "2024 AMC 8 Problems"

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==Problem 2==
 
==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.
 
  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.
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==Problem 4==
 
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What is the sum of the roots of <math>\frac{1}{x}</math> <math>+1=x</math>?
 
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A)0  B)-1  C)1  D)-2  E)2
 
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[[2024 AMC 8 Problems/Problem 10|Solution]]
 
  
 
==Problem 11==
 
==Problem 11==

Revision as of 15:13, 21 January 2024

2024 AMC 8 (Answer Key)
Printable versions: Wiki • AoPS Resources • PDF

Instructions

  1. 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.
  2. You will receive 1 point for each correct answer. There is no penalty for wrong answers.
  3. 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
  4. Figures are not necessarily drawn to scale.
  5. You will have 40 minutes working time to complete the test.
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

==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 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 $\text{x=2024}$. Compute the last three digits of $((x^3-(x-8)^3)^4-(x-69)^2)^5$.

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

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
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