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Middle School Math Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8

Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8

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Middle School Math Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8

Grades 5-8, Ages 10-13, MATHCOUNTS, AMC 8

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#1 h Apr 6, 2025, 11:07 PM

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1. If x squared minus (x squared times pi)/4 equals 3+ 3 root 3 -2pi, solve for x.
2. You're playing a game where you need to roll at least N to win. You can either roll 2 6-sided fair dice or a 12-sided fair die. For what value of n between 1 and 12, inclusive, is the probability of winning equal no matter which dice you choose?
3. Define the polynomial P(x)=(x^3)+1. Find the sum of the coefficients of P(P(P(x))).
4. Jerry chooses 2 positive integers x and y that yield a product of 6^5, or 7776. He then computes the value of n, which is the GCD of (a,b). How many possible values of n can Jerry get?

Provide solutions to answers

Also how hard are these problems: AMC8, AMC10, MathCounts, or AMC12?

This post has been edited 1 time. Last edited by hashbrown2009, Apr 6, 2025, 11:07 PM

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Bocabulary142857

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Bocabulary142857

#2 h Apr 7, 2025, 1:15 AM

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With LaTeX:
1. If $x^2-$ $\frac{x^2*\pi}{4}=3+3\sqrt{3}-2\pi$ , solve for x.
2. You're playing a game where you need to roll at least N to win. You can either roll 2 6-sided fair dice or a 12-sided fair die. For what value of n between 1 and 12, inclusive, is the probability of winning equal no matter which dice you choose?
3. Define the polynomial $P(x)=x^3+1$ . Find the sum of the coefficients of $P(P(P(x)))$ .
4. Jerry chooses 2 positive integers x and y that yield a product of $6^5$ , or 7776. He then computes the value of n, which is the GCD of $(a,b)$ . How many possible values of n can Jerry get? Note

I might solve these later, but these seem like they could be problems in AMC8, Mathcounts, or one of the first problems in AMC10.

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#3 h Apr 7, 2025, 1:18 AM

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all of these are like amc10 p10-18

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#4 h Apr 7, 2025, 1:27 AM

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Bocabulary142857 wrote:

With LaTeX:
1. If $x^2-\frac{\pi x^2}4=3+3\sqrt3-2\pi$ , solve for $x.$
2. You're playing a game where you need to roll at least $N$ to win. You can either roll two $6$ -sided fair dice or a $12$ -sided fair die. For what value of $n$ between $1$ and $12,$ inclusive, is the probability of winning equal, no matter which dice you choose?
3. Define the polynomial $P(x)=x^3+1$ . Find the sum of the coefficients of $P(P(P(x)))$ .
4. Jerry chooses $2$ positive integers $x$ and $y$ that yield a product of $6^5=7776.$ He then computes the value of $n,$ which is $\gcd(x,y).$ How many possible values of $n$ can Jerry get?

FTFYUIJAULWIDSIDFTFY

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iwastedmyusername

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iwastedmyusername

#5 h Apr 7, 2025, 1:40 AM

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hashbrown2009 wrote:

1. If x squared minus (x squared times pi)/4 equals 3+ 3 root 3 -2pi, solve for x.
2. You're playing a game where you need to roll at least N to win. You can either roll 2 6-sided fair dice or a 12-sided fair die. For what value of n between 1 and 12, inclusive, is the probability of winning equal no matter which dice you choose?
3. Define the polynomial P(x)=(x^3)+1. Find the sum of the coefficients of P(P(P(x))).
4. Jerry chooses 2 positive integers x and y that yield a product of 6^5, or 7776. He then computes the value of n, which is the GCD of (a,b). How many possible values of n can Jerry get?

Provide solutions to answers
P1
P2
P3
P4

these are probably like amc 10 p11-15

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