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  • ==Problem== ...6</math> and <math>BC=3</math>. Point <math>E</math> is such that <math>CE=1</math> and <math>AE=5</math>. Construct point <math>F</math> on segment <ma
    3 KB (518 words) - 15:54, 25 November 2015

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  • ...ake. Sometimes, the administrator may ask other people to sign up to write problems for the contest. ...AMC]] competition. There is no guarantee that community members will make Mock AMCs in any given year, but there probably will be one.
    51 KB (6,175 words) - 20:41, 27 November 2024
  • The '''Mock AIME 1 2005-2006''' was written by [[Art of Problem Solving]] community member paladin8. * [[Mock AIME 1 2005-2006/Answer Key|Answer Key]]
    1 KB (135 words) - 16:41, 21 January 2017
  • The '''Mock AIME 1 2006-2007''' was written by [[Art of Problem Solving]] community member Altheman. * [[Mock AIME 1 2006-2007/Problems|Entire Exam]]
    1 KB (155 words) - 15:06, 3 April 2012
  • The '''Mock AIME 2 2006-2007''' was written by [[Art of Problem Solving]] community member 4everwise. * [[Mock AIME 2 2006-2007 Problems|Entire Exam]]
    1 KB (145 words) - 09:55, 4 April 2012
  • ...al{S}</math>, we have that <math>\star (n)=12</math> and <math>0\le n< 10^{7}</math>. If <math>m</math> is the number of elements in <math>\mathcal{S}</ ...us <math>m = 18564 - 7 - 42 - 42 - 105 = 18368</math> so <math>\star(m) = 1 + 8 + 3 + 6 + 8 = 026</math>.
    1 KB (188 words) - 14:53, 3 April 2012
  • Let <math>\triangle ABC</math> have <math>BC=\sqrt{7}</math>, <math>CA=1</math>, and <math>AB=3</math>. If <math>\angle A=\frac{\pi}{n}</math> where ...o <math>3^{2000}\equiv 1 \pmod{1000}</math> and so <math>3^{2007} \equiv 3^7 \equiv 2187 \equiv 187 \pmod{1000}</math>
    963 bytes (135 words) - 14:53, 3 April 2012
  • ...vely. If the <math>x</math>-coordinate of the triangle's centroid is <math>1</math>, find the area of <math>\triangle ABC</math>. ...> and <math>a = (a + b) - b = 12</math>, so our three vertices are <math>(-7, 49), (-2, 4)</math> and <math>(12, 144)</math>.
    1 KB (244 words) - 14:21, 5 November 2012
  • ==Problem== ...math> for [[positive integer]]s <math>a,b,c</math> where <math>\gcd(a,b,c)=1</math>, find <math>a+b+c</math>.
    3 KB (460 words) - 14:52, 3 April 2012
  • ==Problem== label("A",A,(1,0));label("B",B,(-1,0));label("C",C,(-1,0));label("D",D,(1,-1));
    1 KB (244 words) - 13:54, 21 August 2020
  • ==Problem== ...<math>b=\frac{6}{11}</math>, radius <math>c=\frac{2}{5}</math> and <math>r=1</math>, see picture.
    1 KB (236 words) - 22:58, 24 April 2013
  • ==Problem== ...ngth <math>n</math> such that any 3 adjacent place numbers sum to at least 1. For example, <math>00100</math> works, but <math>10001</math> does not. Fi
    2 KB (424 words) - 14:51, 3 April 2012
  • ==Problem== ...7</math>, <math>d_{5}=13</math>, and <math>d_{6}=-16</math>, find <math>d_{7}</math>.
    3 KB (568 words) - 14:50, 3 April 2012
  • ==Problem 1== [[Mock AIME 1 2006-2007 Problems/Problem 1|Solution]]
    8 KB (1,355 words) - 13:54, 21 August 2020
  • == Problem == ...= 144</math> and <math>x_{n+3} = x_{n+2}(x_{n+1}+x_n)</math> for <math>n = 1, 2, 3, 4</math>. Find the last three [[digit]]s of <math>x_7</math>.
    3 KB (470 words) - 23:33, 9 August 2019
  • ...istered to the AoPS community, while others may be sourced from a group of problem writers. Different users may have a different way of participating; some ma ...COUNTS competition. There is no guarantee that community members will make Mock MATHCOUNTS in any given year, but it's usually a good bet that someone will
    26 KB (3,260 words) - 18:28, 15 August 2024
  • ==Problem== ...chael function]], we have <math>\lambda(1000)=100</math>, so <math>3^{100}=1\pmod{1000}</math>. Therefore, letting <math>N=3^{3^3}</math>, we seek to fi
    1 KB (127 words) - 23:15, 4 January 2010
  • ==Problem== <cmath>\begin{eqnarray*} (1 + 1)^{2007} &=& {2007 \choose 0} + {2007 \choose 1} + \ldots + {2007 \choose 2007} = 2^{2007}\
    4 KB (595 words) - 11:14, 25 November 2023
  • ==Problem== ...math>, we see that <math>f(1)=0, f(2)=0, f(3)=0, f(4)=1, f(5)=1, f(6)=2, f(7)=2,
    992 bytes (156 words) - 19:34, 27 September 2019
  • == Problem == ...5</math> and <math>f(101) = 0</math>). Evaluate the remainder when <math>f(1)+f(2)+\cdots+f(99)</math> is divided by <math>1000</math>.
    2 KB (209 words) - 11:43, 10 August 2019
  • In the context of problem-solving, the characteristic polynomial is often used to find closed forms f ...Indeed, if we define <math>T = \lambda I - A</math> and let <math>\bold{T}^1, \bold{T}^2, \ldots, \bold{T}^n</math> denote the column vectors of <math>T
    19 KB (3,412 words) - 13:57, 21 September 2022

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