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• Mock AIME 3 Pre 2005 Problems/Problem 14
  ==Problem== ..._1</math> at <math>C</math> and <math>D</math> respectively. If <math>AD = 3, AP = 6, DP = 4,</math> and <math>PQ = 32</math>, then the area of triangle
  3 KB (563 words) - 02:05, 25 November 2023
• Mock AIME 3 Pre 2005 Problems/Problem 15
  ==Problem== <math>\sum_{k=1}^{40} \cos^{-1}\left(\frac{k^2 + k + 1}{\sqrt{k^4 + 2k^3 + 3k^2 + 2k + 2}}\right)</math>
  2 KB (312 words) - 10:38, 4 April 2012
• Mock AIME 5 2005-2006 Problems/Problem 1
  == 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) - 12:43, 10 August 2019
• Mock AIME 1 Pre 2005 Problems/Problem 1
  == Problem == ...e tens and units digits. Thus the sum of the hundreds places is <math>(1+2+3+\cdots+9)(72) \times 100 = 45 \cdot 72 \cdot 100 = 324000</math>.
  1 KB (194 words) - 13:44, 5 September 2012
• Mock AIME 1 Pre 2005 Problems/Problem 4
  == Problem == When <math>1 + 7 + 7^2 + \cdots + 7^{2004}</math> is divided by <math>1000</math>, a rem
  685 bytes (81 words) - 10:51, 11 June 2013
• Mock AIME 1 Pre 2005 Problems/Problem 7
  == Problem == ...</tt>s amongst the middle five numbers, and so there are <math>6-(5-k) = k+1</math> <tt>C</tt>s amongst the first four numbers.
  1 KB (221 words) - 17:27, 23 February 2013
• Mock AIME 1 Pre 2005 Problems/Problem 8
  == Problem == Thus, the height of <math>P</math> is <math>\sqrt [3]{8} = 2</math> times the height of <math>P'</math>, and thus the height of
  3 KB (446 words) - 00:18, 10 February 2020
• Mock AIME 5 Pre 2005 Problems
  == Problem 1 == <cmath>6g(1 + (1/y)) + 12g(y + 1) = \log_{10} y</cmath>
  6 KB (909 words) - 07:27, 12 October 2022
• Mock AIME 5 Pre 2005 Problems/Problem 12
  == Problem == ...56 = 104060657, \end{aligned}</math> and so the sum of the digits is <math>1+4+6+6+5+7 = \boxed{29}.</math>
  517 bytes (55 words) - 20:01, 23 March 2017
• Mock AIME 1 Pre 2005 Problems/Problem 11
  == Problem == <cmath>\sum_{n=0}^{668} (-1)^{n} {2004 \choose 3n}</cmath>
  2 KB (272 words) - 10:51, 2 July 2015
• Ball-and-urn
  ...ath>3</math> bins. The number of ways to do such is <math>{4+3-1 \choose 3-1} = {6 \choose 2} = 15</math>. ...ath>n</math> bins is <math>{n+k-1 \choose k-1}</math> or <math>\dbinom{n+k-1}n</math>.
  5 KB (775 words) - 23:53, 13 April 2024
• Mock AIME 1 Pre 2005 Problems/Problem 15
  == Problem == ..., we have that <math>\cos B = \frac{7}{16}</math> and <math>\sin B = \frac{3\sqrt{23}}{16}</math>. Since <math>\sin B = \frac{b}{2R}</math>, we have tha
  2 KB (340 words) - 01:44, 3 March 2020
• Mock AIME 5 2005-2006 Problems/Problem 2
  == Problem == {{Mock AIME box|year=2005-2006|n=5|source=76847|num-b=1|num-a=3}}
  752 bytes (117 words) - 21:16, 8 October 2014
• Mock AIME 5 2005-2006 Problems/Problem 4
  == Problem == Let <math>m</math> and <math>n</math> be integers such that <math>1 < m \le 10</math> and <math>m < n \le 100</math>. Given that <math>x = \log
  645 bytes (109 words) - 20:41, 22 March 2016
• Mock AIME 5 2005-2006 Problems/Problem 6
  == Problem == : <math>P_1(x) = 1+x+x^3+x^4+\cdots+x^{96}+x^{97}+x^{99}+x^{100}</math>
  522 bytes (77 words) - 21:17, 8 October 2014
• Mock AIME 5 2005-2006 Problems/Problem 7
  == Problem == ...that <math>P_n > P</math>. Find the value of <math>\left\lfloor \frac{n_0}{3} \right\rfloor</math>.
  853 bytes (134 words) - 21:18, 8 October 2014
• Mock AIME 5 2005-2006 Problems/Problem 14
  == Problem == So <math>Sin^2B=1-Cos^2B=\frac{85^2-13^2}{85^2}=\frac{84^2}{85^2}</math>
  2 KB (282 words) - 10:06, 9 August 2022
• Mock AIME 4 Pre 2005/Problems
  ==Problem 1== For how many integers <math>n>1</math> is it possible to express <math>2005</math> as the sum of <math>n</m
  7 KB (1,094 words) - 15:39, 24 March 2019
• Mock AIME 2 Pre 2005 Problems
  == Problem 1 == [[Mock AIME 2 Pre 2005 Problems/Problem 1|Solution]]
  6 KB (1,052 words) - 13:52, 9 June 2020
• Mock AIME 2 Pre 2005 Problems/Problem 2
  == Problem == ...he property that <math>x+\tfrac1x = 3</math>. Let <math>S_m = x^m + \tfrac{1}{x^m}</math>. Determine the value of <math>S_7</math>.
  883 bytes (128 words) - 16:14, 4 August 2019

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