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• Mock AIME 5 Pre 2005 Problems
  == Problem 1 == [[Mock AIME 5 Pre 2005 Problems/Problem 1|Solution]]
  6 KB (909 words) - 07:27, 12 October 2022
• Mock AIME 5 Pre 2005 Problems/Problem 12
  == Problem == Let <math>m = 101^4 + 256</math>. Find the sum of the digits of <math>m</math>.
  517 bytes (55 words) - 20:01, 23 March 2017
• Ball-and-urn
  ...<math>3</math> bins. The number of ways to do such is <math>{4+3-1 \choose 3-1} = {6 \choose 2} = 15</math>. ...ach urn, then there would be <math>{n \choose k}</math> possibilities; the problem is that you can repeat urns, so this does not work.<math>n</math> and then
  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 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 4 Pre 2005/Problems
  ==Problem 1== [[Mock AIME 4 Pre 2005/Problems/Problem 1 | Solution]]
  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 == <math>x</math> is a real number with the property that <math>x+\tfrac1x = 3</math>. Let <math>S_m = x^m + \tfrac{1}{x^m}</math>. Determine the value of
  883 bytes (128 words) - 16:14, 4 August 2019
• Mock AIME 2 Pre 2005 Problems/Problem 5
  == Problem == ...7 \cdot 3^3 \cdot 37,</cmath> the number <math>10^{12} -1</math> has <math>4 \cdot 2^6 = 256</math> divisors and our answer is <math>256 - 1 = \boxed{25
  1 KB (171 words) - 17:38, 4 August 2019
• Telescoping series
  ...are positive integers. What is <math>a+b</math>? ([[2022 AMC 10B Problems/Problem 9|Source]]) ...math>(2+3)(2^2+3^2)(2^4+3^4)(2^8+3^8)(2^{16}+3^{16})(2^{32}+3^{32})(2^{64}+3^{64})?</math> (Hint: difference of squares!)
  3 KB (500 words) - 14:11, 21 November 2023
• Mock AIME 2 Pre 2005 Problems/Problem 9
  == Problem == ...left(1+2x^{3^2}\right)\cdots \left(1+kx^{3^k}\right) \cdots \left(1+1997x^{3^{1997}}\right) = 1+a_1 x^{k_1} + a_2 x^{k_2} + \cdots + a_m x^{k_m}</cmath>
  2 KB (232 words) - 00:22, 1 January 2021

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