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• 2005 AIME II Problems/Problem 12
  == Problem == ...^2</math> equal and solving for <math>x</math> (it is helpful to scale the problem down by a factor of 50 first), we get <math>x = 250\pm 50\sqrt{7}</math>. S
  13 KB (2,080 words) - 13:14, 23 July 2024
• 2005 AIME I Problems/Problem 12
  == Problem == ...let <math> b </math> denote the number of positive integers <math> n \leq 2005 </math> with <math> S(n) </math> [[even integer | even]]. Find <math> |a-b|
  4 KB (647 words) - 02:29, 4 May 2021
• Mock AIME 3 Pre 2005 Problems/Problem 12
  ==Problem== ...tegers <math>n</math> such that <math>1 \le n \le 1000</math> and <math>n^{12} - 1</math> is divisible by <math>73</math>.
  714 bytes (105 words) - 23:59, 24 April 2013
• Mock AIME 5 Pre 2005 Problems/Problem 12
  == Problem == {{Mock AIME box|year=Pre 2005|n=5|num-b=11|num-a=13|source=28368}}
  517 bytes (55 words) - 20:01, 23 March 2017
• Mock AIME 1 Pre 2005 Problems/Problem 12
  == Problem == {{Mock AIME box|year=Pre 2005|n=1|num-b=11|num-a=13|source=14769}}
  2 KB (376 words) - 22:41, 26 December 2016
• Mock AIME 5 2005-2006 Problems/Problem 12
  == Problem == <math>Or,AD=12</math>
  2 KB (294 words) - 16:24, 24 August 2022

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• Simon's Favorite Factoring Trick
  ...nd make the equation factorable. It can be used to solve more than algebra problems, sometimes going into other topics such as number theory. == Fun Practice Problems ==
  4 KB (682 words) - 10:25, 18 February 2025
• Constructive counting
  This is a problem where constructive counting is not the simplest way to proceed. This next e ...proceed with the construction. If we were to go like before and break the problem down by each box, we'd get a fairly messy solution.
  13 KB (2,018 words) - 15:31, 10 January 2025
• Ellipse
  pair P=(3,12/5), F1=(-4,0), F2=(4,0); ==Problems==
  5 KB (892 words) - 21:52, 1 May 2021
• Complex number
  == Problems == *[[2007 AMC 12A Problems/Problem 18]]
  5 KB (860 words) - 15:36, 10 December 2023
• Without loss of generality
  ...0, AMC 12, and AIME competitions it is very common to use WLOG in geometry problems by assuming one undefined side length to be equal to 1. == Problems using WLOG ==
  2 KB (318 words) - 23:35, 13 September 2024
• Geometric sequence
  == Problems == Here are some problems with solutions that utilize geometric sequences and series.
  4 KB (649 words) - 21:09, 19 July 2024
• Arithmetic sequence
  ...difference <math>-8</math>; however, <math>7, 0, 7, 14</math> and <math>4, 12, 36, 108, \ldots</math> are not arithmetic sequences, as the difference bet == Problems ==
  4 KB (736 words) - 02:00, 7 March 2024
• 2004 AIME II
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2004 AIME II Problems]]
  1 KB (135 words) - 12:24, 22 March 2011
• 2005 AIME I
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2005 AIME I Problems]]
  1 KB (154 words) - 12:30, 22 March 2011
• 2006 AIME I
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2006 AIME I Problems]]
  1 KB (135 words) - 12:31, 22 March 2011
• 2005 AIME II
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2005 AIME II Problems]]
  1 KB (135 words) - 12:30, 22 March 2011
• Mock AMC
  ...ake. Sometimes, the administrator may ask other people to sign up to write problems for the contest. * Look at past [[AMC]]/[[AHSME]] tests to get a feel for what kind of problems you should write and what difficulty level they should be.
  51 KB (6,175 words) - 21:41, 27 November 2024
• 2006 AIME I Problems
  {{AIME Problems|year=2006|n=I}} == Problem 1 ==
  7 KB (1,173 words) - 03:31, 4 January 2023
• Set
  ...describe sets should be used with extreme caution. One way to avoid this problem is as follows: given a property <math>P</math>, choose a known set <math>T< ==Problems==
  11 KB (2,019 words) - 17:20, 7 July 2024
• 2005 AIME II Problems/Problem 4
  == Problem == <math>18^{11} = 2^{11}\cdot3^{22}</math> so <math>18^{11}</math> has <math>12\cdot23 = 276</math> divisors.
  3 KB (377 words) - 18:36, 1 January 2024
• 2005 AIME II Problems/Problem 13
  == Problem == ...olutions so <math>P(x)</math> is at least quadratic. Let us first try this problem out as if <math>P(x)</math> is a quadratic polynomial. Thus <math>P(n)-(n+3
  4 KB (642 words) - 02:14, 1 June 2024
• 2005 AIME II Problems/Problem 5
  == Problem == ...og_a b + 6\log_b a=5, 2 \leq a \leq 2005, </math> and <math> 2 \leq b \leq 2005. </math>
  3 KB (547 words) - 19:15, 4 April 2024
• 2005 AIME II Problems
  {{AIME Problems|year=2005|n=II}} == Problem 1 ==
  7 KB (1,119 words) - 21:12, 28 February 2020
• 2005 AIME II Problems/Problem 7
  == Problem == <cmath>(y^8+1)(y^4+1) =(y^{12}+y^8+y^4+1)</cmath>
  2 KB (279 words) - 12:33, 27 October 2019
• 2005 AIME II Problems/Problem 11
  == Problem == ...</math>, <math>a_{m-1}a_{m-2} = 3</math>; from the recursion given in the problem <math>a_{m-p+1} = a_{m-p-1} - 3/a_{m-p}</math>, so <math>a_{m-p+1} = 3p/a_{
  3 KB (499 words) - 18:52, 21 November 2022

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