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• 2004 AIME I Problems/Problem 3
  == Problem == {{AIME box|year=2004|n=I|num-b=2|num-a=4}}
  1 KB (156 words) - 17:56, 1 January 2016

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• Ptolemy's theorem
  ...lity, with equality holding when <math>A^*, B^*, C^*</math> are collinear, i.e. when <math>A,B,C</math> lie on a circle containing <math>D.</math> Addit ===2023 AIME I Problem 5===
  6 KB (922 words) - 17:34, 13 January 2025
• Overcounting
  An example of a classic problem is as follows: "How many numbers less than or equal to 100 are divisible by either 2 or 3?"
  4 KB (635 words) - 12:19, 2 January 2022
• Constructive counting
  This is a problem where constructive counting is not the simplest way to proceed. This next e === Example 3 ===
  13 KB (2,018 words) - 15:31, 10 January 2025
• Recursion
  ...f the sequence in terms of previous values: <math>F_0=1, F_1=1, F_2=2, F_3=3, F_4=5, F_5=8</math>, and so on. * [[Mock_AIME_2_2006-2007_Problems#Problem_8 | Mock AIME 2 2006-2007 Problem 8]] ([[number theory]])
  2 KB (316 words) - 16:03, 1 January 2024
• Fibonacci sequence
  ...s the sum of the two preceding it. The first few terms are <math>1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...</math>. ...F_1 = F_2 = 1</math> and <math>F_n=F_{n-1}+F_{n-2}</math> for <math>n \geq 3</math>. This is the simplest nontrivial example of a [[linear recursion]]
  7 KB (1,111 words) - 14:57, 24 June 2024
• Complex number
  ...ver, it is possible to define a number, <math> i </math>, such that <math> i = \sqrt{-1} </math>. If we add this new number to the reals, we will have ...rm <math> a + bi </math> where <math> a,b\in \mathbb{R} </math> and <math> i = \sqrt{-1} </math> is the [[imaginary unit]]. The set of complex numbers i
  5 KB (860 words) - 15:36, 10 December 2023
• Arithmetic sequence
  For example, <math>1, 2, 3, 4</math> is an arithmetic sequence with common difference <math>1</math> a * [[2005_AMC_10A_Problems/Problem_17 | 2005 AMC 10A Problem 17]]
  4 KB (736 words) - 02:00, 7 March 2024
• 2004 AIME I
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2004 AIME I Problems]]
  1 KB (135 words) - 18:15, 19 April 2021
• 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
• Mock AMC
  ...A number of '''Mock AMC''' competitions have been hosted on the [[Art of Problem Solving]] message boards. They are generally made by one community member ...amous theorems and formulas and see if there's any way you can make a good problem out of them.
  51 KB (6,175 words) - 21:41, 27 November 2024
• 2005 AIME I Problems
  {{AIME Problems|year=2005|n=I}} == Problem 1 ==
  6 KB (983 words) - 05:06, 20 February 2019
• 2005 AIME I Problems/Problem 2
  == Problem == ...ath>(501,4)</math>, <math>(668,3)</math>, <math>(1002,2)</math> and <math>(2004,1)</math>, and each of these gives a possible value of <math>k</math>. Thus
  2 KB (303 words) - 01:31, 5 December 2022
• 2004 AIME I Problems/Problem 15
  == Problem == ...st <math>n</math> such that <math>x_n=1</math>. (For example, <math>d(100)=3</math> and <math>d(87)=7</math>.) Let <math>m</math> be the number of posit
  9 KB (1,491 words) - 01:23, 26 December 2022
• 2004 AIME I Problems/Problem 14
  == Problem == real x = 20 - ((750)^.5)/3, CE = 8*(6^.5) - 4*(5^.5), CD = 8*(6^.5), h = 4*CE/CD;
  4 KB (729 words) - 01:00, 27 November 2022
• 2004 AIME I Problems/Problem 13
  == Problem == ...oots of the form <math> z_k = r_k[\cos(2\pi a_k)+i\sin(2\pi a_k)], k=1, 2, 3,\ldots, 34, </math> with <math> 0 < a_1 \le a_2 \le a_3 \le \cdots \le a_{3
  2 KB (298 words) - 20:02, 4 July 2013
• 2004 AIME I Problems/Problem 12
  == Problem == ...rac{1}{4}}\right)\left(\frac{\frac{4}{5}}{1-\frac{1}{25}}\right)= \frac{2}{3} \cdot \frac{5}{6} = \frac{5}{9},</cmath> and the answer is <math>m+n = 5 +
  2 KB (303 words) - 18:43, 16 October 2024
• 2004 AIME I Problems/Problem 11
  == Problem == ...the shape of a right circular [[cone]] is 4 inches tall and its base has a 3-inch radius. The entire [[surface]] of the cone, including its base, is pai
  5 KB (839 words) - 22:12, 16 December 2015
• 2004 AIME I Problems/Problem 10
  == Problem == === Solution 3 ===
  5 KB (836 words) - 07:53, 15 October 2023
• 2004 AIME I Problems/Problem 9
  == Problem == Let <math> ABC </math> be a [[triangle]] with sides 3, 4, and 5, and <math> DEFG </math> be a 6-by-7 [[rectangle]]. A segment is
  4 KB (647 words) - 17:43, 23 November 2024

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