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• 2005 AIME I Problems/Problem 10
  == Problem == {{AIME box|year=2005|n=I|num-b=9|num-a=11}}
  5 KB (852 words) - 21:23, 4 October 2023

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• Principle of Inclusion-Exclusion
  ...d only once. In particular, memorizing a formula for PIE is a bad idea for problem solving. ==== Problem ====
  9 KB (1,703 words) - 01:20, 7 December 2024
• Constructive counting
  ...es for each digit to arrive at our answer: <math>9 \cdot 10 \cdot 10 \cdot 10 = 9000</math>. <math>\square</math> This is a problem where constructive counting is not the simplest way to proceed. This next e
  13 KB (2,018 words) - 15:31, 10 January 2025
• 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
  * [[2005_AMC_10A_Problems/Problem_17 | 2005 AMC 10A Problem 17]] * [[2006_AMC_10A_Problems/Problem_19 | 2006 AMC 10A Problem 19]]
  4 KB (736 words) - 02:00, 7 March 2024
• Diophantine equation
  ...re in the form <math>(P_{ia},Q_{ia})</math> for [[positive]] integer <math>i</math>. ...s for any given Diophantine equations. This is known as [[Hilbert's tenth problem]]. The answer, however, is no.
  9 KB (1,434 words) - 01:15, 4 July 2024
• Power of a Point Theorem
  ...}</math> that lies outside of the circle. ([[2020 AMC 12B Problems/Problem 10|Source]]) ...e by the square of a prime, find <math>m+n.</math> ([[2005 AIME I Problems/Problem 15|Source]])
  5 KB (948 words) - 17:04, 21 February 2025
• 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
  ...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
• 2006 AIME I Problems
  {{AIME Problems|year=2006|n=I}} == Problem 1 ==
  7 KB (1,173 words) - 03:31, 4 January 2023
• Set
  ...S'</math> and <math>S''</math> are equal if they include the same objects, i.e., if for every object <math>x</math>, we have <math>x\in S'</math> if and ...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<
  11 KB (2,019 words) - 17:20, 7 July 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 9
  == Problem == ...or equal to <math>1000</math> is <math> (\sin t + i \cos t)^n = \sin nt + i \cos nt </math> true for all real <math> t </math>?
  6 KB (1,154 words) - 03:30, 11 January 2024
• 2005 AIME II Problems/Problem 12
  == Problem == defaultpen(linewidth(0.7)+fontsize(10)); pair A=(0,9), B=(9,9), C=(9,0), D=(0,0), E=(2.5-0.5*sqrt(7),9), F=(6.5-0
  13 KB (2,080 words) - 13:14, 23 July 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 1
  == Problem == [[Image:2005 AIME I Problem 1.png]]
  1 KB (213 words) - 13:17, 22 July 2017
• 2005 AIME I Problems/Problem 2
  == Problem == ...values of <math> k </math> does <math> S_k </math> contain the term <math>2005</math>?
  2 KB (303 words) - 01:31, 5 December 2022
• 2005 AIME I Problems/Problem 4
  == Problem == ...th>. When <math>n = 28</math>, this product is <math>980</math>, and since AIME answers are nonnegative integers less than <math>1000</math>, we don't have
  8 KB (1,249 words) - 21:25, 20 November 2024

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