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• 2005 AIME II Problems/Problem 9
  == Problem == This problem begs us to use the familiar identity <math>e^{it} = \cos(t) + i \sin(t)</ma
  6 KB (1,154 words) - 03:30, 11 January 2024
• 2005 AIME I Problems/Problem 9
  == Problem == [[Image:2005_I_AIME-9.png]]
  4 KB (600 words) - 21:44, 20 November 2023
• Mock AIME 3 Pre 2005 Problems/Problem 9
  ==Problem== {{Mock AIME box|year=Pre 2005|n=3|num-b=8|num-a=10}}
  2 KB (278 words) - 16:32, 27 December 2019
• Mock AIME 1 Pre 2005 Problems/Problem 9
  == Problem == {{Mock AIME box|year=Pre 2005|n=1|num-b=8|num-a=10|source=14769}}
  864 bytes (127 words) - 21:47, 21 February 2010
• Mock AIME 5 2005-2006 Problems/Problem 9
  == Problem == {{Mock AIME box|year=2005-2006|n=5|source=76847|num-b=8|num-a=10}}
  461 bytes (62 words) - 21:18, 8 October 2014
• Mock AIME 2 Pre 2005 Problems/Problem 9
  == Problem == <cmath>k_{1997}={3^{11}}+{3^{10}}+{3^9}+{3^8}+{3^7}+{3^4}+{3^3}+{3^1}.</cmath>
  2 KB (232 words) - 00:22, 1 January 2021
• Mock AIME 4 Pre 2005/Problems/Problem 9
  ==Problem== ...ath>, and <math>2A = 32</math>, yielding <math>A = 16</math> and <math>B = 9</math>. The fact that the ratio between <math>B</math> and <math>A</math> i
  2 KB (319 words) - 01:21, 30 January 2024

Page text matches

• 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
  ...e multiply the possibilities 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
• Ellipse
  D(P--P-(9/5,4)); ==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
• Geometric sequence
  ...<math>-1/2</math>; however, <math>1, 3, 9, -27</math> and <math>-3, 1, 5, 9, \ldots</math> are not geometric sequences, as the ratio between consecutiv == Problems ==
  4 KB (649 words) - 21:09, 19 July 2024
• Arithmetic sequence
  == Problems == Here are some problems with solutions that utilize arithmetic sequences and series.
  4 KB (736 words) - 02:00, 7 March 2024
• Power of a Point Theorem
  == Problems == ...> intersect at <math>R</math>. If <math>AR:BR=1:4</math> and <math>CR:DR=4:9</math>, find the ratio <math>AB:CD</math> .
  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
• 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 1
  == Problem == ...cutive [[integer]]s. Since 720 is close to <math>9^3=729</math>, we try 8, 9, and 10, which works, so <math>n - 3 = 10</math> and <math>n = \boxed{13}</
  1 KB (239 words) - 11:54, 31 July 2023
• 2005 AIME II Problems/Problem 2
  == Problem == *Person 1: <math>\frac{9 \cdot 6 \cdot 3}{9 \cdot 8 \cdot 7} = \frac{9}{28}</math>
  4 KB (628 words) - 11:28, 14 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 == ...10}+y^8+y^6+y^4+y^2+1)(y+1) = (y^{15}+y^{14}+y^{13}+y^{12}+y^{11}+y^{10}+y^9+y^8+y^7+y^6+y^5+y^4+y^3+y^2+y+1)=\frac{y^{16}-1}{y-1}</cmath>
  2 KB (279 words) - 12:33, 27 October 2019
• 2005 AIME II Problems/Problem 8
  == Problem == {{AIME box|year=2005|n=II|num-b=7|num-a=9}}
  4 KB (693 words) - 13:03, 28 December 2021
• 2005 AIME II Problems/Problem 12
  == Problem == ...9), C=(9,0), D=(0,0), E=(2.5-0.5*sqrt(7),9), F=(6.5-0.5*sqrt(7),9), G=(4.5,9), O=(4.5,4.5); draw(A--B--C--D--A);draw(E--O--F);draw(G--O); dot(A^^B^^C^^D
  13 KB (2,080 words) - 13:14, 23 July 2024
• 2005 AIME II Problems/Problem 10
  == Problem == {{AIME box|year=2005|n=II|num-b=9|num-a=11}}
  3 KB (436 words) - 20:35, 13 August 2024

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