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• 2005 AIME II Problems/Problem 1
  {{AIME box|year=2005|n=II|before=First Question|num-a=2}} [[Category:Introductory Combinatorics Problems, Introductory Algebra Problems]]
  1 KB (239 words) - 11:54, 31 July 2023
• 2005 AIME II Problems/Problem 2
  {{AIME box|year=2005|n=II|num-b=1|num-a=3}} [[Category:Intermediate Combinatorics Problems]]
  4 KB (628 words) - 11:28, 14 April 2024
• 2005 AIME II Problems/Problem 3
  An [[infinite]] [[geometric series]] has sum 2005. A new series, obtained by squaring each term of the original series, has 1 ...Then <math>a = 2005 - 2005r</math> and <math>a = 10 + 10r</math> so <math>2005 - 2005r = 10 + 10r</math>, <math>1995 = 2015r</math> and finally <math>r =
  3 KB (581 words) - 21:19, 22 September 2024
• 2005 AIME II Problems/Problem 4
  {{AIME box|year=2005|n=II|num-b=3|num-a=5}} [[Category:Introductory Number Theory Problems]]
  3 KB (377 words) - 18:36, 1 January 2024
• 2005 AIME II Problems/Problem 13
  {{AIME box|year=2005|n=II|num-b=12|num-a=14}} [[Category:Intermediate Algebra Problems]]
  4 KB (642 words) - 02:14, 1 June 2024
• 2005 AIME II Problems/Problem 5
  ...og_a b + 6\log_b a=5, 2 \leq a \leq 2005, </math> and <math> 2 \leq b \leq 2005. </math> ...sible values of <math>b</math>, the values of <math>b^6</math> under <math>2005</math> would have to be subtracted, which would just be <math>2</math> valu
  3 KB (547 words) - 19:15, 4 April 2024
• 2005 AIME II Problems/Problem 6
  {{AIME box|year=2005|n=II|num-b=5|num-a=7}} [[Category:Intermediate Combinatorics Problems]]
  2 KB (384 words) - 00:31, 26 July 2018
• 2005 AIME II Problems
  {{AIME Problems|year=2005|n=II}} [[2005 AIME II Problems/Problem 1|Solution]]
  7 KB (1,119 words) - 21:12, 28 February 2020
• 2005 AIME II Problems/Problem 7
  {{AIME box|year=2005|n=II|num-b=6|num-a=8}} [[Category:Introductory Algebra Problems]]
  2 KB (279 words) - 12:33, 27 October 2019
• 2005 AIME II Problems/Problem 8
  {{AIME box|year=2005|n=II|num-b=7|num-a=9}} [[Category:Intermediate Geometry Problems]]
  4 KB (693 words) - 13:03, 28 December 2021
• 2005 AIME II Problems/Problem 9
  [[Category:Intermediate Algebra Problems]] {{AIME box|year=2005|n=II|num-b=8|num-a=10}}
  6 KB (1,154 words) - 03:30, 11 January 2024
• 2005 AIME II Problems/Problem 12
  {{AIME box|year=2005|n=II|num-b=11|num-a=13}} [[Category:Intermediate Geometry Problems]]
  13 KB (2,080 words) - 13:14, 23 July 2024
• 2005 AIME II Problems/Problem 10
  {{AIME box|year=2005|n=II|num-b=9|num-a=11}} [[Category:Intermediate Geometry Problems]]
  3 KB (436 words) - 20:35, 13 August 2024
• 2005 AIME II Problems/Problem 11
  {{AIME box|year=2005|n=II|num-b=10|num-a=12}} [[Category:Intermediate Algebra Problems]]
  3 KB (499 words) - 18:52, 21 November 2022
• 2005 AIME I Problems
  {{AIME Problems|year=2005|n=I}} [[2005 AIME I Problems/Problem 1|Solution]]
  6 KB (983 words) - 05:06, 20 February 2019
• 2005 AIME I Problems/Problem 1
  [[Image:2005 AIME I Problem 1.png]] {{AIME box|year=2005|n=I|before=First Question|num-a=2}}
  1 KB (213 words) - 13:17, 22 July 2017
• 2005 AIME I Problems/Problem 2
  ...values of <math> k </math> does <math> S_k </math> contain the term <math>2005</math>? ...of the sequence <math>S_k</math> is <math>2005</math>. Then <math>1+(n-1)k=2005</math> so <math>k(n-1)=2004=2^2\cdot 3\cdot 167</math>. The [[ordered pair
  2 KB (303 words) - 01:31, 5 December 2022
• 2005 AIME I Problems/Problem 3
  {{AIME box|year=2005|n=I|num-b=2|num-a=4}} [[Category:Introductory Number Theory Problems]]
  2 KB (249 words) - 09:37, 23 January 2024
• 2005 AIME I Problems/Problem 4
  ...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 {{AIME box|year=2005|n=I|num-b=3|num-a=5}}
  8 KB (1,249 words) - 21:25, 20 November 2024
• 2005 AIME I Problems/Problem 5
  {{AIME box|year=2005|n=I|num-b=4|num-a=6}} [[Category:Intermediate Combinatorics Problems]]
  5 KB (830 words) - 01:51, 1 March 2023

Page text matches

• 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
• Principle of Inclusion-Exclusion
  [[2011 AMC 8 Problems/Problem 6]] [[2017 AMC 10B Problems/Problem 13]]
  9 KB (1,703 words) - 01:20, 7 December 2024
• Combination
  ...as a great introductory video to combinations, permutations, and counting problems in general! [https://bit.ly/CombinationsAndPermutations Permutations & Comb * [[2005_AIME_II_Problems/Problem_1 | 2005 AIME II Problem 1]]
  4 KB (638 words) - 21:55, 5 January 2025
• Brahmagupta's Formula
  == Problems == ...e positive integers. Determine <math>p + q</math>. ([[Mock AIME 3 Pre 2005 Problems/Problem 7|Source]])
  3 KB (543 words) - 19:35, 29 October 2024
• Constructive counting
  ''[[2001 AMC 12 Problems/Problem 16 | 2001 AMC 12 Problem 16]]: A spider has one sock and one shoe f ...on of just how effective a cleverly chosen construction can be to counting problems.
  13 KB (2,018 words) - 15:31, 10 January 2025
• Ellipse
  ==Problems== ...h> are relatively prime integers, find <math> p+q. </math> ([[2005 AIME II Problems/Problem 15|Source]])
  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
• Mathew Crawford
  * Perfect score on the [[AIME]] as a freshman. Crawford also writes competition problems and performs duties for many math competitions:
  2 KB (362 words) - 11:20, 27 September 2024
• 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
  == Problems == Here are some problems with solutions that utilize arithmetic sequences and series.
  4 KB (736 words) - 02:00, 7 March 2024
• Diophantine equation
  == Problems == ...n_2, </math> find the product <math> n_1\cdot n_2</math>. ([[2005 AIME II Problems/Problem 13|Source]])
  9 KB (1,434 words) - 01:15, 4 July 2024
• Power of a Point Theorem
  == Problems == ...math>\overline{MC}</math> that lies outside of the circle. ([[2020 AMC 12B Problems/Problem 10|Source]])
  5 KB (948 words) - 17:04, 21 February 2025
• 2004 AIME II
  ...I''' problems and solutions. The first link 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
  ...I''' problems and solutions. The first link 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
  ...I''' problems and solutions. The first link 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
  ...I''' problems and solutions. The first link 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
• Mock AIME
  A '''Mock AIME''' is a contest that is intended to mimic the [[AIME]] competition. (In more recent years, recurring competitions will be listed ...xOGY2Y2QwOTc3NWZiYjY0LnBkZg==&rn=TWlsZG9yZiBNb2NrIEFJTUUucGRm Mildorf Mock AIME 1]
  8 KB (901 words) - 20:45, 13 January 2025
• AIME Problems and Solutions
  ...olving.com/Forum/resources.php?c=182 AoPS Resources] section. If you find problems that are in the Resources section which are not in the AoPSWiki, please con | 2025 || [[2025 AIME I | AIME I]] || [[2025 AIME II | AIME II]]
  3 KB (400 words) - 20:21, 13 February 2025

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