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• 2005 AIME II Problems/Problem 3
  == Problem == An [[infinite]] [[geometric series]] has sum 2005. A new series, obtained by squaring each term of the original series, has 1
  3 KB (581 words) - 21:19, 22 September 2024
• 2005 AIME I Problems/Problem 3
  == Problem == ...so <math>n</math> must be in the form <math>n=p\cdot q</math> or <math>n=p^3</math> for distinct [[prime number]]s <math>p</math> and <math>q</math>.
  2 KB (249 words) - 09:37, 23 January 2024
• Mock AIME 3 Pre 2005 Problems/Problem 1
  ==Problem== ...rcles are mutually externally tangent. Two of the circles have radii <math>3</math> and <math>7</math>. If the area of the triangle formed by connecting
  795 bytes (129 words) - 10:22, 4 April 2012
• Mock AIME 3 Pre 2005 Problems/Problem 2
  ==Problem== {{Mock AIME box|year=Pre 2005|n=3|num-b=1|num-a=3}}
  950 bytes (137 words) - 10:16, 29 November 2019
• Mock AIME 3 Pre 2005 Problems/Problem 3
  ==Problem== 0 &= x^2 - \frac{3 \times 2004 - 4}{10}x + \frac 52\end{align*}</cmath>
  1 KB (191 words) - 10:22, 4 April 2012
• Mock AIME 3 Pre 2005 Problems/Problem 4
  ==Problem== <cmath>\zeta_1^2+\zeta_2^2+\zeta_3^2=3</cmath>
  2 KB (221 words) - 02:49, 19 March 2015
• Mock AIME 3 Pre 2005 Problems/Problem 5
  ==Problem== ...VC</tt> - the only other combination, two vowels, is impossible due to the problem statement). Then, note that:
  5 KB (795 words) - 16:03, 17 October 2021
• Mock AIME 3 Pre 2005 Problems/Problem 6
  ==Problem== {{Mock AIME box|year=Pre 2005|n=3|num-b=5|num-a=7|source=19349}}
  3 KB (501 words) - 14:48, 29 November 2019
• Mock AIME 3 Pre 2005 Problems/Problem 7
  ==Problem== ...ect at <math>P</math>. If <math>AB = 1, CD = 4,</math> and <math>BP : DP = 3 : 8,</math> then the area of the inscribed circle of <math>ABCD</math> can
  2 KB (330 words) - 10:23, 4 April 2012
• Mock AIME 3 Pre 2005 Problems/Problem 8
  ==Problem== Here are some thoughts on the problem:
  3 KB (520 words) - 12:55, 11 January 2019
• 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 3 Pre 2005 Problems/Problem 10
  ==Problem== {{Mock AIME box|year=Pre 2005|n=3|num-b=9|num-a=11}}
  2 KB (306 words) - 10:36, 4 April 2012
• Mock AIME 3 Pre 2005 Problems/Problem 11
  ==Problem== {{Mock AIME box|year=Pre 2005|n=3|num-b=10|num-a=12}}
  2 KB (379 words) - 01:27, 6 December 2024
• Mock AIME 3 Pre 2005 Problems/Problem 12
  ==Problem== ...</math>, and the rest being the previous: <math>+2, +5, +1, +15, +3, +19, +3, +15, +1, +5, +2</math>. This sequence then repeats itself. We hence find t
  714 bytes (105 words) - 23:59, 24 April 2013
• Mock AIME 3 Pre 2005 Problems/Problem 13
  ==Problem== ...t(\frac{2}{3}\right)^{2005} \cdot \sum_{k=1}^{2005} \frac{k^2}{2^k} \cdot {2005 \choose k}</math>
  3 KB (502 words) - 14:53, 19 July 2020
• Mock AIME 3 Pre 2005 Problems/Problem 14
  ==Problem== ..._1</math> at <math>C</math> and <math>D</math> respectively. If <math>AD = 3, AP = 6, DP = 4,</math> and <math>PQ = 32</math>, then the area of triangle
  3 KB (563 words) - 02:05, 25 November 2023
• Mock AIME 3 Pre 2005 Problems/Problem 15
  ==Problem== <math>\sum_{k=1}^{40} \cos^{-1}\left(\frac{k^2 + k + 1}{\sqrt{k^4 + 2k^3 + 3k^2 + 2k + 2}}\right)</math>
  2 KB (312 words) - 10:38, 4 April 2012
• Mock AIME 1 Pre 2005 Problems/Problem 3
  == Problem == {{Mock AIME box|year=Pre 2005|n=1|num-b=2|num-a=4|source=14769}}
  1 KB (217 words) - 06:18, 2 July 2015
• Mock AIME 5 2005-2006 Problems/Problem 3
  == Problem == {{Mock AIME box|year=2005-2006|n=5|source=76847|num-b=2|num-a=4}}
  795 bytes (133 words) - 08:14, 19 July 2016
• Mock AIME 2 Pre 2005 Problems/Problem 3
  == Problem == {{Mock AIME box|year=Pre 2005|n=2|num-b=2|num-a=4|source=14769}}
  1 KB (170 words) - 17:15, 4 August 2019

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
  ...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
• Combination
  ...as a great introductory video to combinations, permutations, and counting problems in general! [https://bit.ly/CombinationsAndPermutations Permutations & Comb Consider the set of letters A, B, and C. There are <math>3!</math> different [[permutations]] of those letters. Since order doesn't ma
  4 KB (638 words) - 21:55, 5 January 2025
• Brahmagupta's Formula
  == Problems == ...e 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
  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
• Ellipse
  D((-5,0)--(0,0)--(0,-3)); MC(90,"\mbox{semiminor axis}",7,D((0,0)--(0,3),green+linewidth(1)),E);
  5 KB (892 words) - 21:52, 1 May 2021
• Complex number
  ...hat the imaginary part of a complex number is real: for example, <math>\Im(3 + 4i) = 4</math>. So, if <math>z\in \mathbb C</math>, we can write <math>z == Problems ==
  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
  ...mon ratio <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 c == Problems ==
  4 KB (649 words) - 21:09, 19 July 2024
• Arithmetic sequence
  For example, <math>1, 2, 3, 4</math> is an arithmetic sequence with common difference <math>1</math> a == Problems ==
  4 KB (736 words) - 02:00, 7 March 2024
• Diophantine equation
  ...e an integer). However, <math>17</math> will never be a multiple of <math>3</math>, hence, no solutions exist. Case 3: <math>x_0^4 \equiv 1\mod 4, y_0^4 \equiv 0\mod 4</math>, and <math>z_0^2
  9 KB (1,434 words) - 01:15, 4 July 2024
• Power of a Point Theorem
  == Problems == ...rline{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
  ...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
  ...an have multiple indistinct elements, such as the following: <math>\{1,4,5,3,24,4,4,5,6,2\}</math> Such an entity is actually called a multiset. ...>239</math>, for example. (The standard notation for this set is <math>\{1,3,5,239\}</math>. Note that the order in which the terms are listed is comple
  11 KB (2,019 words) - 17:20, 7 July 2024
• 2005 AIME II Problems/Problem 1
  == Problem == ...that can be drawn from the deck is 6 times the number of possible sets of 3 cards that can be drawn. Find <math> n. </math>
  1 KB (239 words) - 11:54, 31 July 2023

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