Create the page "2005 AIME I Problem 12" on this wiki! See also the search results found.

Page title matches

• 2005 AIME I Problems/Problem 12
  == Problem == ...let <math> b </math> denote the number of positive integers <math> n \leq 2005 </math> with <math> S(n) </math> [[even integer | even]]. Find <math> |a-b|
  4 KB (647 words) - 02:29, 4 May 2021

Page text matches

• Constructive counting
  This is a problem where constructive counting is not the simplest way to proceed. This next e ...proceed with the construction. If we were to go like before and break the problem down by each box, we'd get a fairly messy solution.
  13 KB (2,018 words) - 15:31, 10 January 2025
• Ellipse
  pair P=(3,12/5), F1=(-4,0), F2=(4,0); ...latively 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
  ...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
  ...difference <math>-8</math>; however, <math>7, 0, 7, 14</math> and <math>4, 12, 36, 108, \ldots</math> are not arithmetic sequences, as the difference bet * [[2005_AMC_10A_Problems/Problem_17 | 2005 AMC 10A Problem 17]]
  4 KB (736 words) - 02:00, 7 March 2024
• 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
• 2006 AIME I Problems/Problem 15
  == Problem == Suppose <math>b_{i} = \frac {x_{i}}3</math>.
  8 KB (1,334 words) - 17:37, 15 December 2024
• 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 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 == ...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
• 2005 AIME I Problems/Problem 7
  == Problem == In [[quadrilateral]] <math> ABCD,\ BC=8,\ CD=12,\ AD=10, </math> and <math> m\angle A= m\angle B = 60^\circ. </math> Given
  4 KB (567 words) - 20:20, 3 March 2020
• 2005 AIME I Problems/Problem 9
  == Problem == ...a factor of <math>\left(\frac{5}{12}\right)^{12} = \frac{5^{12}}{2^{24}3^{12}}</math>.
  4 KB (600 words) - 21:44, 20 November 2023
• 2005 AIME I Problems/Problem 10
  == Problem == ...ath>. The coordinates of <math> B </math> and <math> C </math> are <math> (12,19) </math> and <math> (23,20), </math> respectively, and the coordinates o
  5 KB (852 words) - 21:23, 4 October 2023
• 2005 AIME I Problems/Problem 11
  == Problem == [[Image:2005 AIME I Problem 11.png]]
  4 KB (707 words) - 11:11, 16 September 2021

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)