Create the page "2005 AIME I Problem 2" on this wiki! See also the search results found.

Page title matches

• 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

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
• Combination
  * <math>\sum_{x=0}^{n} \binom{n}{x} = 2^n</math> ...ath>2^n</math>, and a and b disappear because they are 1, the sum is <math>2^n</math>.
  4 KB (638 words) - 21:55, 5 January 2025
• Constructive counting
  This is a problem where constructive counting is not the simplest way to proceed. This next e === Example 2 ===
  13 KB (2,018 words) - 15:31, 10 January 2025
• Ellipse
  ...llipse is the origin this simplifies to <math>\frac{x^2}{a^2}+\frac{y^2}{b^2}=1</math>. ...<math>P</math>. Then it is true that the bisector of angle <math>F_{1}PF_{2}</math> is perpendicular to <math>\ell</math>.
  5 KB (892 words) - 21:52, 1 May 2021
• Complex number
  ...mplex numbers''' arise when we try to solve [[equation]]s such as <math> x^2 = -1 </math>. ...from this addition, we are not only able to find the solutions of <math> x^2 = -1 </math> but we can now find ''all'' solutions to ''every'' polynomial.
  5 KB (860 words) - 15:36, 10 December 2023
• Arithmetic sequence
  For example, <math>1, 2, 3, 4</math> is an arithmetic sequence with common difference <math>1</math ...-1}, a_n, a_{n+1}</math>. In symbols, <math>a_n = \frac{a_{n-1} + a_{n+1}}{2}</math>. This is mostly used to perform substitutions, though it occasional
  4 KB (736 words) - 02:00, 7 March 2024
• Diophantine equation
  ...ree [[integer]]s that satisfy the [[Pythagorean Theorem]], <math>a^2+b^2=c^2</math>. There are three main methods of finding Pythagorean triples: ...th> is an [[odd]] number, then <math>m, \frac {m^2 -1}{2}, \frac {m^2 + 1}{2}</math> is a Pythagorean triple.
  9 KB (1,434 words) - 01:15, 4 July 2024
• Power of a Point Theorem
  ...s a [[secant line|secant]] (middle figure). In this case, we have <math>AB^2 = BC\cdot BD</math>. <cmath>PX^2=PA_1\cdot PB_1=PA_2\cdot PB_2=\cdots=PA_i\cdot PB_i</cmath>
  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
• AIME Problems and Solutions
  ...in the AoPSWiki, please consider adding them. Also, if you notice that a problem in the Wiki differs from the original wording, feel free to correct it. Fi ! Year || Test I || Test II
  3 KB (400 words) - 20:21, 13 February 2025
• 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
  ...ple 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. ...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
  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 == ..."$x$",E/2+G/2,(0,1));label("$y$",G/2+F/2,(0,1)); label("$450$",(O+G)/2,(-1,1));
  13 KB (2,080 words) - 13:14, 23 July 2024

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