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• 2005 AIME II Problems/Problem 12
  ...math> is not divisible by the [[square]] of any [[prime]], find <math> p+q+r. </math> ...^E^^F^^G^^O); label("\(A\)",A,(-1,1));label("\(B\)",B,(1,1));label("\(C\)",C,(1,-1));label("\(D\)",D,(-1,-1)); label("\(E\)",E,(0,1));label("\(F\)",F,(1
  13 KB (2,080 words) - 21:20, 11 December 2022
• 2005 AIME I Problems
  ...us 30. Let <math> K </math> be the area of the region inside circle <math> C </math> and outside of the six circles in the ring. Find <math> \lfloor K \ ...nonreal roots of <math> x^4-4x^3+6x^2-4x=2005. </math> Find <math> \lfloor P\rfloor. </math>
  6 KB (983 words) - 05:06, 20 February 2019
• 2005 AIME I Problems/Problem 6
  ...nonreal roots of <math> x^4-4x^3+6x^2-4x=2005. </math> Find <math> \lfloor P\rfloor. </math> ...6}</math>. <math>44^2 = 1936 < 2006 < 2025 = 45^2</math> so <math>\lfloor P \rfloor = 1 + 44 = \boxed{045}</math>.
  4 KB (686 words) - 01:55, 5 December 2022
• 2005 AIME I Problems/Problem 9
  ...ath> and <math> c </math> are [[positive integer]]s, find <math> a+b+c+p+q+r. </math>
  4 KB (600 words) - 21:44, 20 November 2023
• 2005 AIME II Problems/Problem 15
  ...p </math> and <math> q </math> are relatively prime integers, find <math> p+q. </math> Let <math>w_3</math> have center <math>(x,y)</math> and radius <math>r</math>. Now, if two circles with radii <math>r_1</math> and <math>r_2</mat
  12 KB (2,000 words) - 13:17, 28 December 2020
• 2005 AIME II Problems/Problem 14
  ...ong \angle CAD. </math> Given that <math> BE=\frac pq </math> where <math> p </math> and <math> q </math> are relatively prime positive integers, find < pair C = rotate(15,A)*(A+dir(-50));
  13 KB (2,129 words) - 18:56, 1 January 2024
• 2004 AIME I Problems/Problem 7
  ...ath> (1 - x)(1 + 2x)(1 - 3x)\cdots(1 + 14x)(1 - 15x). </math> Find <math> |C|. </math> Let our [[polynomial]] be <math>P(x)</math>.
  6 KB (941 words) - 11:37, 27 May 2024
• 2004 AIME II Problems/Problem 15
  ...w it does not change. Otherwise, it changes position (<math>p\mapsto 2^k+1-p</math> for the <math>k</math>-th fold). We just take the number of squares ...d the strip into an array <math>r=2^k</math> squares wide and <math>c=1024/r=2^{10-k}</math> squares tall (so we've made <math>10-k</math> folds). Then
  6 KB (899 words) - 20:58, 12 May 2022
• 2004 AIME II Problems/Problem 14
  ...<math>c</math> <math>777</math>s to sum up to <math>7000</math> (<math>a,b,c \ge 0</math>). Then <math>7a + 77b + 777c = 7000</math>, or dividing by <ma ...es of <math>n</math> for which their only expressions in terms of <math>(b,c)</math> fall into the inequality <math>9b + 108c < 1000 < 11b + 111c</math>
  11 KB (1,857 words) - 21:55, 19 June 2023
• 2004 AIME II Problems/Problem 12
  ...k </math> and <math> p </math> are [[relatively prime]]. Find <math> k+m+n+p. </math> Let the radius of the center circle be <math>r</math> and its center be denoted as <math>O</math>.
  3 KB (431 words) - 23:21, 4 July 2013
• 1983 AIME Problems
  ...ue taken by <math>f(x)</math> for <math>x</math> in the [[interval]] <math>p \leq x\leq15</math>. real r=10;
  7 KB (1,104 words) - 03:13, 27 May 2024
• 1987 AIME Problems
  ...for which <math>[a,b] = 1000</math>, <math>[b,c] = 2000</math>, and <math>[c,a] = 2000</math>. ...h>ABC</math> has right angle at <math>B</math>, and contains a point <math>P</math> for which <math>PA = 10</math>, <math>PB = 6</math>, and <math>\angl
  6 KB (869 words) - 15:34, 22 August 2023
• 1989 AIME Problems
  ..._{}</math> is a perfect cube, what is the smallest possible value of <math>c^{}_{}</math>? pair A=(0,0),B=(10,0),C=6*expi(pi/3);
  7 KB (1,045 words) - 20:47, 14 December 2023
• 1990 AIME Problems
  ...ath> and <math>P_2^{}</math> be a regular <math>s~\mbox{gon}</math> <math>(r\geq s\geq 3)</math> such that each interior angle of <math>P_1^{}</math> is ...e bisector of <math>\angle P</math> can be written in the form <math>ax+2y+c=0_{}^{}</math>. Find <math>a+c_{}^{}</math>.
  6 KB (870 words) - 10:14, 19 June 2021
• 1991 AIME Problems
  Suppose <math>r^{}_{}</math> is a real number for which ...or + \left\lfloor r + \frac{21}{100} \right\rfloor + \cdots + \left\lfloor r + \frac{91}{100} \right\rfloor = 546.
  7 KB (1,106 words) - 22:05, 7 June 2021
• 1992 AIME Problems
  <cmath>\begin{array}{c@{\hspace{8em}} c@{\hspace{6pt}}c@{\hspace{6pt}}c@{\hspace{6pt}}c@{\hspace{4pt}}c@{\hspace{2pt}}
  8 KB (1,117 words) - 05:32, 11 November 2023
• 1993 AIME Problems
  <center><math>\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline n & 0 & 1 & 2 & 3 & \dots & 13 & 14 & 15 \\ :(c) those who caught <math>12</math> or fewer fish averaged <math>5</math> fis
  8 KB (1,275 words) - 06:55, 2 September 2021
• 1994 AIME Problems
  ...r <math>\overline{PQ}\,</math> of length 10 is internally tangent at <math>P^{}_{}</math> to a circle of radius 20. Square <math>ABCD\,</math> is constr ...of <math>n\,</math>. (If <math>n\,</math> has only one digit, then <math>p(n)\,</math> is equal to that digit.) Let
  7 KB (1,141 words) - 07:37, 7 September 2018
• 1996 AIME Problems
  ...h>x^3+rx^2+sx+t=0</math> are <math>a+b</math>, <math>b+c</math>, and <math>c+a</math>. Find <math>t</math>. ...rm {P}=r(\cos{\theta^{\circ}}+i\sin{\theta^{\circ}})</math>, where <math>0<r</math> and <math>0\leq \theta <360</math>. Find <math>\theta</math>.
  6 KB (931 words) - 17:49, 21 December 2018
• 1997 AIME Problems
  ...math> rectangles, of which <math>s</math> are squares. The number <math>s/r</math> can be written in the form <math>m/n,</math> where <math>m</math> an ...is <math>\frac 27.</math> What is the number of possible values for <math>r</math>?
  7 KB (1,098 words) - 17:08, 25 June 2020

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