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• 2015 IMO Problems
  We say that a finite set <math>\mathcal{S}</math> in the plane is <i> balanced </i> if, for any two different points <math>A</math>, <math>B</math> in <math>\mathcal{S}</math>, there is
  4 KB (709 words) - 14:00, 1 June 2024
• Fundamental Theorem of Calculus
  The '''Fundamental Theorem of Calculus''' establishes a link between the two central operations of [[calculus]]: [[derivative|diffe ...imes <math>t=1</math> and <math>t=2</math> geometrically, as an area under a curve.
  11 KB (2,082 words) - 14:23, 2 January 2022
• Mock AMC
  ...an actual [[AMC]] (American Mathematics Competitions 8, 10, or 12) exam. A number of '''Mock AMC''' competitions have been hosted on the [[Art of Prob == Tips for Writing a Mock AMC ==
  51 KB (6,135 words) - 05:44, 2 November 2024
• Modular arithmetic/Introduction
  ...is article is to explain the basics of modular arithmetic while presenting a progression of more difficult and more interesting problems that are easily ...ple, except let's replace the <math>12</math> at the top of the clock with a <math>0</math>.
  16 KB (2,406 words) - 07:56, 10 July 2024
• 2003 AMC 12A Problems
  {{AMC12 Problems|year=2003|ab=A}} ...B) \ } 1\qquad \mathrm{(C) \ } 2\qquad \mathrm{(D) \ } 2003\qquad \mathrm{(E) \ } 4006 </math>
  13 KB (1,955 words) - 20:06, 19 August 2023
• 2003 AMC 12B Problems
  ...2}{3} \qquad \text {(C) } \frac{2}{3} \qquad \text {(D) } 1 \qquad \text {(E) } \frac{14}{3} ...ks. A green pill costs 1 dollar more than a pink pill, and Al's pills cost a total of 546 dollars for the two weeks. How much does one green pill cost?
  13 KB (1,987 words) - 17:53, 10 December 2022
• 2005 AIME II Problems/Problem 15
  ...h> a </math> for which the line <math> y=ax </math> contains the center of a circle that is externally [[tangent (geometry)|tangent]] to <math> w_2 </ma pair A = (-5, 12), B = (5, 12), C = (0, 0);
  12 KB (2,001 words) - 19:26, 23 July 2024
• 2004 AIME I Problems/Problem 14
  ...are [[positive]] [[integer]]s, and <math> c </math> is prime. Find <math> a+b+c. </math> ...= (0,0,0), A=(4*5^.5,-8,4), B=(0,-8,h), C=(Cxy.x,Cxy.y,0), D=(A.x,A.y,0), E=(B.x,B.y,0), O=(O.x,O.y,h);
  4 KB (729 words) - 00:00, 27 November 2022
• 2004 AIME I Problems/Problem 2
  ...The absolute value of the difference between the greatest element of <math>A</math> and the greatest element of <math>B</math> is <math>99</math>. Find ...e median) must be <math>2</math>. Therefore, the largest element in <math>A</math> is <math>2 + \frac{m-1}{2}</math>.
  8 KB (1,437 words) - 20:53, 19 May 2023
• 2004 AIME II Problems/Problem 7
  ...and <math> n </math> are relatively prime positive integers. Find <math> m+n. </math> ...(25,70/3), D=(0,70/3), E=(8,0), F=(22,70/3), Bp=reflect(E,F)*B, Cp=reflect(E,F)*C;
  9 KB (1,500 words) - 19:06, 8 October 2024
• 1993 AIME Problems
  ...etc. If the candidate went <math>\frac{n^{2}}{2}</math> miles on the <math>n^{\mbox{th}}_{}</math> day of this tour, how many miles was he from his star ...many contestants caught <math>n\,</math> fish for various values of <math>n\,</math>.
  8 KB (1,275 words) - 05:55, 2 September 2021
• 1983 AIME Problems/Problem 11
  The solid shown has a square base of side length <math>s</math>. The upper edge is parallel to th triple A=(0,0,0),B=(s,0,0),C=(s,s,0),D=(0,s,0),E=(-s/2,s/2,6),F=(3*s/2,s/2,6);
  6 KB (971 words) - 14:35, 27 May 2024
• 1983 AIME Problems/Problem 15
  ...rational number. If this number is expressed as a fraction <math>\frac{m}{n}</math> in lowest terms, what is the product <math>mn</math>? pair A=(-0.91,-0.41);
  20 KB (3,497 words) - 14:37, 27 May 2024
• 1986 AIME Problems/Problem 9
  pair C=(0,0),A=(510,0),B=IP(circle(C,450),circle(A,425)); pair Da=IP(Circle(A,289),A--B),E=IP(Circle(C,324),B--C),Ea=IP(Circle(B,270),B--C);
  11 KB (1,873 words) - 12:08, 29 July 2024
• 1989 AIME Problems/Problem 15
  ...d <math>CPF</math> are drawn with <math>D</math> on <math>BC</math>, <math>E</math> on <math>AC</math>, and <math>F</math> on <math>AB</math> (see the f ...>, and line <math>XP</math> intersects line <math>YZ</math> at point <math>L</math>, then <math>\dfrac{XP}{PL} = \frac{[XPY] + [ZPX]}{[YPZ]}.</math>
  14 KB (2,234 words) - 22:46, 30 June 2024
• 1995 AIME Problems/Problem 12
  ...> where <math>m_{}</math> and <math>n_{}</math> are integers, find <math>m+n.</math> // n = normal to plane
  8 KB (1,172 words) - 20:57, 22 September 2022
• 1995 AIME Problems/Problem 3
  ...h> and <math>n</math> are relatively prime positive integers, find <math>m+n.</math> ...math> steps, then it must have gone two steps <tt>N</tt> and two steps <tt>E</tt>, in some permutation. There are <math>\frac{4!}{2!2!} = 6</math> ways
  3 KB (602 words) - 22:15, 16 June 2019
• 1999 AIME Problems/Problem 15
  ...The vertices of its midpoint triangle are the [[midpoint]]s of its sides. A triangular [[pyramid]] is formed by folding the triangle along the sides of ..."\(D\)",foot(A,B,C),NE);label("\(E\)",foot(B,A,C),SW);label("\(F\)",foot(C,A,B),NW);label("\(P\)",P,NW);label("\(Q\)",Q,NE);label("\(R\)",R,SE);</asy><a
  7 KB (1,175 words) - 12:26, 3 September 2024
• 2001 AIME I Problems/Problem 12
  ...and <math>n</math> are relatively prime positive integers. Find <math>m + n.</math> triple A = (6,0,0), B = (0,4,0), C = (0,0,2), D = (0,0,0);
  8 KB (1,241 words) - 12:47, 1 October 2024
• 2001 AIME I Problems/Problem 6
  ...</math> are [[relatively prime]] [[positive]] [[integer]]s. Find <math>m + n</math>. ...n the diagram below, the lowest <math>y</math>-coordinate at each of <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math> corresponds to t
  11 KB (1,731 words) - 02:16, 24 August 2024

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