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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
• Base numbers
  ...the number 2746. This number can be rewritten as <math>2746_{10}=2\cdot10^3+7\cdot10^2+4\cdot10^1+6\cdot10^0.</math> ...<math>10^2</math>'s, and the fourth digit tells us there are two <math>10^3</math>'s.
  4 KB (547 words) - 16:23, 30 December 2020
• Fundamental Theorem of Calculus
  The '''Fundamental Theorem of Calculus''' establishes a link between the two central operations of [[calculus]]: [[derivative|diffe * Evaluate: <math>\int_2^5 x^3 dx</math> and <math>\int_{.2}^{.4} \cos(x) dx</math>. (The next few questi
  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
• Riemann zeta function
  The '''Riemann zeta function''' is a function very important in [[number theory]]. In particular, the [[Riemann Hypothesis]] is a conjecture
  9 KB (1,547 words) - 02:04, 13 January 2021
• 2006 AIME I Problems
  In quadrilateral <math> ABCD , \angle B </math> is a right angle, diagonal <math> \overline{AC} </math> is perpendicular to <mat ...th> and let <math> S </math> be the sum of the elements of <math> \mathcal{A}. </math> Find the number of possible values of <math> S. </math>
  7 KB (1,173 words) - 02:31, 4 January 2023
• 2003 AMC 12A Problems
  {{AMC12 Problems|year=2003|ab=A}} <math> \mathrm{(A) \ } 0\qquad \mathrm{(B) \ } 1\qquad \mathrm{(C) \ } 2\qquad \mathrm{(D) \
  13 KB (1,955 words) - 20:06, 19 August 2023
• 2003 AMC 12B Problems
  <cmath>\frac{2-4+6-8+10-12+14}{3-6+9-12+15-18+21}?</cmath> ...ext {(C) } \frac{2}{3} \qquad \text {(D) } 1 \qquad \text {(E) } \frac{14}{3}
  13 KB (1,987 words) - 17:53, 10 December 2022
• 2005 AIME II Problems/Problem 15
  ...p </math> and <math> q </math> are relatively prime integers, find <math> p+q. </math> pair A = (-5, 12), B = (5, 12), C = (0, 0);
  12 KB (2,001 words) - 19:26, 23 July 2024
• 1988 AIME Problems
  ...rder -- the correct five buttons. The sample shown below has <math>\{1, 2, 3, 6, 9\}</math> as its combination. Suppose that these locks are redesigned == Problem 3 ==
  6 KB (902 words) - 07:57, 19 June 2021
• 1992 AIME Problems
  A positive integer is called ascending if, in its decimal representation, the == Problem 3 ==
  8 KB (1,117 words) - 04:32, 11 November 2023
• 1993 AIME Problems
  ...n for office, a candidate made a tour of a country which we assume lies in a plane. On the first day of the tour he went east, on the second day he went == Problem 3 ==
  8 KB (1,275 words) - 05:55, 2 September 2021
• 1983 AIME Problems/Problem 15
  ...r arc <math>AB</math> is a rational number. If this number is expressed as a fraction <math>\frac{m}{n}</math> in lowest terms, what is the product <mat pair A=(-0.91,-0.41);
  20 KB (3,497 words) - 14:37, 27 May 2024
• 1986 AIME Problems/Problem 14
  ..., and <math>\frac{15}{\sqrt{10}}</math>. Determine the [[volume]] of <math>P</math>. ...en <math>AC</math> and that corner, which is <math>\frac {wl}{\sqrt {w^2 + l^2}}</math>.
  2 KB (346 words) - 12:13, 22 July 2020
• 1986 AIME Problems/Problem 9
  ...t]] <math>P</math> is then drawn, and [[segment]]s are drawn through <math>P</math> [[parallel]] to the sides of the [[triangle]]. If these three segmen pair C=(0,0),A=(510,0),B=IP(circle(C,450),circle(A,425));
  11 KB (1,873 words) - 12:08, 29 July 2024
• 1989 AIME Problems/Problem 15
  ...ven that <math>AP=6</math>, <math>BP=9</math>, <math>PD=6</math>, <math>PE=3</math>, and <math>CF=20</math>, find the area of <math>\triangle ABC</math> ...>, 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
• 1993 AIME Problems/Problem 12
  ...int, then <math>P_{n + 1}^{}</math> is the midpoint of <math>\overline{P_n L}</math>. Given that <math>P_7 = (14,92)\,</math>, what is <math>k + m\,</m ...the midpoint of <math>(u,v)</math> and <math>(p,q)</math>, then <math>u=2r-p</math> and <math>v=2s-q</math>. So we start with the point they gave us and
  4 KB (611 words) - 12:59, 15 July 2023
• 1995 AIME Problems/Problem 12
  // p = point on line triple lineintersectplan(triple p, triple d, triple q, triple n)
  8 KB (1,172 words) - 20:57, 22 September 2022
• 1995 AIME Problems/Problem 3
  ...object reaches <math>(2,2)</math> in six or fewer steps. Given that <math>p</math> can be written in the form <math>m/n,</math> where <math>m</math> an ...math>2!</math> ways to determine the order of the remaining two steps, for a total of <math>12</math> sequences that we have to exclude. This gives <mat
  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 ...;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><asy>import three; defaul
  7 KB (1,175 words) - 12:26, 3 September 2024

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