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• Mock AIME 3 Pre 2005 Problems
  ...igits are in increasing order. Determine the remainder obtained when <math>N</math> is divided by <math>1000</math>. (Repeated digits are allowed.) A function <math>f(x)</math> is defined for all real numbers <math>x</math>.
  7 KB (1,135 words) - 23:53, 24 March 2019
• Mock AIME 3 Pre 2005 Problems/Problem 5
  ...math>-letter Zuminglish words. Determine the remainder obtained when <math>N</math> is divided by <math>1000</math>. ...te the number of <math>n</math>-letter words ending in a vowel followed by a constant (<tt>VC</tt> - the only other combination, two vowels, is impossib
  5 KB (795 words) - 16:03, 17 October 2021
• 2007 AIME II Problems/Problem 15
  ...nd <math>n</math> are [[relatively prime]] positive integers. Find <math>m+n.</math> pair A,B,C,X,Y,Z,P,Q,R;
  11 KB (2,099 words) - 17:51, 4 January 2024
• 2007 USAMO Problems/Problem 2
  ...sists of all [[point]]s <math>(m,n)</math>, where <math>m</math> and <math>n</math> are [[integer]]s. Is it possible to cover all grid points by an inf ...ngent]] circles with radius greater than or equal to 5, one can always fit a circle with radius greater than <math>\frac{1}{\sqrt{2}}</math> between tho
  5 KB (754 words) - 03:41, 7 August 2014
• Circumradius
  ...very triangle is [[cyclic]], every triangle has a circumscribed circle, or a [[circumcircle]]. ==Formula for a Triangle==
  4 KB (729 words) - 16:52, 19 February 2024
• 2005 AMC 12A Problems/Problem 15
  ...\overline{DC} \perp \overline{AB}</math> and <math>\overline{DE}</math> is a second diameter. What is the [[ratio]] of the area of <math>\triangle DCE</ pair O=(0,0), C=(-1/3.0), B=(1,0), A=(-1,0);
  14 KB (1,970 words) - 17:02, 18 August 2023
• 2006 AIME II Problems/Problem 12
  ...visible]] by the [[perfect square | square]] of any prime, find <math> p+q+r. </math> pair A=(0,0),B=(-3^.5,-3),C=(3^.5,-3),D=13*expi(-2*pi/3),E1=11*expi(-pi/3),F=E1+D;
  6 KB (1,033 words) - 02:36, 19 March 2022
• 1971 Canadian MO Problems
  ...of a circle such that <math>DE=3</math> and <math>EB=5 .</math> Let <math>O</math> be the center of the circle. Join <math>OE</math> and extend <math>O <math>ABCD</math> is a quadrilateral with <math>AD=BC</math>. If <math>\angle ADC</math> is greate
  3 KB (519 words) - 08:58, 13 September 2012
• 2007 AMC 12B Problems
  <math> \mathrm{(A) \ } 678\qquad \mathrm{(B) \ } 768\qquad \mathrm{(C) \ } 786\qquad \mathrm{ A college student drove his compact car 120 miles home for the weekend and av
  12 KB (1,814 words) - 12:58, 19 February 2020
• Asymptote: Useful functions
  The bundled <code>markers</code> package provides a useful function for marking angles. The exact same function exists in the < Label ''L''="", int ''n''=1, real ''radius''=0, real ''space''=0,<br/>
  4 KB (646 words) - 21:18, 26 March 2024
• 2000 AMC 12 Problems/Problem 24
  ...ters at <math>B</math> and <math>A</math>, respectively, then there exists a circle tangent to both <math>\overarc {AC}</math> and <math>\overarc{BC}</m label("A", (0,0), W);
  2 KB (263 words) - 19:59, 18 April 2024
• 1995 AHSME Problems
  ...7, 83, and 88 on her first three mathematics examinations. If Kim receives a score of 90 on the fourth exam, then her average will <math> \mathrm{(A) \ \text{remain the same} } \qquad \mathrm{(B) \ \text{increase by 1} } \qq
  17 KB (2,387 words) - 22:44, 26 May 2021
• 1951 AHSME Problems
  The percent that <math>M</math> is greater than <math>N</math> is: ...\textbf{(D) \ } \frac {M - N}{M} \qquad \textbf{(E) \ } \frac {100(M + N)}{N} </math>
  23 KB (3,647 words) - 13:29, 6 June 2024
• 1966 AHSME Problems
  <math>\text{(A)} \ \frac 18 \qquad \text{(B)} \ \frac 73 \qquad \text{(C)} \ \frac78 \qqua When the base of a triangle is increased 10% and the altitude to this base is decreased 10%, t
  19 KB (3,159 words) - 22:10, 11 March 2024
• 2004 AMC 12B Problems/Problem 19
  ...d cone has horizontal bases with radii <math>18</math> and <math>2</math>. A sphere is tangent to the top, bottom, and lateral surface of the truncated <math>\mathrm{(A)}\ 6
  3 KB (520 words) - 19:12, 20 November 2023
• 2007 AMC 10B Problems/Problem 11
  ...s of an isosceles triangle that has two sides of length <math>3</math> and a base of length <math>2</math>. What is the area of this circle? <math>\textbf{(A) } 2\pi \qquad\textbf{(B) } \frac{5}{2}\pi \qquad\textbf{(C) } \frac{81}{32
  5 KB (851 words) - 22:02, 26 July 2021
• 2008 AMC 10A Problems
  {{AMC10 Problems|year=2008|ab=A}} A bakery owner turns on his doughnut machine at <math>\text{8:30}\ {\small\te
  14 KB (2,138 words) - 15:08, 18 February 2023
• 2008 AMC 12A Problems/Problem 13
  ...rcle]] centered at <math>O</math>, and <math>\angle AOB = 60^\circ</math>. A second circle is internally [[tangent]] to the first and tangent to both <m <math>\mathrm{(A)}\ \frac{1}{16}\qquad\mathrm{(B)}\ \frac{1}{9}\qquad\mathrm{(C)}\ \frac{1}{
  4 KB (630 words) - 20:32, 4 June 2021
• 2008 AMC 12A Problems/Problem 20
  <math>\mathrm{(A)}\ \frac{1}{28}\left(10-\sqrt{2}\right)\qquad\mathrm{(B)}\ \frac{3}{56}\lef pair C=(0,0),A=(0,3),B=(4,0),D=(4-2.28571,1.71429);
  6 KB (951 words) - 16:31, 2 August 2019
• 2008 AMC 12B Problems
  A basketball player made <math>5</math> baskets during a game. Each basket was worth either <math>2</math> or <math>3</math> points. <math>\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 3 \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ 5 \
  14 KB (2,199 words) - 13:43, 28 August 2020

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