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• 2006 AIME II Problems
  ...th> and <math>\angle D</math> are right angles, and <math>\angle B, \angle C, \angle E,</math> and <math>\angle F</math> are congruent. The area of the ...\log_{10} 75</math>, and <math>\log_{10} n</math>, where <math>n</math> is a positive integer. Find the number of possible values for <math>n</math>.
  8 KB (1,350 words) - 12:00, 4 December 2022
• 1988 IMO Problems/Problem 6
  ...>b</math> be positive integers such that <math>ab + 1</math> divides <math>a^{2} + b^{2}</math>. Show that \frac {a^{2} + b^{2}}{ab + 1}
  4 KB (720 words) - 12:26, 7 April 2024
• 1999 PMWC Problems
  label("$C$", (7.8,0), NE * labelscalefactor); label("$A$", (3.9,6.75), NE * labelscalefactor);
  6 KB (703 words) - 21:21, 21 April 2014
• 2000 PMWC Problems
  <math>y</math> is a number that has <math>8</math> different factors (including the number <mat Given that <math>A^4=75600\times B</math>. If <math>A</math> and <math>B</math> are positive integers, find the smallest value of
  11 KB (1,713 words) - 22:47, 13 July 2023
• 2002 PMWC Problems
  label("$\textbf{A}$",(-1,0)); label("$\textbf{C}$",(0,-sqrt(3)));
  5 KB (725 words) - 16:07, 23 April 2014
• 1971 Canadian MO Problems
  ...Join <math>OE</math> and extend <math>OE</math> to cut the circle at <math>C.</math> Given <math>EC=1,</math> find the radius of the circle <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
• 1989 USAMO Problems/Problem 4
  ...math>,<math>E</math>,<math>F</math> on <math>a</math>,<math>b</math>,<math>c</math>, respectively. We notice that <math>IO</math> passes through sides <math>a</math> and <math>c</math> if and only if <math>I</math> belongs to either regions <math>AOF</m
  2 KB (290 words) - 19:11, 18 July 2016
• 2007 AMC 12B Problems
  <math> \mathrm{(A) \ } 678\qquad \mathrm{(B) \ } 768\qquad \mathrm{(C) \ } 786\qquad \mathrm{(D) \ } 867\qquad \mathrm{(E) \ } 876</math> 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
• Cramer's Rule
  '''Cramer's Rule''' is a method of solving systems of equations using [[matrix|matrices]]. ...the [http://en.wikipedia.org/wiki/Determinant matrix determinant] to solve a system of ''n'' linear equations in ''n'' variables.
  2 KB (352 words) - 18:22, 11 October 2023
• Asymptote: Useful functions
  The bundled <code>markers</code> package provides a useful function for marking angles. The exact same function exists in the < ...e functions, you can replace <code>line l1, line l2</code> with <code>pair A, pair O, pair B</code>, which would mark the angle <math>\angle AOB</math>.
  4 KB (646 words) - 21:18, 26 March 2024
• Asymptote: CSE5
  ...of two paths without common points, which may be useful if you try to draw a picture just from its verbal description and do not want to make any calcul CSE5 contains doubles of each function; a function with a full name and a function with an abbreviated name.
  4 KB (607 words) - 15:09, 30 June 2020
• Intermediate Value Theorem
  Take a function <math>f</math> and interval <math>[a,b]</math> such that the following hold: <math>f:[a,b]\rightarrow\mathbb{R},</math>
  811 bytes (143 words) - 18:08, 1 February 2021
• Summation
  A '''summation''' is the [[sum]] of a number of terms (addends). Summations are often written using sigma notatio ...+c_{b}</math>. Here <math>i</math> refers to the index of summation, <math>a</math> is the lower bound, and <math>b</math> is the upper bound.
  3 KB (482 words) - 16:39, 8 October 2023
• 1962 IMO Problems
  (a) Its decimal representation has 6 as the last digit. ...> begin their motion at the same instant from the starting positions <math>A</math> and <math>B'</math>, respectively. Determine and draw the locus of t
  3 KB (431 words) - 21:17, 20 August 2020
• Relation
  ...e structure that can be placed on a pair or collection of [[set]]s to give a notion of "relatedness" to the [[element]]s of those sets. ...al number]]s that indicates that a first number is exactly one larger than a second number, or the relation betweem the [[integer]]s and the set <math>\
  2 KB (445 words) - 08:16, 21 August 2009
• 2004 AMC 12A Problems/Problem 14
  ...ath>20</math> is added to the third term, the three resulting numbers form a [[geometric progression]]. What is the smallest possible value for the thir <math>\text {(A)}\ 1 \qquad \text {(B)}\ 4 \qquad \text {(C)}\ 36 \qquad \text {(D)}\ 49 \qquad \text {(E)}\ 81</math>
  4 KB (689 words) - 03:35, 16 January 2023
• Celsius
  ...emperature at which water freezes at 1 [[atm]], and <math>100^\circ\mathrm{C}</math> as the temperature at which water boils at 1 atm. ...ly, to be <math>-273.15^\circ\mathrm{C}</math> and <math>0.01^\circ\mathrm{C}</math>.
  4 KB (357 words) - 22:40, 17 April 2024
• De Longchamps point
  label("C",(29,25),(1,1)); ...<math>H</math>) reflected <br /> through the [[circumcenter]]<br /> (<math>C</math>).}}
  10 KB (1,780 words) - 09:23, 17 November 2022
• 1976 USAMO Problems/Problem 5
  If <math>P(x)</math>, <math>Q(x)</math>, <math>R(x)</math>, and <math>S(x)</math> are all [[polynomial]]s such that <cmath> P(x^5) + xQ(x^5) + x^2 R(x^5) = (x^4 + x^3 + x^2 + x +1) S(x), </cmath>
  3 KB (572 words) - 17:14, 16 August 2015
• 2000 AMC 12 Problems/Problem 10
  ...bout the <math>x</math>-axis to produce <math>R</math>, and finally, <math>R</math> is translated by 5 units in the positive-<math>y</math> direction to \text {(A) } (1,7, - 3) \qquad \text {(B) } ( - 1,7, - 3) \qquad \text {(C) } ( - 1, - 2,8) \qquad \text {(D) } ( - 1,3,3) \qquad \text {(E) } (1,3,3)
  1 KB (173 words) - 08:56, 21 August 2023

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