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• Graph (graph theory)
  ...[[empty set | nonempty]] [[set]] of [[vertex|vertices]] that are joined by a number (possibly zero) of [[edge]]s. Graphs are frequently represented gra ...multiple edges, see [[multigraph]]. If the edges are directed, then <math>E</math> may be defined using ordered pairs from the [[product set]] <math>V
  8 KB (1,428 words) - 10:26, 27 August 2020
• 2007 AMC 10A Problems
  {{AMC10 Problems|year=2007|ab=A}} ...ath>25\%</math> discount. Pam buys 5 tickets using a coupon that gives her a <math>30\%</math> discount. How many more dollars does Pam pay than Susan?
  13 KB (2,058 words) - 17:54, 29 March 2024
• 1959 AHSME Problems
  Each edge of a cube is increased by <math>50</math>%. The percent of increase of the surfa ...xtbf{(B)}\ 125\qquad\textbf{(C)}\ 150\qquad\textbf{(D)}\ 300\qquad\textbf{(E)}\ 750 </math>
  22 KB (3,345 words) - 20:12, 15 February 2023
• 2007 AMC 10A Problems/Problem 18
  ...f its sides has length <math>4</math>, and each two consecutive sides form a right angle. Suppose that <math>\overline{AG}</math> and <math>\overline{CH ..., D=(3,2), Ep=(3,1), F=(2,1), G=(2,0), H=(1,0), I=(1,1), J=(0,1), K=(0,2), L=(1,2);
  6 KB (867 words) - 00:17, 20 May 2023
• 2008 USAMO Problems/Problem 3
  (''Gabriel Carroll'') Let <math>n</math> be a positive integer. Denote by <math>S_n</math> the set of points <math>(x, y) <cmath>\left|x\right| + \left|y + \frac {1}{2}\right| < n</cmath>
  9 KB (1,585 words) - 01:00, 14 August 2014
• Normal subgroup
  ...he notation <math>\mathbb{Z}/n\mathbb{Z}</math> for the integers mod <math>n</math>.) ...s means <math>aN=Na</math> but it does not imply that for every <math>n\in N</math>, <math>an=na</math>.
  15 KB (2,840 words) - 12:22, 9 April 2019
• Millennium Problems
  ...set of seven problems for which the [[Clay Mathematics Institute]] offered a US \$7 million prize fund (\$1 million per problem) to celebrate the new mi ...24, 2000 at the [[Collège de France]]. [[Timothy Gowers]] first presented a lecture titled ''The Importance of Mathematics'' as an introduction. After
  13 KB (1,969 words) - 17:57, 22 February 2024
• 2005 AMC 8 Problems
  Connie multiplies a number by 2 and gets 60 as her answer. However, she should ...textbf{(B)}\ 15\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 120\qquad\textbf{(E)}\ 240 </math>
  13 KB (1,821 words) - 22:18, 5 December 2023
• 2004 AMC 12B Problems/Problem 14
  ...<math>AC=5</math>, and <math>BC=12</math>. Points <math>M</math> and <math>N</math> lie on <math>AC</math> and <math>BC</math>, respectively, with <math pair C=(0,0), A=(0,5), B=(12,0), M=(0,4), N=(4,0);
  7 KB (1,083 words) - 22:41, 23 November 2020
• 2009 AMC 10B Problems/Problem 22
  ...pieces as shown in this top view, where <math>M</math> is the midpoint of a top edge. The piece whose top is triangle <math>B</math> contains <math>c</ label("$A$",(-0.4,0.7));
  12 KB (1,868 words) - 03:36, 30 September 2023
• 2000 AMC 8 Problems
  ...\mathrm{(B)}\ 16\qquad\mathrm{(C)}\ 17\qquad\mathrm{(D)}\ 21\qquad\mathrm{(E)}\ 37</math> ...uad \text{(B)}\ -1 \qquad \text{(C)}\ 0 \qquad \text{(D)}\ 1 \qquad \text{(E)}\ 2</math>
  15 KB (2,165 words) - 18:29, 5 June 2024
• Radical axis
  The theory of radical axis is a priceless geometric tool that can solve formidable geometric problems fairl ...rtains to that situation. I hope after you read this text, you will become a better math student, armed with another tool to solve difficult problems. B
  12 KB (2,125 words) - 08:38, 23 May 2024
• 1968 AHSME Problems/Problem 35
  MP("a",(5,0),S); MP("J",(0,10),N);
  3 KB (597 words) - 01:52, 16 August 2023
• 2009 USAMO Problems/Problem 5
  pair A = (-.6, .8), B = (.6, .8), C = (.9, -sqrt(.19)), D = (-.9, -sqrt(.19)), G = draw(A--B--C--D--cycle); draw(B--D);
  6 KB (973 words) - 19:24, 18 October 2018
• 2009 IMO Problems/Problem 2
  ...ctively, and let <math>\Gamma</math> be the circle passing through <math>K,L</math> and <math>M</math>. Suppose that the line <math>PQ</math> is tangent dot("O", (50, 38), N);
  2 KB (280 words) - 01:16, 19 November 2023
• 2009 IMO Problems
  ...th>a_i(a_{i+1}-1)</math> for <math>i=1,\ldots,k-1</math>. Prove that <math>n</math> doesn't divide <math>a_k(a_1-1)</math>. ...ctively, and let <math>\Gamma</math> be the circle passing through <math>K,L</math> and <math>M</math>. Suppose that the line <math>PQ</math> is tangent
  3 KB (509 words) - 09:23, 10 September 2020
• 1992 AJHSME Problems
  ...quad \text{(B)}\ 1 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 10</math> ...\text{(C)}\ 1\dfrac{3}{12} \qquad \text{(D)}\ 1\dfrac{1}{5} \qquad \text{(E)}\ 1\dfrac{10}{40}</math>
  17 KB (2,346 words) - 13:36, 19 February 2020
• 2010 AMC 12A Problems/Problem 21
  ...xtbf{(B)}\ 5 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 7 \qquad \textbf{(E)}\ 8</math> [Quick note: Since we don't know <math>a</math>, <math>b</math>, and <math>c</math>, we really don't even need the l
  5 KB (969 words) - 21:33, 22 June 2022
• 2010 AMC 12A Problems/Problem 12
  In a magical swamp there are two species of talking amphibians: toads, whose sta Chris: "LeRoy is a frog."
  2 KB (413 words) - 20:08, 31 January 2024
• 2010 AMC 12B Problems
  ...f{(B)}\ 20 \qquad \textbf{(C)}\ 25 \qquad \textbf{(D)}\ 30 \qquad \textbf{(E)}\ 35</math> A big <math>L</math> is formed as shown. What is its area?
  12 KB (1,845 words) - 13:00, 19 February 2020

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