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• Mock AMC
  | [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9321 Initial Discussion] | [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9353 Problems]
  51 KB (6,175 words) - 20:58, 6 December 2023
• 1985 AIME Problems/Problem 12
  ...rom vertex <math>V</math> and ending at vertex <math>A,</math> where <math>V\in\{A,B,C,D\}</math> and <math>k</math> is a positive integer. We wish to f ...math>V</math> to <math>A</math> and the paths from <math>A</math> to <math>V</math> have one-to-one correspondence. So, we must get <cmath>A_k+B_k+C_k+D
  19 KB (3,128 words) - 00:53, 22 June 2024
• P versus NP
  ...akes to solve a problem as a function of input, usually expressed with big-O notation) and [[space]] (how much memory it takes to solve a problem). In s ...ch as "What is the length of the longest path from <math>s</math> to <math>t</math>?"). More formally, a decision problem may be thought of as a languag
  6 KB (1,104 words) - 15:11, 25 October 2017
• 2007 iTest Problems
  ...}{4}\quad\mathrm{(E)}\,\frac{4}{3}\quad\mathrm{(F)}\,\sqrt{3}\quad\mathrm{(G)}\,\frac{\sqrt6}{2}</math> ...ad\mathrm{(D)}\,10\quad\mathrm{(E)}\,12\quad\mathrm{(F)}\,2.4\quad\mathrm{(G)}\,25.2\quad\mathrm{(H)}\,123456789</math>
  30 KB (4,794 words) - 23:00, 8 May 2024
• 2020 AMC 10A Problems
  label("V", (2, 6), NE); pair G = (0.924, 0.403);
  13 KB (1,968 words) - 18:32, 29 February 2024
• Mock AIME 5 Pre 2005 Problems
  Function <math>g(y)</math> is given such way that for all <math>y</math>, If <math>g(9) + g(26) + g(126) + g(401) = \frac {m}{n}</math> where <math>m</math> and <math>n</math> are rela
  6 KB (909 words) - 07:27, 12 October 2022
• 1988 IMO Problems/Problem 1
  ...dii <math>R</math> and <math>r</math> (<math>R>r</math>) with center <math>O</math>. Fix <math>P</math> on the small circle and consider the variable c ...ble positions of the midpoints <math>U</math> of <math>AB</math> and <math>V</math> of <math>AC</math> as <math>A</math> varies?</li>
  3 KB (545 words) - 11:32, 30 January 2021
• Characteristic polynomial
  ...det(tI - A)</math>, which is a <math>n</math>th degree polynomial in <math>t</math>. Here, <math>I</math> refers to the <math>n\times n</math> [[identit ..._{2n} \\ \vdots & \vdots & \ddots & \vdots \\ -a_{n1} & -a_{n2} & \cdots & t-a_{nn}\end{vmatrix}</cmath></center>
  19 KB (3,412 words) - 14:57, 21 September 2022
• Mock Amc 12
  | [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9321 Initial Discussion] | [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9353 Problems]
  18 KB (2,206 words) - 19:41, 24 December 2020
• 2010 AMC 8 Problems
  ...-4), P=(1,-3.8), Q=(1,-3.6), R=(1,-3.4), S=(1,-3.2), T=(1,-3), U=(1,-2.8), V=(1,-2.6), W=(1,-2.4), Z=(1,-2.2), E_1=(1.4,-2.6), F_1=(1.8,-2.6), O_1=(14,- ...)); D(T--(8,-3),linewidth(0.4)); D(B--(8,-2),linewidth(0.4)); D(B--S_1); D(T--R_1); D(N--Q_1); D(H--P_1); D(A--O_1); D(C_1--E_1); D(E_1--F_1); D(F_1--D_
  18 KB (2,768 words) - 21:05, 9 January 2024
• 2011 AMC 8 Problems
  ...,-2), M=(0,-6), O=(0,-4), P=(4,-4), Q=(2,-2), R=(2,-6), T=(6,4), U=(10,0), V=(10,4), Z=(10,2), A_1=(8,4), B_1=(8,0), C_1=(6,-2), D_1=(10,-2), E_1=(6,-6) ...--cycle,linewidth(1.6)); draw(M--O--Q--R--cycle,linewidth(1.6)); draw(A_1--V--Z--cycle,linewidth(1.6)); draw(G_1--K_1--J_1--E_1--cycle,linewidth(1.6));
  16 KB (2,371 words) - 17:34, 9 January 2024
• 2011 AMC 8 Problems/Problem 7
  ...,-2), M=(0,-6), O=(0,-4), P=(4,-4), Q=(2,-2), R=(2,-6), T=(6,4), U=(10,0), V=(10,4), Z=(10,2), A_1=(8,4), B_1=(8,0), C_1=(6,-2), D_1=(10,-2), E_1=(6,-6) ...--cycle,linewidth(1.6)); draw(M--O--Q--R--cycle,linewidth(1.6)); draw(A_1--V--Z--cycle,linewidth(1.6)); draw(G_1--K_1--J_1--E_1--cycle,linewidth(1.6));
  4 KB (557 words) - 00:30, 4 January 2023
• 2002 Romanian NMO Problems
  ...EF]</math> be a frustum of a regular pyramid. Let <math>G</math> and <math>G'</math> be the centroids of bases <math>ABC</math> and <math>DEF</math> res ...triangles <math>OXY</math> and <math>OZT</math> are right-angled at <math>O</math> and isosceles.
  10 KB (1,695 words) - 10:03, 10 May 2012
• 1973 AHSME Problems
  Of the following five statements, I to V, about the binary operation of averaging (arithmetic mean), <math>\text{V. Averaging has an identity element }</math>
  18 KB (2,788 words) - 13:55, 20 February 2020
• 1988 AHSME Problems
  pair A=(0,0), B=(16,0), C=(16,16), D=(0,16), E=(32,0), F=(48,0), G=(48,16), H=(32,16), I=(0,8), J=(10,8), K=(10,16), L=(32,6), M=(40,6), N=(40 draw(A--B--C--D--A^^E--F--G--H--E^^I--J--K^^L--M--N);
  17 KB (2,535 words) - 13:45, 19 February 2020
• 2007 iTest Problems/Problem 22
  \text{(G) } 6 \quad \text{(O) } 14 \quad
  929 bytes (137 words) - 22:05, 10 January 2019
• 2007 iTest Problems/Problem 25
  \text{(G) } 6\qquad \text{(O) } 14\qquad
  2 KB (270 words) - 14:35, 29 July 2018
• 2007 iTest Problems/Problem 23
  \text{(G) } -3\quad \text{(O) } 3-2i\quad</math>
  1 KB (202 words) - 16:48, 24 November 2018
• 2007 iTest Problems/Problem 24
  \text{(G) }6 \quad \text{(O) }14 \quad
  2 KB (340 words) - 19:49, 30 June 2018
• 2014 IMO Problems/Problem 3
  ...ar from <math>A</math> to <math>BD</math>. Points <math>S</math> and <math>T</math> lie on sides <math>AB</math> and <math>AD</math>, respectively, such pair T = IP(D--A,circle4, 0);
  6 KB (1,071 words) - 03:58, 8 September 2018

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