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ICTM Math Contest
...consists of five members who work together on 20 questions for 25 minutes. A school may field as many five member teams as it wishes. The individual com A school team will qualify by taking first place in a region with four or more schools competing.

8 KB (1,182 words) - 13:26, 3 April 2024
Ptolemy's theorem
...orem''' gives a relationship between the side lengths and the diagonals of a [[cyclic quadrilateral]]; it is the [[equality condition | equality case]] Given a [[cyclic quadrilateral]] <math>ABCD</math> with side lengths <math>{a},{b},{c},{d}</math> and [[diagonal]]s <math>{e},{f}</math>:

7 KB (1,198 words) - 23:28, 19 September 2024
LaTeX:Symbols
This article provides a short list of commonly used LaTeX symbols. .../math> on the web, (technically an AJAX library simulating it.)) maintains a [http://docs.mathjax.org/en/latest/tex.html#supported-latex-commands list o

16 KB (2,315 words) - 19:35, 4 November 2024
2004 AMC 12A Problems
{{AMC12 Problems|year=2004|ab=A}} <math>\text{(A) } 0.0029 \qquad \text{(B) } 0.029 \qquad \text{(C) } 0.29 \qquad \text{(D)

13 KB (1,953 words) - 23:31, 25 January 2023
2006 AMC 10A Problems/Problem 17
pair A,B,C,D,E,F,G,H,W,X,Y,Z; A=(0,2); B=(1,2); C=(2,2); D=(3,2);

6 KB (1,106 words) - 09:20, 4 November 2024
2005 AIME II Problems/Problem 12
...> AB </math> with <math> AE<BF </math> and <math> E </math> between <math> A </math> and <math> F, m\angle EOF =45^\circ, </math> and <math> EF=400. </m ...D--A);draw(E--O--F);draw(G--O); dot(A^^B^^C^^D^^E^^F^^G^^O); label("\(A\)",A,(-1,1));label("\(B\)",B,(1,1));label("\(C\)",C,(1,-1));label("\(D\)",D,(-1,

13 KB (2,080 words) - 12:14, 23 July 2024
2005 AIME II Problems/Problem 15
...h> a </math> for which the line <math> y=ax </math> contains the center of a circle that is externally [[tangent (geometry)|tangent]] to <math> w_2 </ma pair A = (-5, 12), B = (5, 12), C = (0, 0);

12 KB (2,001 words) - 19:26, 23 July 2024
2004 AIME II Problems/Problem 7
<math> ABCD </math> is a rectangular sheet of paper that has been folded so that corner <math> B </m pair A=origin, B=(25,0), C=(25,70/3), D=(0,70/3), E=(8,0), F=(22,70/3), Bp=reflect

9 KB (1,500 words) - 19:06, 8 October 2024
1992 AIME Problems
A positive integer is called ascending if, in its decimal representation, the ...she has won by the total number of matches she has played. At the start of a weekend, her win ratio is exactly <math>0.500</math>. During the weekend, s

8 KB (1,117 words) - 04:32, 11 November 2023
1983 AIME Problems/Problem 11
The solid shown has a square base of side length <math>s</math>. The upper edge is parallel to th triple A=(0,0,0),B=(s,0,0),C=(s,s,0),D=(0,s,0),E=(-s/2,s/2,6),F=(3*s/2,s/2,6);

6 KB (971 words) - 14:35, 27 May 2024
1984 AIME Problems/Problem 3
A [[point]] <math>P</math> is chosen in the interior of <math>\triangle ABC</ pair A=(0,0),B=(12,0),C=(4,5);

4 KB (726 words) - 12:39, 13 August 2023
1985 AIME Problems/Problem 4
A small [[square (geometry) | square]] is constructed inside a square of [[area]] 1 by dividing each side of the unit square into <math>n< ...qrt{2n^2 - 2n + 1}</math>, so the parallelogram has height <math>h = \frac{A}{l} = \frac{1}{\sqrt{2n^2 - 2n + 1}}</math>. But the height of the paralle

3 KB (484 words) - 20:40, 2 March 2020
1991 AIME Problems/Problem 12
...--B--C--D--cycle);draw(P--R..Q--S); draw(P--Q--R--S--cycle); label("\(A\)",A,NW);label("\(B\)",B,NE);label("\(C\)",C,SE);label("\(D\)",D,SW); label("\(P ...bus; <math>PQ = \sqrt{15^2 + 20^2} = 25</math>. Since the [[diagonal]]s of a rhombus are [[perpendicular bisector]]s, we have that <math>OP = 15, OQ = 2

8 KB (1,270 words) - 22:36, 27 August 2023
1992 AIME Problems/Problem 14
...AC^{}_{}</math>, and <math>AB^{}_{}</math>, respectively. Given that <math>AA'</math>, <math>BB'</math>, and <math>CC'</math> are concurrent at the point ...and <math>ABC</math> having the same base, <cmath>\frac{AO}{OA'}+1=\frac{AA'}{OA'}=\frac{[ABC]}{[BOC]}=\frac{K_A+K_B+K_C}{K_A}.</cmath> Therefore, we

4 KB (667 words) - 00:26, 16 August 2023
1996 AIME Problems/Problem 15
...=(0,0), A=expi(pi/4), C=IP(A--A + 2*expi(17*pi/12), B--(3,0)), D=A+C, O=IP(A--C,B--D); D(MP("A",A,N)--MP("B",B)--MP("C",C)--MP("D",D,N)--cycle); D(B--D); D(A--C); D(MP("O",O,SE));

5 KB (710 words) - 20:04, 14 September 2020
1997 AIME Problems/Problem 8
...umn must have 2 1's and 2 -1's. Let's consider the first column. There are a total of <math>6</math> ways to arrange 2 1's and 2 -1's. Let's consider th ...e that first there are <math>\binom{4}{2}</math> values of the fixed <math>A</math>. We then have the following cases:

4 KB (638 words) - 15:41, 22 January 2024
1998 AIME Problems/Problem 8
...[negative]] term encounted. What positive integer <math>x</math> produces a sequence of maximum length? ...ont> || <math>1000 - x</math> || <math>2x - 1000</math><font color="white">a</font> || <math>2000 - 3x</math> || <math>5x - 3000</math> || <math>5000 -

2 KB (354 words) - 12:11, 25 November 2024
1999 AIME Problems/Problem 14
pair A=(0,0),B=(13,0),C=IP(circle(A,15),circle(B,14)); D(MP("A",A)--MP("B",B)--MP("C",C,N)--cycle);

7 KB (1,184 words) - 12:25, 22 December 2022
2001 AIME I Problems/Problem 7
...), I=incenter(A,B,C), D=IP((0,I.y)--(20,I.y),A--B), E=IP((0,I.y)--(20,I.y),A--C); D(MP("A",A,N)--MP("B",B)--MP("C",C)--cycle); D(MP("I",I,NE)); D(MP("E",E,NE)--MP("D",D

11 KB (1,829 words) - 05:57, 30 September 2024
2002 AIME I Problems/Problem 15
...CD</math> is a square with <math>AB = 12;</math> face <math>ABFG</math> is a trapezoid with <math>\overline{AB}</math> parallel to <math>\overline{GF},< triple A=(-6,-6,0), B = (-6,6,0), C = (6,6,0), D = (6,-6,0), E = (2,0,12), H=(-6+2*s

7 KB (1,181 words) - 14:56, 1 July 2024

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