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• Math books
  ...https://artofproblemsolving.com/community/user/243060 cargeek9], currently a junior in high school. It covers the basics of algebra, geometry, combinato .../www.amazon.com/exec/obidos/ASIN/0817636773/artofproblems-20 Algebra] by I.M. Gelfand and Alexander Shen.
  24 KB (3,182 words) - 11:10, 31 August 2024
• 2015 IMO Problems
  We say that a finite set <math>\mathcal{S}</math> in the plane is <i> balanced </i> if, for any two different points <math>A</math>, <math>B</math> in <math>\mathcal{S}</math>, there is
  4 KB (709 words) - 15:00, 1 June 2024
• Function
  A '''function''' is a rule that maps one set of values to another set of values, assigning to eac ...is a ''function from <math>A</math> to <math>B</math>'' (written <math>f: A \to B</math>) if and only if
  10 KB (1,761 words) - 03:16, 12 May 2023
• Circle
  A '''circle''' is a geometric figure commonly used in Euclidean [[geometry]]. {{asy image|<asy>unitsize(2cm);draw(unitcircle,blue);</asy>|right|A basic circle.}}
  9 KB (1,585 words) - 13:46, 2 September 2024
• Mock AMC
  ...an actual [[AMC]] (American Mathematics Competitions 8, 10, or 12) exam. A number of '''Mock AMC''' competitions have been hosted on the [[Art of Prob == Tips for Writing a Mock AMC ==
  51 KB (6,220 words) - 21:22, 17 July 2024
• 2006 AMC 12A Problems
  {{AMC12 Problems|year=2006|ab=A}} ...B) \ } 32\qquad \mathrm{(C) \ } 33\qquad \mathrm{(D) \ } 34\qquad \mathrm{(E) \ } 35 </math>
  15 KB (2,223 words) - 13:43, 28 December 2020
• 2005 AMC 12A Problems
  {{AMC12 Problems|year=2005|ab=A}} ...B}) \ 2 \qquad (\mathrm {C})\ 5 \qquad (\mathrm {D}) \ 10 \qquad (\mathrm {E})\ 20
  13 KB (1,965 words) - 22:18, 7 September 2024
• 2005 AMC 12B Problems
  A scout troop buys <math>1000</math> candy bars at a price of five for <math>2</math> dollars. They sell all the candy bars at t \mathrm{(A)}\ 100 \qquad
  12 KB (1,781 words) - 14:59, 19 July 2024
• 2005 AIME II Problems/Problem 12
  ...math> is not divisible by the [[square]] of any [[prime]], find <math> p+q+r. </math> ...)",F,(1,1));label("\(G\)",G,(-1,1));label("\(O\)",O,(1,-1)); label("\(x\)",E/2+G/2,(0,1));label("\(y\)",G/2+F/2,(0,1)); label("\(450\)",(O+G)/2,(-1,1));
  13 KB (2,080 words) - 13:14, 23 July 2024
• 2005 AIME II Problems/Problem 14
  ...is on <math> \overline{BC} </math> with <math> CD=6. </math> Point <math> E </math> is on <math> \overline{BC} </math> such that <math> \angle BAE\cong pair A = origin;
  14 KB (2,340 words) - 16:38, 21 August 2024
• 2004 AIME I Problems/Problem 9
  ...nd <math> n</math> are [[relatively prime]] positive integers. Find <math> m+n. </math> .../math> or <math>\overline{FG}</math>. <math>V_2</math> is a trapezoid with a right angle then, from which it follows that <math>V_1</math> contains one
  4 KB (618 words) - 20:01, 4 July 2013
• 1983 AIME Problems
  ...th> and <math>z</math> all exceed <math>1</math> and let <math>w</math> be a positive number such that <math>\log_xw=24</math>, <math>\log_y w = 40</mat ...hat of <math>BC</math> is <math>2</math> cm. The angle <math>ABC</math> is a right angle. Find the square of the distance (in centimeters) from <math>B<
  7 KB (1,104 words) - 03:13, 27 May 2024
• 2002 AIME I Problems
  ...ath> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. ...gram shows twenty congruent circles arranged in three rows and enclosed in a rectangle. The circles are tangent to one another and to the sides of the r
  8 KB (1,374 words) - 21:09, 27 July 2023
• 2001 AIME II Problems
  ...rom left to right, each pair of consecutive digits of <math>N</math> forms a perfect square. What are the leftmost three digits of <math>N</math>? ...he largest number of students who could study both languages. Find <math>M-m</math>.
  8 KB (1,282 words) - 21:12, 19 February 2019
• 1983 AIME Problems/Problem 14
  ...<math>P</math>, one of the points of intersection, a line is drawn in such a way that the chords <math>QP</math> and <math>PR</math> have equal length. ...2); draw(Q--R); label("$Q$",Q,NW); label("$P$",P,1.5*dir(80)); label("$R$",R,NE); label("12",waypoint(O1--O2,0.4),S);</asy>
  13 KB (2,151 words) - 17:48, 27 May 2024
• 1990 AIME Problems/Problem 14
  ...ments <math>\overline{CP}</math> and <math>\overline{DP}</math>, we obtain a [[triangular pyramid]], all four of whose faces are [[isosceles triangle]]s pair D=origin, A=(13,0), B=(13,12), C=(0,12), P=(6.5, 6);
  7 KB (1,086 words) - 08:16, 29 July 2023
• 1992 AIME Problems/Problem 9
  ...nd <math>n^{}_{}</math> are relatively prime positive integers, find <math>m+n^{}_{}</math>. ...ath> bisects <math>\angle AXB;</math> let it meet <math>CD</math> at <math>E.</math> Using the angle bisector theorem, we let <math>XB=y(92-x), XA=xy</m
  5 KB (874 words) - 10:27, 22 August 2021
• 1999 AIME Problems/Problem 15
  ...The vertices of its midpoint triangle are the [[midpoint]]s of its sides. A triangular [[pyramid]] is formed by folding the triangle along the sides of ...F\)",foot(C,A,B),NW);label("\(P\)",P,NW);label("\(Q\)",Q,NE);label("\(R\)",R,SE);</asy><asy>import three; defaultpen(linewidth(0.6));
  7 KB (1,175 words) - 13:26, 3 September 2024
• 2001 AIME I Problems/Problem 6
  ...th>n</math> are [[relatively prime]] [[positive]] [[integer]]s. Find <math>m + n</math>. ...n the diagram below, the lowest <math>y</math>-coordinate at each of <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math> corresponds to t
  11 KB (1,731 words) - 03:16, 24 August 2024
• 2006 Romanian NMO Problems
  ...<math>2 \cdot \frac{CN}{BC} = \frac{AM}{AB}</math>. Let <math>P</math> be a point on the line <math>AC</math>. Prove that the lines <math>MN</math> and ...nimal <math>n</math>, such that for each coloring, there exists a line and a column with at least 3 unit squares of the same color (on the same line or
  11 KB (1,779 words) - 14:57, 7 May 2012

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