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• 2006 AMC 8 Problems/Problem 7
  ...math> Y </math> has a circumference of <math> 8 \pi </math>. Circle <math> Z </math> has an area of <math> 9 \pi </math>. List the circles in order from ...quad\textbf{(C)}\ Y, X, Z\qquad\textbf{(D)}\ Z, Y, X\qquad\textbf{(E)}\ X, Z, Y </math>
  868 bytes (153 words) - 19:35, 14 January 2024
• 1985 AHSME Problems
  <math> \mathrm{(A)\ } 15 \qquad \mathrm{(B) \ }16 \qquad \mathrm{(C) \ } 17 \qquad \mathrm{( In an arcade game, the "monster" is the shaded sector of a circle of radius <math>1</math> cm, as shown in the figure. The missing pie
  17 KB (2,488 words) - 03:26, 20 March 2024
• 1985 AHSME Problems/Problem 15
  ...at <math>a^b = b^a</math> and <math>b = 9a</math>, then the value of <math>a</math> is <math> \mathrm{(A)\ } 9 \qquad \mathrm{(B) \ }\frac{1}{9} \qquad \mathrm{(C) \ } \sqrt[9]{9}
  1,012 bytes (163 words) - 21:35, 19 March 2024
• 1985 AHSME Problems/Problem 17
  ...parallel lines <math>L</math> and <math>L'</math> that pass through <math>A</math> and <math>C</math> and are perpendicular to <math>DB</math>. The are real x=sqrt(6), y=sqrt(3), a=0.4;
  2 KB (340 words) - 22:39, 19 March 2024
• 2010 AMC 8 Problems
  <math> \textbf{(A)}\ 26 \qquad\textbf{(B)}\ 27\qquad\textbf{(C)}\ 28\qquad\textbf{(D)}\ 29\qq If <math>a @ b = \frac{a\times b}{a+b}</math> for <math>a,b</math> positive integers, then what is <math>5 @ 10</math>?
  18 KB (2,768 words) - 21:05, 9 January 2024
• 2011 AMC 8 Problems
  ...math> apples at a cost of <math> 50 </math> cents per apple. She paid with a 5-dollar bill. How much change did Margie receive? <math>\textbf{(A) }\ \textdollar 1.50 \qquad \textbf{(B) }\ \textdollar 2.00 \qquad \textbf{
  16 KB (2,371 words) - 17:34, 9 January 2024
• 2011 AMC 8 Problems/Problem 17
  ...<math>z</math> be whole numbers. If <math>2^w \cdot 3^x \cdot 5^y \cdot 7^z = 588</math>, then what does <math>2w + 3x + 5y + 7z</math> equal? <math> \textbf{(A) } 21\qquad\textbf{(B) }25\qquad\textbf{(C) }27\qquad\textbf{(D) }35\qquad\
  924 bytes (137 words) - 15:08, 17 December 2023
• 1970 Canadian MO Problems/Problem 1
  Find all number triples <math> (x,y,z)</math> such that when any of these numbers is added to the product of the z + yx &=& 2 \end{matrix}</math>
  1 KB (196 words) - 06:54, 30 December 2012
• 1973 Canadian MO Problems/Problem 7
  State a general law suggested by these examples, and prove it. Thus, by induction, the formula holds for all <math>n \in \mathbb{Z^{+}}</math>
  2 KB (351 words) - 18:56, 27 May 2022
• Alcumus
  Alcumus is a free, educational system that asks questions from the AoPS staff, books, or ...follow a book from AoPS, use "All Available Topics" or "Let Alcumus Choose a Topic".
  3 KB (533 words) - 10:55, 7 February 2023
• Barycentric coordinates
  ...triangle <math> \Delta{A_1}{A_2}{A_3} </math>. These masses then determine a point <math> P </math>, which is the geometric centroid of the three masses The Central NC Math Group published a lecture concerning this topic at https://www.youtube.com/watch?v=KQim7-wrwL
  25 KB (5,106 words) - 11:00, 24 May 2024
• Mock Geometry AIME 2011 Problems/Problem 5
  ...<math>D</math> and the circumcircle at <math>E</math> different from <math>A</math>. Calculate the value of <math>DE^2</math> label("$A$",(0,24sqrt(2)),NNW);
  4 KB (665 words) - 03:40, 25 December 2022
• 2011 AMC 8 Problems/Problem 7
  ...,-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), F_1=(10, ...ycle,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
• Pre-Olympiad Level Tournament By Mathtime
  ...with the first term equal to <math>a_1</math>, with <math>a_1>0</math>, an a second term of <math>3</math> and each term after that, <math>a_n</math> eq In a cyclic quadrilateral with sides <math>AB, BC, CD, AC</math> prove that:
  1 KB (235 words) - 16:06, 7 January 2012
• 1989 AHSME Problems
  <math> \textrm{(A)}\ -7\qquad\textrm{(B)}\ -2\qquad\textrm{(C)}\ 0\qquad\textrm{(D)}\ 1\qquad <math> \textrm{(A)}\ \frac{1}5\qquad\textrm{(B)}\ \frac{1}4\qquad\textrm{(C)}\ \frac{2}7\qqua
  15 KB (2,247 words) - 13:44, 19 February 2020
• 1989 AHSME Problems/Problem 9
  <math> \textrm{(A)}\ 276\qquad\textrm{(B)}\ 300\qquad\textrm{(C)}\ 552\qquad\textrm{(D)}\ 600 ...two distinct letters other than Z (as the last name will automatically be Z), there is only one possible way to arrange them in alphabetical order, thu
  728 bytes (109 words) - 07:48, 22 October 2014
• 2012 AMC 10A Problems/Problem 25
  .... The probability that no two of <math>x</math>, <math>y</math>, and <math>z</math> are within 1 unit of each other is greater than <math>\frac {1}{2}</ <math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\
  13 KB (2,133 words) - 01:22, 6 February 2024
• 2012 AMC 10A Problems/Problem 21
  Let points <math>A</math> = <math>(0 ,0 ,0)</math>, <math>B</math> = <math>(1, 0, 0)</math>, < <math> \textbf{(A)}\ \sqrt{2}\qquad\textbf{(B)}\ \frac{2\sqrt{5}}{3}\qquad\textbf{(C)}\ \frac
  3 KB (526 words) - 19:05, 30 June 2022
• 2012 AMC 10A Problems
  {{AMC10 Problems|year=2012|ab=A}} Cagney can frost a cupcake every <math>20</math> seconds and Lacey can frost a cupcake every <math>30</math> seconds. Working together, how many cupcakes
  13 KB (1,994 words) - 01:31, 22 December 2023
• 2012 AMC 12A Problems
  {{AMC12 Problems|year=2012|ab=A}} A bug crawls along a number line, starting at <math>-2</math>. It crawls to <math>-6</math>, the
  14 KB (2,197 words) - 13:34, 12 August 2020

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