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• 1952 AHSME Problems
  Two high school classes took the same test. One class of <math> 20 </math> stud Two equal circles in the same plane cannot have the following number of common
  23 KB (3,556 words) - 15:35, 30 December 2023
• 1953 AHSME Problems
  \textbf{(B)}\ \frac{440}{\pi} \qquad \textbf{(C)}\ \frac{880}{\pi} \qquad
  21 KB (3,123 words) - 14:24, 20 February 2020
• 1955 AHSME Problems
  The ratio of the areas of two concentric circles is <math>1: 3</math>. If the radius of the smaller is <m Two numbers whose sum is <math>6</math> and the absolute value of whose differe
  22 KB (3,509 words) - 21:29, 31 December 2023
• 1998 USAMO Problems/Problem 6
  ..., we can easily alternate them, but if <math>n</math> is odd, we must have two adjacent sides be the same length, and that length must be the larger side
  5 KB (871 words) - 18:59, 10 May 2023
• 2012 AMC 10B Problems/Problem 16
  ...xtbf{(C)}\ 12\pi+\sqrt{3}\qquad\textbf{(D)}\ 10\pi+9\qquad\textbf{(E)}\ 13\pi</math> ...<math>\dfrac{1}{2}</math>, we get <math>2\sqrt{3}</math>. Since there are two 30-60-90 triangles in the equilateral triangle, we multiply the area of the
  4 KB (675 words) - 03:58, 23 January 2023
• 1986 USAMO Problems
  Two distinct circles <math>K_1</math> and <math>K_2</math> are drawn in the pla ...lar to a line through a point on or off the line), find a construction for two points <math>C</math> and <math>D</math> on <math>K_1</math> such that <mat
  3 KB (500 words) - 19:00, 23 October 2019
• 2008 AMC 8 Problems/Problem 21
  ...(6) = 96\pi</math>. The volume of the wedge is half this which is <math>48\pi \approx \boxed{\textbf{(C)}\ 151}</math>.
  1 KB (198 words) - 20:54, 29 October 2023
• 2008 AMC 8 Problems
  In <math>2005</math> Tycoon Tammy invested <math>100</math> dollars for two years. During the first year investment showed a <math>20\%</math> gain. Over the two-year period, what was the change
  14 KB (2,034 words) - 19:14, 20 June 2024
• 2012 AMC 8 Problems
  A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inche ...ass. Her goal is to achieve an average grade of 95 on the tests. Her first two test scores were 97 and 91. After seeing her score on the third test, she r
  13 KB (1,835 words) - 08:51, 8 March 2024
• 2012 AMC 8 Problems/Problem 24
  ...D)}\hspace{.05in}\frac{\pi-1}{\pi}\qquad\textbf{(E)}\hspace{.05in}\frac{3}\pi </math> ...two areas, we find the answer is <math> \boxed{\textbf{(A)}\ \frac{4-\pi}{\pi}} </math>.
  2 KB (310 words) - 16:18, 10 November 2023
• 2004 AMC 8 Problems/Problem 25
  ...rsecting sides, as shown. The circle's diameter is the segment between the two points of intersection. What is the area of the shaded region created by re ...uad \text{(C)}\ 28-4\pi \qquad \text{(D)}\ 28-2\pi \qquad \text{(E)}\ 32-2\pi</math>
  2 KB (268 words) - 09:28, 17 June 2024
• 2012 AMC 10B Problems/Problem 17
  ...m two sectors, the smaller having a central angle of 120 degrees. He makes two circular cones, using each sector to form the lateral surface of a cone. Wh ...s <math>\dfrac{1}{3} \times 4^2\pi \times 8\sqrt{2}=\dfrac{128\sqrt{2}}{3}\pi</math>.
  2 KB (364 words) - 00:51, 17 January 2021
• 2013 AMC 12A Problems/Problem 24
  <math>a_k = 2\sin ( \frac{k\pi}{12} )</math>. <math>2a_2 = 2 = a_6</math>. Thus any two segments with at least one them longer than <math>a_2</math> have a sum gre
  3 KB (395 words) - 15:54, 8 November 2022
• 2013 AMC 12A Problems
  ...on <math>20\%</math> of her three-point shots and <math>30\%</math> of her two-point shots. Shenille attempted <math>30</math> shots. How many points did ...operty that every term beginning with the third is the sum of the previous two. That is, <cmath> S_n = S_{n-2} + S_{n-1} \text{ for } n \ge 3. </cmath> S
  14 KB (2,206 words) - 19:31, 15 May 2024
• 2013 AMC 10A Problems
  ...One afternoon two of his brothers whose ages sum to 16 went to the movies, two brothers younger than 10 went to play baseball, and Joey and the 5-year-old ...on <math>20\%</math> of her three-point shots and <math>30\%</math> of her two-point shots. Shenille attempted <math>30</math> shots. How many points di
  12 KB (1,894 words) - 15:59, 3 January 2024
• 2013 AMC 12A Problems/Problem 23
  ...ath> P </math>, sweeping out a region whose area is <math> \frac{1}{c} (a \pi + b) </math>, where <math>a </math>, <math>b</math>, and <math> c </math> a ...h>. It must be that <math> \overline{AP} </math> divides the diagonal into two segments in the ratio <math>\sqrt{3}</math> to <math>1</math>. It is not di
  4 KB (603 words) - 16:51, 3 April 2020
• 2013 AMC 10B Problems/Problem 7
  ...e is the diameter, the opposite angle is a right angle. Also, because the two adjacent angles are one sixth of the circle apart, the angle opposite them ...ch arc is <math>\frac{\pi}{3}</math>, because the circumference is <math>2\pi</math>. Once we draw the triangle (as is explained in solution 1), we see t
  3 KB (417 words) - 20:21, 12 January 2024
• 2013 AIME I Problems
  ...into two squares and two nonsquare rectangles. The sum of the areas of the two squares is <math>\frac{9}{10}</math> of the area of square <math>ABCD.</mat ...uted in equal numbers to each student, there are exactly three blocks left over.
  9 KB (1,580 words) - 13:07, 24 February 2024
• 2013 AIME I Problems/Problem 14
  For <math>\pi \le \theta < 2\pi</math>, let ...>\sin \theta = -17/19, 1/3.</math> Since we're given <math>\pi\leq\theta<2\pi,</math> <math>\sin\theta</math> is nonpositive. We therefore use the negati
  10 KB (1,654 words) - 13:24, 13 June 2024
• 1991 AHSME Problems
  <math>|3-\pi|=</math> ...4 \qquad \textbf{(C) }3-\pi \qquad \textbf{(D) }3+\pi \qquad \textbf{(E) }\pi-3 </math>
  16 KB (2,451 words) - 04:27, 6 September 2021

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