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2014 AIME II Problems/Problem 3
...of 24, the hexagon has the same area as the original rectangle. Find <math>a^2</math>. pair A,B,C,D,E,F,R,S,T,X,Y,Z;

3 KB (454 words) - 22:00, 24 January 2024
2014 AIME II Problems/Problem 5
...0</math>. Find the sum of all possible values of <math>|b|</math>.</onlyinclude> ...</math> in <math>p(x)</math> and <math>q(x)</math> are both equal to <math>a</math>, and equating the two coefficients gives

6 KB (1,069 words) - 15:51, 31 December 2023
2016 AMC 10A Problems
{{AMC10 Problems|year=2016|ab=A}} <math>\textbf{(A)}\ 99\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 110\qquad\textbf{(D)}\ 121\

14 KB (2,104 words) - 21:35, 7 June 2024
1975 IMO Problems/Problem 6
...nteger <math>n</math> and all real <math>t, x, y</math> <cmath>P(tx, ty) = t^nP(x, y)</cmath> (that is, <math>P</math> is homogeneous of degree <math>n< (ii) for all real <math>a, b, c</math>, <cmath>P(b + c, a) + P(c + a, b) + P(a + b, c) = 0,</cmath>

3 KB (563 words) - 16:21, 29 January 2021
1962 AHSME Problems/Problem 13
...c37</math>. Find <math>S</math> when <math>R = \sqrt {48}</math> and <math>T = \sqrt {75}</math>. <math> \textbf{(A)}\ 28\qquad\textbf{(B)}\ 30\qquad\textbf{(C)}\ 40\qquad\textbf{(D)}\ 42\qqu

969 bytes (143 words) - 22:19, 10 April 2023
1962 AHSME Problems/Problem 18
...decagon (<math>12</math> sides) is inscribed in a circle with radius <math>r</math> inches. The area of the dodecagon, in square inches, is: ...bf{(B)}\ 2r^2\qquad\textbf{(C)}\ \frac{3r^2\sqrt{3}}{4}\qquad\textbf{(D)}\ r^2\sqrt{3}\qquad\textbf{(E)}\ 3r^2\sqrt{3} </math>

902 bytes (147 words) - 22:17, 3 October 2014
1962 AHSME Problems
<math>\textbf{(A)}\ \frac{4y-1}{8} \qquad <math>\textbf{(A)}\ \frac{\sqrt{3}}{6} \qquad

17 KB (2,459 words) - 22:40, 10 April 2023
2013 AMC 8 Problems
<math>\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \ ...lf-pound packages for just \$3 per package." What is the regular price for a full pound of fish, in dollars? (Assume that there are no deals for bulk)

15 KB (2,162 words) - 20:05, 8 May 2023
2013 AMC 8 Problems/Problem 11
...mill on 3 days this week. He went 2 miles each day. On Monday he jogged at a speed of 5 miles per hour. He walked at the rate of 3 miles per hour on Wed <math>\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \

2 KB (323 words) - 17:57, 5 May 2022
1981 AHSME Problems
<math> \textbf{(A)}\ \sqrt{2}\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 4\qquad\textbf{(D)}\ 8\ <math> \textbf{(A)}\ \sqrt{3}\qquad\textbf{(B)}\ \sqrt{5}\qquad\textbf{(C)}\ 3\qquad\textbf{(

17 KB (2,633 words) - 15:44, 16 September 2023
2014 AMC 10A Problems/Problem 4
Walking down Jane Street, Ralph passed four houses in a row, each painted a different color. He passed the orange house before the red house, and he pa <math>\textbf{(A)}\ 2\qquad\textbf{(B)}\ 3\qquad\textbf{(C)}\ 4\qquad\textbf{(D)}\ 5\qquad\t

3 KB (532 words) - 17:28, 5 May 2024
2000 PMWC Problems/Problem T3
...th> is a square, <math>P</math>, <math>Q</math>, <math>R</math>, and <math>S</math> are midpoints of the sides <math>AB</math>, <math>BC</math>, <math>C label("A",(0,2),NW);

1 KB (158 words) - 19:59, 30 January 2023
2018 AIME I Problems/Problem 14
...1P_2P_3EP_4P_5</math> be a heptagon. A frog starts jumping at vertex <math>S</math>. From any vertex of the heptagon except <math>E</math>, the frog may ...f left/right (L/R) paths of length <math>\le 11</math> that start at <math>S</math> and end at either <math>P_4</math> or <math>P_3</math>.

4 KB (649 words) - 17:29, 22 December 2023
1960 AHSME Problems
If <math>2</math> is a solution (root) of <math>x^3+hx+10=0</math>, then <math>h</math> equals: <math>\textbf{(A)}10\qquad

21 KB (3,242 words) - 21:27, 30 December 2020
2014 AMC 12B Problems
...d have the same number of pennies and nickels. In cents, how much are Leah's coins worth? <math> \textbf{(A)}\ 33\qquad\textbf{(B)}\ 35\qquad\textbf{(C)}\ 37\qquad\textbf{(D)}\ 39\qqu

13 KB (2,066 words) - 14:08, 1 November 2022
2014 AMC 10B Problems
...ld have the same number of pennies as nickels. In cents, how much are Leah's coins worth? <math> \textbf {(A) } 33 \qquad \textbf {(B) } 35 \qquad \textbf {(C) } 37 \qquad \textbf {(D)

13 KB (2,011 words) - 21:54, 8 November 2022
2014 AMC 10B Problems/Problem 23
A sphere is inscribed in a truncated right circular cone as shown. The volume of the truncated cone is <math>\text{(A) } \dfrac32 \quad \text{(B) } \dfrac{1+\sqrt5}2 \quad \text{(C) } \sqrt3 \q

6 KB (1,060 words) - 19:15, 11 August 2023
2014 AMC 12B Problems/Problem 19
A sphere is inscribed in a truncated right circular cone as shown. The volume of the truncated cone is real r=(3+sqrt(5))/2;

4 KB (703 words) - 16:24, 9 September 2022
2014 AIME II Problems
...s Abe. Abe begins to paint the room and works alone for the first hour and a half. Then Bea joins Abe, and they work together until half the room is pai ...has none of the three risk factors given that he does not have risk factor A is <math>\frac{p}{q}</math>, where <math>p</math> and <math>q</math> are re

8 KB (1,410 words) - 00:04, 29 December 2021
2014 AIME I Problems/Problem 4
Jon and Steve ride their bicycles along a path that parallels two side-by-side train tracks running the east/west dir ...arly, the second train has to cover a distance equal to its own length, at a rate of <math>r_2 + \dfrac{1}{3}</math>. Since the times are equal and <mat

5 KB (784 words) - 13:59, 30 November 2021

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