Recent changes

From AoPSWiki

Track the most recent changes to the wiki on this page.

7 January 2009

• (diff) (hist) . . N 1999 AHSME Problems/Problem 9‎; 21:59 . . (+1,146) . . Misof (Talk | contribs) (New page: == Problem == Before Ashley started a three-hour drive, her car's odometer reading was 29792, a palindrome. (A palindrome is a number that reads te same way from left to right as it does f...)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 15‎; 21:56 . . (+162) . . BOGTRO (Talk | contribs) (New page: <math>ab=a-b</math> <math>\frac{a}{b}+\frac{b}{a}-ab=\frac{a^2+b^2}{ab}-ab=\frac{-a^2b^2+a^2+b^2}{ab}</math> <math>\frac{-a^2+2ab-b^2+a^2+b^2}{ab}=2</math>. E.)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 14‎; 21:54 . . (+616) . . BOGTRO (Talk | contribs) (New page: 71, 76, 80, 82, 91. The sum of the first 2 must be even, so we must choose 2 evens or the 2 odds. Let us look at the numbers (mod 3). 2,1,2,1,1. If we choose the two odds, the next num...)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 13‎; 21:49 . . (+256) . . BOGTRO (Talk | contribs) (New page: The question is rather ambiguous, however I will assume that the pegs of the same color are distinguishable. Clearly, there is only 1 possible ordering if the colors are indistinguishable...)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 12‎; 21:47 . . (+269) . . BOGTRO (Talk | contribs) (New page: We have a recursion: <math>A_n=A_{n-1}+4(n-1)</math>. I.E. we add increasing multiples of <math>4</math> each time we go up a figure. So, to go from Figure 0 to 100, we add <math>4 \cd...)
• (diff) (hist) . . 1985 AJHSME Problems‎; 21:45 . . (+825) . . 5849206328x (Talk | contribs) (→Problem 7: )
• (diff) (hist) . . N 1999 AHSME Problems/Problem 17‎; 21:37 . . (+1,545) . . Misof (Talk | contribs) (New page: == Problem == Let <math>P(x)</math> be a polynomial such that when <math>P(x)</math> is divided by <math>x-19</math>, the remaidner is <math>99</math>, and when <math>P(x)</math> is divide...)
• (diff) (hist) . . 1985 AJHSME Problems‎; 21:14 . . (+307) . . 5849206328x (Talk | contribs) (→Problem 6: )
• (diff) (hist) . . 1985 AJHSME Problems‎; 21:08 . . (+458) . . 5849206328x (Talk | contribs) (→Problem 4: )
• (diff) (hist) . . 1985 AJHSME Problems‎; 20:49 . . (+164) . . 5849206328x (Talk | contribs) (→Problem 3: )
• (diff) (hist) . . N 1999 AHSME Problems/Problem 18‎; 20:44 . . (+1,835) . . Misof (Talk | contribs) (New page: == Problem == How many zeros does <math>f(x) = \cos(\log x)</math> have on the interval <math>0 < x < 1</math>? <math> \mathrm{(A) \ } 0 \qquad \mathrm{(B) \ } 1 \qquad \mathrm{(C) \ } 2 ...)
• (diff) (hist) . . 1985 AJHSME Problems‎; 20:42 . . (+171) . . 5849206328x (Talk | contribs) (→Problem 2: )
• (diff) (hist) . . N 1999 AHSME Problems/Problem 20‎; 20:00 . . (+902) . . Misof (Talk | contribs) (New page: == Problem == The sequence <math>a_{1},a_{2},a_{3},\ldots</math> statisfies <math>a_{1} = 19,a_{9} = 99</math>, and, for all <math>n\geq 3</math>, <math>a_{n}</math> is the arithmetic mean...)
• (diff) (hist) . . 1985 AJHSME Problems‎; 19:14 . . (+220) . . 5849206328x (Talk | contribs) (→Problem 1: )
• (diff) (hist) . . 2000 AMC 10 Problems/Problem 1‎; 19:11 . . (+69) . . 5849206328x (Talk | contribs)
• (diff) (hist) . . N 1999 AHSME Problems/Problem 21‎; 19:10 . . (+1,454) . . Misof (Talk | contribs) (New page: == Problem == A circle is circumscribed about a triangle with sides <math>20,21,</math> and <math>29,</math> thus dividing the interior of the circle into four regions. Let <math>A,B,</mat...)
• (diff) (hist) . . 2000 AMC 10 Problems/Problem 1‎; 19:07 . . (+445) . . 5849206328x (Talk | contribs)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 11‎; 19:06 . . (+426) . . BOGTRO (Talk | contribs) (New page: Two prime numbers between <math>4</math> and <math>18</math> are both odd. odd*odd=odd. odd-odd-odd=odd. Thus, we can discard the even choices. <math>ab-a-b=(a-1)(b-1)-1</math>. <mat...)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 10‎; 19:03 . . (+197) . . BOGTRO (Talk | contribs) (New page: The largest possible value for <math>x</math> is <math>9</math>. The smallest is <math>3</math>. <math>9-3=6</math>. <math>8</math> is the smallest that cannot be made (of the choices li...)
• (diff) (hist) . . 2000 AMC 10 Problems/Problem 9‎; 19:03 . . (+4) . . BOGTRO (Talk | contribs)
• (diff) (hist) . . N 1999 AHSME Problems/Problem 24‎; 19:03 . . (+947) . . Misof (Talk | contribs) (New page: == Problem == Six points on a circle are given. Four of the chords joining pairs of the six points are selected at random. What is the probability that the four chords form a convex quadri...)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 9‎; 19:02 . . (+105) . . BOGTRO (Talk | contribs) (New page: <math>|x-2|=p</math> <math>x<2</math>, so <math>2-x=p</math>. <math>x+p=2</math>. <math>x-p=2-2p</math>.)
• (diff) (hist) . . 2000 AMC 10 Problems/Problem 8‎; 19:02 . . (+3) . . BOGTRO (Talk | contribs)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 8‎; 19:01 . . (+188) . . BOGTRO (Talk | contribs) (New page: Let <math>f</math> be the number of freshman and s be the number of sophomores. <math>\frac{2}{5}f=\frac{4}{5}s</math>. <math>f=2s</math>. There are twice as many freshman as sophomores.)
• (diff) (hist) . . 2000 AMC 10 Problems/Problem 7‎; 19:00 . . (+4) . . BOGTRO (Talk | contribs)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 7‎; 19:00 . . (+576) . . BOGTRO (Talk | contribs) (New page: <asy> draw((0,2)--(3.4,2)--(3.4,0)--(0,0)--cycle); draw((0,0)--(1.3,2)); draw((0,0)--(3.4,2)); dot((0,0)); dot((0,2)); dot((3.4,2)); dot((3.4,0)); dot((1.3,2)); label("$A$",(0,2),NW); labe...)
• (diff) (hist) . . m 1999 AHSME Problems‎; 18:58 . . (0) . . Misof (Talk | contribs) (→Problem 24: )
• (diff) (hist) . . 2000 AMC 10 Problems‎; 18:58 . . (+1,098) . . 5849206328x (Talk | contribs) (→Problem 16: )
• (diff) (hist) . . 2000 AMC 10 Problems/Problem 6‎; 18:57 . . (0) . . BOGTRO (Talk | contribs)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 6‎; 18:57 . . (+158) . . BOGTRO (Talk | contribs) (New page: The pattern of the units digits are 1,1,2,3,5,8,3,1,4,5,9,4,3,7,0,7,7,4,1,5,6 In order of appearance: <math>1,2,3,5,8,4,9,7,0,6</math>. 6 is the last. D.)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 5‎; 18:55 . . (+414) . . BOGTRO (Talk | contribs) (New page: (a) Clearly does not change, as <math>MN=\frac{1}{2}AB</math>. Since <math>AB</math> does not change, neither does <math>MN</math>. (b) Obviously, the perimetar changes. (c) The area cle...)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 4‎; 18:53 . . (+214) . . BOGTRO (Talk | contribs) (New page: Let <math>x</math> be the fixed fee, and <math>y</math> be the amount she pays for the minutes she used in the first month. <math>x+y=12.48</math> <math>x+2y=17.54</math>. <math>y=5.06</...)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 3‎; 18:52 . . (+124) . . BOGTRO (Talk | contribs) (New page: <math>x \cdot .8 \cdot .8=32</math> <math>x \cdot .64=32</math> <math>x \cdot \frac{32}{50}=32</math> <math>x=50</math>. B.)
• (diff) (hist) . . 2000 AMC 10 Problems/Problem 2‎; 18:51 . . (0) . . BOGTRO (Talk | contribs)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 2‎; 18:51 . . (+91) . . BOGTRO (Talk | contribs) (New page: <math>2000 \cdot 2000^{2000}=2000^1 \cdot 2000^{2000}=2000^{2000+1}=2000^{2001}</math>. B.)
• (diff) (hist) . . N 2000 AMC 10 Problems/Problem 1‎; 18:50 . . (+103) . . BOGTRO (Talk | contribs) (New page: 2001=1*3*667=3*23*29 1+3+667=671 3+23+29=55 1+29+69=99 1+23+87=111 Clearly, 671, or E is the largest.)
• (diff) (hist) . . N 1999 AHSME Problems/Problem 28‎; 18:05 . . (+2,469) . . Misof (Talk | contribs) (New page: == Problem == Let <math>x_1, x_2, \ldots , x_n</math> be a sequence of integers such that (i) <math>-1 \le x_i \le 2</math> for <math>i = 1,2, \ldots n</math> (ii) <math>x_1 + \cdots + x_...)
• (diff) (hist) . . 2000 AMC 10 Problems‎; 17:45 . . (+656) . . 5849206328x (Talk | contribs) (→Problem 13: )
• (diff) (hist) . . m 1999 AHSME Problems‎; 17:28 . . (0) . . Misof (Talk | contribs) (→Problem 28: )
• (diff) (hist) . . N 1998 AHSME Problems/Problem 11‎; 17:12 . . (+914) . . Misof (Talk | contribs) (New page: == Problem == Let <math>R</math> be a rectangle. How many circles in the plane of <math>R</math> have a diameter both of whose endpoints are vertices of <math>R</math>? <math> \mathrm{(A)...)
• (diff) (hist) . . N 1998 AHSME Problems/Problem 13‎; 16:59 . . (+1,242) . . Misof (Talk | contribs) (New page: == Problem == Walter rolls four standard six-sided dice and finds that the product of the numbers of the upper faces is <math>144</math>. Which of he following could '''not ''' be the sum ...)
• (diff) (hist) . . 1998 AHSME Problems‎; 16:55 . . (0) . . Misof (Talk | contribs) (fixed a bug in the options)
• (diff) (hist) . . N 1998 AHSME Problems/Problem 18‎; 16:47 . . (+1,099) . . Misof (Talk | contribs) (New page: == Problem == A right circular cone of volume <math>A</math>, a right circular cylinder of volume <math>M</math>, and a sphere of volume <math>C</math> all have the same radius, and the co...)
• (diff) (hist) . . 2000 AMC 10 Problems‎; 16:14 . . (+1,129) . . 5849206328x (Talk | contribs) (→Problem 12: )
• (diff) (hist) . . N 1998 AHSME Problems/Problem 19‎; 16:08 . . (+1,843) . . Misof (Talk | contribs) (New page: == Problem == How many triangles have area <math>10</math> and vertices at <math>(-5,0),(5,0)</math> and <math>(5\cos \theta, 5\sin \theta)</math> for some angle <math>\theta</math>? <mat...)
• (diff) (hist) . . N 1998 AHSME Problems/Problem 20‎; 15:52 . . (+2,095) . . Misof (Talk | contribs) (New page: == Problem == Three cards, each with a positive integer written on it, are lying face-down on a table. Casey, Stacy, and Tracy are told that : (a) the numbers are all different, : (b) the...)
• (diff) (hist) . . N 1998 AHSME Problems/Problem 21‎; 15:30 . . (+1,195) . . Misof (Talk | contribs) (New page: == Problem == In an <math>h-</math> meter race, Sunny is exactly <math>d</math> meters ahead of Windy when Sunny finishes the race. The next time they race, Sunny sportingly starts <math>d...)
• (diff) (hist) . . m 2000 AMC 10 Problems‎; 15:28 . . (+26) . . 5849206328x (Talk | contribs) (→Problem 18: )
• (diff) (hist) . . m 1998 AHSME Problems‎; 15:23 . . (0) . . Misof (Talk | contribs) (→Problem 21: )
• (diff) (hist) . . N 1998 AHSME Problems/Problem 23‎; 15:19 . . (+1,222) . . Misof (Talk | contribs) (New page: == Problem == The graphs of <math>x^2 + y^2 = 4 + 12x + 6y</math> and <math>x^2 + y^2 = k + 4x + 12y</math> intersect when <math>k</math> satisfies <math>a \le k \le b</math>, and for no o...)