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(Latest | Earliest) View (newer 50) (older 50) (20 | 50 | 100 | 250 | 500)- 21:59, 7 January 2009 1999 AHSME Problems/Problem 9 (hist) [1,146 bytes] 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...)
- 21:56, 7 January 2009 2000 AMC 10 Problems/Problem 15 (hist) [162 bytes] 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.)
- 21:54, 7 January 2009 2000 AMC 10 Problems/Problem 14 (hist) [616 bytes] 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...)
- 21:49, 7 January 2009 2000 AMC 10 Problems/Problem 13 (hist) [256 bytes] 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...)
- 21:47, 7 January 2009 2000 AMC 10 Problems/Problem 12 (hist) [269 bytes] 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...)
- 21:37, 7 January 2009 1999 AHSME Problems/Problem 17 (hist) [1,545 bytes] 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...)
- 20:44, 7 January 2009 1999 AHSME Problems/Problem 18 (hist) [1,835 bytes] 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 ...)
- 20:00, 7 January 2009 1999 AHSME Problems/Problem 20 (hist) [902 bytes] 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...)
- 19:10, 7 January 2009 1999 AHSME Problems/Problem 21 (hist) [1,454 bytes] 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...)
- 19:06, 7 January 2009 2000 AMC 10 Problems/Problem 11 (hist) [426 bytes] 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...)
- 19:03, 7 January 2009 2000 AMC 10 Problems/Problem 10 (hist) [197 bytes] 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...)
- 19:03, 7 January 2009 1999 AHSME Problems/Problem 24 (hist) [947 bytes] 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...)
- 19:02, 7 January 2009 2000 AMC 10 Problems/Problem 9 (hist) [109 bytes] 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>.)
- 19:01, 7 January 2009 2000 AMC 10 Problems/Problem 8 (hist) [191 bytes] 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.)
- 19:00, 7 January 2009 2000 AMC 10 Problems/Problem 7 (hist) [580 bytes] 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...)
- 18:57, 7 January 2009 2000 AMC 10 Problems/Problem 6 (hist) [158 bytes] 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.)
- 18:55, 7 January 2009 2000 AMC 10 Problems/Problem 5 (hist) [414 bytes] 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...)
- 18:53, 7 January 2009 2000 AMC 10 Problems/Problem 4 (hist) [214 bytes] 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</...)
- 18:52, 7 January 2009 2000 AMC 10 Problems/Problem 3 (hist) [124 bytes] 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.)
- 18:51, 7 January 2009 2000 AMC 10 Problems/Problem 2 (hist) [91 bytes] BOGTRO (Talk | contribs) (New page: <math>2000 \cdot 2000^{2000}=2000^1 \cdot 2000^{2000}=2000^{2000+1}=2000^{2001}</math>. B.)
- 18:50, 7 January 2009 2000 AMC 10 Problems/Problem 1 (hist) [617 bytes] 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.)
- 18:05, 7 January 2009 1999 AHSME Problems/Problem 28 (hist) [2,469 bytes] 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_...)
- 17:12, 7 January 2009 1998 AHSME Problems/Problem 11 (hist) [914 bytes] 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)...)
- 16:59, 7 January 2009 1998 AHSME Problems/Problem 13 (hist) [1,242 bytes] 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 ...)
- 16:47, 7 January 2009 1998 AHSME Problems/Problem 18 (hist) [1,099 bytes] 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...)
- 16:08, 7 January 2009 1998 AHSME Problems/Problem 19 (hist) [1,843 bytes] 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...)
- 15:52, 7 January 2009 1998 AHSME Problems/Problem 20 (hist) [2,095 bytes] 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...)
- 15:30, 7 January 2009 1998 AHSME Problems/Problem 21 (hist) [1,195 bytes] 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...)
- 15:19, 7 January 2009 1998 AHSME Problems/Problem 23 (hist) [1,222 bytes] 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...)
- 14:56, 7 January 2009 1998 AHSME Problems/Problem 25 (hist) [3,155 bytes] Misof (Talk | contribs) (New page: == Problem == A piece of graph paper is folded once so that <math>(0,2)</math> is matched with <math>(4,0)</math>, and <math>(7,3)</math> is matched with <math>(m,n)</math>. Find <math>m+n...)
- 13:23, 7 January 2009 1998 AHSME Problems/Problem 30 (hist) [2,909 bytes] Misof (Talk | contribs) (New page: == Problem == For each positive integer <math>n</math>, let <center><math>a_n = \frac{(n+9)!}{(n-1)!}</math></center> Let <math>k</math> denote the smallest positive integer for which t...)
- 03:14, 7 January 2009 2004 AMC 12B Problems/Problem 20 (hist) [1,339 bytes] Azjps (Talk | contribs) (solution)
- 03:06, 7 January 2009 2004 AMC 12B Problems/Problem 22 (hist) [2,920 bytes] Azjps (Talk | contribs) (solution)
- 14:32, 6 January 2009 2004 AMC 12B Problems/Problem 8 (hist) [575 bytes] Misof (Talk | contribs) (New page: == Problem == A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many rows ...)
- 14:30, 6 January 2009 2004 AMC 12B Problems/Problem 7 (hist) [733 bytes] Misof (Talk | contribs) (New page: == Problem 7 == A square has sides of length 10, and a circle centered at one of its vertices has radius 10. What is the area of the union of the regions enclosed by the square and the cir...)
- 14:25, 6 January 2009 2004 AMC 12B Problems/Problem 6 (hist) [807 bytes] Misof (Talk | contribs) (New page: == Problem == Minneapolis-St. Paul International Airport is 8 miles southwest of downtown St. Paul and 10 miles southeast of downtown Minneapolis. Which of the following is closest to the ...)
- 14:20, 6 January 2009 2004 AMC 12B Problems/Problem 5 (hist) [1,149 bytes] Misof (Talk | contribs) (New page: == Problem == On a trip from the United States to Canada, Isabella took <math>d</math> U.S. dollars. At the border she exchanged them all, receiving 10 Canadian dollars for every 7 U.S. do...)
- 14:07, 6 January 2009 2004 AMC 12B Problems/Problem 4 (hist) [954 bytes] Misof (Talk | contribs) (New page: == Problem == An integer <math>x</math>, with <math>10\leq x\leq 99</math>, is to be chosen. If all choices are equally likely, what is the probability that at least one digit of <math>x<...)
- 11:26, 6 January 2009 2004 AMC 12B Problems/Problem 3 (hist) [438 bytes] Misof (Talk | contribs) (New page: == Problem == If <math>x</math> and <math>y</math> are positive integers for which <math>2^x3^y=1296</math>, what is the value of <math>x+y</math>? <math>(\mathrm {A}) 8\qquad (\mathrm {B...)
- 11:23, 6 January 2009 2004 AMC 12B Problems/Problem 2 (hist) [976 bytes] Misof (Talk | contribs) (New page: == Problem 2 == In the expression <math>c\cdot a^b-d</math>, the values of <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math> are 0, 1, 2, and 3, although not necessarily i...)
- 00:39, 6 January 2009 AoPSML Main Page (hist) [362 bytes] Levans (Talk | contribs) (New page: The '''AoPSML''', short for Art of Problem Solving Markup Language provides a way for you to incorporate AoPS data into your page without having to rely on API calls. AoPSML is both a supe...)
- 21:08, 3 January 2009 1976 USAMO Problems (hist) [3,160 bytes] Minsoens (Talk | contribs) (New page: Problems from the '''1976 USAMO'''. ==Problem 1== <asy> void fillsq(int x, int y){ fill((x,y)--(x+1,y)--(x+1,y+1)--(x,y+1)--cycle, ...)
- 21:03, 3 January 2009 1976 USAMO Problems/Problem 4 (hist) [377 bytes] Minsoens (Talk | contribs) (New page: ==Problem== If the sum of the lengths of the six edges of a trirectangular tetrahedron <math>PABC</math> (i.e., <math>\angle APB=\angle BPC=\angle CPA=90^o</math>) is <math>S</math>, deter...)
- 20:41, 3 January 2009 1976 USAMO Problems/Problem 2 (hist) [1,270 bytes] Minsoens (Talk | contribs) (New page: ==Problem== If <math>A</math> and <math>B</math> are fixed points on a given circle and <math>XY</math> is a variable diameter of the same circle, determine the locus of the point of inter...)
- 15:35, 3 January 2009 1992 AIME Answer Key (hist) [249 bytes] 1=2 (Talk | contribs) (New page: Return to 1992 AIME (1992 AIME Problems) # 400 # 502 # 164 # 062 # 660 # 156 # 320 # 819 # 164 # 572 # 945 # 792 # 820 # 094 # 396 {{AIME box|year=1992|before=[[1991 AIME Answ...)
- 15:30, 3 January 2009 1993 AIME Answer Key (hist) [248 bytes] 1=2 (Talk | contribs) (New page: Return to 1993 AIME (1993 AIME Problems) 1# 728 2# 580 3# 943 4# 870 5# 763 6# 495 7# 005 8# 365 9# 118 10# 240 11# 093 12# 344 13# 163 14# 448 15# 997 {{AIME box|year=1993|bef...)
- 14:15, 2 January 2009 2003 AMC 10B (hist) [1,254 bytes] 1=2 (Talk | contribs) (New page: '''2003 AMC 10B''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. * 2003 AMC 10B Problems * [...)
- 06:00, 2 January 2009 2000 AMC 10 Problems (hist) [13,801 bytes] Chenhsi (Talk | contribs) (Start page, most answers are wrong)
- 05:43, 2 January 2009 2000 AMC 10 (hist) [1,228 bytes] Chenhsi (Talk | contribs) (New page: '''2000 AMC 10''' problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution. * 2000 AMC 10 Problems * [[2...)
- 21:43, 1 January 2009 2001 AMC 10 Problems (hist) [735 bytes] Modx07 (Talk | contribs) (First 5 problems of 2001 AMC 10)
