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• Joining an ARML team
  Team selection for the [[American Regions Mathematics League]] varies from team to team. ...ge Xinke's AoPS account "hurdler", if you are interested in trying out for the Alabama team.
  22 KB (3,533 words) - 20:58, 2 June 2024
• Simon's Favorite Factoring Trick
  ==The General Statement== ...s the product of the variables, <math>66x</math> and <math>-88y</math> are the variables in linear terms.
  7 KB (1,157 words) - 01:49, 27 July 2024
• Combination
  ...objects are chosen is irrelevant. We are generally concerned with finding the number of combinations of size <math>r</math> from an original set of size The common forms of denoting the number of combinations of <math>{r}</math> objects from a set of <math>{n}<
  4 KB (615 words) - 11:43, 21 May 2021
• 2006 AMC 12B Problems/Problem 20
  ...x</math> be chosen at random from the interval <math>(0,1)</math>. What is the probability that Here <math>\lfloor x\rfloor</math> denotes the greatest integer that is less than or equal to <math>x</math>.
  3 KB (485 words) - 14:09, 21 May 2021
• 2006 AMC 12A Problems/Problem 20
  ...ll choices are independent. What is the probability that after seven moves the bug will have visited every vertex exactly once? Call this cube <math>ABCDEFGH</math>, with <math>A</math> being the starting point.
  5 KB (908 words) - 19:23, 22 September 2022
• 2006 AMC 12A Problems/Problem 25
  ...pty]] [[subset]]s <math>S</math> of <math>\{1,2,3,\ldots ,15\}</math> have the following two properties? ...finding. We give a somewhat more general attack, based on the solution to the following problem:
  8 KB (1,405 words) - 11:52, 27 September 2022
• 2005 AMC 12B Problems/Problem 25
  ...equal [[probability]]. What is the probability that no two ants arrive at the same vertex? ...ways ants can do their desired migration, and then multiply this number by the probability that each case occurs.
  10 KB (1,840 words) - 15:01, 4 July 2024
• Set
  ...nkel Axioms]]. In this article we shall present just a brief discussion of the most common properties of sets and operations related to them. ...misconception is that a set can have multiple indistinct elements, such as the following: <math>\{1,4,5,3,24,4,4,5,6,2\}</math> Such an entity is actually
  11 KB (2,019 words) - 17:20, 7 July 2024
• 2004 AIME II Problems/Problem 10
  ...o <math>1</math>'s. If a number is chosen at random from <math> S, </math> the [[probability]] that it is divisible by <math>9</math> is <math> p/q, </mat ...se <math>2^{40}</math> has 41) with leading zeroes if necessary. Therefore the number of sets where there are exactly two 1’s in this binary representat
  8 KB (1,283 words) - 19:19, 8 May 2024
• 1983 AIME Problems/Problem 7
  ...math>P</math> is written as a fraction in lowest terms, what is the sum of the numerator and denominator? ...an use [[complementary counting]], by finding the probability that none of the three knights are sitting next to each other and subtracting it from <math>
  9 KB (1,392 words) - 20:37, 19 January 2024
• 1983 AIME Problems/Problem 10
  The numbers <math>1447</math>, <math>1005</math> and <math>1231</math> have som ...ther three digits can be <math>1</math>. This means the possible forms for the number are
  5 KB (855 words) - 20:26, 14 January 2023
• 1985 AIME Problems/Problem 12
  ...tex <math>A</math> when it has crawled exactly <math>7</math> meters. Find the value of <math>n</math>. ...ive integers <math>k,</math> let <math>P(k)</math> be the probability that the bug is at vertex <math>A</math> when it has crawled exactly <math>k</math>
  19 KB (3,128 words) - 21:38, 23 July 2024
• 1988 AIME Problems/Problem 10
  ...any [[segment]]s joining vertices of the polyhedron lie in the interior of the polyhedron rather than along an [[edge]] or a [[face]]? The polyhedron described looks like this, a truncated cuboctahedron.
  6 KB (902 words) - 17:40, 19 May 2024
• Integration by parts
  ...ation by parts is to replace a difficult [[integral]] with an easier one. The formula is ...th> as <math>v</math> in the integral on the RHS, <math>u</math> should be chosen such that it has an "easy" (or "easier") [[derivative]] and <math>dv</math>
  1 KB (235 words) - 17:01, 11 March 2022
• Hampshire College Summer Studies in Mathematics
  ...tics''', abbreviated '''HCSSiM''', is a 6-week summer program intended for the studies of mathematics founded in 1971 by [[David C. Kelly]]. HCSSiM takes A typical day of the program (Mon-Sat) includes three meals, 4 hours of learning mathematics, a
  2 KB (253 words) - 21:57, 13 May 2017
• 2004 AMC 10A Problems
  ...charity, dividing the fundraising equally. How many dollars will each of you need to raise? ...h>a</math>, <math>b</math>, and <math>c</math>, with <math>b\neq c</math>, the operation <math>\otimes</math> is defined by:
  15 KB (2,092 words) - 20:32, 15 April 2024
• 2005 AMC 12A Problems/Problem 24
  We can write the problem as ...values of <math>Q(1)</math>, <math>Q(2)</math>, and <math>Q(3)</math> are chosen.
  5 KB (833 words) - 18:17, 8 April 2024
• 2008 USAMO Problems/Problem 6
  ...aticians may be split between the two rooms is a power of two (i.e., is of the form <math>2^k</math> for some positive integer <math>k</math>). .... Let <math>V</math> be the [[vector space]] of all such functions. Define the linear operator <math>A : V \to V</math> as
  13 KB (2,414 words) - 14:37, 11 July 2016
• KGS math club
  ...ething, I'm afraid you need to register to the AoPS wiki first. After that you're good to go. ...ollar signs, it seems) where required, e.g. <math>f''(x)</math>. Still, if you don't, somebody else will; all additions are appreciated.
  22 KB (3,358 words) - 15:17, 18 July 2017
• 2008 iTest Problems
  ...s. Michael is their oldest child, and Wendy their oldest daughter. Tony is the youngest child. Twins Joshua and Alexis are <math>12</math> years old. When the Kubiks went on vacation to San Diego last year, they spent a day at the San Diego Zoo.
  71 KB (11,749 words) - 01:31, 2 November 2023

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