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- The '''United States of America Mathematical Olympiad''' ('''USAMO''') is the third test in a series of exams used to challenge bright students on th ...rican Mathematics Competitions]] (AMC). [[Art of Problem Solving]] (AoPS) is a proud sponsor of the AMC and of the recent expansion of USAMO participant6 KB (869 words) - 12:52, 20 February 2024
- ...if they have a hard time following the rest of this article). This theorem is credited to [[Pierre de Fermat]]. ...n [[integer]], <math>{p}</math> is a [[prime number]] and <math>{a}</math> is not [[divisibility|divisible]] by <math>{p}</math>, then <math>a^{p-1}\equi16 KB (2,658 words) - 16:02, 8 May 2024
- If <math>\tan x+\tan y=25</math> and <math>\cot x + \cot y=30</math>, what is <math>\tan(x+y)</math>? Since <math>\cot</math> is the reciprocal function of <math>\tan</math>:3 KB (545 words) - 23:44, 12 October 2023
- ...icular]] to <math>y=2x</math>, so the slope of <math>\overline{PP'}</math> is <math>\frac{-1}{2}</math>. Thus <math>\frac{y' - y}{x' - x} = \frac{-1}{2} ...math>, which is unchanged by the reflection, into the expression. But this is not necessary. We see that <math>b=-7</math>, <math>c=-12</math>, so <math>4 KB (700 words) - 17:21, 3 May 2021
- ...<math>20k + 8 \equiv 88 \pmod{100}</math>. This is true if the tens digit is either <math>4</math> or <math>9</math>. Casework: ...le value for the hundreds digit is <math>4</math>, and so <math>442</math> is a valid solution.6 KB (893 words) - 08:15, 2 February 2023
- ...r D\rfloor</math>? (For real <math>x</math>, <math>\lfloor x\rfloor</math> is the [[floor function|greatest integer]] less than or equal to <math>x</math ...> (in other words, <math>x \in [1,1000]</math>). Indeed, <math>D(x)</math> is symmetric about <math>x = 500.5</math>; consider replacing all of numbers <5 KB (851 words) - 18:01, 28 December 2022
- The probability that one team wins all games is <math>5\cdot \left(\frac{1}{2}\right)^4=\frac{5}{16}</math>. Similarity, the probability that one team loses all games is <math>\frac{5}{16}</math>.3 KB (461 words) - 00:33, 16 May 2024
- ...values. The [[probability]] that all three players obtain an [[odd]] sum is <math>m/n,</math> where <math>m</math> and <math>n</math> are [[relatively ...that it matters in what order the people pick the tiles; the final answer is the same if we assume the opposite, that order doesn't matter.)5 KB (917 words) - 02:37, 12 December 2022
- Therefore the desired sum is <math>34\cdot7+21\cdot6+13\cdot5+8\cdot4+5\cdot3+3 \cdot2+2\cdot1+1\cdot0=\ Finding <math>7x</math> isn't hard, and we see that it is equal to <math>609</math>:2 KB (317 words) - 00:09, 9 January 2024
- ...h> and <math>C_{3}</math> can be written as <math>\sqrt {10n}</math>. What is <math>n</math>? ...> and <math>b</math> are the legs of the right triangle and <math>c</math> is the hypotenuse. (This formula should be used ''only for right triangles''.)7 KB (1,112 words) - 02:15, 26 December 2022
- A [[circle]] is [[inscribe]]d in [[quadrilateral]] <math>ABCD</math>, [[tangent]] to <math> which is nowhere near as hard of a calculation. In fact, this is basically the same exact calculation done at the end of solution 1, just wi2 KB (399 words) - 17:37, 2 January 2024
- ...N{1!18!}</math></center> find the [[floor function|greatest integer]] that is less than <math>\frac N{100}</math>. ...ing these up we have <math>13796</math> therefore <math>\boxed{137}</math> is the desired answer.2 KB (281 words) - 12:09, 5 April 2024
- ...3c+c^3a", "a^2+b^2=20c^2", "f(xf(y))f(y)=yf(xy)" than the following ones: "hard geometry", "please help me!!", "what to do with this one?", "don't know how ...tp://www.artofproblemsolving.com/Forum/index.php?f=149 High School Basics] is for problems that would be considered part of the standard U.S. high school9 KB (1,420 words) - 01:14, 1 September 2023
- A [[sequence]] is defined over [[non-negative]] integral indexes in the following way: <math> ...<math>a_1/a_0 = 1</math>, this means that the sequence <math>(a_n)</math> is increasing. Since <math>a_3=672</math> already, we must have <math>a_{2006}13 KB (2,185 words) - 23:30, 5 December 2022
- ..., where <math>p</math> and <math>q</math> are rational, and <math>r</math> is an [[integer]] not divisible by the [[square]] of a [[prime]]. Find <math> [[Image:AIME I 2007-15.png]]4 KB (673 words) - 22:14, 6 August 2022
- ...ld also try to strengthen in the areas you are not as good at. This guide is intended to help you get started. * Art of Problem Solving Volume 2 - [[AMC 12]], [[AIME]], [[USAMO]], [[MOP]]13 KB (1,926 words) - 11:22, 30 November 2023
- ...<math>AC = 12</math>, <math>BC = 35</math>, and <math>\overline{CD}</math> is the altitude to <math>\overline{AB}</math>. Let <math>\omega</math> be the ...ve length <math>x</math>. Then the perimeter of <math>\triangle ABI</math> is equal to <cmath>2(x+AD+DB)=2(x+37).</cmath> It remains to compute <math>\df12 KB (1,970 words) - 22:53, 22 January 2024
- ...lty level of various [[List of mathematics competitions|competitions]]. It is designed with the intention of introducing contests of similar difficulty l ...to variances within a contest, ranges shown may overlap. A sample problem is provided with each entry, with a link to a solution.41 KB (6,720 words) - 13:58, 9 May 2024
- This is a community created list of Frequently Asked Questions about Art of Problem ...PS will not change your username for other reasons (e.g., current username is too "cringy").25 KB (4,184 words) - 21:16, 13 May 2024
- There is a very, very small chance that anyone is reading this right now. But either way, here are my achievements: ...alculating my projected score after guessing to see if I could qualify for AIME. My projected score was something around 122, so I got lucky.)4 KB (701 words) - 19:50, 31 August 2011
