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• The figure shows a square of side $y$ units divided into a square of side $x$ units and four congruent rectangles. What is the perimeter, in units, of one of the four congruent rectangles? Express your answer in terms of $y$.
  0 bytes (0 words) - 22:13, 4 March 2020

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• Pythagorean Theorem
  ...f geometry problems can be solved by building right triangles and applying the Pythagorean Theorem. ...Geometric inequality#Pythagorean_Inequality | Pythagorean Inequality]] and the [[Law of Cosines]].
  5 KB (886 words) - 21:12, 22 January 2024
• 2016 AMC 10A Problems/Problem 7
  ...0, 100, x, 40, 50, 200, 90</math> are all equal to <math>x</math>. What is the value of <math>x</math>? Since <math>x</math> is the mean,
  2 KB (268 words) - 18:19, 27 September 2023
• 2016 AMC 10A Problems/Problem 10
  ...<math>1</math> foot wide on all four sides. What is the length in feet of the inner rectangle? Let the length of the inner rectangle be <math>x</math>.
  2 KB (337 words) - 14:56, 25 June 2023
• 2016 AMC 10A Problems/Problem 11
  Find the area of the shaded region. ...h>, <math>2</math>, and <math>\frac{5}{4}</math>, which add to the area of the shaded region, which is <math>\boxed{6\frac{1}{2}}</math>.
  8 KB (1,016 words) - 00:17, 31 December 2023
• 2016 AMC 10A Problems/Problem 13
  ...moved two seats to the right, Ceci had moved one seat to the left, and Dee and Edie had switched seats, leaving an end seat for Ada. In which seat had Ada ...cupied and the positioning would not work. So, Edie and Dee are in seats 4 and 5. This means that Bea was originally in seat 1. Ceci must have been in sea
  2 KB (402 words) - 14:54, 25 June 2023
• List of mathematics competitions
  ...l links to more helpful pages about mathematics competitions. This is not the place to list individual competitions. ...an mathematics competitions are categorized in two, one for public schools and other for particular schools.
  4 KB (406 words) - 11:20, 26 February 2021
• Alabama mathematics competitions
  ...nd there are a number of quality contests around the state for both middle and high school students. ...298 middle school math forums] where students can discuss contest problems and mathematics.
  3 KB (411 words) - 21:32, 8 December 2014
• MathILy (serious mathematics infused with levity)
  ...r undergraduate math students. The math content covered is undergraduate- and graduate-level. ...3, with MathILy at Bryn Mawr College and MathILy-Er at Arcadia University. The program fee will be \$5300.
  5 KB (706 words) - 23:49, 29 January 2024
• Mathematics, science, and technology scholarships
  This page is for listing of '''Mathematics, science, and technology scholarships''' that are not subject specific. Links to scholar == Mathematics, science, and technology scholarships ==
  7 KB (851 words) - 10:54, 29 January 2022
• Proton Energy Scholarship
  ...of science and technology. They must also be planning further education in the field. ...th>\textdollar</math>100,000, though only one had been originally promised the scholarship.
  894 bytes (123 words) - 15:48, 13 June 2022
• MATHCOUNTS
  ...of Teachers of Mathematics], and others including Art of Problem Solving, the focus of MATHCOUNTS is on mathematical problem solving. Students are eligib ...]], [[geometry]], [[number theory]], [[probability]], and [[statistics]]. The focus of MATHCOUNTS curriculum is in developing [[mathematical problem solv
  10 KB (1,497 words) - 11:42, 10 March 2024
• ASIA TEAM Problems/Problem 1
  ...er of <math>2n-1</math> is one more than the order of <math>2n</math>, and the answer is <math>\frac{1000}{2}=\boxed{500}</math>.
  227 bytes (40 words) - 05:42, 16 February 2024
• ICTM Math Contest
  ...ade School (Grades 3, 4, 5, 6, 7, 8 + Algebra 1) and High School (Regional and State Finals). ...schools at each grade level will receive certificates and be recognized in the ICTM Bulletin.
  8 KB (1,182 words) - 14:26, 3 April 2024
• Resources for mathematics competitions
  ...Many also have links to books, websites, and other resources relevant to the topic. == Quick Start Video Introduction to the AMC ==
  24 KB (3,269 words) - 00:43, 24 April 2024
• Math books
  ...re recommended by [[Art of Problem Solving]] administrators and members of the [http://aops.com/community AoPS Community]. Levels of reading and math ability are loosely defined as follows:
  24 KB (3,177 words) - 12:53, 20 February 2024
• Physics
  ...is considered to be the most fundamental of all the sciences, and is also the oldest. ...e 19th century is called <strong>Classical Physics</strong>. Physics after the 19th century is know as <strong>Modern Physics</strong>.
  9 KB (1,355 words) - 07:29, 29 September 2021
• Mathematics
  ...mportant to people in most modern technical discplines such as engineering and economics. ...2\,3\,4\,5\,6\,7\,8\,9\,0</math>|right|The ten [[digit]]s making up <br /> the base ten number system.}}
  6 KB (902 words) - 12:53, 3 September 2019
• AMC historical results
  <!-- Post AMC statistics and lists of high scorers here so that the AMC page doesn't get cluttered. --> ...he '''AMC historical results''' page. This page should include results for the [[AIME]] as well. For [[USAMO]] results, see [[USAMO historical results]].
  17 KB (1,921 words) - 13:00, 28 April 2024
• Inequality
  ...] methods. While most of the subject of inequalities is often left out of the ordinary educational track, they are common in [[mathematics Olympiads]]. Inequalities are arguably a branch of [[elementary algebra]], and relate slightly to [[number theory]]. They deal with [[relations]] of [[var
  12 KB (1,798 words) - 16:20, 14 March 2023
• United States of America Mathematical Talent Search
  ...ics competition]] in which students are challenged to write full solutions and mathematical proofs to exploratory math problems. ...the [[Art of Problem Solving Foundation]] with support and sponsorship by the [[National Security Agency]] (NSA).
  4 KB (613 words) - 13:08, 18 July 2023
• Academic scholarships
  ...ve guides to '''academic scholarships'''. Get started by clicking through the links below by subject area. ...a category rather than a list, please create a new page for that category and list it here.
  3 KB (337 words) - 03:35, 7 September 2020
• AMC 10
  ...on the path towards choosing the team that represents the United States at the [[International Mathematics Olympiad]] (IMO). High scoring AMC 10 and AMC 12 students are invited to take the [[American Invitational Mathematics Examination]] (AIME).
  4 KB (574 words) - 15:28, 22 February 2024
• 1955 AHSME Problems/Problem 38
  ...numbers <math>29, 23, 21</math>, and <math>17</math> are obtained. One of the original integers is: ...ath> to be the four numbers. In order to satisfy the following conditions, the system of equation should be constructed. (It doesn't matter which variable
  1 KB (200 words) - 23:35, 28 August 2020
• American Invitational Mathematics Examination
  ...on the path toward choosing the team that represents the United States at the [[International Mathematics Olympiad]] (IMO). While most AIME participants ...America Junior Mathematics Olympiad (USAJMO) for qualification from taking the AMC 10.
  8 KB (1,057 words) - 12:02, 25 February 2024
• American Mathematics Competitions
  ...bbreviation for American Math Contest, used to refer to the AMC 8, AMC 10, and AMC 12. * [[AMC 8]] &mdash; for students grades 8 and under.
  5 KB (696 words) - 03:47, 24 December 2019
• United States of America Mathematical Olympiad
  ...on the path toward choosing the team that represents the United States at the [[International Mathematics Olympiad]] (IMO). ...). [[Art of Problem Solving]] (AoPS) is a proud sponsor of the AMC and of the recent expansion of USAMO participants from around 250 to around 500.
  6 KB (869 words) - 12:52, 20 February 2024
• American Regions Mathematics League
  The '''American Regions Math League''' (ARML) is a [[mathematical problem solvi ...details. If your area does not already have a team, ask ARML how to start one.
  2 KB (267 words) - 17:06, 7 March 2020
• 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.
  21 KB (3,500 words) - 18:41, 23 April 2024
• Proof writing
  ...a proof, they intend a different meaning to how the word is understood by the wider population. Students who spend time studying maths can develop proof- ...good proof are precision, accuracy, and clarity. A single word can change the intended meaning of a proof, so it is best to be as precise as possible.
  3 KB (502 words) - 18:16, 18 January 2016
• Community Service Scholarships
  ...rship programs in other countries. Just make that reorganization as clear and as clean as possible. ...[[Mathew Crawford]] using the email crawford@artofproblemsolving.com with the scholarship listing you wish to contribute.
  3 KB (350 words) - 01:18, 19 June 2016
• California MathCounts
  ...nts]] team is made up of the top four students during the written round of the state competition. ...won eight national championships (1986, 1992, 2000, 2002, 2003, 2010, 2011 and 2014), more than any other team.
  644 bytes (87 words) - 02:05, 25 March 2015
• Mu Alpha Theta
  ...itions]] and each year a national Mu Alpha Theta convention is held during the summer that includes a large competition. == The Competition ==
  4 KB (632 words) - 17:09, 11 October 2020
• Wilson's Theorem
  ...ath> if and only if <math>p</math> is prime. It was stated by John Wilson. The French mathematician Lagrange proved it in 1771. ...entary one that rests close to basic principles of [[modular arithmetic]], and an elegant method that relies on more powerful [[algebra]]ic tools.
  4 KB (639 words) - 01:53, 2 February 2023
• Trivial Inequality
  ...uare of any real number is nonnegative. Its name comes from its simplicity and straightforwardness. ...>x<0</math>, then <math>x^2 = (-x)(-x) > 0,</math> again by the closure of the set of positive numbers under multiplication.
  3 KB (560 words) - 22:51, 13 January 2024
• Heron's Formula
  ...formula | formula]] for finding the [[area]] of a [[triangle]] given only the three side lengths. ...s <math>{a}, {b}, {c}</math>, the area <math>{A}</math> can be found using the following formula:
  4 KB (675 words) - 00:05, 22 January 2024
• Polynomial
  ...s and multiplied by [[coefficient]]s from a predetermined [[set]] (usually the set of integers; [[rational]], [[real]] or [[complex]] numbers; but in [[ab * <math>4x^2 + 6x - 9</math>, in the variable <math>x</math>
  6 KB (1,100 words) - 01:44, 17 January 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 (1,107 words) - 07:35, 26 March 2024
• Factoring
  ...r]] or [[polynomial]]) as a product of different terms. This often allows one to find information about an expression that was not otherwise obvious. ==Differences and Sums of Powers==
  3 KB (532 words) - 22:00, 13 January 2024
• Proof by contradiction
  ...ue usually works well on problems where not a lot of information is known, and thus we can create some using proof by contradiction. ===Proof that the square root of 2 is irrational===
  2 KB (374 words) - 14:01, 21 August 2022
• Mathematical problem solving
  ...thinking. Mathematical [[problem solving]] involves using all the tools at one's disposal to attack a problem in a new way. ...eresting example of this kind of thinking is the calculation of the sum of the [[series]] <math>\frac11 + \frac14 + \frac19 + \cdots + \frac{1}{n^2} + \cd
  2 KB (314 words) - 06:45, 1 May 2014
• Pigeonhole Principle
  ...if <math>n+1</math> or more pigeons are placed into <math>n</math> holes, one hole must contain two or more pigeons. This seemingly trivial statement may ...> boxes and <math>n>k</math>, then at least one box must contain more than one ball.
  11 KB (1,985 words) - 21:03, 5 August 2023
• Quadratic equation
  ...one of three main strategies: [[factoring]], [[completing the square]] and the [[quadratic formula]]. The purpose of factoring is to turn a general quadratic into a product of [[bin
  2 KB (264 words) - 12:04, 15 July 2021
• 1965 AHSME Problems/Problem 40
  ...<math>x</math> such that <math>P = x^4 + 6x^3 + 11x^2 + 3x + 31</math> is the square of an integer. Then <math>n</math> is: ...ginning of <math>P</math>, we notice <math>x^4+6x^3</math>, which gives us the idea to use <math>(x^2+3x)^2=x^4+6x^3+9x^2</math>.
  3 KB (571 words) - 00:42, 22 October 2021
• Minnesota MathCounts
  ...held every year at the Crowne Plaza Minneapolis West Hotel in Plymouth on the second weekend of March (Friday-Saturday). == Past Winners and Schools ==
  995 bytes (131 words) - 18:02, 12 March 2023
• Combinatorics
  ...ive]] formula for the [[Fibonacci numbers]], and so too methods of solving the [[Rubiks cube]]. Mathematicians who spend their careers studying combinator ...mathematics, notably in [[theoretical computer science]], [[statistics]], and various fields of science.
  1 KB (208 words) - 02:12, 4 October 2020
• Principle of Inclusion-Exclusion
  ...the size of each set, and the size of all possible [[intersection]]s among the sets. ...t and undercount, in the end making sure every element is counted once and only once. In particular, memorizing a formula for PIE is a bad idea for problem
  9 KB (1,703 words) - 07:25, 24 March 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 ...pe! It serves as a great introductory video to combinations, permutations, and counting problems in general! [https://bit.ly/CombinationsAndPermutations P
  4 KB (615 words) - 11:43, 21 May 2021
• Cauchy-Schwarz Inequality
  ...s. In high-school competitions, its applications are limited to elementary and linear algebra. ...auchy-Schwarz forms the foundation for inequality problems in intermediate and olympiad competitions. It is particularly crucial in proof-based contests.
  13 KB (2,048 words) - 15:28, 22 February 2024
• Factorial
  ...mportant function in [[combinatorics]] and [[analysis]], used to determine the number of ways to arrange objects. ...{i=1}^n i</math>. Alternatively, a [[recursion|recursive definition]] for the factorial is <math>n!=n \cdot (n-1)!</math>.
  10 KB (809 words) - 16:40, 17 March 2024
• Discriminant
  ...ive, the equation has two [[nonreal]] roots; and if the discriminant is 0, the equation has a real [[double root]]. ...(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_0</math> of degree <math>n</math> with all the coefficients being real. But for polynomials of degree 4 or higher it can b
  4 KB (734 words) - 19:19, 10 October 2023

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