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  • ...n Theorem is one of the most frequently used theorems in [[geometry]], and is one of the many tools in a good geometer's arsenal. A very large number of This is generalized by the [[Geometric inequality#Pythagorean_Inequality | Pythagor
    5 KB (886 words) - 21:12, 22 January 2024
  • ...s</math> is tangent to both axes and to the second and third circles. What is <math>r/s</math>? dotfactor=3;
    2 KB (305 words) - 23:01, 26 January 2024
  • ...so we can write <math>\$12.50\cdot (4+3)=\$ 87.50.</math> Then the answer is <math>\boxed{\text{(C)}}.</math>
    1 KB (176 words) - 10:58, 16 June 2023
  • ...o <math>\tfrac{x}{y}</math>. What is the value of <math>\text{rem} (\tfrac{3}{8}, -\tfrac{2}{5} )</math>? ...xtbf{(B) } -\frac{1}{40} \qquad \textbf{(C) } 0 \qquad \textbf{(D) } \frac{3}{8} \qquad \textbf{(E) } \frac{31}{40}</math>
    2 KB (257 words) - 10:57, 16 June 2023
  • A rectangular box has integer side lengths in the ratio <math>1: 3: 4</math>. Which of the following could be the volume of the box? ...ath>x \cdot 3x \cdot 4x =12x^3</math>. If <math>x=2</math>, then <math>12x^3 = 96 \implies \boxed{\textbf{(D) } 96.}</math>
    1 KB (184 words) - 13:58, 22 August 2023
  • .../math>. Star adds her numbers and Emilio adds his numbers. How much larger is Star's sum than Emilio's? ...2 appears 3 times as a units digit, the answer is <math>10\cdot 10+1\cdot 3=\boxed{\textbf{(D) }103.}</math>
    967 bytes (143 words) - 03:18, 27 June 2023
  • ...h>60, 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
  • ...ow, and so on up to <math>N</math> coins in the <math>N</math>th row. What is the sum of the digits of <math>N</math>? ...\frac{63\cdot 64}{2}=2016,</math> we have <math>N=63,</math> so our answer is <math>\boxed{\textbf{(D) } 9}.</math>
    2 KB (315 words) - 15:34, 18 June 2022
  • ...the two shaded regions is <math>1</math> foot wide on all four sides. What is the length in feet of the inner rectangle? filldraw(rectangle((2,2),(5,3)),white);
    2 KB (337 words) - 14:56, 25 June 2023
  • label("$4$",(8,3),dir(0)); <math>\textbf{(A)}\ 4\dfrac{3}{5} \qquad \textbf{(B)}\ 5\qquad \textbf{(C)}\ 5\dfrac{1}{4} \qquad \textbf
    8 KB (1,016 words) - 00:17, 31 December 2023
  • ...bout the probability <math>p</math> that the product of the three integers is odd? ...rac{1}{3}\qquad\textbf{(D)}\ p=\dfrac{1}{3}\qquad\textbf{(E)}\ p>\dfrac{1}{3}</math>
    2 KB (297 words) - 14:54, 25 June 2023
  • <math>\textbf{(A) }1 \qquad \textbf{(B) } 2 \qquad \textbf{(C) } 3 \qquad \textbf{(D) } 4\qquad \textbf{(E) } 5</math> ...This means that Bea was originally in seat 1. Ceci must have been in seat 3 to keep seat 1 open, which leaves seat 2.
    2 KB (402 words) - 14:54, 25 June 2023
  • * [[AMC 8]] hosted by the [[American Mathematics Competitions]] is a very large middle school math contest taken in-school. ([http://www.maa.o *[http://www.imc-impea.org IMC-IMPEA] is an offline/online math contest for all grades level. The contest offers ind
    7 KB (777 words) - 11:32, 15 March 2024
  • ...ors are graduate or undergraduate math students. The math content covered is undergraduate- and graduate-level. Our 2024 programs will be taking place online from June 30-August 3, with MathILy at Bryn Mawr College and MathILy-Er at Arcadia University. Th
    5 KB (706 words) - 23:49, 29 January 2024
  • ...ics], and others including Art of Problem Solving, the focus of MATHCOUNTS is on mathematical problem solving. Students are eligible for up to three year ...>Countdown</u>: 0.5 (School/Chapter), 1 (State/National)<br><u>Sprint</u>: 1-1.5 (School/Chapter), 2-2.5 (State/National)<br><u>Target:</u> 1.5 (School),
    10 KB (1,497 words) - 11:42, 10 March 2024
  • ...</math>, and <math>2013_{10}=133131</math>, so the answer is <math>1+3+3+1+3+1=\boxed{12}</math>.
    190 bytes (26 words) - 06:13, 16 February 2024
  • ...ers of Mathematics offers two areas of math contests: Grade School (Grades 3, 4, 5, 6, 7, 8 + Algebra 1) and High School (Regional and State Finals). ...Committee offers in-school contests at six different grade levels (grades 3-8). The season consists of three contests to be given at your school. Each
    8 KB (1,178 words) - 22:48, 17 October 2015
  • * The [http://www.kalva.demon.co.uk/ Kalva site] is one of the best resources for math problems on the planet. (Currently offli * [https://brilliant.org/ Brilliant] is a website where one can solve problems to gain points and go to higher leve
    24 KB (3,269 words) - 22:58, 18 March 2024
  • The '''William Lowell Putnam Mathematical Competition''' is a highly challenging, proof-oriented [[mathematics competition]] for underg ...f|difficulty=7 - 9|breakdown=<u>Problem A/B, 1/2</u>: 7<br><u>Problem A/B, 3/4</u>: 8<br><u>Problem A/B, 5/6</u>: 9}}
    4 KB (623 words) - 13:11, 20 February 2024
  • '''Mathematics''' is the [[science]] of structure and change. Mathematics is important to the other sciences because it provides rigourous methods for d ==Overview=={{asy image|<math>1\,2\,3\,4\,5\,6\,7\,8\,9\,0</math>|right|The ten [[digit]]s making up <br /> the b
    6 KB (902 words) - 12:53, 3 September 2019
  • This is the '''AMC historical results''' page. This page should include results for *Mean: 68.3
    17 KB (1,921 words) - 12:33, 20 March 2024
  • ...with [[optimization]] methods. While most of the subject of inequalities is often left out of the ordinary educational track, they are common in [[math ...f <math>a</math> is greater than <math>b</math>, that is, <math>a-b</math> is positive.
    12 KB (1,798 words) - 16:20, 14 March 2023
  • The '''United States of America Mathematical Talent Search''' ('''USAMTS''') is a [[mathematics competition]] in which students are challenged to write ful The USAMTS is administered by the [[Art of Problem Solving Foundation]] with support and
    4 KB (613 words) - 13:08, 18 July 2023
  • ...rican Mathematics Contest 10''' ('''AMC 10'''), along with the [[AMC 12]], is one of the first exams in the series of exams used to challenge bright stud ...rican Mathematics Competitions]] (AMC). [[Art of Problem Solving]] (AoPS) is a proud sponsor of the AMC.
    4 KB (574 words) - 15:28, 22 February 2024
  • The '''American Mathematics Contest 12''' ('''AMC 12''') is the first exam in the series of exams used to challenge bright students, gr ...rican Mathematics Competitions]] (AMC). [[Art of Problem Solving]] (AoPS) is a proud sponsor of the AMC!
    4 KB (520 words) - 12:11, 13 March 2024
  • ...21</math>, and <math>17</math> are obtained. One of the original integers is: ...ystem of equation should be constructed. (It doesn't matter which variable is which.)
    1 KB (200 words) - 23:35, 28 August 2020
  • The '''American Invitational Mathematics Examination''' ('''AIME''') is the second exam in the series of exams used to challenge bright students on ...matical Association of America]] (MAA). [[Art of Problem Solving]] (AoPS) is a proud sponsor of the AMC!
    8 KB (1,057 words) - 12:02, 25 February 2024
  • dotfactor=3; pair A=(-3*sqrt(3)/32,9/32), B=(3*sqrt(3)/32, 9/32), C=(0,9/16);
    3 KB (415 words) - 18:01, 24 May 2020
  • We say that a finite set <math>\mathcal{S}</math> in the plane is <i> balanced </i> ...t points <math>A</math>, <math>B</math> in <math>\mathcal{S}</math>, there is
    4 KB (692 words) - 22:33, 15 February 2021
  • 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 participant
    6 KB (869 words) - 12:52, 20 February 2024
  • ...e Spring Semester to determine the team each year. The 6 practices include 3 individual tests to help determine the team and some lectures on certain ma ...ent process of selecting team members has yet to be decided upon. The team is organized by and practices at the San Diego Math Circle (SDMC), and most of
    21 KB (3,477 words) - 16:43, 1 January 2024
  • ...hosts classes for outstanding middle and high school students. The school is also accredited by the Western Association of Schools and Colleges. Each of ...ine School/Intermediate Algebra | Intermediate Algebra]] (formerly Algebra 3) — [https://artofproblemsolving.com/school/course/catalog/intermediate-al
    8 KB (965 words) - 03:41, 17 September 2020
  • ...)! + 1</math> is divisible by <math>p</math> if and only if <math>p</math> is prime. It was stated by John Wilson. The French mathematician Lagrange prov ...h> is composite. Then <math>p</math> has a factor <math>d > 1</math> that is less than or equal to <math>p-1</math>. Then <math>d</math> divides <math>
    4 KB (639 words) - 01:53, 2 February 2023
  • ...ity''' is an [[inequality]] that states that the square of any real number is nonnegative. Its name comes from its simplicity and straightforwardness. ...al inequality is one of the most commonly used theorems in mathematics. It is very well-known and does not require proof.
    3 KB (560 words) - 22:51, 13 January 2024
  • The '''arithmetic mean''' of a [[set]] of numbers (or variables) is the sum of all the numbers, divided by the number of numbers - the [[averag is the arithmetic mean of the <math>{n}</math> numbers <math>x_1,x_2,\ldots,x_
    699 bytes (110 words) - 12:44, 20 September 2015
  • The idea of '''completing the square''' is to add something to an equation to make that equation a [[perfect square]]. ...math> was added to this, then we would have a [[perfect square]], <math>(x-3)^2=x^2-6x+9</math>. To do this, add <math>7</math> to each side of the equ
    2 KB (422 words) - 16:20, 5 March 2023
  • '''Heron's Formula''' (sometimes called Hero's formula) is a [[mathematical formula | formula]] for finding the [[area]] of a [[triang ...serve as a reason for why the area <math>A</math> is never imaginary. This is equivalent of ending at step <math>4</math> in the proof and distributing.
    4 KB (675 words) - 00:05, 22 January 2024
  • ...abstract algebra]] often an arbitrary [[field]]). Note that a [[constant]] is also a polynomial. * <math>x^3 + 3x^2y + 3xy^2 + y^3</math>, in the variables <math>x</math> and <math>y</math>
    6 KB (1,100 words) - 01:44, 17 January 2024
  • ...3333</cmath>where <math>23333</math> is the constant term, <math>xy</math> is the product of the variables, <math>66x</math> and <math>-88y</math> are th ...>a</math> are integer constants, and the coefficient of xy must be 1(If it is not 1, then divide the coefficient off of the equation.). According to Simo
    7 KB (1,107 words) - 07:35, 26 March 2024
  • ...mathematical toolbox. To factor, or to break an expression into factors, is to write the expression (often an [[integer]] or [[polynomial]]) as a produ This leads to the difference of cubes factorization, <cmath>a^3-b^3=(a-b)(a^2+ab+b^2)</cmath>
    3 KB (532 words) - 22:00, 13 January 2024
  • ...ehind The [[Art of Problem Solving]] as well as many [[math competitions]] is the use of creative methods to solve problems. In a way, students are disco An interesting example of this kind of thinking is the calculation of the sum of the [[series]] <math>\frac11 + \frac14 + \fra
    2 KB (314 words) - 06:45, 1 May 2014
  • ...principle'''. A common phrasing of the principle uses balls and boxes and is that if <math>n</math> balls are to be placed in <math>k</math> boxes and < An intuitive proof of the pigeonhole principle is as follows: suppose for contradiction that there exists a way to place <mat
    11 KB (1,985 words) - 21:03, 5 August 2023
  • ...+ 11x^2 + 3x + 31</math> is the square of an integer. Then <math>n</math> is: \textbf{(B) }\ 3 \qquad
    3 KB (571 words) - 00:42, 22 October 2021
  • ...while the geometric mean of the numbers <math>b</math> and <math>c</math> is the number <math>g</math> such that <math>g\cdot g = b\cdot c</math>. ...nd 2 is <math>\sqrt[4]{6\cdot 4\cdot 1 \cdot 2} = \sqrt[4]{48} = 2\sqrt[4]{3}</math>.
    2 KB (282 words) - 22:04, 11 July 2008
  • ...is counted once and only once. In particular, memorizing a formula for PIE is a bad idea for problem solving. Here, we will illustrate how PIE is applied with various numbers of sets.
    9 KB (1,703 words) - 07:25, 24 March 2024
  • ...om a set of <math>n</math> where the order in which the objects are chosen is irrelevant. We are generally concerned with finding the number of combinat This video is a great introduction to permutations, combinations, and constructive counti
    4 KB (615 words) - 11:43, 21 May 2021
  • ...htarrow (a-1)(b-1)=2</math> from whence we have <math>(a,b,c)\in\{(2,3,1),(3,2,1)\}</math>. ...c|a+b</math>; hence <math>a+b</math> is a multiple of <math>c</math> which is no more than <math>2c+6</math>. It follows that <math>a+b\in\{c,2c,3c,4c,5c
    2 KB (332 words) - 09:37, 30 December 2021
  • ...Bunyakovsky–Schwarz Inequality''' or informally as '''Cauchy-Schwarz''', is an [[inequality]] with many ubiquitous formulations in abstract algebra, ca ...tion 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
  • The '''factorial''' is an important function in [[combinatorics]] and [[analysis]], used to determ ...h>. 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
  • ...negative, the equation has two [[nonreal]] roots; and if the discriminant is 0, the equation has a real [[double root]]. We know that the discriminant of a polynomial is the product of the squares of the differences of the polynomial roots <math
    4 KB (734 words) - 19:19, 10 October 2023

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