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• 2006 AMC 12A Problems/Problem 2
  Define <math>x\otimes y=x^3-y</math>. What is <math>h\otimes (h\otimes h)</math>? ...bf{(B)}\ 0\qquad\textbf{(C)}\ h\qquad\textbf{(D)}\ 2h\qquad\textbf{(E)}\ h^3</math>
  694 bytes (110 words) - 14:03, 27 July 2023
• 2006 AMC 12A Problems/Problem 3
  ...lems|2006 AMC 12A #3]] and [[2006 AMC 10A Problems/Problem 3|2006 AMC 10A #3]]}} ...ice's age is <math>3:5</math>. Alice is <math>30</math> years old. How old is Mary?
  1 KB (155 words) - 17:30, 16 December 2021
• 2006 AMC 12A Problems/Problem 6
  ...e two hexagons can be repositioned without overlap to form a square. What is <math>y</math>? label("$y$",(3,4),S);
  3 KB (528 words) - 18:29, 7 May 2024
• 2006 AMC 12A Problems/Problem 8
  <math> \textbf{(A) } 1\qquad \textbf{(B) } 2\qquad \textbf{(C) } 3\qquad \textbf{(D) } 4\qquad \textbf{(E) } 5</math> ...e must be either <math>1, 3, </math> or <math>5</math>, and <math>1</math> is clearly not possible. The other two possibilities both work:
  3 KB (450 words) - 02:00, 13 January 2024
• 2006 AMC 12A Problems/Problem 9
  ...more than an eraser, and both items cost a [[whole number]] of cents. What is the total cost, in cents, of one pencil and one eraser? ...1 \pmod 3</math> so <math>p</math> leaves a remainder of 1 on division by 3.
  3 KB (429 words) - 18:14, 26 September 2020
• Diagonal
  A '''diagonal''' of a [[polygon]] is any segment joining two [[vertex|vertices]] other than an [[edge]]. ...als of a polygon with <math>n</math> vertices is given by <math>\frac{n(n-3)}{2}</math>.
  2 KB (374 words) - 00:37, 25 January 2015
• Equation
  An '''equation''' is a [[relation]] which states that two [[expression]]s are equal, identical, A unique aspect to equations is the ability to modify an original equation by performing operations (such a
  5 KB (932 words) - 12:57, 26 July 2023
• Harvard-MIT Mathematics Tournament
  ...998. The contest takes place alternatively at Harvard or MIT each year. It is composed of two tournaments, the ''February Tournament'' and the ''November The February Tournament is the more difficult of the two tournaments, with its problems ranging from m
  4 KB (539 words) - 16:58, 19 February 2023
• Radius
  ...ons hold for the [[sphere]] and [[hypersphere]]. The plural form of radius is radii. The radius of a circle is often denoted using R or r.
  929 bytes (156 words) - 22:49, 5 January 2023
• Intersection
  ...math>\{1, 2, 3\}</math> and <math>\{1, 3, 5\}</math> is the set <math>\{1, 3\}</math>. ....e. <math>\bigcap_{i = 1}^n A_i = A_1 \cap A_2 \cap \ldots \cap A_n</math> is the intersection of the <math>n</math> sets <math>A_1, A_2, \ldots, A_n</ma
  1 KB (221 words) - 22:41, 11 April 2019
• Word problem
  A '''word problem''' is a problem posed in plain language, as opposed to a problem with only "math" Because word problems are based on a contextualized scenario, the context is important in interpreting the results. For instance, when determining the
  1 KB (200 words) - 15:05, 10 April 2020
• Multinomial Theorem
  where <math>\binom{n}{j_1; j_2; \ldots ; j_k}</math> is the [[multinomial coefficient]] <math>\binom{n}{j_1; j_2; \ldots ; j_k}=\df Note that this is a direct generalization of the [[Binomial Theorem]], when <math>k = 2</math
  3 KB (476 words) - 19:37, 4 January 2023
• Quadratic reciprocity
  <cmath> \genfrac{(}{)}{}{}{a}{p} =\begin{cases} 1 & \text{if } a \text{ is a quadratic residue modulo } p, \\ We say that <math>a</math> is a '''quadratic residue''' modulo <math>p</math> if there exists an integer
  7 KB (1,182 words) - 16:46, 28 April 2016
• 2006 AMC 10B Problems
  What is <math> (-1)^{1} + (-1)^{2} + ... + (-1)^{2006} </math> ? ...define <math> x \mathop{\spadesuit} y = (x+y)(x-y) </math>. What is <math> 3 \mathop{\spadesuit} (4 \mathop{\spadesuit} 5) </math>?
  14 KB (2,059 words) - 01:17, 30 January 2024
• 2005 AMC 10B Problems
  ...e property that <math>x\%</math> of <math>x</math> is <math>4</math>. What is <math>x</math>? == Problem 3 ==
  12 KB (1,874 words) - 21:20, 23 December 2020
• Noncommutative
  More formally, if <math>\star</math> is some [[binary operation]] on a [[set]], and <math>x</math> and <math>y</mat ...commutative]]. For example, <math>4\cdot3=3\cdot4=12</math>, and <math>2+3=3+2=5</math>.
  2 KB (257 words) - 15:30, 26 December 2017
• Platonic solid
  A '''Platonic solid''' is a [[polyhedron]], or 3 dimensional figure, in which all [[face]]s are [[congruent (geometry)|congr It is easy to verify that all five Platonic solids satisfy [[Euler's polyhedral f
  8 KB (1,184 words) - 22:53, 27 August 2024
• Law of Tangents
  ...'''Law of Tangents''' is a rather obscure [[trigonometric identity]] that is sometimes used in place of its better-known counterparts, the [[law of sine ...n a triangle, any ratio of linear combinations applied to lengths of sides is equal to the ratio of the same linear combinations applied to the sines of
  2 KB (306 words) - 16:11, 21 February 2023
• 2000 AMC 12 Problems/Problem 3
  ...0 AMC 12 Problems|2000 AMC 12 #3]] and [[2000 AMC 10 Problems|2000 AMC 10 #3]]}} ...h>. If she ate <math>20\%</math> of the jellybeans, then <math>80\%</math> is remaining. Hence, after day 1, there are:
  1 KB (177 words) - 00:36, 15 July 2024
• 2000 AMC 12 Problems/Problem 8
  Figures <math>0</math>, <math>1</math>, <math>2</math>, and <math>3</math> consist of <math>1</math>, <math>5</math>, <math>13</math>, and <mat draw((9,0)--(10,0)--(10,3)--(9,3)--cycle);
  8 KB (1,226 words) - 23:15, 25 July 2024

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