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• Order of operations
  The '''order of operations''' is a [[mathematical convention]] for [[arithmetic]] computation. The below li ...m PEMDAS. An AoPS mnemonic you can use to remember the order of operations is "Please Evaluate, My Dear AoPS Students".
  2 KB (271 words) - 13:19, 5 March 2022
• Octahedron
  An '''octahedron''' is a type of [[polyhedron]]. ...eometry]], an octahedron is any polyhedron with eight [[face]]s. The term is most frequently to refer to a polyhedron with eight [[triangular]] faces, w
  1 KB (155 words) - 12:19, 21 July 2023
• Circumradius
  ...f the [[circle]] that [[circumscribe]]s the triangle. Since every triangle is [[cyclic]], every triangle has a circumscribed circle, or a [[circumcircle] ...rea of the triangle. Then, the measure of the circumradius of the triangle is simply <math>R=\frac{abc}{4A}</math>. This can be rewritten as <math>A=\fra
  4 KB (729 words) - 16:52, 19 February 2024
• Sum and difference of powers
  If <math>p</math> is a positive integer and <math>x</math> and <math>y</math> are real numbers, <math>x^3-y^3=(x-y)(x^2+xy+y^2)</math>
  3 KB (450 words) - 06:25, 6 May 2024
• LaTeX:Layout
  ...style are items that are set in the preamble. Often, much of the preamble is placed in a separate file and included using the \usepackage statement. Th ...defaults. One option that might need modification is the font size, which is 10pt by default but can be increased to 11pt or 12pt. A reference on other
  30 KB (5,171 words) - 10:16, 4 April 2021
• LaTeX:Packages
  ...ds or a basic preamble that you can include in any of your LaTeX documents is simple. Just follow these steps: ...X 2.9\tex\latex'''. (If you have an older MiKTeX installation, this folder is probably '''C:\texmf\tex\latex'''.)</li>
  9 KB (1,544 words) - 06:05, 24 February 2021
• LaTeX:Commands
  | <math>a^{i+1}_3</math>||a^{i+1}_3||<math>x^{3^2}</math>||x^{3^2} |<math>\sqrt{3}</math>||\sqrt{3}
  12 KB (1,894 words) - 21:24, 7 June 2024
• Imaginary number
  An '''imaginary number''' is a [[complex number]] whose [[real part]] is equal to 0. In the [[complex plane]], these numbers lie on the [[imaginary ...= \sqrt{-1}</math> is the [[imaginary unit]] and <math>\textrm{Im}</math> is the [[imaginary part]] [[function]].
  2 KB (283 words) - 00:18, 8 March 2012
• Science Olympiad
  '''Science Olympiad''' is a national team-based science competition primarily for middle high school ...school is allowed to have up to five ninth graders on its team. Division C is generally for high school students in grades 10-12, though ninth graders ar
  3 KB (443 words) - 11:27, 25 May 2023
• Chicken McNugget Theorem
  ...e form <math>am + bn</math> for [[nonnegative]] integers <math>a, b</math> is <math>mn-m-n</math>. ...t in each pair of the form <math>(k, mn-m-n-k)</math>, exactly one element is expressible.
  17 KB (2,748 words) - 19:22, 24 February 2024
• Dodecagon
  ...dodecagon''' is a 12-sided [[polygon]]. The sum of its internal [[angle]]s is <math>1800^{\circ}</math>. Each of its exterior angles has measure <math>3 D=dir(360/12*3);
  1 KB (219 words) - 13:08, 15 June 2018
• Triangular number
  The <math>n^{th}</math> triangular number is the sum of all natural numbers from one to n. That is, the <math>n^{th}</math> triangle number is
  2 KB (275 words) - 08:39, 7 July 2021
• 2005 AMC 12A Problems/Problem 24
  ...math>Q(x)</math> does there exist a polynomial <math>R(x)</math> of degree 3 such that <math>P(Q(x))=P(x) \cdot R(x)</math>? <math>P(Q(x))=(Q(x)-1)(Q(x)-2)(Q(x)-3)=P(x)\cdot R(x)=(x-1)(x-2)(x-3)\cdot R(x)</math>.
  5 KB (833 words) - 18:17, 8 April 2024
• 2005 AMC 12A Problems/Problem 23
  ...}\}</math>. What is the [[probability]] that <math>\mathrm{log}_a b</math> is an [[integer]]? ...<math>\sum_{x=1}^{12} \lfloor\frac {25}x-1\rfloor = 24 + 11 + 7 + 5 + 4 + 3 + 2 + 2 + 1 + 1 + 1 + 1 = 62</math>.
  1 KB (175 words) - 20:35, 7 November 2013
• 2007 AMC 12A Problems/Problem 2
  ...with a rectangular base that measures 40 cm by 20 cm and a height of 10 cm is placed in the aquarium. By how many centimeters does the water rise? ...th>4000 cm^3</math>; therefore, when the volume increases by <math>8000 cm^3</math>, the water level rises <math>2 cm \Rightarrow\fbox{D}</math>
  895 bytes (140 words) - 21:30, 3 July 2013
• 2007 AMC 12A Problems/Problem 3
  The larger of two consecutive odd integers is three times the smaller. What is their sum? *Thus, the answer is <math>1+(1+2)=4 \mathrm{(A)}</math>
  585 bytes (81 words) - 02:09, 16 February 2021
• 2007 AMC 12A Problems/Problem 6
  ...measures 40 degrees, and angle <math>ADC</math> measures 140 degrees. What is the degree measure of angle <math>BAD</math>? Since triangle <math>ABC</math> is isosceles we know that angle <math>\angle BAC = \angle BCA</math>.
  2 KB (265 words) - 00:20, 30 October 2022
• 2007 AMC 12A Problems/Problem 18
  ...</math> has real coefficients, and <math>f(2i) = f(2 + i) = 0.</math> What is <math>a + b + c + d?</math> <math>x^4 - 4x^3 + 9x^2 - 16x + 20 = 0</math></div>
  2 KB (319 words) - 00:37, 25 March 2024
• 2007 AMC 12A Problems/Problem 9
  ...s fast as he walks, and both choices require the same amount of time. What is the [[ratio]] of Yan's distance from his home to his distance from the stad ...-1 = \frac{4}{3}</math>, so the answer is <math>\boxed{\mathrm{(B)}\ \frac{3}{4}}</math>
  5 KB (804 words) - 14:55, 21 August 2022
• Proportion
  Direct proportion is a proportion in which one number is a multiple of the other. Direct proportion between two numbers <math>x</mat where <math>k</math> is some [[real number]].
  2 KB (325 words) - 16:34, 1 June 2022

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