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• Pythagorean Theorem
  ...a good geometer's arsenal. A very large number of geometry problems can be solved by building right triangles and applying the Pythagorean Theorem.
  5 KB (886 words) - 21:12, 22 January 2024
• Inequality
  Linear inequalities can be solved much like linear equations to get implicit restrictions upon a variable. H
  12 KB (1,798 words) - 16:20, 14 March 2023
• AMC 10
  ...ity]] and other secondary school math topics. Problems are designed to be solved by students without any background in calculus or trigonometry.
  4 KB (574 words) - 15:28, 22 February 2024
• United States of America Mathematical Olympiad
  ...his two day, 9 hour exam (two 4.5 hour sessions). All six questions can be solved using precalculus methods, but an extensive understanding of the material a
  6 KB (869 words) - 12:52, 20 February 2024
• Completing the square
  ...ving a lot of equations easy. In fact, all [[quadratic equation]]s can be solved by completing the square. All quadratic equations in the form <math>(x+a)^2=b</math> can be solved by taking the [[square root]] of <math>b</math> and subtracting <math>a</ma
  2 KB (422 words) - 16:20, 5 March 2023
• Factoring
  These factorizations are useful for problems that could otherwise be solved by [[Newton sums]] or problems that give a polynomial and ask a question ab
  3 KB (532 words) - 22:00, 13 January 2024
• Quadratic equation
  ...ath>) and <math>x</math> is the unknown variable. Quadratic equations are solved using one of three main strategies: [[factoring]], [[completing the square]
  2 KB (264 words) - 12:04, 15 July 2021
• Contest strategies
  ...wishful thinking” — trying to make a problem look like a similar one solved before.
  3 KB (538 words) - 13:13, 16 January 2021
• Induction
  ...aren't any problems in other areas, such as [[Inequalities]], that can be solved with induction. ...cs Olympiad | IMO]]. A good example of an upper-level problem that can be solved with induction is [http://www.artofproblemsolving.com/Forum/viewtopic.php?p
  5 KB (768 words) - 20:45, 1 September 2022
• Orthic triangle
  .... Problems written in either excenters or the orthic triangle can often be solved by shifting perspective to the other, via the medium of this lemma. Also, n
  8 KB (1,408 words) - 11:54, 8 December 2021
• Constructive counting
  ...olving ability becomes more advanced, there are fewer problems that can be solved by constructive counting alone; the list of examples terminates at a late-i
  12 KB (1,896 words) - 23:55, 27 December 2023
• Casework
  ...Unlike the selections in this article, most problems cannot be completely solved through casework. However, it is crucial as an intermediate step across all
  5 KB (709 words) - 10:28, 19 February 2024
• Common factorizations
  These factorizations are useful for problem that could otherwise be solved by [[Newton sums]] or problems that give a polynomial, and ask a question a
  2 KB (327 words) - 02:06, 28 April 2024
• Math Bee
  ...in 35 minutes, while the second phase has 20 free-response questions to be solved in 15 minutes.
  1 KB (197 words) - 10:59, 14 April 2024
• Functional equation
  ...n''', roughly speaking, is an equation in which some of the unknowns to be solved for are [[function]]s. For example, the following are functional equations
  2 KB (361 words) - 14:40, 24 August 2021
• Trigonometry
  ...lving the trigonometric functions appear frequently on contests. These are solved by clever usage of the trigonometric functions' countless [[Trigonometric i
  8 KB (1,217 words) - 20:15, 7 September 2023
• Modular arithmetic/Introduction
  ...rogression of more difficult and more interesting problems that are easily solved using modular arithmetic.
  15 KB (2,396 words) - 20:24, 21 February 2024
• 2006 AIME I Problems/Problem 10
  ...ight)</math> and <math>\left(\frac 32,2\right)</math>, which can be easily solved to be <math>6x = 2y + 5</math>. Thus, <math>a^2 + b^2 + c^2 = \boxed{065}</
  4 KB (731 words) - 17:59, 4 January 2022
• 2006 AMC 12A Problems/Problem 25
  This question can be solved fairly directly by casework and pattern-finding. We give a somewhat more g
  8 KB (1,405 words) - 11:52, 27 September 2022
• 2005 AMC 12B Problems/Problem 24
  The slope <math>BC</math> can also be solved similarly, noting that it makes a <math>120^{\circ}</math> angle with <math
  4 KB (761 words) - 09:10, 1 August 2023

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