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• Inequality
  Inequalities are arguably a branch of [[elementary algebra]], and relate slightly to [[number theory]]. For two [[number]]s <math>a</math> and <math>b</math>:
  12 KB (1,806 words) - 05:07, 19 June 2024
• Divisibility rules
  ...its of the number are divisible by <math>2^n</math>. Thus, in particular, a number is divisible by 2 if and only if its units digit is divisible by 2, A number is divisible by 3 or 9 if and only if the sum of its digits is divis
  10 KB (1,572 words) - 21:11, 22 September 2024
• Prime factorization
  ...ental Theorem of Arithmetic]] tells us that every [[positive integer]] has a unique prime factorization, up to changing the order of the terms. The form of a prime factorization is
  3 KB (496 words) - 21:14, 5 January 2024
• Fraction
  A '''fraction''' is the [[ratio]] of two [[number]]s. Most commonly, we cons ...erator is greater than the denominator is called an [[improper fraction]]. A fraction where the numerator is the same as the denominator such as <math>\
  3 KB (432 words) - 18:34, 11 June 2020
• Exponentiation
  ...math>a^b</math>, where <math>b</math> is the exponent (or power) and <math>a</math> is the [[base]]. In the [[order of operations]], it is the second operation performed if a equation has [[parentheses]] or the first one performed when there is no pa
  5 KB (803 words) - 15:25, 10 August 2020
• 2006 AMC 12B Problems/Problem 7
  \text {(A) } 4 \qquad \text {(B) } 12 \qquad \text {(C) } 16 \qquad \text {(D) } 24 \ \boxed{12}</math> possible seating arrangements. ~ aopsav (Credit to AoPS Alcumus)
  1 KB (213 words) - 14:33, 9 April 2024
• 2006 AMC 12B Problems/Problem 9
  \text {(A) } 21 \qquad \text {(B) } 34 \qquad \text {(C) } 51 \qquad \text {(D) } 72 ==Solution 1 (Alcumus Edition)==
  3 KB (409 words) - 16:10, 30 April 2024
• 2006 AMC 12A Problems/Problem 17
  ...ies on the circle, on the same side of <math>\overline{BE}</math> as <math>A</math>. Segment <math>AF</math> is tangent to the circle, and <math>AF=\sqr label("A", (-s,0), W);
  6 KB (958 words) - 22:29, 28 September 2023
• 2006 AMC 12A Problems/Problem 23
  ...h>S=(a_1,a_2,\ldots ,a_n)</math> of <math>n</math> real numbers, let <math>A(S)</math> be the sequence ...ath>x>0</math>, and let <math>S=(1,x,x^2,\ldots ,x^{100})</math>. If <math>A^{100}(S)=(1/2^{50})</math>, then what is <math>x</math>?
  3 KB (466 words) - 21:40, 29 September 2023
• 2005 AMC 12B Problems/Problem 7
  \mathrm{(A)}\ 6 \qquad ...lowing 4 equations (using the logic that if <math>|a|=b</math>, then <math>a</math> is either <math>b</math> or <math>-b</math>):
  2 KB (357 words) - 19:15, 27 December 2020
• 2005 AMC 12B Problems/Problem 23
  ...y^{3}=a \cdot 10^{3z} + b \cdot 10^{2z}.</math> What is the value of <math>a+b?</math> \textbf{(A)}\ \frac {15}{2} \qquad
  5 KB (786 words) - 10:36, 19 May 2024
• 2006 AMC 10A Problems/Problem 15
  ...ns counterclockwise at <math>300 m/min</math> and uses the outer lane with a radius of <math>60</math> meters, starting on the same radial line as Odell <math>\textbf{(A) } 29\qquad\textbf{(B) } 42\qquad\textbf{(C) } 45\qquad\textbf{(D) } 47\qqu
  3 KB (533 words) - 23:24, 23 October 2024
• 2005 AIME II Problems/Problem 13
  Let <math> P(x) </math> be a polynomial with integer coefficients that satisfies <math> P(17)=10 </math> ...it has roots at <math>17</math> and <math>24</math>. Hence <math>P(x)-x+7=A(x-17)(x-24)</math>. In particular, this means that
  4 KB (642 words) - 01:14, 1 June 2024
• 2006 AMC 10B Problems/Problem 21
  ...in the ratio <math>1:2:3:4:5:6</math>. What is the probability of rolling a total of <math>7</math> on the two dice? <math> \mathrm{(A) \ } \frac{4}{63}\qquad \mathrm{(B) \ } \frac{1}{8}\qquad \mathrm{(C) \ } \
  4 KB (512 words) - 03:05, 21 October 2024
• 2003 AIME I Problems/Problem 2
  ...]s with [[radius | radii]] <math> 1, 2, 3, \dots, 100 </math> are drawn in a plane. The interior of the circle of radius <math>1</math> is colored red, For any <math>a</math>, <math>a^{2}-(a-1)^{2}=a^{2}-(a^{2}-2a+1)=2a-1</math>. We can cancel the [[divisor | factor]] of [[pi]] fr
  4 KB (523 words) - 14:49, 8 March 2021
• 2003 AIME II Problems/Problem 3
  ...<math>C</math>, and <math>C</math> is never immediately followed by <math>A</math>. How many seven-letter good words are there? ...ot2^6=\boxed{192}</math> seven-letter good words. ~ aopsav (Credit to AoPS Alcumus)
  2 KB (336 words) - 16:29, 30 July 2022
• 2002 AIME II Problems/Problem 15
  ...me, and <math>a</math> and <math>c</math> are relatively prime. Find <math>a + b + c</math>. ...<math>b</math> respectively. We know that the point <math>(9,6)</math> is a point on both circles, so we have that
  7 KB (1,188 words) - 16:46, 23 June 2024
• Ratio
  ...b</math>, <math>a:b</math>, <math>a</math> to <math>b</math>, or simply as a decimal. ...rtional) if the two ratios equal each other. In other words, <math>\tfrac{a}{b} = \tfrac{c}{d}</math>.
  666 bytes (100 words) - 19:25, 29 December 2023
• 2004 AMC 12A Problems/Problem 4
  ...ome of her daughters have 6 daughters, and the rest have none. Bertha has a total of 30 daughters and granddaughters, and no great-granddaughters. How <math>\mathrm{(A) \ } 22 \qquad \mathrm{(B) \ } 23 \qquad \mathrm{(C) \ } 24 \qquad \mathrm{
  2 KB (232 words) - 12:56, 19 January 2021
• 2003 AMC 10A Problems/Problem 21
  Pat is to select six cookies from a tray containing only chocolate chip, oatmeal, and peanut butter cookies. Th <math> \mathrm{(A) \ } 22\qquad \mathrm{(B) \ } 25\qquad \mathrm{(C) \ } 27\qquad \mathrm{(D)
  7 KB (993 words) - 20:06, 29 September 2024

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