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• Mathematics summer program
  ...demic year. Selection is important in creating the best experience for any math student. ...programs listed below offer [[mathematics scholarships]] or financial aid. A few of them are free. When you discover more that do, please add that infor
  14 KB (1,869 words) - 20:06, 18 May 2024
• Mathematics, science, and technology scholarships
  * [[Intel Science Talent Search]]. One of the oldest and largest math and science scholarship programs. Intel STS winners receive scholarships of ...t important such competition in the world. The 3 ISEF winners each receive a <dollar/>50,000 scholarship. [http://www.sciserv.org/isef website]
  7 KB (851 words) - 10:54, 29 January 2022
• Texas mathematics competitions
  ...ts [http://www.artofproblemsolving.com/Forum/index.php?f=298 middle school math forums] where students can discuss contest problems and mathematics. *[[Texas A&M University math Contest]] [http://www.math.tamu.edu/teaching/undergrad/highschoolcontest/ website]
  2 KB (255 words) - 07:55, 2 March 2023
• Math books
  These '''math books''' are recommended by [[Art of Problem Solving]] administrators and m Levels of reading and math ability are loosely defined as follows:
  24 KB (3,177 words) - 12:53, 20 February 2024
• Math Olympiads for Elementary and Middle Schools
  '''Math Olympiads for Elementary and Middle Schools''' ('''MOEMS''') is a large and popular [[mathematics competition]] for students in grades 4 thro ...e=Free Response|difficulty=1|breakdown=<u>Division E</u>: 1<br><u>Division M</u>: 1}}
  2 KB (215 words) - 02:54, 18 November 2020
• Math textbooks
  ...ics -- not problem books, contest books, or general interest books. See [[math books]] for more titles. == Math textbooks by subject ==
  7 KB (901 words) - 14:11, 6 January 2022
• United States of America Mathematical Talent Search
  ...challenged to write full solutions and mathematical proofs to exploratory math problems. Each problems are graded on a scale from 0 to 5. The full 5 points are awarded for correct, concise solut
  4 KB (613 words) - 13:08, 18 July 2023
• Knowledge bowl competitions
  * [https://www.internationalmathbowl.com/ International Math Bowl] * [[Texas A&M Regional Science Bowl]] [http://outreach.science.tamu.edu/sciencebowl.asp w
  2 KB (212 words) - 17:15, 2 April 2024
• Joining an ARML team
  ...3 individual tests to help determine the team and some lectures on certain math topics not commonly taught in school, as well as practices of previous year ...lto:eric.brattain@gmail.com eric.brattain@gmail.com] and visit [http://www.math.ucdavis.edu/~exploration/arml/contact.php the team website].
  21 KB (3,435 words) - 00:56, 23 May 2024
• Base numbers
  ...rewritten as <math>2746_{10}=2\cdot10^3+7\cdot10^2+4\cdot10^1+6\cdot10^0.</math> ...ath>10^2</math>'s, and the fourth digit tells us there are two <math>10^3</math>'s.
  4 KB (547 words) - 17:23, 30 December 2020
• Law of Cosines
  ...sines''' is a theorem which relates the side-[[length]]s and [[angle]]s of a [[triangle]]. It can be derived in several different ways, the most common ...opposite [[angle]]s of measure <math>A</math>, <math>B</math> and <math>C</math>, respectively, the Law of Cosines states:
  6 KB (1,003 words) - 00:02, 20 May 2024
• Law of Sines
  The '''Law of Sines''' is a useful identity in a [[triangle]], which, along with the [[law of cosines]] and the [[law of tan ...th>B</math>, <math>c</math> opposite to <math>C</math>, and where <math>R</math> is the circumradius:
  4 KB (658 words) - 16:19, 28 April 2024
• Mock AMC
  ...an actual [[AMC]] (American Mathematics Competitions 8, 10, or 12) exam. A number of '''Mock AMC''' competitions have been hosted on the [[Art of Prob == Tips for Writing a Mock AMC ==
  51 KB (6,175 words) - 20:58, 6 December 2023
• 2006 AIME I Problems
  ...21, </math> and <math> CD=14. </math> Find the perimeter of <math> ABCD. </math> ...th> \mathcal{A}. </math> Find the number of possible values of <math> S. </math>
  7 KB (1,173 words) - 03:31, 4 January 2023
• 2006 AMC 12B Problems
  What is <math>( - 1)^1 + ( - 1)^2 + \cdots + ( - 1)^{2006}</math>? <math>
  13 KB (2,058 words) - 12:36, 4 July 2023
• 2006 AMC 12A Problems
  {{AMC12 Problems|year=2006|ab=A}} ...ny dollars will it cost to purchase <math>5</math> sandwiches and <math>8</math> sodas?
  15 KB (2,223 words) - 13:43, 28 December 2020
• 2005 AMC 12A Problems
  {{AMC12 Problems|year=2005|ab=A}} ...th>x</math> and <math>20 \%</math> of <math>y</math>. What is <math>x - y</math>?
  13 KB (1,971 words) - 13:03, 19 February 2020
• 2000 AMC 12 Problems
  ...01 </math>. What is the largest possible value of the sum <math>I + M + O</math>? ...\qquad \textbf{(C)}\ 99 \qquad \textbf{(D)}\ 111 \qquad \textbf{(E)}\ 671</math>
  13 KB (1,948 words) - 12:26, 1 April 2022
• 2004 AMC 12B Problems
  ...6 \qquad (\mathrm {C}) 9 \qquad (\mathrm {D}) 12 \qquad (\mathrm {E}) 15</math> ...the values of <math>a</math>, <math>b</math>, <math>c</math>, and <math>d</math> are 0, 1, 2, and 3, although not necessarily in that order. What is the ma
  13 KB (2,049 words) - 13:03, 19 February 2020
• 2005 AMC 12B Problems
  ...th> dollars. They sell all the candy bars at the price of two for <math>1</math> dollar. What was their profit, in dollars? <math>
  12 KB (1,781 words) - 12:38, 14 July 2022
• 2006 AMC 10A Problems
  {{AMC10 Problems|year=2006|ab=A}} ...st <math> \textdollar 3 </math> each and sodas cost <math> \textdollar 2 </math> each. How many dollars will it cost to purchase 5 sandwiches and 8 sodas?
  13 KB (2,028 words) - 16:32, 22 March 2022
• 2005 AIME II Problems
  ...the number of possible sets of 3 cards that can be drawn. Find <math> n. </math> ...th> and <math> n </math> are relatively prime integers, find <math> m+n. </math>
  7 KB (1,119 words) - 21:12, 28 February 2020
• 2005 AIME I Problems
  ...d outside of the six circles in the ring. Find <math> \lfloor K \rfloor. </math> ...,\ldots. </math> For how many values of <math> k </math> does <math> S_k </math> contain the term 2005?
  6 KB (983 words) - 05:06, 20 February 2019
• 1984 AIME Problems/Problem 14
  ...</math>, ... , and in general <math>9 + 6n</math> for nonnegative <math>n</math> are odd composites. We now have 3 cases: ...some nonnegative <math>n</math>. Note that <math>9</math> and <math>9+6n</math> are both odd composites.
  8 KB (1,346 words) - 01:16, 9 January 2024
• 1990 AIME Problems/Problem 13
  ...t its first (leftmost) digit is 9, how many [[element]]s of <math>T_{}^{}</math> have 9 as their leftmost digit? ...tive integers n, there's exactly one n-digit power of 9 that does not have a left-most digit 9
  5 KB (762 words) - 01:18, 10 February 2023
• 1991 AIME Problems/Problem 11
  ...math> is not divisible by the square of any prime. Find <math>a+b+c^{}_{}</math>. for (int a=1; a<24; a+=2)
  4 KB (740 words) - 17:46, 24 May 2024
• 1992 AIME Problems/Problem 13
  Triangle <math>ABC</math> has <math>AB=9</math> and <math>BC: AC=40: 41</math>. What's the largest area that this triangle can have? ...<math>\frac{ \sqrt{a^2 + b^2} }{ \sqrt{ (a-9)^2 + b^2 } } = \frac{40}{41}</math>.
  4 KB (703 words) - 02:40, 29 December 2023
• 2005 AMC 10B Problems
  ...2</math>. They sell all the candy bars at a price of two for &#36;<math>1</math>. What was the profit, in dollars? ...0 \qquad \mathrm{(C)} 300 \qquad \mathrm{(D)} 400 \qquad \mathrm{(E)} 500</math>
  12 KB (1,874 words) - 21:20, 23 December 2020
• University of South Carolina High School Math Contest/1993 Exam/Problems
  If the width of a particular rectangle is doubled and the length is increased by 3, then the <cmath> \mathrm{(A) \ } 1 \qquad \mathrm{(B) \ } 2 \qquad \mathrm{(C) \ } 3 \qquad \mathrm{(D)
  14 KB (2,102 words) - 22:03, 26 October 2018
• Balkan MO Problems and Solutions, with authors
  Triangle ABC has a right angle at C. The internal bisectors of angles BAC and ABC meet BC and CA at P and Q respectively. The points M and N are the feet of the perpendiculars from P and Q
  4 KB (371 words) - 16:41, 1 January 2024
• 2007 Cyprus MO/Lyceum/Problems
  ...th>x-y=1</math>, then the value of the expression <math>K=x^2+x-2xy+y^2-y</math> is ...{(B)}\ -2\qquad\mathrm{(C)}\ 1\qquad\mathrm{(D)}\ -1\qquad\mathrm{(E)}\ 0</math>
  13 KB (1,990 words) - 08:29, 19 December 2009
• LaTeX:Layout
  ...his allows you to use the same code in many source files by just including a single line in each source file. ...font size, which is 10pt by default but can be increased to 11pt or 12pt. A reference on other options for this command can be found [http://www.nada.k
  30 KB (5,171 words) - 10:16, 4 April 2021
• LaTeX:Commands
  This page introduces various useful commands for rendering math in LaTeX, as well as instructions for building your own commands. |<math>2^{2}</math>||2^2||<math>\textstyle a_i</math>||a_i
  12 KB (1,898 words) - 15:31, 22 February 2024
• LaTeX:Help
  ==== I'm using a Macintosh. What do I do? ==== ...stall LaTeX and imagemagick on your server to use this. That site also has a TeX Converter that doesn't require LaTeX and Imagemagick.
  7 KB (1,109 words) - 20:01, 8 September 2022
• Chicken McNugget Theorem
  ...bn</math> for [[nonnegative]] integers <math>a, b</math> is <math>mn-m-n</math>. ...of is based on the fact that 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
• 2006 AIME II Problems
  ...a of the hexagonal region is <math>2116(\sqrt{2}+1).</math> Find <math>AB</math>. ...th> is a positive integer. Find the number of possible values for <math>n</math>.
  8 KB (1,350 words) - 12:00, 4 December 2022
• Mandelbrot historical results
  The following is a collection of results for the [[Mandelbrot Competition]]. <tr><td>Jeffrey Chen</td><td>A&M Consolidated High School</td><td align=center>14</td><td align=center>44</t
  16 KB (2,223 words) - 14:34, 25 November 2009
• 2007 AMC 10A Problems
  {{AMC10 Problems|year=2007|ab=A}} ...> discount. Pam buys 5 tickets using a coupon that gives her a <math>30\%</math> discount. How many more dollars does Pam pay than Susan?
  13 KB (2,058 words) - 17:54, 29 March 2024
• 2008 AIME I Problems/Problem 15
  ...not divisible by the <math>n</math>th power of any prime. Find <math>m+n</math>. import three; import math; import cse5; import olympiad;
  6 KB (1,041 words) - 00:54, 1 February 2024
• KGS math club
  A group of people on [http://www.gokgs.com Kiseido Go Server] Mathematics roo ...re and save hints and solution suggestions. In order to write something, I'm afraid you need to register to the AoPS wiki first. After that you're good
  22 KB (3,358 words) - 15:17, 18 July 2017
• 2008 iTest Problems
  ...aughter. Tony is the youngest child. Twins Joshua and Alexis are <math>12</math> years old. When the Kubiks went on vacation to San Diego last year, they spent a day at the San Diego Zoo.
  71 KB (11,749 words) - 01:31, 2 November 2023
• 1989 AJHSME Problems
  <math>(1+11+21+31+41)+(9+19+29+39+49)=</math> ...199 \qquad \text{(C)}\ 200 \qquad \text{(D)}\ 249 \qquad \text{(E)}\ 250</math>
  13 KB (1,765 words) - 11:55, 22 November 2023
• Radical axis
  ...competitions, including the prestigious [[USAMO]]. Therefore, any aspiring math olympian should peruse this material carefully, as it may contain the keys ...that situation. I hope after you read this text, you will become a better math student, armed with another tool to solve difficult problems. But, anyway,
  12 KB (2,125 words) - 08:38, 23 May 2024
• 2002 AMC 12A Problems/Problem 22
  ...ath> at <math>D</math>. What is the probability that <math> BD > 5\sqrt2 </math>? import math;
  2 KB (308 words) - 11:11, 18 July 2023
• 2010 AMC 12A Problems/Problem 7
  ...town. The city's water tower stands 40 meters high, and the top portion is a sphere that holds 100,000 liters of water. Logan's miniature water tower ho ...extbf{(C)}\ 0.4 \qquad \textbf{(D)}\ \frac{4}{\pi} \qquad \textbf{(E)}\ 4</math>
  1 KB (198 words) - 18:08, 28 June 2021
• 2002 AMC 10B Problems/Problem 25
  ...the enlarged list, the mean of the enlarged list is decreased by <math>1</math>. How many integers were in the original list? ...\qquad \mathrm{(C) \ } 6\qquad \mathrm{(D) \ } 7\qquad \mathrm{(E) \ } 8 </math>
  4 KB (679 words) - 19:11, 17 September 2023
• 2010 AMC 12B Problems
  ...during her <math>9</math>-hour work day. The first meeting took <math>45</math> minutes and the second meeting took twice as long. What percent of her wor ...0 \qquad \textbf{(C)}\ 25 \qquad \textbf{(D)}\ 30 \qquad \textbf{(E)}\ 35</math>
  12 KB (1,845 words) - 13:00, 19 February 2020
• Math, Science, and Technology Scholarships
  * [[Intel Science Talent Search]]. One of the oldest and largest math and science scholarship programs. Intel STS winners receive scholarships of ...t important such competition in the world. The 3 ISEF winners each receive a <dollar/>50,000 scholarship. [http://www.sciserv.org/isef website]
  2 KB (278 words) - 22:14, 15 June 2010
• 2010 AMC 12B Problems/Problem 25
  .../math>. What is the largest integer <math>m</math> such that <math>2010^m</math> divides <math>\prod_{n=2}^{5300}\text{pow}(n)</math>?
  4 KB (579 words) - 21:26, 16 February 2021
• 2011 AIME I Problems/Problem 7
  ...<math>x_0</math>, <math>x_1</math> , <math>\dots</math> , <math>x_{2011}</math> such that <cmath>m^{x_0} = \sum_{k = 1}^{2011} m^{x_k}.</cmath>
  10 KB (1,677 words) - 19:59, 29 May 2024
• Olympiad books
  Here is a list of '''Olympiad Books''' that have Olympiad-level problems used to trai *''Inequalities: A Mathematical Olympiad Approach'' - '''Radmila Bulajich Manfrino, Jose Anton
  17 KB (2,261 words) - 00:30, 22 April 2024
• Mock Amc 12
  ...an actual [[AMC]] (American Mathematics Competitions 8, 10, or 12) exam. A number of '''Mock AMC''' competitions have been hosted on the [[Art of Prob ...r more information on Mock AMCs, as well as tips on how to write them, and a complete list of all Mock AMC 10s and Mock AMC 12s.
  18 KB (2,206 words) - 19:41, 24 December 2020
• 2010 AMC 8 Problems
  ...rmain's class, <math>8</math> students in Mr. Newton's class, and <math>9</math> students in Mrs. Young's class taking the AMC 8 this year. How many mathem ...)}\ 27\qquad\textbf{(C)}\ 28\qquad\textbf{(D)}\ 29\qquad\textbf{(E)}\ 30 </math>
  18 KB (2,768 words) - 21:05, 9 January 2024
• Barycentric coordinates
  ...h>, and <math> (0,0,1) </math>. Barycentric coordinates were discovered by Möbius in 1827 (Coxeter 1969, p. 217; Fauvel et al. 1993). The Central NC Math Group published a lecture concerning this topic at https://www.youtube.com/watch?v=KQim7-wrwL
  25 KB (5,106 words) - 11:00, 24 May 2024
• 2017 AMC 8 Problems
  ...textbf{(D) }2+0+1 \times 7\qquad\textbf{(E) }2 \times 0 \times 1 \times 7</math> ...were distributed among the three candidates. If Brenda received <math>36</math> votes, then how many votes were cast all together?
  12 KB (1,771 words) - 21:13, 20 January 2024
• 1974 AHSME Answer Key
  #A #A
  2 KB (233 words) - 06:08, 20 January 2023
• 1950 AHSME Answer Key
  #A #A<!--5-->
  3 KB (443 words) - 06:25, 20 January 2023
• 2012 AMC 8 Problems
  ...many pounds of meat does she need to make <math> 24 </math> hamburgers for a neighborhood picnic? ...ac{1}2\qquad\textbf{(D)}\hspace{.05in}8\qquad\textbf{(E)}\hspace{.05in}9 </math>
  13 KB (1,835 words) - 08:51, 8 March 2024
• 2013 AIME I Problems
  ...les twice as fast as he runs. Tom completes the AIME Triathlon in four and a quarter hours. How many minutes does he spend bicycling? Find the number of five-digit positive integers, <math>n</math>, that satisfy the following conditions:
  9 KB (1,580 words) - 13:07, 24 February 2024
• 2013 AIME I Problems/Problem 6
  ...and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. ...>m=3</math> and <math>n=44</math>. Therefore, <math>m+n=3+44=\boxed{047}</math>.
  5 KB (831 words) - 17:20, 9 January 2024
• 2013 AIME I Problems/Problem 11
  ...math> registered students. The classroom has a very large number, <math>N</math>, of play blocks which satisfies the conditions: (a) If <math>16</math>, <math>15</math>, or <math>14</math> students are present in the class, then in each case all the blocks can be
  9 KB (1,539 words) - 12:48, 20 December 2022
• 2013 AIME II Problems/Problem 10
  ...>c</math> is not divisible by the square of any prime. Find <math>a+b+c+d</math>. import math;
  5 KB (823 words) - 17:57, 29 December 2023
• 2013 IMO Problems/Problem 4
  ...ameter of <math>\omega_2</math>. Prove that <math>X, Y</math> and <math>H</math> are collinear. Draw a good diagram, or use the one below. What do you notice? (In particular, wha
  11 KB (1,991 words) - 01:31, 19 November 2023
• Mock AIME I 2015 Problems
  ...d A. If <math>k</math> is the number that Palmer says, what is <math>20k</math>? ...nd <math>b</math> are positive relatively prime integers. Find <math>a+b</math>.
  9 KB (1,463 words) - 14:48, 12 February 2017
• 2013 AMC 8 Problems
  ...}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5</math> ...lf-pound packages for just \$3 per package." What is the regular price for a full pound of fish, in dollars? (Assume that there are no deals for bulk)
  15 KB (2,162 words) - 20:05, 8 May 2023
• 2014 AIME I Problems/Problem 14
  Let <math>m</math> be the largest real solution to the equation <math>\frac{3}{x-3}+\frac{5}{x-5}+\frac{17}{x-17}+\frac{19}{x-19}=x^2-11x-4</math>
  2 KB (391 words) - 15:09, 13 August 2022
• 2007 iTest Problems/Problem 19
  ...rechaun calls out, "hey, stupid, this is your only chance to win gold from a leprechaun!" ...son a fair coin and tells him to clop it as many times as it takes to flip a head. For each tail Jason flips, the leprechaun promises one gold coin.
  3 KB (397 words) - 01:18, 29 October 2023
• 1964 AHSME Problems
  What is the value of <math>[\log_{10}(5\log_{10}100)]^2</math>? <math>\textbf{(A)}\ \log_{10}50 \qquad
  19 KB (2,907 words) - 14:16, 20 February 2020
• 2013 UNCO Math Contest II Problems
  Twenty-first Annual UNC Math Contest Final Round January 19, 2013. The positive integers are <math>1, 2, 3, 4, \ldots</math>
  11 KB (1,648 words) - 09:55, 20 December 2021
• 2013 UNCO Math Contest II Problems/Problem 10
  Dav designs a robot, which he calls FrankenCoder, to print nonsense text by scrambling el <math>\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|}
  4 KB (536 words) - 03:30, 13 January 2019
• 2011 UNCO Math Contest II Problems
  ...factorial, is computed as <math>n! = 1 \cdot 2 \cdot 3 \cdot 4 \cdots n</math> • The factorials are <math>1, 2, 6, 24, 120, 720,\ldots</math>
  5 KB (846 words) - 22:10, 7 November 2014
• 2014 UNCO Math Contest II Problems/Problem 10
  The March Hare invites <math>11</math> guests to a tea party. He randomly cake. The guests decide to play a game. Each one tries to guess
  2 KB (297 words) - 03:33, 13 January 2019
• 2009 UNCO Math Contest II Problems
  ...such that <math>a+b=c</math> For example, <math>202</math> and <math>178</math> ...but <math>245</math> and <math>317</math> do not have that property. Find A-B*c+3 square.
  5 KB (753 words) - 20:35, 8 February 2024
• 2009 UNCO Math Contest II Problems/Problem 6
  Let each of <math>m</math> distinct points on the positive <math>x</math>-axis be joined to each of <math>n</math> distinct points on
  1 KB (165 words) - 13:46, 12 February 2017
• 2011 UNCO Math Contest II Problems/Problem 2
  Let <math>m</math> and <math>n</math> be positive integers. List all the integers in the set ...math>\underline{cannot}</math> be written in the form <math>m+n+m \cdot n</math>.
  547 bytes (74 words) - 03:20, 13 January 2019
• 2011 UNCO Math Contest II Problems/Problem 4
  ...2+1,\cdots\right\}</math> be the set of all positive squares plus <math>1</math> and ...0,\cdots\right\}</math> be the set of all positive squares plus <math>100</math>.
  1 KB (173 words) - 21:00, 28 August 2015
• 2011 UNCO Math Contest II Problems/Problem 10
  ...n on the blackboard. Select any two, call them <math>m</math> and <math>n</math> and replace these two with the one number <math>m+n+mn</math>. Continue doing this until only one number remains and
  2 KB (398 words) - 15:55, 31 January 2023
• 2011 UNCO Math Contest II Problems/Problem 11
  ...hat are one less than a prime cannot be written in the form <math>m +n +m</math>. {{UNCO Math Contest box|n=II|year=2011|num-b=10|after=Last Question}}
  337 bytes (49 words) - 03:23, 13 January 2019
• 2007 UNCO Math Contest II Problems/Problem 2
  ...egon <math>\frac{4}{5}</math> of the men are married to <math>\frac{3}{7}</math> of the women. What fraction of the adult population is married? Give a possible generalization.
  1 KB (216 words) - 18:49, 29 January 2018
• 2007 UNCO Math Contest II Problems/Problem 6
  (a) Demonstrate that every odd number <math>2n+1</math> can be expressed as a difference of two squares. (b) Demonstrate which even numbers can be expressed as a difference of two squares.
  1 KB (203 words) - 18:49, 29 January 2018
• 2007 UNCO Math Contest II Problems/Problem 9
  A circle is inscribed in an equilateral triangle whose side length is <math>2</math>. Then another circle is inscribed externally
  3 KB (412 words) - 18:49, 29 January 2018
• 2006 UNCO Math Contest II Problems
  If a dart is thrown at the <math>6\times 6</math> target, what is the probability that it will hit the shaded area? [[2006 UNCO Math Contest II Problems/Problem 1|Solution]]
  5 KB (725 words) - 22:15, 7 November 2014
• 2006 UNCO Math Contest II Problems/Problem 7
  ...=e</math> and <math>c=d</math>; in addition, <math>55225=235^2=(235)(235)</math>. ...number <math>abcde</math> that satisfies <math>a=b=e</math> and <math>c=d</math>.
  510 bytes (84 words) - 02:33, 13 January 2019
• 2014 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 8
  ...ions equivalent to <math>\textdollar{15}</math> and <math>\textdollar{44}</math>. The ATM machines in this country can give at a single withdrawer any amount you request as long
  2 KB (355 words) - 21:04, 20 October 2022
• 2014 AMC 8 Problems
  ...is <math>H</math> and Terry's answer is <math>T</math>, what is <math>H-T</math>? ...tbf{(B) }-6\qquad\textbf{(C) }0\qquad\textbf{(D) }6\qquad \textbf{(E) }10</math>
  13 KB (1,957 words) - 12:08, 13 January 2024
• 2015 UNCO Math Contest II Problems
  Twenty-third Annual UNC Math Contest Final Round January 31, 2015. The positive integers are <math>1, 2, 3, 4, \ldots </math> A polynomial is quadratic if its highest power term has power two.
  7 KB (1,151 words) - 15:11, 20 August 2020
• 2015 UNCO Math Contest II Problems/Problem 6
  ...e the property that their product <math>mn</math> is less than <math>2015</math>? ...s 3 cases, and m = 44 contributes 1 case. This sums to <math>\boxed{1197}</math>.
  926 bytes (128 words) - 09:43, 6 March 2024
• Gmaas
  ...999999999999999999999999999999999^{9999999999999999999999999999999999999}</math> years and counting. That's older than he is. EDIT: It is not older than he ...ke and reciprocated the fee," you must pay <math>1,000,000</math> to solve a problem using the Games theorem. You wouldn't waste that much money to solv
  69 KB (11,805 words) - 20:49, 18 December 2019
• 2006 iTest Problems
  <math>\mathrm{(A)}\, 8</math> <math>\mathrm{(A)}\, 15\quad\mathrm{(B)}\, \frac{40}{3}</math>
  31 KB (4,811 words) - 00:02, 4 November 2023
• 1954 AHSME Problems/Problem 37
  ...ath>, <math>PQ</math> extended to <math>D</math> and <math>\angle n</math> a right angle, then: path anglemark2(pair A, pair B, pair C, real t=8, bool flip=false)
  3 KB (560 words) - 10:11, 3 May 2020
• 2017 AMC 12B Problems/Problem 21
  Last year, Isabella took 7 math tests and received 7 different scores, each an integer between 91 and 100, ...)}\ 94\qquad\textbf{(C)}\ 96\qquad\textbf{(D)}\ 98\qquad\textbf{(E)}\ 100</math>
  8 KB (1,381 words) - 20:33, 9 November 2023
• 2018 AMC 10A Problems/Problem 13
  ..., as shown, is folded so that point <math>A</math> falls on point <math>B</math>. What is the length in inches of the crease? label("$A$", (0,0), SW);
  8 KB (1,193 words) - 15:12, 3 July 2023
• 2018 AMC 10A Problems/Problem 4
  ...ecutive periods? (What courses the student takes during the other <math>3</math> periods is of no concern here.) ...tbf{(B) }6\qquad\textbf{(C) }12\qquad\textbf{(D) }18\qquad\textbf{(E) }24</math>
  4 KB (586 words) - 15:57, 2 January 2024
• 2006 iTest Problems/Problem U3
  ...n of the [[2006 iTest]], where solving this problem required the answer of a previous problem. When the problem is rewritten, the T-value is substituted ...math>n</math> are relatively prime positive integers. Compute <math>m + n</math>.
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• 2016 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 7
  For a positive integer <math>n</math> let <math>S(n)</math> denote the function which assigns the sum of all divisors of ...math> are relatively prime positive integers then <math>S(mn) = S(m) S(n)</math>. For
  630 bytes (98 words) - 04:33, 12 January 2019
• 2016 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 8
  Find all non-negative integer solutions of the equation <cmath>n(n+1)=9(m-1)(m+1)</cmath>. {{UNM-PNM Math Contest box|year=2016|n=II|num-b=7|num-a=9}}
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• 2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 4
  ...3),p(5)</math>, and <math>p(7)</math> are perfect squares, but <math>p(2)</math> is not. ...},\overline{c}) = (0,4,-2,18),(1,3,-1,10),(2,6,-4,40),(3,5,-2,27),\ldots </math>
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• 2019 AIME II Problems/Problem 1
  ...and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. pair A = (0,0);
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• 2019 AIME I Problems/Problem 7
  There are positive integers <math>x</math> and <math>y</math> that satisfy the system of equations ...me factors in the prime factorization of <math>y</math>. Find <math>3m+2n</math>.
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• 2019 AIME I Problems/Problem 15
  ...and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. pair O, A, B, P, O1, O2, Q, X, Y;
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• Pascal's Triangle and Pythagorean Theorem
  <math>{n \choose k}={n-1\choose k-1}+{n-1\choose k}</math> ...n}{k}</math> is the binomial coefficient <math>\binom{n}{k} = nCk = C_k^n</math>.
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• 2020 AMC 8 Problems/Problem 6
  Aaron, Darren, Karen, Maren, and Sharon rode on a small train that has five cars that seat one person each. Maren sat in the ...{Karen} \qquad \textbf{(D) }\text{Maren}\qquad \textbf{(E) }\text{Sharon}</math>
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• What is the definition of Pure Mathematics?
  ...is welcomed to edit, BUT ONLY IN GOOD WAYS! The AoPS Secret Governemtn has a backup of this page. That may be true for some areas of math. However, what about geometry, trigonometry, and calculus? And what is the
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• 2020 AIME I Problems/Problem 12
  ...\cdot7^7.</math> Find the number of positive integer divisors of <math>n.</math> ...(n)</math> the highest power of prime <math>p</math> that divides <math>n</math>.
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• Math M Addicts
  ...gularly every Saturday (non-holidays). Math-M-Addicts is also constructing a school program, called Group Z, to build mathematical foundations in school ...l, there are five tiers, increasing in prestige and level: Y, S, L, I, and A. Students are encouraged to go in that order, but students are permitted to
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• 2020 AIME II Problems/Problem 1
  ...of positive integers <math>(m,n)</math> such that <math>{m^2n = 20 ^{20}}</math>. ...m to finding the number of unique perfect square factors of <math>20^{20}</math>.
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• GMAAS
  ...999999999999999999999999999999999^{9999999999999999999999999999999999999}</math> years and counting. That's older than he is. EDIT: It is not older than he
  85 KB (13,971 words) - 18:02, 16 May 2024
• 2019 AMC 8 Problems/Problem 24
  ...e ABC</math> is <math>360</math>, what is the area of <math>\triangle EBF</math>? pair A,B,C,DD,EE,FF;
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• 2020 AMC 10A Problems/Problem 15
  ...<math>n</math> are relatively prime positive integers. What is <math>m+n</math>? ...(B)}\ 5\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 23</math>
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• 2020 AMC 10A Problems/Problem 20
  ...ath> and <math>AE=5.</math> What is the area of quadrilateral <math>ABCD?</math> ...qquad \textbf{(C) } 350 \qquad \textbf{(D) } 360 \qquad \textbf{(E) } 370</math>
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• 2020 AMC 12A Problems/Problem 10
  ...} = \log_4{(\log_4{n})}.</cmath>What is the sum of the digits of <math>n?</math> ...7 \qquad \textbf{(C) } 8 \qquad \textbf{(D) } 11 \qquad \textbf{(E) } 13</math>
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• 2020 AMC 12A Problems/Problem 25
  ...itive integers, has the property that the sum of all real numbers <math>x</math> satisfying <cmath> \lfloor x \rfloor \cdot \{x\} = a \cdot x^2</cmath>
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• 2021 HMC 10
  ...expressed as <math>\frac{m}{n}</math> in the simplest form. Find <math>m</math>. ...\qquad\textbf{(C)} ~179 \qquad\textbf{(D)} ~180 \qquad\textbf{(E)} ~181 </math>
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• 2020 AIME II Problems/Problem 3
  ...and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. ..., we get <math>x=\frac{3}{100}</math> and the answer is <math>\boxed{103}</math>.
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• 2020 AIME II Problems/Problem 4
  ...h>\triangle ABC</math> to <math>\triangle A'B'C'</math>. Find <math>m+x+y</math>. ...h> and <math>A'</math>, <math>x+y=18</math>. Thus <math>90+18=\boxed{108}</math>.
  10 KB (1,542 words) - 13:29, 19 January 2024
• 2020 AIME II Problems/Problem 10
  ...ots +n^3</math> is divided by <math>n+5</math>, the remainder is <math>17</math>. for any positive integer <math>k</math>.
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• Superagh's Olympiad Notes
  ...o this thing is almost the exact same format as Lcz's :P ). (Ok, actually, a LOT of credits to Lcz) NEVERYMIND I"M DOING THIS ON MY BLOG SINCE IT"LL LOAD
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• 2021 AIME I Problems/Problem 10
  ...</math> for relatively prime positive integers <math>m</math> and <math>n</math>, then ...in the form <math>\frac{t}{t+1}</math> for some positive integer <math>t</math>.
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• 2021 AIME I Problems/Problem 11
  ...nd <math>n</math> are relatively prime positive integers. Find <math>m+n.</math> pair A, B, C, D, A1, B1, C1, D1;
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• 2021 AIME I Problems/Problem 12
  ...and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. ...order). Without the loss of generality, assume that <math>a\leq b\leq c.</math>
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• 2021 AIME I Problems/Problem 13
  ...distance between the centers of <math>\omega_1</math> and <math>\omega_2</math>. ...>D\equiv\omega\cap\omega_{1}</math> and <math>E\equiv\omega\cap\omega_{2}</math>. The solution relies on the following key claim:
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• 2021 AIME I Problems/Problem 14
  .... Find the sum of the prime factors in the prime factorization of <math>n</math>. ...y Dirichlet's Theorem (Refer to the <b>Remark</b> section.), such <math>a</math> always exists.
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• 2021 AMC 10B Problems
  How many integer values of <math>x</math> satisfy <math>|x| < 3\pi</math>? ...~10 \qquad\textbf{(C)} ~18 \qquad\textbf{(D)} ~19 \qquad\textbf{(E)} ~20</math>
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• 2022 AIME I Problems/Problem 15
  Let <math>x,</math> <math>y,</math> and <math>z</math> be positive real numbers satisfying the system of equations: ...nd <math>n</math> are relatively prime positive integers. Find <math>m+n.</math>
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• 2020 CIME I Problems
  ...th>. Find the number of ways the knight can reach the point <math>(15,15)</math>. ...es tax of <math>7.5\%</math> is applied on all items. If the total cost of a purchase, after tax, is an integer number of cents, find the minimum possib
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• 2021 AMC 12A Problems/Problem 15
  ...lected. What is the remainder when <math>N</math> is divided by <math>100</math>? ...8\qquad\textbf{(C) } 83\qquad\textbf{(D) } 95\qquad\textbf{(E) } 96\qquad</math>
  8 KB (1,183 words) - 00:36, 27 May 2024
• 2021 AMC 12A Problems/Problem 18
  .../math>. For which of the following numbers <math>x</math> is <math>f(x)<0</math>? ...(C) }\frac79 \qquad \textbf{(D) }\frac76\qquad \textbf{(E) }\frac{25}{11}</math>
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• 2021 AMC 12B Problems/Problem 15
  ...>m</math> and <math>n</math> are positive integers. What is <math>m + n ?</math> pair A=(-2.4638,4.10658);
  4 KB (537 words) - 13:49, 25 February 2024
• 2021 AMC 12B Problems
  How many integer values of <math>x</math> satisfy <math>|x|<3\pi?</math> ...}10 \qquad \textbf{(C) }18 \qquad \textbf{(D) }19 \qquad \textbf{(E) }20</math>
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• 2020 AMC 8 Problems/Problem 24
  ...t is the ratio <math>\frac{d}{s}</math> for this larger value of <math>n?</math> ...{9}{25} \qquad \textbf{(D) }\frac{7}{16} \qquad \textbf{(E) }\frac{9}{16}</math>
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• 2021 April MIMC 10
  ...petition. Feel free to add more solutions beneath the official solution.}</math> What is the sum of <math>2^{3}-(-3^{4})-3^{4}+1</math>?
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• Jason321
  ...the world to remember who I am. One Day My ideas will change the world in a way nobody of you guys ever imagined. See ya in the Top
  550 bytes (102 words) - 06:58, 27 December 2020
• 2021 AMC 12B Problems/Problem 4
  ...ass to the number of students in the afternoon class is <math>\frac{3}{4}</math>. What is the mean of the scores of all the students? ...~75 \qquad\textbf{(C)} ~76 \qquad\textbf{(D)} ~77 \qquad\textbf{(E)} ~78</math>
  3 KB (450 words) - 23:50, 18 July 2023
• 2021 AMC 12B Problems/Problem 12
  ...</math>. What is the average value of all the integers in the set <math>S</math>? ...4 \qquad \textbf{(C) }36.6\qquad \textbf{(D) }36.8 \qquad \textbf{(E) }37</math>
  5 KB (878 words) - 09:56, 20 May 2023
• 2021 AMC 12B Problems/Problem 14
  ...tive integers (in this order). What is the volume of pyramid <math>MABCD?</math> ...textbf{(C) }28\sqrt5\qquad \textbf{(D) }66 \qquad \textbf{(E) }8\sqrt{70}</math>
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• 2021 AIME II Problems/Problem 13
  ...n</math> for which <math>2^n + 5^n - n</math> is a multiple of <math>1000</math>. ...25</math> both divide it. It should be fairly obvious that <math>n \geq 3</math>; so we may break up the initial condition into two sub-conditions.
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• 2021 Fall MIMC 10
  <math>\textit{This is a mock contest of the actual AMC competition.}</math> What is the sum of <math>2^{3}-(-3^{4})-3^{4}+1</math>?
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• 2022 AMC 8 Problems/Problem 24
  ...triangular prism. Suppose that <math>AH = EF = 8</math> and <math>GH = 14</math>. What is the volume of the prism? pair G = (0,0), F = (r,0), C = (r,s), B = (0,s), M = (C+F)/2, I = M + s/2 * dir(-theta);
  3 KB (527 words) - 15:03, 23 November 2023
• 2022 AMC 8 Problems
  ...h Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches? label("$\textbf{Math}$", (2.1,3.7)--(3.9,3.7));
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• 2022 AMC 8 Problems/Problem 4
  ...ted over the line <math>q</math> and then reflected over the line <math>p</math>. What is the resulting image? draw((-1,0)--(1,0)); draw((0,-1)--(0,1)); label("$\textbf{\textsf{M}}$",(0.25,0.6));
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• 2022 AMC 8 Problems/Problem 13
  ..._____ more than twice another, and the sum of the two numbers is <math>28</math>.” ...} 7 \qquad \textbf{(C) } 8 \qquad \textbf{(D) } 9 \qquad \textbf{(E) } 10</math>
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• 2022 AMC 8 Problems/Problem 22
  ...s and Zia start at the same time toward the library, with the bus <math>3</math> stops behind. After how many minutes will Zia board the bus? ...9 \qquad \textbf{(C) } 20 \qquad \textbf{(D) } 21 \qquad \textbf{(E) } 23</math>
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• 2022 AMC 10A Problems/Problem 16
  ...lar box is formed by lengthening each edge of the original box by <math>2</math> ...textbf{(C) } \frac{81}{5} \qquad \textbf{(D) } 30 \qquad \textbf{(E) } 48</math>
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• 2022 AMC 12A Problems/Problem 23
  .... For how many integers with <math>1\le{n}\le{22}</math> is <math>k_n<L_n</math>? ...tbf{(B) }3 \qquad\textbf{(C) }7 \qquad\textbf{(D) }8\qquad\textbf{(E) }10</math>
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• 2022 AMC 12A Problems/Problem 21
  ...+ 1.</cmath> Which of the following polynomials is a factor of <math>P(x)</math>? ...\qquad\textbf{(D)} \, x^6 - x^3 + 1 \qquad\textbf{(E)} \, x^6 + x^3 + 1 </math>
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• 2022 AMC 10A Problems/Problem 22
  ...of the <math>13!</math> possible orderings of the cards will the <math>13</math> cards be picked up in exactly two passes? ...ad \textbf{(C) } 4096 \qquad \textbf{(D) } 8178 \qquad \textbf{(E) } 8191</math>
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• 2022 AMC 12A Problems/Problem 12
  ...in regular tetrahedron <math>ABCD</math>. What is <math>\cos(\angle CMD)</math>? ...ac25 \qquad \textbf{(D) } \frac12 \qquad \textbf{(E) } \frac{\sqrt{3}}{2}</math>
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• 2023 AMC 8 Problems/Problem 15
  ...detour, walking <math>3</math> blocks of equal length instead of <math>1</math> block to reach the next corner. From the time he starts his detour, at wha ...\qquad \textbf{(C)}\ 4.5 \qquad \textbf{(D)}\ 4.8 \qquad \textbf{(E)}\ 5</math>
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• 2024 AMC 8 Problems
  ...bf{(B) } 2\qquad\textbf{(C) } 4\qquad\textbf{(D) } 6\qquad\textbf{(E) } 8</math> ...04\qquad\textbf{(C) } 6.54\qquad\textbf{(D) } 6.9\qquad\textbf{(E) } 6.94</math>
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• 2023 AMC 8 Problems/Problem 16
  ...w many <math>\text{P}</math>s, <math>\text{Q}</math>s, and <math>\text{R}</math>s will appear in the completed table? <math>\textbf{(A)}~132\text{ Ps, }134\text{ Qs, }134\text{ Rs}</math>
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• 2023 AIME I Problems/Problem 1
  ...nd <math>n</math> are relatively prime positive integers. Find <math>m+n.</math> ...only differ by rotations or reflections. In this way, there are <math>14!</math> arrangements without restrictions.
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• 2023 AIME I Problems/Problem 8
  ...ath> and <math>16,</math> respectively. Find the perimeter of <math>ABCD.</math> /* Made by MRENTHUSIASM; inspired by Math Jams. */
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• Daniel Zhou's Profile
  Hi! I'm Daniel Zhou. I post on AOPS solutions to various problems including IMO, US <math>\textbf{IMO}</math>
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• Know the Facts: Gmaas
  ...e contributors section. WARNING: Security details will be checking once in a while, so please edit this page appropriately! ..., though his godly power can turn him into anything, he just prefers to be a cat. As you read on, you will discover more things about him then you will
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• 1993 IMO Problems/Problem 3
  ...piece which has been jumped over is removed. Find those values of <math>n</math> for which the game can end with only one piece remaining on the board. This is a very beautifully done video solution by YouTuber Mr. Math: https://www.youtube.com/watch?v=eAROaUpkgRo
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• 2006 iTest Problems/Ultimate Question
  ...n of the [[2006 iTest]], where solving this problem required the answer of a previous problem. When the problem is rewritten, the T-value is substituted Find the real number <math>x</math> such that
  4 KB (612 words) - 11:13, 4 April 2024
• 2023 AMC 12A Problems/Problem 8
  ...ath> on each of the next three quizzes, her mean will increase by <math>2</math>. What is the mean of her quiz scores currently? ...textbf{(B) }5\qquad\textbf{(C) }6\qquad\textbf{(D) }7\qquad\textbf{(E) }8</math>
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• 2024 AMC 8 Problems/Problem 14
  ...e marked. Traveling along these routes, what is the shortest distance from A to Z in kilometers? ...9 \qquad \textbf{(C)}\ 30 \qquad \textbf{(D)}\ 31 \qquad \textbf{(E)}\ 32</math>
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• 2024 AIME I Problems/Problem 11
  ...<math>n</math> are relatively prime positive integers. What is <math>m+n</math>? ...tion of all the blues now were not previously red.) Thus, we have <math>1</math>.
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• Feuerbach point
  The incircle and nine-point circle of a triangle are tangent to each other at the Feuerbach point of the triangle. <math>1998, 24^{th}</math> Russian math olympiad
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• 2005 iTest Problems
  ...number of distinct permutations of <math>KATHRYN</math>, find <math>K -J</math>. Find the sum of the solutions of <math>x^3 + x + 182 = 0</math>.
  25 KB (3,738 words) - 10:53, 23 April 2024