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• International Mathematical Olympiad
  ...le (inclusive and integers only). Full credit is only given for complete, correct solutions. Each solution is intended to be in the form of a [[proof writin
  3 KB (490 words) - 03:32, 23 July 2023
• American High School Mathematics Examination
  For every correct answer: 5 points
  3 KB (388 words) - 23:07, 5 February 2024
• AIME Problems and Solutions
  ...inally, additions to and improvements on the solutions in the AoPSWiki are always welcome.
  3 KB (391 words) - 16:00, 21 February 2024
• 2004 AMC 12A Problems
  On the AMC 12, each correct answer is worth <math>6</math> points, each incorrect answer is worth <math
  13 KB (1,953 words) - 00:31, 26 January 2023
• 2003 AMC 12A Problems
  ...ssumes he is the first to arrive. If each takes what he believes to be the correct share of candy, what fraction of the candy goes unclaimed?
  13 KB (1,955 words) - 21:06, 19 August 2023
• 2002 AMC 12A Problems
  ..., and <math>R</math> the area of the red square. Which of the following is correct?
  12 KB (1,792 words) - 13:06, 19 February 2020
• 2003 AMC 12B Problems
  Cassandra sets her watch to the correct time at noon. At the actual time of 1:00 PM, she notices that her watch rea
  13 KB (1,987 words) - 18:53, 10 December 2022
• 2005 AMC 12B Problems/Problem 22
  Inductive Step: Suppose the formula is correct for <math>z_k</math>, then ...z|</math>. Therefore, the magnitude of <math>\frac{iz_n}{|z_n|}</math> is always <math>1</math>, meaning that all of the numbers in the sequence <math>z_k</
  4 KB (660 words) - 17:40, 24 January 2021
• 2004 AIME I Problems/Problem 6
  ...4}</math> But, this over-counts since it counts numbers like 0213. We can correct for this over-counting. Lock the first digit as 0 and permute 3 other chose
  3 KB (562 words) - 18:12, 4 March 2022
• 2004 AIME II Problems/Problem 7
  ...clear from the problem setup that <math>0<\theta<\frac\pi2</math>, so the correct value is <math>\tan(\theta)=\frac53</math>. Next, extend rays <math>\overri
  9 KB (1,501 words) - 05:34, 30 October 2023
• 1984 AIME Problems
  ...the formula <math>s=30+4c-w</math>, where <math>c</math> is the number of correct answers and <math>w</math> is the number of wrong answers. Students are not
  6 KB (933 words) - 01:15, 19 June 2022
• 1988 AIME Problems
  ...ailable ten-button lock may be opened by depressing -- in any order -- the correct five buttons. The sample shown below has <math>\{1, 2, 3, 6, 9\}</math> as
  6 KB (902 words) - 08:57, 19 June 2021
• 2002 AIME II Problems
  ...bsent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive
  7 KB (1,177 words) - 15:42, 11 August 2023
• 1984 AIME Problems/Problem 10
  ...the formula <math>s=30+4c-w</math>, where <math>c</math> is the number of correct answers and <math>w</math> is the number of wrong answers. (Students are no Let Mary's score, number correct, and number wrong be <math>s,c,w</math> respectively. Then
  7 KB (1,163 words) - 23:53, 28 March 2022
• 1988 AIME Problems/Problem 8
  Since this is an AIME problem, there is exactly one correct answer, and thus, exactly one possible value of <math>f(14,52)</math>.
  4 KB (538 words) - 13:24, 12 October 2021
• 1988 AIME Problems/Problem 1
  ...available ten-button lock may be opened by pressing -- in any order -- the correct five buttons. The sample shown below has <math>\{1,2,3,6,9\}</math> as its
  1 KB (181 words) - 18:23, 26 August 2019
• 2006 AMC 10B Problems/Problem 7
  ...As no other option choice fits, <math>\boxed{\textbf{(A)}-x}</math> is the correct solution.
  1 KB (179 words) - 10:33, 19 August 2022
• 1991 AIME Problems/Problem 6
  THIS SOLUTION IS INCORRECT, PLEASE CORRECT IT IF YOU HAVE TIME!
  3 KB (447 words) - 17:02, 24 November 2023
• 1991 AIME Problems/Problem 1
  ...r of <math>11</math> is <math>(5,11)</math>, and checking shows that it is correct.
  4 KB (628 words) - 22:05, 7 June 2021
• 2006 AMC 10B Problems/Problem 25
  ...way to do the problem is by the process of elimination. The only possible correct choices are the highest powers of each prime, <math>2^3=8</math>, <math>3^2
  5 KB (878 words) - 14:39, 3 December 2023
• 2000 AIME I Problems/Problem 15
  ...th> to <math>96</math> alternate in fake-real-fake-real, where we have the correct order of cards once the first <math>96</math> have moved and we can start p ...the spacing of the cards moved, <math>a</math> is an integer such that the correct first card is moved, and <math>k</math> is an integer greater than or equal
  15 KB (2,673 words) - 19:16, 6 January 2024
• 2000 AIME I Problems/Problem 5
  ...ing <math>2</math> and <math>7</math> for <math>w_1</math> does not give a correct product. Thus, <math>\frac{27}{50}</math> must be a reduced form of the ac
  7 KB (1,011 words) - 20:09, 4 January 2024
• 2001 AIME I Problems/Problem 6
  ...ination counts only one of the permutations; we can say that it counts the correct (ascending order) permutation. ...sformations of the problem, a recursion formula can be a robust way to the correct answer.
  11 KB (1,729 words) - 20:50, 28 November 2023
• 2003 AIME II Problems/Problem 13
  ...th> and <math>C</math>. Oh wait they are symmetric. So then if this is the correct answer, why am I wrong, or what happened to that factor of <math>3</math>?"
  15 KB (2,406 words) - 23:56, 23 November 2023
• 2002 AIME II Problems/Problem 10
  ...bsent-minded professor failed to notice that his calculator was not in the correct angular mode. He was lucky to get the right answer. The two least positive
  2 KB (336 words) - 19:30, 24 June 2020
• 2000 AIME II Problems/Problem 13
  ...math>, so no real solution exists for <math>x</math>. Thus our solution is correct.
  6 KB (1,060 words) - 17:36, 26 April 2024
• 2005 AMC 10B Problems/Problem 24
  ...math>11</math> while <math>(a-b)</math> is a factor of nine (1 or 9). The correct guesses are <math>a = 6, b = 5</math> causing <math>x = 65, y = 56,</math>
  5 KB (845 words) - 19:23, 17 September 2023
• 2006 AMC 12A Problems/Problem 3
  ...h>, we see <math>6\cdot8=30+18</math>. Therefore, we can see our answer is correct.
  1 KB (155 words) - 17:30, 16 December 2021
• 2006 AMC 12A Problems/Problem 8
  Thus, the correct answer is <math>\boxed{\textbf{(C) }3}.</math> Note to readers: make sure to always read the problem VERY carefully before attempting; it could mean the differ
  3 KB (450 words) - 02:00, 13 January 2024
• 2006 AMC 12A Problems/Problem 9
  ...= 72</math>. 28 is not divisible by 3, so we know that this number is not correct. Moving on to 7, <math>13 \cdot 7 = 91</math>. We know that 9 is a multiple
  3 KB (429 words) - 18:14, 26 September 2020
• Furman University Wylie Mathematics Tournament
  The test is scored as 1 point for each correct answer, 0 points for blank answers, and -.25 for incorrect answers except f
  2 KB (365 words) - 21:21, 18 March 2017
• University of South Carolina High School Math Contest/1993 Exam/Problem 20
  ...lifying of the brackets. Open the brackets and you should notice why it is correct. If you are also wondering whether or not if we got all the sets in the abo
  2 KB (263 words) - 18:13, 19 October 2021
• Pierre de Fermat
  ...rn techniques. However, a flaw was discovered soon after. Wiles managed to correct the proof by October 1994, thus solving the last of Fermat's problems. It i
  5 KB (860 words) - 17:10, 21 March 2023
• P versus NP
  The [[Clay Mathematics Institute]] has offered a USD \$1,000,000 prize for a correct solution, as it has listed it as one of its [[Millennium Problems]].
  6 KB (1,104 words) - 15:11, 25 October 2017
• Congruent (geometry)
  ...given side of <math>A'</math> on the straight line <math>a'</math>, we can always find one and only one point <math>B'</math> so that the segment <math>AB</m Every segment is congruent to itself; that is, we always have
  10 KB (1,655 words) - 21:43, 24 March 2022
• 2005 AMC 10A Problems/Problem 4
  So our correct answer choice is <math>\boxed{\textbf{(B) }\frac{2}{5}x^2}</math>
  2 KB (265 words) - 19:07, 25 December 2022
• Derangement
  ...c{1}{1} + \frac{1}{2} - \frac{1}{6}\right) = 2</math>, which we know to be correct.
  3 KB (473 words) - 12:57, 20 February 2024
• Cobb County Math Meets
  ...ive minute, twenty-five question multiple-choice test worth six points per correct response, and ten ciphering questions. Each ciphering question is worth te
  2 KB (307 words) - 20:25, 12 March 2012
• United States of America Computing Olympiad
  ...s. Every test case has equal weight within the problem. For each test case correct, you receive the points for the test case. Programs get 4 seconds per test Each test case will give feedback on how well your program did. Correct test cases show how much time and memory used. Incorrect test cases are dif
  2 KB (297 words) - 01:41, 21 January 2023
• Cyprus Mathematical Olympiad
  ...ts must answer 30 multiple choice mathematics problems in 60 minutes. Each correct answer gives 4 points, each wrong answer subtracts 1 point and no answer gi
  2 KB (366 words) - 14:26, 4 September 2017
• 1999 AMC 8 Problems/Problem 16
  Altogether, Tori answered <math>7 + 12 + 21 = 40</math> questions correct. ...e needed to answer <math>45 - 40 = 5</math> more questions to pass, so the correct answer is <math>\boxed{(B) 5}</math>
  1 KB (167 words) - 20:30, 11 January 2024
• Special relativity
  ...ciple of Relativity says it is impossible to ascertain that one of them is correct while the other is wrong.
  3 KB (538 words) - 23:39, 2 March 2008
• 2001 AMC 8 Problems
  On a twenty-question test, each correct answer is worth 5 points, each unanswered question is worth 1 point and eac
  13 KB (1,994 words) - 13:04, 18 February 2024
• Georgia Tech High School Math Competition
  ...ng questions, each of which contestants have three minutes to answer. Each correct answer is worth five points. Each team's score is determined by the top fou
  3 KB (475 words) - 21:51, 31 December 2013
• Georgia Junior Varsity State Tournament
  ...twenty-five question multiple-choice test. Four points are given for each correct answer, and 1.1 points are given for each blank answer. On this round a [[
  2 KB (324 words) - 10:23, 24 April 2007
• Vestavia Hills High School Math Tournament
  ...ears. The tests consist of 25 questions which are worth 4 point each for a correct answer, minus 1 point for an incorrect answer. Ciphering rounds- 4 of them,
  1 KB (160 words) - 12:31, 27 December 2006
• GCTM State Math Tournament
  ...ons and five free-response questions; a student's score is five points per correct questions, plus one point per answer left blank; there is no penalty for in
  2 KB (353 words) - 17:02, 7 June 2009
• Georgia Southern Invitational Mathematics Tournament
  ...nior high division; a student's score is forty points plus four points per correct question minus one point per incorrect question. No calculators are permit
  1 KB (154 words) - 09:45, 21 March 2010
• Mock AIME 4 2006-2007 Problems/Problem 10
  ...o we divide the whole sum by 3 and we add or subtract <math>q(n)</math> to correct for the integer based on the modularity of the sum with 3
  4 KB (595 words) - 12:14, 25 November 2023
• 2007 AIME II Problems/Problem 14
  The answer is clearly correct, but the proof has a gap, i.e. there is no reason that <math>f(-2)\neq1</ma
  7 KB (1,335 words) - 17:44, 25 January 2022

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