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1998 AIME Problems/Problem 2
== Problem == [[Image:AIME_1998-2.png|thumb|300px|right]]

6 KB (913 words) - 16:34, 6 August 2020
1998 AHSME Problems/Problem 2
== Problem 2 == ...and <math>D</math> represent four different digits selected from <math>0,1,2,\ldots ,9.</math> If <math>(A+B)/(C+D)</math> is an integer that is as larg

1,008 bytes (167 words) - 14:28, 5 July 2013
1998 AJHSME Problems/Problem 2
== Problem == ...{c}</math>, what is the value of <math>\begin{tabular}{r|l}3&4 \\ \hline 1&2\end{tabular}</math>?

797 bytes (126 words) - 15:40, 20 October 2016
1998 USAMO Problems/Problem 2
== Problem == C1=circle(O,2);

4 KB (656 words) - 17:26, 20 June 2019
1998 IMO Problems/Problem 2
==Problem== contestants. Prove that k/a ≥ (b − 1)/(2b).

451 bytes (79 words) - 23:47, 18 November 2023
1998 JBMO Problems/Problem 2
==Problem 2== <math>\cos X = \frac{AC ^ {2} + AD ^ {2} - DC ^ {2}}{ 2 \cdot AC \cdot AD }</math>

3 KB (554 words) - 08:31, 2 July 2020
1998 CEMC Gauss (Grade 7) Problems/Problem 2
== Problem == == Solution 2==

651 bytes (98 words) - 16:14, 15 June 2022
1998 APMO Problems/Problem 2
== Problem == ...<math>b</math>, <math>(36a + b)(36b + a)</math> cannot be a power of <math>2</math>.

2 KB (297 words) - 12:50, 22 July 2021
1998 OIM Problems/Problem 2
== Problem ==

564 bytes (96 words) - 15:39, 13 December 2023

Page text matches

MATHCOUNTS
...cluding Art of Problem Solving, the focus of MATHCOUNTS is on mathematical problem solving. Students are eligible for up to three years, but cannot compete be ...er), 2-2.5 (State/National) Target: 1.5 (School), 2 (Chapter), 2-2.5 (State/National)}}

10 KB (1,497 words) - 11:42, 10 March 2024
American Invitational Mathematics Examination
...ministered by the [[Mathematical Association of America]] (MAA). [[Art of Problem Solving]] (AoPS) is a proud sponsor of the AMC! ...blem 1-5: 3 Problem 6-10: 4 Problem 10-12: 5 Problem 12-15: 6}}

8 KB (1,057 words) - 12:02, 25 February 2024
Constructive counting
This is a problem where constructive counting is not the simplest way to proceed. This next e === Example 2 ===

12 KB (1,896 words) - 23:55, 27 December 2023
Fibonacci sequence
...m is the sum of the two preceding it. The first few terms are <math>1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...</math>. ...ion|recursively]] as <math>F_1 = F_2 = 1</math> and <math>F_n=F_{n-1}+F_{n-2}</math> for <math>n \geq 3</math>. This is the simplest nontrivial example

6 KB (957 words) - 23:49, 7 March 2024
Complex number
...mplex numbers''' arise when we try to solve [[equation]]s such as <math> x^2 = -1 </math>. ...from this addition, we are not only able to find the solutions of <math> x^2 = -1 </math> but we can now find ''all'' solutions to ''every'' polynomial.

5 KB (860 words) - 15:36, 10 December 2023
AIME Problems and Solutions
...in the AoPSWiki, please consider adding them. Also, if you notice that a problem in the Wiki differs from the original wording, feel free to correct it. Fi | colspan="2"| [[1999 AIME | AIME]]

3 KB (391 words) - 16:00, 21 February 2024
Olimpiada de Mayo/1997
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1997 I Problems/Problem 1|Problem 1]]

856 bytes (98 words) - 14:53, 3 July 2009
1999 AIME
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1999 AIME Problems/Problem 1|Problem 1]]

1 KB (118 words) - 08:41, 7 September 2011
1998 AIME
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1998 AIME Problems]]

1 KB (114 words) - 08:39, 7 September 2011
1997 AIME
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1997 AIME Problems/Problem 1|Problem 1]]

1 KB (114 words) - 08:39, 7 September 2011
1997 AIME Problems
== Problem 1 == [[1997 AIME Problems/Problem 1|Solution]]

7 KB (1,098 words) - 17:08, 25 June 2020
1998 AIME Problems
{{AIME Problems|year=1998}} == Problem 1 ==

7 KB (1,084 words) - 02:01, 28 November 2023
1999 AIME Problems
== Problem 1 == [[1999 AIME Problems/Problem 1|Solution]]

7 KB (1,094 words) - 13:39, 16 August 2020
1985 AIME Problems/Problem 5
== Problem == ..., a_2, a_3, \ldots</math> is chosen so that <math>a_n = a_{n - 1} - a_{n - 2}</math> for each <math>n \ge 3</math>. What is the sum of the first 2001 te

2 KB (410 words) - 13:37, 1 May 2022
1998 AIME Problems/Problem 15
== Problem == ...have to leave the vertex, so every vertex reached is equivalent to adding 2 more segments. So the degree of each vertex must be even, with the exceptio

9 KB (1,671 words) - 22:10, 15 March 2024
1998 AIME Problems/Problem 14
== Problem == ...angular box has half the volume of an <math>(m + 2)\times(n + 2)\times(p + 2)</math> rectangular box, where <math>m, n,</math> and <math>p</math> are in

2 KB (390 words) - 21:05, 29 May 2023
1998 AIME Problems/Problem 13
== Problem == ...the sum of the complex power sums of all nonempty [[subset]]s of <math>\{1,2,\ldots,n\}.</math> Given that <math>S_8 = - 176 - 64i</math> and <math> S_

2 KB (384 words) - 19:02, 20 October 2023
1998 AIME Problems/Problem 12
== Problem == ...ivisible by the square of any [[prime]]. What is <math>a^{2} + b^{2} + c^{2}</math>?

5 KB (876 words) - 20:27, 9 June 2022
1998 AIME Problems/Problem 11
== Problem == ...that it is of the same length of a face diagonal, making it <math>20\sqrt{2}</math>.

7 KB (1,084 words) - 11:48, 13 August 2023
1998 AIME Problems/Problem 10
== Problem == <cmath>x^2 + (r-100)^2 = (r+100)^2 \Longrightarrow x = 20\sqrt{r}</cmath>

3 KB (496 words) - 13:02, 5 August 2019
1998 AIME Problems/Problem 9
== Problem == label(rotate(45)*"$M_1-M_2\le m$",((m+60)/2,(60-m)/2),NW,fontsize(9));

4 KB (624 words) - 18:34, 18 February 2018
1998 AIME Problems/Problem 8
== Problem == | 0 || 1 || 2 || 3 || 4 || 5 || 6

2 KB (354 words) - 19:37, 24 September 2023
1998 AIME Problems/Problem 7
== Problem == Note that this is an algebraic bijection, we have simplified the problem and essentially removed the odd condition, so now we can finish with plain

5 KB (684 words) - 11:41, 13 August 2023
1998 AIME Problems/Problem 6
== Problem == <math>0 = RC^2 - 112\cdot847</math>

2 KB (254 words) - 19:38, 4 July 2013
1998 AIME Problems/Problem 5
== Problem == Given that <math>A_k = \frac {k(k - 1)}2\cos\frac {k(k - 1)\pi}2,</math> find <math>|A_{19} + A_{20} + \cdots + A_{98}|.</math>

1 KB (225 words) - 02:20, 16 September 2017
1998 AIME Problems/Problem 4
== Problem == Nine tiles are numbered <math>1, 2, 3, \cdots, 9,</math> respectively. Each of three players randomly selects

5 KB (917 words) - 02:37, 12 December 2022
1998 AIME Problems/Problem 3
== Problem == The graph of <math> y^2 + 2xy + 40|x|= 400</math> partitions the plane into several regions. What

1 KB (198 words) - 20:13, 23 February 2018
1998 AIME Problems/Problem 2
== Problem == [[Image:AIME_1998-2.png|thumb|300px|right]]

6 KB (913 words) - 16:34, 6 August 2020
1998 AIME Problems/Problem 1
== Problem == ...<math>k</math> has only 2s and 3s in its prime factorization, or <math>k = 2^a3^b</math>.

2 KB (289 words) - 22:50, 23 April 2024
2000 AIME I Problems/Problem 3
== Problem == ...e [[relatively prime]] positive integers, the [[coefficient]]s of <math>x^{2}</math> and <math>x^{3}</math> are equal. Find <math>a + b</math>.

679 bytes (98 words) - 00:51, 2 November 2023
2000 AIME II Problems/Problem 14
== Problem == ...on <math>(f_1,f_2,f_3,\ldots,f_m)</math>, meaning that <math>k=1!\cdot f_1+2!\cdot f_2+3!\cdot f_3+\cdots+m!\cdot f_m</math>, where each <math>f_i</math

7 KB (1,131 words) - 14:49, 6 April 2023
IMO Problems and Solutions
* [[1959 IMO Problems/Problem 1 | Problem 1]] proposed by Poland * [[1959 IMO Problems/Problem 2 | Problem 2]] proposed by Constantin Ionescu-Tiu, Romania

35 KB (4,009 words) - 20:25, 21 February 2024
Balkan Mathematical Olympiad
...u>Problem 1: 6 Problem 2: 6.5 Problem 3: 7.5 Problem 4: 8}} *In every competition or test there are four problem usually covering [[geometry]], [[number theory]], [[algebra]], and [[combin

4 KB (578 words) - 00:12, 29 August 2018
Junior Balkan Mathematical Olympiad
...ficulty=4 - 6|breakdown=Problem 1: 4 Problem 2/3: 5 Problem 4: 6}} *In every competition or test there are four problem usually covering [[geometry]], [[number theory]], [[algebra]], and [[combin

3 KB (472 words) - 18:49, 2 February 2019
JBMO Problems and Solutions, with authors
* [[1997 JBMO Problems/Problem 1 | Problem 1]] proposed by Bulgaria * [[1997 JBMO Problems/Problem 2 | Problem 2]] proposed by Cyprus

6 KB (524 words) - 17:17, 17 August 2018
Balkan MO Problems and Solutions, with authors
* [[1984 BMO Problems/Problem 1 | Problem 1]] * [[1984 BMO Problems/Problem 2 | Problem 2]]

4 KB (371 words) - 16:41, 1 January 2024
2007 AMC 12A Problems/Problem 22
...ate|[[2007 AMC 12A Problems|2007 AMC 12A #22]] and [[2007 AMC 10A Problems/Problem 25|2007 AMC 10A #25]]}} == Problem ==

15 KB (2,558 words) - 19:33, 4 February 2024
1998 PMWC Problems
== Problem I1 == Calculate: <math>\frac{1*2*3+2*4*6+3*6*9+4*8*12+5*10*15}{1*3*5+2*6*10+3*9*15+4*12*20+5*15*25}</math>

11 KB (1,738 words) - 19:25, 10 March 2015
1997 PMWC Problems/Problem T3
==Problem== ...0 thousands and multiply it by 2 and subtract 5, since we are leaving out 1998 and 1999.

1 KB (202 words) - 14:39, 20 April 2014
1999 AHSME Problems
== Problem 1 == <math>1 - 2 + 3 -4 + \cdots - 98 + 99 = </math>

13 KB (1,945 words) - 18:28, 19 June 2023
1999 USAMO
...contains the full set of test problems. The rest contain each individual problem and its solution. ** [[1999 USAMO Problems/Problem 1 | Problem 1]]

808 bytes (95 words) - 15:27, 29 April 2020
1998 AHSME Problems/Problem 24
== Problem == ...that each <math>d_i</math> can be any of the ten decimal digits <math>0,1,2, \ldots, 9</math>, the number of different memorable telephone numbers is

2 KB (330 words) - 10:14, 10 August 2016
1998 AHSME Problems/Problem 22
== Problem == \qquad\mathrm{(D)}\ 2

1 KB (138 words) - 10:41, 22 April 2016
1998 AHSME Problems/Problem 17
== Problem == : (b) <math>f(0) = 2</math>.

656 bytes (94 words) - 22:16, 28 March 2024
1998 AHSME Problems/Problem 26
== Problem == pair D=(0,0), C=(0,24*3^0.5), A=(46,0), E=(72,0), B=(46+13/2,13*3^.5/2);

3 KB (391 words) - 14:30, 5 July 2013
1998 AHSME Problems/Problem 27
== Problem == [[Image:1998 AHSME num. 27.png]]

3 KB (403 words) - 23:00, 10 August 2020
APMO Problems and Solutions
** [[1989 APMO Problems/Problem 1 | Problem 1]] ** [[1989 APMO Problems/Problem 2 | Problem 2]]

7 KB (626 words) - 21:52, 19 August 2023
1998 APMO
...contains the full set of test problems. The rest contain each individual problem and its solution. * [[1998 APMO Problems|Problems]]

549 bytes (60 words) - 09:45, 30 May 2012
1999 AHSME
...contains the full set of test problems. The rest contain each individual problem and its solution. ** [[1999 AHSME Problems/Problem 1|Problem 1]]

2 KB (178 words) - 13:28, 20 February 2020
1998 AHSME Problems
|year = 1998 == Problem 1 ==

15 KB (2,222 words) - 10:40, 11 August 2020

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