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2016 AMC 10A Problems/Problem 12

2 KB (302 words) - 01:57, 18 October 2024
2001 AMC 12 Problems/Problem 1
...te|[[2001 AMC 12 Problems|2001 AMC 12 #1]] and [[2001 AMC 10 Problems|2001 AMC 10 #3]]}} ...\textbf{(C)}\ 3S + 6 \qquad\textbf{(D)}\ 2S + 6 \qquad \textbf{(E)}\ 2S + 12</math>

904 bytes (136 words) - 16:10, 15 July 2024
2001 AMC 12 Problems/Problem 2
...te|[[2001 AMC 12 Problems|2001 AMC 12 #2]] and [[2001 AMC 10 Problems|2001 AMC 10 #6]]}}

1,007 bytes (165 words) - 20:31, 27 October 2024
2001 AMC 12 Problems/Problem 3
...te|[[2001 AMC 12 Problems|2001 AMC 12 #3]] and [[2001 AMC 10 Problems|2001 AMC 10 #9]]}}

2 KB (221 words) - 21:40, 15 July 2024
2000 AMC 12 Problems/Problem 1
...te|[[2000 AMC 12 Problems|2000 AMC 12 #1]] and [[2000 AMC 10 Problems|2000 AMC 10 #1]]}} [[Category:Introductory Algebra Problems]]

2 KB (320 words) - 19:37, 30 November 2024
AMC 12 Problems and Solutions
[[AMC 12]] problems and solutions. | 2024 || [[2024_AMC_12A | AMC 12A]] || [[2024_AMC_12B | AMC 12B]]

2 KB (264 words) - 18:26, 8 November 2024
2000 AMC 12 Problems
{{AMC12 Problems|year=2000|ab=}} [[2000 AMC 12 Problems/Problem 1|Solution]]

13 KB (1,948 words) - 10:35, 16 June 2024
2001 AMC 12 Problems
{{AMC12 Problems|year=2001|ab=}} ...2\qquad \text{(C)}\ 3S + 6 \qquad\text{(D)} 2S + 6 \qquad \text{(E)}\ 2S + 12</math>

13 KB (1,957 words) - 12:53, 24 January 2024
2006 AMC 12B Problems/Problem 12
[[Category:Introductory Algebra Problems]]

1 KB (239 words) - 13:29, 17 December 2024
2005 AMC 12B Problems/Problem 12
...[2005 AMC 12B Problems|2005 AMC 12B #12]] and [[2005 AMC 10B Problems|2005 AMC 10B #16]]}} [[Category:Introductory Algebra Problems]]

2 KB (322 words) - 02:57, 11 November 2024
2006 AMC 10A Problems/Problem 12
 MP('8', (16,-12),W);

3 KB (424 words) - 10:14, 17 December 2021
2006 AMC 12A Problems/Problem 12
...2A Problems|2006 AMC 12A #12]] and [[2006 AMC 10A Problems/Problem 14|2006 AMC 10A #14]]}} D((12,-10)--(12,10)); MP('20',(12,0),E);

2 KB (292 words) - 11:56, 17 December 2021
2006 AMC 10B Problems/Problem 12
[[Category:Introductory Algebra Problems]]

1 KB (220 words) - 20:07, 27 November 2023
2005 AMC 10B Problems/Problem 12
...ft(\frac{1}{12}\right)^{12} \qquad \textbf{(B) } \left(\frac{1}{6}\right)^{12} \qquad \textbf{(C) } 2\left(\frac{1}{6}\right)^{11} \qquad \textbf{(D) } \ ...ity is <math>\dfrac{3}{6}\times\left(\dfrac{1}{6}\right)^{11}\times\dbinom{12}{1} = \dfrac{1}{2}\times\left(\dfrac{1}{6}\right)^{11}\times12=\left(\dfrac

3 KB (385 words) - 14:03, 16 June 2022
AMC 12 Problems and Solutions/Tasks
* Problems ** [[2001 AMC 12]]

649 bytes (76 words) - 20:56, 15 February 2011
2000 AMC 12 Problems/Problem 2
...te|[[2000 AMC 12 Problems|2000 AMC 12 #2]] and [[2000 AMC 10 Problems|2000 AMC 10 #2]]}} [[Category:Introductory Algebra Problems]]

1 KB (171 words) - 21:36, 22 December 2024
2000 AMC 12 Problems/Problem 3
...te|[[2000 AMC 12 Problems|2000 AMC 12 #3]] and [[2000 AMC 10 Problems|2000 AMC 10 #3]]}} [[Category:Introductory Algebra Problems]]

1 KB (177 words) - 00:36, 15 July 2024
2000 AMC 12 Problems/Problem 5
...te|[[2000 AMC 12 Problems|2000 AMC 12 #5]] and [[2000 AMC 10 Problems|2000 AMC 10 #9]]}} [[Category:Introductory Algebra Problems]]

1 KB (232 words) - 00:20, 6 September 2024
2000 AMC 12 Problems/Problem 8
...0 AMC 12 Problems|2000 AMC 12 #8]] and [[2000 AMC 10 Problems|2000 AMC 10 #12]]}} ...ecursion from solution 1, we see that the first differences of <math>4, 8, 12, ...</math> form an arithmetic progression, and consequently that the secon

8 KB (1,221 words) - 11:34, 27 November 2024
2000 AMC 12 Problems/Problem 6
...te|[[2000 AMC 12 Problems|2000 AMC 12 #6]] and [[2000 AMC 10 Problems|2000 AMC 10 #11]]}} {{AMC10 box|year=2000|num-b=10|num-a=12}}

2 KB (244 words) - 02:47, 13 August 2024

Page text matches

Pythagorean Theorem
...e many tools in a good geometer's arsenal. A very large number of geometry problems can be solved by building right triangles and applying the Pythagorean Theo <cmath>5-12-13</cmath>

6 KB (978 words) - 12:02, 6 March 2025
List of United States high school mathematics competitions
* [[American Mathematics Competitions]] (AMC) are the largest series of national high school competitions in the United **[[AMC 10]]

6 KB (625 words) - 23:27, 13 January 2025
Resources for mathematics competitions
...tions]]. Look around the AoPSWiki. Individual articles often have sample problems and solutions for many levels of problem solvers. Many also have links to ...ets [//competifyhub.com/resources/ Free Competition Resources for Grades 1-12]

14 KB (1,913 words) - 23:52, 6 March 2025
Mathematics books
...Started is recommended for students who are participating in contests like AMC 8/10 and [[MATHCOUNTS]]. * Intermediate is recommended for students who can expect to pass the AMC 10/12.

23 KB (3,036 words) - 16:38, 1 March 2025
AMC 8
...8 and below, hosted annually by the [[American Mathematics Competitions]] (AMC) to students all over the United States. ...more challenging [[AMC 10]] exam. However, there is no requirement for the AMC 10 besides the fact that you have to be 10<math>^\text{th}</math> grade or

4 KB (584 words) - 19:59, 19 February 2025
AMC 10
...'''American Mathematics Contest 10''' ('''AMC 10'''), along with the [[AMC 12]], are the first exams in the series of exams used to challenge bright stud High scoring AMC 10 and AMC 12 students are invited to take the [[American Invitational Mathematics Examin

4 KB (596 words) - 04:53, 3 February 2025
AMC 12
The '''American Mathematics Contest 12''' ('''AMC 12'''), along with the [[AMC 10]], are the first exams in the series of exams used to challenge bright s High scoring AMC 12 students are invited to take the more challenging [[American Invitational M

5 KB (646 words) - 04:52, 3 February 2025
American Invitational Mathematics Examination
...unior Mathematical Olympiad]] (USAJMO) for qualification from taking the [[AMC 10]]. ...rica]] (MAA). [[Art of Problem Solving]] (AoPS) is a proud sponsor of the AMC.

5 KB (669 words) - 17:19, 11 March 2025
Math Jam
...sessions for discussion of the problems from each year's [[AMC 10]], [[AMC 12]], and [[AIME]] exams.

891 bytes (116 words) - 18:36, 31 January 2025
American Mathematics Competitions
...ion for American Math Contest, used to refer to the AMC 8, AMC 10, and AMC 12. == AMC Contests ==

5 KB (696 words) - 03:47, 24 December 2019
United States of America Mathematical Olympiad
The top 12 students of the USAMO are invited to an awards ceremony in Washington, D.C. ...]] exams. The competition takes place over 2 consecutive days. Each day, 3 problems are given to the students to work for 4.5 hours. Responses are assessed bas

6 KB (836 words) - 04:57, 3 February 2025
Joining an ARML team
...are not planning on extending invites to new students unless scores on the AMC exams or the San Diego Math Olympiad (SDMO) are particularly high. * Performance on problems at practice sessions.

22 KB (3,532 words) - 11:25, 27 September 2024
Simon's Favorite Factoring Trick
...nd make the equation factorable. It can be used to solve more than algebra problems, sometimes going into other topics such as number theory. == Fun Practice Problems ==

4 KB (682 words) - 10:25, 18 February 2025
Discriminant
== Example Problems == * (AMC 12 2005) There are two values of <math>a</math> for which the equation <math>4

4 KB (768 words) - 17:56, 24 June 2024
Fermat's Little Theorem
In contest problems, Fermat's Little Theorem is often used in conjunction with the [[Chinese Re ...ts, x_n) = \left(a + \frac 12 - x_1, a + \frac 12 - x_2, \ldots, a + \frac 12 - x_p\right),</cmath>

15 KB (2,618 words) - 12:03, 19 February 2025
Harmonic mean
...we would be trying to calculate <math>\frac 3{\frac 13 + \frac 16 - \frac 12} = \frac 30</math>, which is obviously problematic. == Problems ==

1 KB (196 words) - 10:25, 23 February 2025
Contest strategies
It's a bad idea to stay up all night solving problems or playing video games because it's easy to get drowsy during the test. Ge ...l aid can help solvers visualize and look for clues. Even in non-geometry problems, drawing pictures can help formulate ideas.

3 KB (544 words) - 14:14, 26 August 2024
Constructive counting
''[[2001 AMC 12 Problems/Problem 16 | 2001 AMC 12 Problem 16]]: A spider has one sock and one shoe for each of its eight legs ...leg has <math>_{14} C_2</math> places in the boxes, the third has <math>_{12} C_2</math>, and so on. The final answer is then the product of the leg's c

13 KB (2,018 words) - 15:31, 10 January 2025
Complementary counting
...don't want, then subtracts that from the total number of possibilities. In problems that involve complex or tedious [[casework]], complementary counting is oft ''[[2006 AMC 10A Problems/Problem 21 | 2006 AMC 10A Problem 21]]: How many four-digit positive integers have at least one d

8 KB (1,192 words) - 17:20, 16 June 2023
2001 AMC 12 Problems/Problem 1
...te|[[2001 AMC 12 Problems|2001 AMC 12 #1]] and [[2001 AMC 10 Problems|2001 AMC 10 #3]]}} ...\textbf{(C)}\ 3S + 6 \qquad\textbf{(D)}\ 2S + 6 \qquad \textbf{(E)}\ 2S + 12</math>

904 bytes (136 words) - 16:10, 15 July 2024

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