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User contributions
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Mock AMC
2018-04-23T20:42:28Z
<p>Blue8931: /* Mock AMC 10 */</p>
<hr />
<div>A '''Mock AMC''' is a contest intended to mimic an actual [[AMC]] exam. A number of '''Mock AMC''' competitions have been hosted on the [[Art of Problem Solving]] message boards. They are generally made by one community member and then administered for any of the other community members to take. Sometimes, the administrator may ask other people to sign up to write problems for the contest.<br />
<br />
Mock AMC's are usually very popular in the months leading up to the actual [[AMC]] competition. There is no guarantee that community members will make Mock AMC's in any given year, but it's usually a good bet that someone will.<br />
<br />
Feel free to remove mock tests which are not of good quality, or recommend others.<br />
<br />
== Tips for Writing a Mock AMC ==<br />
Anyone can write a Mock AMC and administer it. If you are interested in writing one, here are some tips:<br />
<br />
* Look at past [[AMC]]/[[AHSME]] tests to get a feel for what kind of problems you should write and what difficulty level they should be.<br />
* Look at famous theorems and formulas and see if there's any way you can make a good problem out of them.<br />
* If you're running out of creative juice and decide to pull problems from contests, try using problems from obscure contests first, if possible. This way, even the more experienced test takers will hopefully find problems that they do not already know how to do.<br />
* Pair up with another user on AoPS and write it together. Two minds are much better than one. With just one person, the problems might be biased toward one subject, but with two people, the chances of this happening are smaller.<br />
<br />
== Past Mock AMCs ==<br />
<br />
Listed below are the [higher-quality] Mock AMCs which have been hosted over AoPS in the past. Feel free to add, remove, or recommend.<br />
<br />
Note that the "level" column represents the originally intended difficulty. In other words, if a person makes a mock [[AMC 12]], the level would be "12", even if the problems themselves are much easier. Recommended mock tests are starred.<br />
<br />
=== Mock AMC 12 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" width=80 | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC #1'''<br />
| mathfanatic<br />
| 2003<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9321 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9353 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9572 1-5]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9573 6-10]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9574 11-15]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9575 16-20]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9576 21-25]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9365 Results]<br />
|-<br />
! scope="row" | '''Mock AMC #2'''<br />
| mathfanatic<br />
| 2004<br />
| [http://www.artofproblemsolving.com/community/c5h10497p67837 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10497 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10497 Solutions]<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| JSRosen3<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14138 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14361 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=102483#p102483 Answers] [http://www.artofproblemsolving.com/community/c5h14516 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14489 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC B'''<br />
| beta<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14735 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14764 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14894 Answers] [http://www.artofproblemsolving.com/community/c5h14884 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=105741#p105741 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC C'''<br />
| JGeneson<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15001 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15134 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15251 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15251 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC D'''<br />
| joml88<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=16886 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17888 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17891 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17891 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC E'''<br />
| Silverfalcon<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=21997 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22141 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22344 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22344 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC F'''<br />
| joml88<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22049 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23163 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23177 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23177 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC G'''<br />
| Lucky707<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=24355 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=24974 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=25087 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h25087p157983 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC H'''<br />
| Silverfalcon<br />
| 2005<br />
| [http://www.artofproblemsolving.com/community/c5h24437p154514 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h24437p154514 Problems]<br />
| throughout thread<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC I'''<br />
| white_horse_king88<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=21280 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=25181 Problems]<br />
| n/a<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC J'''<br />
| Silverfalcon<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=47625 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=48129 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=304246#p304246 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=48132 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC K'''<br />
| amirhtlusa<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=49958 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=50515 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=321102#p321102 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=321102#p321102 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC L'''<br />
| amirhtlusa<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=61330 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63041 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63258 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63258 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC M'''<br />
| Silverfalcon<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63542 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=78982 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=79749 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=79749 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC N'''<br />
| chess64<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=98894 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99307 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99344 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99344 Results] / [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99566 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC O'''<br />
| mustafa<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=121312 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=122126 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126071 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126071 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC P'''<br />
| Anirudh<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125029 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=709655#p709655 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=716240#p716240 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=716262#p716262 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125029 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC Q'''<br />
| calc rulz<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125194 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125886 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128102 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128102 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC R'''<br />
| rnwang2<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126107 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=715597#p715597 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127421 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127421 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC S'''<br />
| mysmartmouth<br />
| 2007<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127221 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128689 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131403 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131403 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC T'''<br />
| paladin8<br />
| 2007<br />
| [http://www.artofproblemsolving.com/community/c5h127979p726003 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127979 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC U'''<br />
| Silverfalcon<br />
| 2008<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=184067 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185233 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185238 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185236 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185238 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC V'''<br />
| gfour84<br />
| 2009<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=298452 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1634175#p1634175 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1637429#p1637429 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1637006#p1637006 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=302030 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 12'''<br />
| MathTwo<br />
| 2010<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=319184 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1759276#p1759276 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1778080#p1778080 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=328510 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 2/11'''<br />
| Caelestor<br />
| 2011<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=390907 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2183293#p2183293 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=390907 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 1/12'''<br />
| Lord.of.AMC<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h456321p2563731 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2605537#p2605537 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2610048#p2610048 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2610048#p2610048 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 12'''<br />
| Diehard<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459149 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459710 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2580327#p2580327 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459710 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 12 2012'''<br />
| python123<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=456256 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2576205#p2576205 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h456256p2580610 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h456256p2580610 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| Binomial-theorem<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=473867 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2692082#p2692082 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2717578#p2717578 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2707954#p2707954 Results]<br />
|-<br />
! scope = "row" | '''Almost 2016 Mock AMC 11.5'''<br />
| whatshisbucket<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Problems]<br />
| [http://artofproblemsolving.com/community/c209194_almost_2016_mock_amc_11.5 Solutions]<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Results / Discussion]<br />
|-<br />
! scope = "row" | '''December 2015 Mock AMC 1^3*(3+7)'''<br />
| mathisawesome2169<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5647504 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5647504 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5707101 Results / Discussion]<br />
|-<br />
! scope="row" | '''hnkevin42 Mock AMC 12'''<br />
| hnkevin42<br />
| 2016<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5913294 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Results/Discussion]<br />
|-<br />
! scope="row" | '''Last-Minute Mock AMC 12'''<br />
| CountofMC<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Problems]<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Answers]<br />
| [https://artofproblemsolving.com/community/c4t334444f4_lastminute_mock_amc_12 Results/Discussion]<br />
|}<br />
<br />
=== Mock AMC 10 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 10'''<br />
| #H34N1<br />
| 2008<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=212730 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=214081 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=213727 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=213732 Results/Discussion]<br />
|-<br />
! scope="row" | '''agent's Mock AMC 10'''<br />
| agentcx<br />
| 2009<br />
| [http://www.artofproblemsolving.com/community/c5h331823p1775678 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1781208#p1781208 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/community/c5h331823p1782769 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10 Set'''<br />
| AwesomeToad<br />
| 2010<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=311120 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1762829#p1762829 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1778740#p1778740 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 10/12'''<br />
| djmathman<br />
| 2013<br />
| [http://www.artofproblemsolving.com/community/c5h556673s1_first_mock_amcs_of_the_20132014_season Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3294854 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3324794 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3324794 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10 2014-2015*'''<br />
| AlcumusGuy<br />
| 2014<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=618080&hilit=AlcumusGuy%27s+mock+amc+10 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=618080&hilit=AlcumusGuy%27s+mock+amc+10 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h618080p3710795 Answers/Results]<br />
| [http://artofproblemsolving.com/community/c56018 Problem Discussion]<br />
|-<br />
! scope="row" | '''Kelvin the Frog v2015'''<br />
| BOGTRO<br />
| 2015<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=623373&hilit=Kelvin+the+frog Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=623373&hilit=Kelvin+the+frog Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3731642#p3731642 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3731642#p3731642 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 10/12'''<br />
| joey8189681<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h624714p3741743 Initial Discussion]<br />
| [https://www.dropbox.com/s/1c8hhl6yt2awpix/Mock%20AMC%2010.pdf?dl=0 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h624714p3754593 Answers]<br />
| [http://www.artofproblemsolving.com/community/q2h626092p3756574 Results]<br />
|-<br />
! scope="row" | '''May Mock AMC 10 Contest'''<br />
| azmath333<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1082684_mock_amc_1012_contest Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684_mock_amc_1012_contest Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684p4812575 Answers] [http://www.artofproblemsolving.com/community/c5h1082684p4825662 Solutions]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684p4812575 Results / Discussion] <br />
|-<br />
! scope="row" | '''2015 Mock AMC 10*'''<br />
| droid347<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p4893513 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p4893513 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p5051006 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p5045295 Results / Discussion]<br />
|-<br />
! scope="row" | '''July Mock AMC 10 Contest'''<br />
| akshaygowrish<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1104125_july_mock_amc_10_contest Initial Discussion]<br />
| [https://docs.google.com/document/d/12OXd-mmS_T7SyMcqw1hfvykNlcj-4TR4mMXlRJ09uBg/edit?usp=sharing Problems]<br />
| [https://docs.google.com/document/d/1-Q_w5XNKcRaffvpCLSdoJ51TpRpcDAgYLmV9OlczBCs/edit?usp=sharing Answer Key]<br />
| [http://artofproblemsolving.com/community/c5h1104125p5154283 Results / Discussion]<br />
|-<br />
! scope = "row" |'''August Mock AMC 10'''<br />
| azmath333<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1115462_august_mock_amc_10 Initial Discussion]<br />
| [http://latex.artofproblemsolving.com/miscpdf/augustmockamc10.pdf Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1115462p5270430 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1115462p5270430 Results] / [http://www.artofproblemsolving.com/community/c121880_august_mock_amc_10_discussion_forum Discussion]<br />
|-<br />
! scope = "row" | '''September Mock AMC 10'''<br />
| cpma213<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1137447p5320386 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1137447p5320386 Problems]<br />
| n/a<br />
| [http://artofproblemsolving.com/community/c5h1137447p5479954 Results / Discussion]<br />
|-<br />
! scope = "row" | '''New Year's Mock AMC10*'''<br />
| checkmatetang<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1171366p5627439 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5627439 Problems]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5711384 Answers]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5711384 Results] / [http://artofproblemsolving.com/community/c202656_new_years_mock_amc10_discussion Discussion]<br />
|-<br />
! scope = "row" | '''2015-2016 Mock AMC 10*'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Problems]<br />
| [http://artofproblemsolving.com/community/c147536h1182005_mock_amc10_wrapup Answers]<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 10 2015-2016*'''<br />
| AlcumusGuy<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1177413p5687990 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1177413_mock_amc_10_20152016_released Problems]<br />
| [http://artofproblemsolving.com/community/c212844_mock_amc_10_20152016 Solutions]<br />
| [http://artofproblemsolving.com/community/c5h1177413p5769839 Results / Discussion]<br />
|-<br />
! scope = "row" | '''January 2016 Mock AMC 10*'''<br />
| atmchallenge<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5700377 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5700377 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5838468 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5838468 Results/Discussion]<br />
|-<br />
! scope = "row" | '''2015-2016 Mock AMC 10* #2'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1188467 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1188467 Problems]<br />
| [http://artofproblemsolving.com/community/c147536h1175930 Solutions]<br />
| [http://artofproblemsolving.com/community/c5h1188467 Results / Discussion]<br />
|-<br />
<br />
! scope="row" | '''MeepyMeepMeep Mock AMC 10'''<br />
| MeepyMeepMeep, speck<br />
| 2016<br />
| [http://artofproblemsolving.com/community/c5h1195432p5852002 Initial Discussion]<br />
| [https://www.dropbox.com/s/uw0herhuqk8zbp5/Mock%20AMC%2010.pdf?dl=0 Problems]<br />
| n/a<br />
| n/a<br />
|- <br />
<br />
!scope="row" | eisirrational's Mock AMC 10<br />
| eisirrational, illogical_21, whatshisbucket<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1372991_eisirrationals_mock_amc_10 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c5h1372991_eisirrationals_mock_amc_10 Problems]<br />
| [http://artofproblemsolving.com/community/c418591h1392426p7811150 Answer Key]<br />
| [https://artofproblemsolving.com/community/c418591_mock_amc_10_discussion Discussion]<br />
|-<br />
<br />
!scope="row" | Summer Mock AMC 10<br />
| Rowechen, OmicronGamma, FedeX333X, KenV, kvedula2004, ItzVineeth<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1471834_summer_mock_amc_series Initial Discussion]<br />
| [https://drive.google.com/file/d/0B3M-fxa6QG0_ODNpSnJZcEt3djQ/view Problems]<br />
| [http://latex.artofproblemsolving.com/miscpdf/hehdrwpi.pdf?t=1500270651030 Answers]<br />
| [https://artofproblemsolving.com/community/c481237_2017_summer_mock_amc_10_discussion_forum Statistics / Discussion]<br />
|-<br />
<br />
!scope="row" | scrabbler94's Mock AMC 10<br />
| scrabbler94<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Problems]<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Answers]<br />
| [http://artofproblemsolving.com/community/c5h1569848p9704902 Results] / [https://artofproblemsolving.com/community/c593716_scrabbler94s_mock_amc_10_discussion Discussion]<br />
|-<br />
! scope="row" | '''2018 Mock AMC 10'''<br />
| blue8931<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c594864h1606066 Initial Discussion]<br />
| [https://artofproblemsolving.com/downloads/printable_post_collections/628064 Problems]<br />
| [https://artofproblemsolving.com/community/c628116h1632436_official_answer_key Answer Key]<br />
| [https://artofproblemsolving.com/community/c628116_2018_mock_amc_10_discussion_forum Results / Discussion]<br />
|-<br />
<br />
|}<br />
<br />
=== Mock AMC 8 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" width=80 | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| mathfanatic<br />
| 2004<br />
| [http://www.artofproblemsolving.com/community/c5h15878p111575 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15878 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=114070#p114070 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h15878p114404 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| 13375P34K43V312<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=107507 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=108455 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=630802#p630802 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h108455p623522 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| ahaanomegas<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h459346p2577870 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2598111#p2598111 Problems]<br />
| n/a<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| utahjazz<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h485041p2717878 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2728186#p2728186 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2731391#p2731391 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| iNomOnCountdown<br />
| 2014<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&hilit=iNomonCountdown%27s+mock+amc+8 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&hilit=iNomonCountdown%27s+mock+amc+8 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&start=0 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&start=0 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8'''<br />
| Tan<br />
| 2014<br />
| [http://www.artofproblemsolving.com/community/c5h613297p3648226 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h613297p3648227 Problems]<br />
| [https://docs.google.com/spreadsheets/d/1U1QJ9r4r2xFbRByk9gXOhEVV48ScjoLWZp4IFanbKF0/edit#gid=1475864782 Answers]<br />
| [https://docs.google.com/spreadsheets/d/1U1QJ9r4r2xFbRByk9gXOhEVV48ScjoLWZp4IFanbKF0/edit#gid=1475864782 Results / Discussion]<br />
|-<br />
! scope = "row" | '''2015 Hard Mock AMC 8*'''<br />
| Not_a_Username, 8invalid8<br />
| 2015<br />
| [http://artofproblemsolving.com/community/q1h1128391p5227860 Initial Discussion]<br />
| [http://latex.artofproblemsolving.com/miscpdf/kashimyo.pdf Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1128391p5423312 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1128391p5423312 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c3h1152332p5457736 Initial Discussion]<br />
| [http://artofproblemsolving.com/downloads/printable_post_collections/163667 Problems]<br />
| [http://artofproblemsolving.com/community/category-admin/165328 Forum]<br />
| [http://artofproblemsolving.com/community/c165328h1155882p5484131 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8 #2'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c3h1167425p5586244 Initial Discussion]<br />
| [http://artofproblemsolving.com/downloads/printable_post_collections/165838 Problems]<br />
| [http://artofproblemsolving.com/community/c147536_the_mock_amc_8_forum Forum]<br />
| [http://artofproblemsolving.com/community/c3h1167425p5586244 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8 2015'''<br />
| Alberty44<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c194276_discusssion Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1168822p5674003 Problems]<br />
| n/a<br />
| [http://artofproblemsolving.com/community/c194276h1175928p5673996 Results/Discussion]<br />
|-<br />
! scope = "row" | '''Christmas AMC 8'''<br />
| Mudkipswims42<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1177489p5688588 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1177489p5688588 Problems]<br />
| [http://www.artofproblemsolving.com/community/c229455_christmas_amc8_discussion_forum Forum]<br />
| [http://artofproblemsolving.com/community/c5h1177489p5880200 Results/Discussion]<br />
|- <br />
<br />
! scope = "row" | '''Mock AMC 8!'''<br />
| eisirrational, pretzel, AOPS12142015, Th3Numb3rThr33, e_power_pi_times_i<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1526187_mock_amc_8 Initial Discussion]<br />
| [http://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvYi84LzFkNzUyMWYwZTViOTQ1MzRmZmU3ODE0NmI2MzIzMGUxNjA2MTcwLnBkZg==&rn=TW9jayBBTUMgOCB2Ny5wZGY= Problems]<br />
| [http://artofproblemsolving.com/community/c3h1545004p9368333 Answer Key/Solutions]<br />
| [https://artofproblemsolving.com/community/c561318_mock_amc_8_2017_discussion Discussion]<br />
|}<br />
<br />
----<br />
<br />
== See also ==<br />
* [[American Mathematics Competitions]]<br />
* [[Math books]]<br />
* [[Mathematics competitions]]<br />
* [[Mock AIME]]<br />
* [[Mock MathCounts]]<br />
* [[Mock USAMO]]<br />
* [[Mock USAJMO]]<br />
* [[Resources for mathematics competitions]]<br />
* [[AoPS Past Contests]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AMC&diff=94183
Mock AMC
2018-04-23T20:42:13Z
<p>Blue8931: /* Mock AMC 10 */</p>
<hr />
<div>A '''Mock AMC''' is a contest intended to mimic an actual [[AMC]] exam. A number of '''Mock AMC''' competitions have been hosted on the [[Art of Problem Solving]] message boards. They are generally made by one community member and then administered for any of the other community members to take. Sometimes, the administrator may ask other people to sign up to write problems for the contest.<br />
<br />
Mock AMC's are usually very popular in the months leading up to the actual [[AMC]] competition. There is no guarantee that community members will make Mock AMC's in any given year, but it's usually a good bet that someone will.<br />
<br />
Feel free to remove mock tests which are not of good quality, or recommend others.<br />
<br />
== Tips for Writing a Mock AMC ==<br />
Anyone can write a Mock AMC and administer it. If you are interested in writing one, here are some tips:<br />
<br />
* Look at past [[AMC]]/[[AHSME]] tests to get a feel for what kind of problems you should write and what difficulty level they should be.<br />
* Look at famous theorems and formulas and see if there's any way you can make a good problem out of them.<br />
* If you're running out of creative juice and decide to pull problems from contests, try using problems from obscure contests first, if possible. This way, even the more experienced test takers will hopefully find problems that they do not already know how to do.<br />
* Pair up with another user on AoPS and write it together. Two minds are much better than one. With just one person, the problems might be biased toward one subject, but with two people, the chances of this happening are smaller.<br />
<br />
== Past Mock AMCs ==<br />
<br />
Listed below are the [higher-quality] Mock AMCs which have been hosted over AoPS in the past. Feel free to add, remove, or recommend.<br />
<br />
Note that the "level" column represents the originally intended difficulty. In other words, if a person makes a mock [[AMC 12]], the level would be "12", even if the problems themselves are much easier. Recommended mock tests are starred.<br />
<br />
=== Mock AMC 12 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" width=80 | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC #1'''<br />
| mathfanatic<br />
| 2003<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9321 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9353 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9572 1-5]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9573 6-10]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9574 11-15]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9575 16-20]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9576 21-25]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9365 Results]<br />
|-<br />
! scope="row" | '''Mock AMC #2'''<br />
| mathfanatic<br />
| 2004<br />
| [http://www.artofproblemsolving.com/community/c5h10497p67837 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10497 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10497 Solutions]<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| JSRosen3<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14138 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14361 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=102483#p102483 Answers] [http://www.artofproblemsolving.com/community/c5h14516 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14489 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC B'''<br />
| beta<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14735 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14764 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14894 Answers] [http://www.artofproblemsolving.com/community/c5h14884 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=105741#p105741 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC C'''<br />
| JGeneson<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15001 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15134 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15251 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15251 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC D'''<br />
| joml88<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=16886 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17888 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17891 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17891 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC E'''<br />
| Silverfalcon<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=21997 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22141 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22344 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22344 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC F'''<br />
| joml88<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22049 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23163 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23177 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23177 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC G'''<br />
| Lucky707<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=24355 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=24974 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=25087 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h25087p157983 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC H'''<br />
| Silverfalcon<br />
| 2005<br />
| [http://www.artofproblemsolving.com/community/c5h24437p154514 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h24437p154514 Problems]<br />
| throughout thread<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC I'''<br />
| white_horse_king88<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=21280 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=25181 Problems]<br />
| n/a<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC J'''<br />
| Silverfalcon<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=47625 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=48129 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=304246#p304246 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=48132 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC K'''<br />
| amirhtlusa<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=49958 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=50515 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=321102#p321102 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=321102#p321102 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC L'''<br />
| amirhtlusa<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=61330 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63041 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63258 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63258 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC M'''<br />
| Silverfalcon<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63542 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=78982 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=79749 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=79749 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC N'''<br />
| chess64<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=98894 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99307 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99344 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99344 Results] / [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99566 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC O'''<br />
| mustafa<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=121312 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=122126 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126071 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126071 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC P'''<br />
| Anirudh<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125029 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=709655#p709655 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=716240#p716240 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=716262#p716262 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125029 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC Q'''<br />
| calc rulz<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125194 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125886 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128102 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128102 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC R'''<br />
| rnwang2<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126107 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=715597#p715597 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127421 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127421 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC S'''<br />
| mysmartmouth<br />
| 2007<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127221 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128689 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131403 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131403 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC T'''<br />
| paladin8<br />
| 2007<br />
| [http://www.artofproblemsolving.com/community/c5h127979p726003 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127979 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC U'''<br />
| Silverfalcon<br />
| 2008<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=184067 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185233 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185238 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185236 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185238 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC V'''<br />
| gfour84<br />
| 2009<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=298452 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1634175#p1634175 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1637429#p1637429 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1637006#p1637006 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=302030 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 12'''<br />
| MathTwo<br />
| 2010<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=319184 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1759276#p1759276 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1778080#p1778080 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=328510 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 2/11'''<br />
| Caelestor<br />
| 2011<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=390907 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2183293#p2183293 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=390907 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 1/12'''<br />
| Lord.of.AMC<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h456321p2563731 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2605537#p2605537 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2610048#p2610048 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2610048#p2610048 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 12'''<br />
| Diehard<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459149 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459710 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2580327#p2580327 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459710 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 12 2012'''<br />
| python123<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=456256 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2576205#p2576205 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h456256p2580610 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h456256p2580610 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| Binomial-theorem<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=473867 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2692082#p2692082 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2717578#p2717578 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2707954#p2707954 Results]<br />
|-<br />
! scope = "row" | '''Almost 2016 Mock AMC 11.5'''<br />
| whatshisbucket<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Problems]<br />
| [http://artofproblemsolving.com/community/c209194_almost_2016_mock_amc_11.5 Solutions]<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Results / Discussion]<br />
|-<br />
! scope = "row" | '''December 2015 Mock AMC 1^3*(3+7)'''<br />
| mathisawesome2169<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5647504 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5647504 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5707101 Results / Discussion]<br />
|-<br />
! scope="row" | '''hnkevin42 Mock AMC 12'''<br />
| hnkevin42<br />
| 2016<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5913294 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Results/Discussion]<br />
|-<br />
! scope="row" | '''Last-Minute Mock AMC 12'''<br />
| CountofMC<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Problems]<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Answers]<br />
| [https://artofproblemsolving.com/community/c4t334444f4_lastminute_mock_amc_12 Results/Discussion]<br />
|}<br />
<br />
=== Mock AMC 10 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 10'''<br />
| #H34N1<br />
| 2008<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=212730 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=214081 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=213727 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=213732 Results/Discussion]<br />
|-<br />
! scope="row" | '''agent's Mock AMC 10'''<br />
| agentcx<br />
| 2009<br />
| [http://www.artofproblemsolving.com/community/c5h331823p1775678 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1781208#p1781208 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/community/c5h331823p1782769 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10 Set'''<br />
| AwesomeToad<br />
| 2010<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=311120 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1762829#p1762829 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1778740#p1778740 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 10/12'''<br />
| djmathman<br />
| 2013<br />
| [http://www.artofproblemsolving.com/community/c5h556673s1_first_mock_amcs_of_the_20132014_season Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3294854 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3324794 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3324794 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10 2014-2015*'''<br />
| AlcumusGuy<br />
| 2014<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=618080&hilit=AlcumusGuy%27s+mock+amc+10 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=618080&hilit=AlcumusGuy%27s+mock+amc+10 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h618080p3710795 Answers/Results]<br />
| [http://artofproblemsolving.com/community/c56018 Problem Discussion]<br />
|-<br />
! scope="row" | '''Kelvin the Frog v2015'''<br />
| BOGTRO<br />
| 2015<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=623373&hilit=Kelvin+the+frog Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=623373&hilit=Kelvin+the+frog Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3731642#p3731642 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3731642#p3731642 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 10/12'''<br />
| joey8189681<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h624714p3741743 Initial Discussion]<br />
| [https://www.dropbox.com/s/1c8hhl6yt2awpix/Mock%20AMC%2010.pdf?dl=0 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h624714p3754593 Answers]<br />
| [http://www.artofproblemsolving.com/community/q2h626092p3756574 Results]<br />
|-<br />
! scope="row" | '''May Mock AMC 10 Contest'''<br />
| azmath333<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1082684_mock_amc_1012_contest Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684_mock_amc_1012_contest Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684p4812575 Answers] [http://www.artofproblemsolving.com/community/c5h1082684p4825662 Solutions]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684p4812575 Results / Discussion] <br />
|-<br />
! scope="row" | '''2015 Mock AMC 10*'''<br />
| droid347<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p4893513 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p4893513 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p5051006 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p5045295 Results / Discussion]<br />
|-<br />
! scope="row" | '''July Mock AMC 10 Contest'''<br />
| akshaygowrish<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1104125_july_mock_amc_10_contest Initial Discussion]<br />
| [https://docs.google.com/document/d/12OXd-mmS_T7SyMcqw1hfvykNlcj-4TR4mMXlRJ09uBg/edit?usp=sharing Problems]<br />
| [https://docs.google.com/document/d/1-Q_w5XNKcRaffvpCLSdoJ51TpRpcDAgYLmV9OlczBCs/edit?usp=sharing Answer Key]<br />
| [http://artofproblemsolving.com/community/c5h1104125p5154283 Results / Discussion]<br />
|-<br />
! scope = "row" |'''August Mock AMC 10'''<br />
| azmath333<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1115462_august_mock_amc_10 Initial Discussion]<br />
| [http://latex.artofproblemsolving.com/miscpdf/augustmockamc10.pdf Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1115462p5270430 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1115462p5270430 Results] / [http://www.artofproblemsolving.com/community/c121880_august_mock_amc_10_discussion_forum Discussion]<br />
|-<br />
! scope = "row" | '''September Mock AMC 10'''<br />
| cpma213<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1137447p5320386 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1137447p5320386 Problems]<br />
| n/a<br />
| [http://artofproblemsolving.com/community/c5h1137447p5479954 Results / Discussion]<br />
|-<br />
! scope = "row" | '''New Year's Mock AMC10*'''<br />
| checkmatetang<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1171366p5627439 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5627439 Problems]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5711384 Answers]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5711384 Results] / [http://artofproblemsolving.com/community/c202656_new_years_mock_amc10_discussion Discussion]<br />
|-<br />
! scope = "row" | '''2015-2016 Mock AMC 10*'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Problems]<br />
| [http://artofproblemsolving.com/community/c147536h1182005_mock_amc10_wrapup Answers]<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 10 2015-2016*'''<br />
| AlcumusGuy<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1177413p5687990 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1177413_mock_amc_10_20152016_released Problems]<br />
| [http://artofproblemsolving.com/community/c212844_mock_amc_10_20152016 Solutions]<br />
| [http://artofproblemsolving.com/community/c5h1177413p5769839 Results / Discussion]<br />
|-<br />
! scope = "row" | '''January 2016 Mock AMC 10*'''<br />
| atmchallenge<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5700377 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5700377 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5838468 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5838468 Results/Discussion]<br />
|-<br />
! scope = "row" | '''2015-2016 Mock AMC 10* #2'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1188467 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1188467 Problems]<br />
| [http://artofproblemsolving.com/community/c147536h1175930 Solutions]<br />
| [http://artofproblemsolving.com/community/c5h1188467 Results / Discussion]<br />
|-<br />
<br />
! scope="row" | '''MeepyMeepMeep Mock AMC 10'''<br />
| MeepyMeepMeep, speck<br />
| 2016<br />
| [http://artofproblemsolving.com/community/c5h1195432p5852002 Initial Discussion]<br />
| [https://www.dropbox.com/s/uw0herhuqk8zbp5/Mock%20AMC%2010.pdf?dl=0 Problems]<br />
| n/a<br />
| n/a<br />
|- <br />
<br />
!scope="row" | eisirrational's Mock AMC 10<br />
| eisirrational, illogical_21, whatshisbucket<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1372991_eisirrationals_mock_amc_10 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c5h1372991_eisirrationals_mock_amc_10 Problems]<br />
| [http://artofproblemsolving.com/community/c418591h1392426p7811150 Answer Key]<br />
| [https://artofproblemsolving.com/community/c418591_mock_amc_10_discussion Discussion]<br />
|-<br />
<br />
!scope="row" | Summer Mock AMC 10<br />
| Rowechen, OmicronGamma, FedeX333X, KenV, kvedula2004, ItzVineeth<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1471834_summer_mock_amc_series Initial Discussion]<br />
| [https://drive.google.com/file/d/0B3M-fxa6QG0_ODNpSnJZcEt3djQ/view Problems]<br />
| [http://latex.artofproblemsolving.com/miscpdf/hehdrwpi.pdf?t=1500270651030 Answers]<br />
| [https://artofproblemsolving.com/community/c481237_2017_summer_mock_amc_10_discussion_forum Statistics / Discussion]<br />
|-<br />
<br />
!scope="row" | scrabbler94's Mock AMC 10<br />
| scrabbler94<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Problems]<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Answers]<br />
| [http://artofproblemsolving.com/community/c5h1569848p9704902 Results] / [https://artofproblemsolving.com/community/c593716_scrabbler94s_mock_amc_10_discussion Discussion]<br />
|-<br />
! scope="row" | '''2018 Mock AMC 10'''<br />
| blue8931<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c594864h1606066 Initial Discussion]<br />
| [https://artofproblemsolving.com/downloads/printable_post_collections/628064 Problems]<br />
| [https://artofproblemsolving.com/community/c628116h1632436_official_answer_key Answer Key]<br />
| [https://artofproblemsolving.com/community/c628116_2018_mock_amc_10_discussion_forum Results/Discussion]<br />
|-<br />
<br />
|}<br />
<br />
=== Mock AMC 8 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" width=80 | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| mathfanatic<br />
| 2004<br />
| [http://www.artofproblemsolving.com/community/c5h15878p111575 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15878 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=114070#p114070 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h15878p114404 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| 13375P34K43V312<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=107507 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=108455 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=630802#p630802 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h108455p623522 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| ahaanomegas<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h459346p2577870 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2598111#p2598111 Problems]<br />
| n/a<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| utahjazz<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h485041p2717878 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2728186#p2728186 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2731391#p2731391 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| iNomOnCountdown<br />
| 2014<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&hilit=iNomonCountdown%27s+mock+amc+8 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&hilit=iNomonCountdown%27s+mock+amc+8 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&start=0 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&start=0 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8'''<br />
| Tan<br />
| 2014<br />
| [http://www.artofproblemsolving.com/community/c5h613297p3648226 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h613297p3648227 Problems]<br />
| [https://docs.google.com/spreadsheets/d/1U1QJ9r4r2xFbRByk9gXOhEVV48ScjoLWZp4IFanbKF0/edit#gid=1475864782 Answers]<br />
| [https://docs.google.com/spreadsheets/d/1U1QJ9r4r2xFbRByk9gXOhEVV48ScjoLWZp4IFanbKF0/edit#gid=1475864782 Results / Discussion]<br />
|-<br />
! scope = "row" | '''2015 Hard Mock AMC 8*'''<br />
| Not_a_Username, 8invalid8<br />
| 2015<br />
| [http://artofproblemsolving.com/community/q1h1128391p5227860 Initial Discussion]<br />
| [http://latex.artofproblemsolving.com/miscpdf/kashimyo.pdf Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1128391p5423312 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1128391p5423312 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c3h1152332p5457736 Initial Discussion]<br />
| [http://artofproblemsolving.com/downloads/printable_post_collections/163667 Problems]<br />
| [http://artofproblemsolving.com/community/category-admin/165328 Forum]<br />
| [http://artofproblemsolving.com/community/c165328h1155882p5484131 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8 #2'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c3h1167425p5586244 Initial Discussion]<br />
| [http://artofproblemsolving.com/downloads/printable_post_collections/165838 Problems]<br />
| [http://artofproblemsolving.com/community/c147536_the_mock_amc_8_forum Forum]<br />
| [http://artofproblemsolving.com/community/c3h1167425p5586244 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8 2015'''<br />
| Alberty44<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c194276_discusssion Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1168822p5674003 Problems]<br />
| n/a<br />
| [http://artofproblemsolving.com/community/c194276h1175928p5673996 Results/Discussion]<br />
|-<br />
! scope = "row" | '''Christmas AMC 8'''<br />
| Mudkipswims42<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1177489p5688588 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1177489p5688588 Problems]<br />
| [http://www.artofproblemsolving.com/community/c229455_christmas_amc8_discussion_forum Forum]<br />
| [http://artofproblemsolving.com/community/c5h1177489p5880200 Results/Discussion]<br />
|- <br />
<br />
! scope = "row" | '''Mock AMC 8!'''<br />
| eisirrational, pretzel, AOPS12142015, Th3Numb3rThr33, e_power_pi_times_i<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1526187_mock_amc_8 Initial Discussion]<br />
| [http://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvYi84LzFkNzUyMWYwZTViOTQ1MzRmZmU3ODE0NmI2MzIzMGUxNjA2MTcwLnBkZg==&rn=TW9jayBBTUMgOCB2Ny5wZGY= Problems]<br />
| [http://artofproblemsolving.com/community/c3h1545004p9368333 Answer Key/Solutions]<br />
| [https://artofproblemsolving.com/community/c561318_mock_amc_8_2017_discussion Discussion]<br />
|}<br />
<br />
----<br />
<br />
== See also ==<br />
* [[American Mathematics Competitions]]<br />
* [[Math books]]<br />
* [[Mathematics competitions]]<br />
* [[Mock AIME]]<br />
* [[Mock MathCounts]]<br />
* [[Mock USAMO]]<br />
* [[Mock USAJMO]]<br />
* [[Resources for mathematics competitions]]<br />
* [[AoPS Past Contests]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AMC&diff=93291
Mock AMC
2018-03-16T22:12:13Z
<p>Blue8931: /* Mock AMC 10 */</p>
<hr />
<div>A '''Mock AMC''' is a contest intended to mimic an actual [[AMC]] exam. A number of '''Mock AMC''' competitions have been hosted on the [[Art of Problem Solving]] message boards. They are generally made by one community member and then administered for any of the other community members to take. Sometimes, the administrator may ask other people to sign up to write problems for the contest.<br />
<br />
Mock AMC's are usually very popular in the months leading up to the actual [[AMC]] competition. There is no guarantee that community members will make Mock AMC's in any given year, but it's usually a good bet that someone will.<br />
<br />
Feel free to remove mock tests which are not of good quality, or recommend others.<br />
<br />
== Tips for Writing a Mock AMC ==<br />
Anyone can write a Mock AMC and administer it. If you are interested in writing one, here are some tips:<br />
<br />
* Look at past [[AMC]]/[[AHSME]] tests to get a feel for what kind of problems you should write and what difficulty level they should be.<br />
* Look at famous theorems and formulas and see if there's any way you can make a good problem out of them.<br />
* If you're running out of creative juice and decide to pull problems from contests, try using problems from obscure contests first, if possible. This way, even the more experienced test takers will hopefully find problems that they do not already know how to do.<br />
* Pair up with another user on AoPS and write it together. Two minds are much better than one. With just one person, the problems might be biased toward one subject, but with two people, the chances of this happening are smaller.<br />
<br />
== Past Mock AMCs ==<br />
<br />
Listed below are the [higher-quality] Mock AMCs which have been hosted over AoPS in the past. Feel free to add, remove, or recommend.<br />
<br />
Note that the "level" column represents the originally intended difficulty. In other words, if a person makes a mock [[AMC 12]], the level would be "12", even if the problems themselves are much easier. Recommended mock tests are starred.<br />
<br />
=== Mock AMC 12 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" width=80 | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC #1'''<br />
| mathfanatic<br />
| 2003<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9321 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9353 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9572 1-5]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9573 6-10]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9574 11-15]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9575 16-20]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9576 21-25]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9365 Results]<br />
|-<br />
! scope="row" | '''Mock AMC #2'''<br />
| mathfanatic<br />
| 2004<br />
| [http://www.artofproblemsolving.com/community/c5h10497p67837 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10497 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10497 Solutions]<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| JSRosen3<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14138 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14361 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=102483#p102483 Answers] [http://www.artofproblemsolving.com/community/c5h14516 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14489 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC B'''<br />
| beta<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14735 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14764 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14894 Answers] [http://www.artofproblemsolving.com/community/c5h14884 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=105741#p105741 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC C'''<br />
| JGeneson<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15001 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15134 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15251 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15251 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC D'''<br />
| joml88<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=16886 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17888 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17891 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17891 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC E'''<br />
| Silverfalcon<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=21997 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22141 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22344 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22344 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC F'''<br />
| joml88<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22049 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23163 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23177 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23177 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC G'''<br />
| Lucky707<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=24355 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=24974 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=25087 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h25087p157983 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC H'''<br />
| Silverfalcon<br />
| 2005<br />
| [http://www.artofproblemsolving.com/community/c5h24437p154514 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h24437p154514 Problems]<br />
| throughout thread<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC I'''<br />
| white_horse_king88<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=21280 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=25181 Problems]<br />
| n/a<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC J'''<br />
| Silverfalcon<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=47625 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=48129 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=304246#p304246 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=48132 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC K'''<br />
| amirhtlusa<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=49958 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=50515 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=321102#p321102 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=321102#p321102 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC L'''<br />
| amirhtlusa<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=61330 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63041 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63258 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63258 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC M'''<br />
| Silverfalcon<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63542 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=78982 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=79749 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=79749 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC N'''<br />
| chess64<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=98894 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99307 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99344 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99344 Results] / [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99566 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC O'''<br />
| mustafa<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=121312 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=122126 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126071 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126071 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC P'''<br />
| Anirudh<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125029 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=709655#p709655 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=716240#p716240 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=716262#p716262 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125029 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC Q'''<br />
| calc rulz<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125194 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125886 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128102 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128102 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC R'''<br />
| rnwang2<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126107 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=715597#p715597 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127421 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127421 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC S'''<br />
| mysmartmouth<br />
| 2007<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127221 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128689 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131403 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131403 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC T'''<br />
| paladin8<br />
| 2007<br />
| [http://www.artofproblemsolving.com/community/c5h127979p726003 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127979 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC U'''<br />
| Silverfalcon<br />
| 2008<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=184067 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185233 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185238 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185236 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185238 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC V'''<br />
| gfour84<br />
| 2009<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=298452 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1634175#p1634175 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1637429#p1637429 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1637006#p1637006 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=302030 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 12'''<br />
| MathTwo<br />
| 2010<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=319184 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1759276#p1759276 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1778080#p1778080 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=328510 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 2/11'''<br />
| Caelestor<br />
| 2011<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=390907 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2183293#p2183293 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=390907 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 1/12'''<br />
| Lord.of.AMC<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h456321p2563731 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2605537#p2605537 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2610048#p2610048 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2610048#p2610048 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 12'''<br />
| Diehard<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459149 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459710 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2580327#p2580327 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459710 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 12 2012'''<br />
| python123<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=456256 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2576205#p2576205 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h456256p2580610 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h456256p2580610 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| Binomial-theorem<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=473867 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2692082#p2692082 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2717578#p2717578 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2707954#p2707954 Results]<br />
|-<br />
! scope = "row" | '''Almost 2016 Mock AMC 11.5'''<br />
| whatshisbucket<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Problems]<br />
| [http://artofproblemsolving.com/community/c209194_almost_2016_mock_amc_11.5 Solutions]<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Results / Discussion]<br />
|-<br />
! scope = "row" | '''December 2015 Mock AMC 1^3*(3+7)'''<br />
| mathisawesome2169<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5647504 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5647504 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5707101 Results / Discussion]<br />
|-<br />
! scope="row" | '''hnkevin42 Mock AMC 12'''<br />
| hnkevin42<br />
| 2016<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5913294 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Results/Discussion]<br />
|-<br />
! scope="row" | '''Last-Minute Mock AMC 12'''<br />
| CountofMC<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Problems]<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Answers]<br />
| [https://artofproblemsolving.com/community/c4t334444f4_lastminute_mock_amc_12 Results/Discussion]<br />
|}<br />
<br />
=== Mock AMC 10 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 10'''<br />
| #H34N1<br />
| 2008<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=212730 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=214081 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=213727 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=213732 Results/Discussion]<br />
|-<br />
! scope="row" | '''agent's Mock AMC 10'''<br />
| agentcx<br />
| 2009<br />
| [http://www.artofproblemsolving.com/community/c5h331823p1775678 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1781208#p1781208 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/community/c5h331823p1782769 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10 Set'''<br />
| AwesomeToad<br />
| 2010<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=311120 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1762829#p1762829 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1778740#p1778740 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 10/12'''<br />
| djmathman<br />
| 2013<br />
| [http://www.artofproblemsolving.com/community/c5h556673s1_first_mock_amcs_of_the_20132014_season Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3294854 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3324794 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3324794 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10 2014-2015*'''<br />
| AlcumusGuy<br />
| 2014<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=618080&hilit=AlcumusGuy%27s+mock+amc+10 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=618080&hilit=AlcumusGuy%27s+mock+amc+10 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h618080p3710795 Answers/Results]<br />
| [http://artofproblemsolving.com/community/c56018 Problem Discussion]<br />
|-<br />
! scope="row" | '''Kelvin the Frog v2015'''<br />
| BOGTRO<br />
| 2015<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=623373&hilit=Kelvin+the+frog Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=623373&hilit=Kelvin+the+frog Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3731642#p3731642 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3731642#p3731642 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 10/12'''<br />
| joey8189681<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h624714p3741743 Initial Discussion]<br />
| [https://www.dropbox.com/s/1c8hhl6yt2awpix/Mock%20AMC%2010.pdf?dl=0 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h624714p3754593 Answers]<br />
| [http://www.artofproblemsolving.com/community/q2h626092p3756574 Results]<br />
|-<br />
! scope="row" | '''May Mock AMC 10 Contest'''<br />
| azmath333<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1082684_mock_amc_1012_contest Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684_mock_amc_1012_contest Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684p4812575 Answers] [http://www.artofproblemsolving.com/community/c5h1082684p4825662 Solutions]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684p4812575 Results / Discussion] <br />
|-<br />
! scope="row" | '''2015 Mock AMC 10*'''<br />
| droid347<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p4893513 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p4893513 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p5051006 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p5045295 Results / Discussion]<br />
|-<br />
! scope="row" | '''July Mock AMC 10 Contest'''<br />
| akshaygowrish<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1104125_july_mock_amc_10_contest Initial Discussion]<br />
| [https://docs.google.com/document/d/12OXd-mmS_T7SyMcqw1hfvykNlcj-4TR4mMXlRJ09uBg/edit?usp=sharing Problems]<br />
| [https://docs.google.com/document/d/1-Q_w5XNKcRaffvpCLSdoJ51TpRpcDAgYLmV9OlczBCs/edit?usp=sharing Answer Key]<br />
| [http://artofproblemsolving.com/community/c5h1104125p5154283 Results / Discussion]<br />
|-<br />
! scope = "row" |'''August Mock AMC 10'''<br />
| azmath333<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1115462_august_mock_amc_10 Initial Discussion]<br />
| [http://latex.artofproblemsolving.com/miscpdf/augustmockamc10.pdf Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1115462p5270430 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1115462p5270430 Results] / [http://www.artofproblemsolving.com/community/c121880_august_mock_amc_10_discussion_forum Discussion]<br />
|-<br />
! scope = "row" | '''September Mock AMC 10'''<br />
| cpma213<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1137447p5320386 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1137447p5320386 Problems]<br />
| n/a<br />
| [http://artofproblemsolving.com/community/c5h1137447p5479954 Results / Discussion]<br />
|-<br />
! scope = "row" | '''New Year's Mock AMC10*'''<br />
| checkmatetang<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1171366p5627439 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5627439 Problems]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5711384 Answers]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5711384 Results] / [http://artofproblemsolving.com/community/c202656_new_years_mock_amc10_discussion Discussion]<br />
|-<br />
! scope = "row" | '''2015-2016 Mock AMC 10*'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Problems]<br />
| [http://artofproblemsolving.com/community/c147536h1182005_mock_amc10_wrapup Answers]<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 10 2015-2016*'''<br />
| AlcumusGuy<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1177413p5687990 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1177413_mock_amc_10_20152016_released Problems]<br />
| [http://artofproblemsolving.com/community/c212844_mock_amc_10_20152016 Solutions]<br />
| [http://artofproblemsolving.com/community/c5h1177413p5769839 Results / Discussion]<br />
|-<br />
! scope = "row" | '''January 2016 Mock AMC 10*'''<br />
| atmchallenge<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5700377 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5700377 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5838468 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5838468 Results/Discussion]<br />
|-<br />
! scope = "row" | '''2015-2016 Mock AMC 10* #2'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1188467 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1188467 Problems]<br />
| [http://artofproblemsolving.com/community/c147536h1175930 Solutions]<br />
| [http://artofproblemsolving.com/community/c5h1188467 Results / Discussion]<br />
|-<br />
<br />
! scope="row" | '''MeepyMeepMeep Mock AMC 10'''<br />
| MeepyMeepMeep, speck<br />
| 2016<br />
| [http://artofproblemsolving.com/community/c5h1195432p5852002 Initial Discussion]<br />
| [https://www.dropbox.com/s/uw0herhuqk8zbp5/Mock%20AMC%2010.pdf?dl=0 Problems]<br />
| n/a<br />
| n/a<br />
|- <br />
<br />
!scope="row" | eisirrational's Mock AMC 10<br />
| eisirrational, illogical_21, whatshisbucket<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1372991_eisirrationals_mock_amc_10 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c5h1372991_eisirrationals_mock_amc_10 Problems]<br />
| [http://artofproblemsolving.com/community/c418591h1392426p7811150 Answer Key]<br />
| [https://artofproblemsolving.com/community/c418591_mock_amc_10_discussion Discussion]<br />
|-<br />
<br />
!scope="row" | Summer Mock AMC 10<br />
| Rowechen, OmicronGamma, FedeX333X, KenV, kvedula2004, ItzVineeth<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1471834_summer_mock_amc_series Initial Discussion]<br />
| [https://drive.google.com/file/d/0B3M-fxa6QG0_ODNpSnJZcEt3djQ/view Problems]<br />
| [http://latex.artofproblemsolving.com/miscpdf/hehdrwpi.pdf?t=1500270651030 Answers]<br />
| [https://artofproblemsolving.com/community/c481237_2017_summer_mock_amc_10_discussion_forum Statistics / Discussion]<br />
|-<br />
<br />
!scope="row" | scrabbler94's Mock AMC 10<br />
| scrabbler94<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Problems]<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Answers]<br />
| [http://artofproblemsolving.com/community/c5h1569848p9704902 Results] / [https://artofproblemsolving.com/community/c593716_scrabbler94s_mock_amc_10_discussion Discussion]<br />
|-<br />
! scope="row" | '''2018 Mock AMC 10'''<br />
| blue8931<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c594864h1606066 Initial Discussion]<br />
| [https://artofproblemsolving.com/downloads/printable_post_collections/628064 Problems]<br />
| Coming Soon<br />
| Coming Soon<br />
|-<br />
<br />
|}<br />
<br />
=== Mock AMC 8 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" width=80 | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| mathfanatic<br />
| 2004<br />
| [http://www.artofproblemsolving.com/community/c5h15878p111575 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15878 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=114070#p114070 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h15878p114404 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| 13375P34K43V312<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=107507 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=108455 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=630802#p630802 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h108455p623522 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| ahaanomegas<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h459346p2577870 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2598111#p2598111 Problems]<br />
| n/a<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| utahjazz<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h485041p2717878 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2728186#p2728186 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2731391#p2731391 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| iNomOnCountdown<br />
| 2014<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&hilit=iNomonCountdown%27s+mock+amc+8 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&hilit=iNomonCountdown%27s+mock+amc+8 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&start=0 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&start=0 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8'''<br />
| Tan<br />
| 2014<br />
| [http://www.artofproblemsolving.com/community/c5h613297p3648226 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h613297p3648227 Problems]<br />
| [https://docs.google.com/spreadsheets/d/1U1QJ9r4r2xFbRByk9gXOhEVV48ScjoLWZp4IFanbKF0/edit#gid=1475864782 Answers]<br />
| [https://docs.google.com/spreadsheets/d/1U1QJ9r4r2xFbRByk9gXOhEVV48ScjoLWZp4IFanbKF0/edit#gid=1475864782 Results / Discussion]<br />
|-<br />
! scope = "row" | '''2015 Hard Mock AMC 8*'''<br />
| Not_a_Username, 8invalid8<br />
| 2015<br />
| [http://artofproblemsolving.com/community/q1h1128391p5227860 Initial Discussion]<br />
| [http://latex.artofproblemsolving.com/miscpdf/kashimyo.pdf Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1128391p5423312 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1128391p5423312 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c3h1152332p5457736 Initial Discussion]<br />
| [http://artofproblemsolving.com/downloads/printable_post_collections/163667 Problems]<br />
| [http://artofproblemsolving.com/community/category-admin/165328 Forum]<br />
| [http://artofproblemsolving.com/community/c165328h1155882p5484131 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8 #2'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c3h1167425p5586244 Initial Discussion]<br />
| [http://artofproblemsolving.com/downloads/printable_post_collections/165838 Problems]<br />
| [http://artofproblemsolving.com/community/c147536_the_mock_amc_8_forum Forum]<br />
| [http://artofproblemsolving.com/community/c3h1167425p5586244 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8 2015'''<br />
| Alberty44<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c194276_discusssion Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1168822p5674003 Problems]<br />
| n/a<br />
| [http://artofproblemsolving.com/community/c194276h1175928p5673996 Results/Discussion]<br />
|-<br />
! scope = "row" | '''Christmas AMC 8'''<br />
| Mudkipswims42<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1177489p5688588 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1177489p5688588 Problems]<br />
| [http://www.artofproblemsolving.com/community/c229455_christmas_amc8_discussion_forum Forum]<br />
| [http://artofproblemsolving.com/community/c5h1177489p5880200 Results/Discussion]<br />
|- <br />
<br />
! scope = "row" | '''Mock AMC 8!'''<br />
| eisirrational, pretzel, AOPS12142015, Th3Numb3rThr33, e_power_pi_times_i<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1526187_mock_amc_8 Initial Discussion]<br />
| [http://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvYi84LzFkNzUyMWYwZTViOTQ1MzRmZmU3ODE0NmI2MzIzMGUxNjA2MTcwLnBkZg==&rn=TW9jayBBTUMgOCB2Ny5wZGY= Problems]<br />
| [http://artofproblemsolving.com/community/c3h1545004p9368333 Answer Key/Solutions]<br />
| [https://artofproblemsolving.com/community/c561318_mock_amc_8_2017_discussion Discussion]<br />
|}<br />
<br />
----<br />
<br />
== See also ==<br />
* [[American Mathematics Competitions]]<br />
* [[Math books]]<br />
* [[Mathematics competitions]]<br />
* [[Mock AIME]]<br />
* [[Mock MathCounts]]<br />
* [[Mock USAMO]]<br />
* [[Mock USAJMO]]<br />
* [[Resources for mathematics competitions]]<br />
* [[AoPS Past Contests]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AMC&diff=93290
Mock AMC
2018-03-16T22:11:42Z
<p>Blue8931: /* Mock AMC 10 */</p>
<hr />
<div>A '''Mock AMC''' is a contest intended to mimic an actual [[AMC]] exam. A number of '''Mock AMC''' competitions have been hosted on the [[Art of Problem Solving]] message boards. They are generally made by one community member and then administered for any of the other community members to take. Sometimes, the administrator may ask other people to sign up to write problems for the contest.<br />
<br />
Mock AMC's are usually very popular in the months leading up to the actual [[AMC]] competition. There is no guarantee that community members will make Mock AMC's in any given year, but it's usually a good bet that someone will.<br />
<br />
Feel free to remove mock tests which are not of good quality, or recommend others.<br />
<br />
== Tips for Writing a Mock AMC ==<br />
Anyone can write a Mock AMC and administer it. If you are interested in writing one, here are some tips:<br />
<br />
* Look at past [[AMC]]/[[AHSME]] tests to get a feel for what kind of problems you should write and what difficulty level they should be.<br />
* Look at famous theorems and formulas and see if there's any way you can make a good problem out of them.<br />
* If you're running out of creative juice and decide to pull problems from contests, try using problems from obscure contests first, if possible. This way, even the more experienced test takers will hopefully find problems that they do not already know how to do.<br />
* Pair up with another user on AoPS and write it together. Two minds are much better than one. With just one person, the problems might be biased toward one subject, but with two people, the chances of this happening are smaller.<br />
<br />
== Past Mock AMCs ==<br />
<br />
Listed below are the [higher-quality] Mock AMCs which have been hosted over AoPS in the past. Feel free to add, remove, or recommend.<br />
<br />
Note that the "level" column represents the originally intended difficulty. In other words, if a person makes a mock [[AMC 12]], the level would be "12", even if the problems themselves are much easier. Recommended mock tests are starred.<br />
<br />
=== Mock AMC 12 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" width=80 | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC #1'''<br />
| mathfanatic<br />
| 2003<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9321 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9353 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9572 1-5]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9573 6-10]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9574 11-15]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9575 16-20]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9576 21-25]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9365 Results]<br />
|-<br />
! scope="row" | '''Mock AMC #2'''<br />
| mathfanatic<br />
| 2004<br />
| [http://www.artofproblemsolving.com/community/c5h10497p67837 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10497 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10497 Solutions]<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| JSRosen3<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14138 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14361 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=102483#p102483 Answers] [http://www.artofproblemsolving.com/community/c5h14516 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14489 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC B'''<br />
| beta<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14735 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14764 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14894 Answers] [http://www.artofproblemsolving.com/community/c5h14884 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=105741#p105741 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC C'''<br />
| JGeneson<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15001 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15134 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15251 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15251 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC D'''<br />
| joml88<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=16886 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17888 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17891 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17891 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC E'''<br />
| Silverfalcon<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=21997 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22141 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22344 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22344 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC F'''<br />
| joml88<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22049 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23163 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23177 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23177 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC G'''<br />
| Lucky707<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=24355 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=24974 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=25087 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h25087p157983 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC H'''<br />
| Silverfalcon<br />
| 2005<br />
| [http://www.artofproblemsolving.com/community/c5h24437p154514 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h24437p154514 Problems]<br />
| throughout thread<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC I'''<br />
| white_horse_king88<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=21280 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=25181 Problems]<br />
| n/a<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC J'''<br />
| Silverfalcon<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=47625 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=48129 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=304246#p304246 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=48132 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC K'''<br />
| amirhtlusa<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=49958 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=50515 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=321102#p321102 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=321102#p321102 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC L'''<br />
| amirhtlusa<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=61330 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63041 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63258 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63258 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC M'''<br />
| Silverfalcon<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63542 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=78982 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=79749 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=79749 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC N'''<br />
| chess64<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=98894 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99307 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99344 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99344 Results] / [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99566 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC O'''<br />
| mustafa<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=121312 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=122126 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126071 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126071 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC P'''<br />
| Anirudh<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125029 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=709655#p709655 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=716240#p716240 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=716262#p716262 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125029 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC Q'''<br />
| calc rulz<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125194 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125886 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128102 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128102 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC R'''<br />
| rnwang2<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126107 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=715597#p715597 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127421 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127421 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC S'''<br />
| mysmartmouth<br />
| 2007<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127221 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128689 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131403 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131403 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC T'''<br />
| paladin8<br />
| 2007<br />
| [http://www.artofproblemsolving.com/community/c5h127979p726003 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127979 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC U'''<br />
| Silverfalcon<br />
| 2008<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=184067 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185233 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185238 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185236 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185238 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC V'''<br />
| gfour84<br />
| 2009<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=298452 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1634175#p1634175 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1637429#p1637429 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1637006#p1637006 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=302030 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 12'''<br />
| MathTwo<br />
| 2010<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=319184 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1759276#p1759276 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1778080#p1778080 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=328510 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 2/11'''<br />
| Caelestor<br />
| 2011<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=390907 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2183293#p2183293 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=390907 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 1/12'''<br />
| Lord.of.AMC<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h456321p2563731 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2605537#p2605537 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2610048#p2610048 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2610048#p2610048 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 12'''<br />
| Diehard<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459149 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459710 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2580327#p2580327 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459710 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 12 2012'''<br />
| python123<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=456256 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2576205#p2576205 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h456256p2580610 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h456256p2580610 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| Binomial-theorem<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=473867 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2692082#p2692082 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2717578#p2717578 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2707954#p2707954 Results]<br />
|-<br />
! scope = "row" | '''Almost 2016 Mock AMC 11.5'''<br />
| whatshisbucket<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Problems]<br />
| [http://artofproblemsolving.com/community/c209194_almost_2016_mock_amc_11.5 Solutions]<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Results / Discussion]<br />
|-<br />
! scope = "row" | '''December 2015 Mock AMC 1^3*(3+7)'''<br />
| mathisawesome2169<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5647504 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5647504 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5707101 Results / Discussion]<br />
|-<br />
! scope="row" | '''hnkevin42 Mock AMC 12'''<br />
| hnkevin42<br />
| 2016<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5913294 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Results/Discussion]<br />
|-<br />
! scope="row" | '''Last-Minute Mock AMC 12'''<br />
| CountofMC<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Problems]<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Answers]<br />
| [https://artofproblemsolving.com/community/c4t334444f4_lastminute_mock_amc_12 Results/Discussion]<br />
|}<br />
<br />
=== Mock AMC 10 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 10'''<br />
| #H34N1<br />
| 2008<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=212730 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=214081 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=213727 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=213732 Results/Discussion]<br />
|-<br />
! scope="row" | '''agent's Mock AMC 10'''<br />
| agentcx<br />
| 2009<br />
| [http://www.artofproblemsolving.com/community/c5h331823p1775678 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1781208#p1781208 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/community/c5h331823p1782769 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10 Set'''<br />
| AwesomeToad<br />
| 2010<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=311120 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1762829#p1762829 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1778740#p1778740 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 10/12'''<br />
| djmathman<br />
| 2013<br />
| [http://www.artofproblemsolving.com/community/c5h556673s1_first_mock_amcs_of_the_20132014_season Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3294854 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3324794 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3324794 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10 2014-2015*'''<br />
| AlcumusGuy<br />
| 2014<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=618080&hilit=AlcumusGuy%27s+mock+amc+10 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=618080&hilit=AlcumusGuy%27s+mock+amc+10 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h618080p3710795 Answers/Results]<br />
| [http://artofproblemsolving.com/community/c56018 Problem Discussion]<br />
|-<br />
! scope="row" | '''Kelvin the Frog v2015'''<br />
| BOGTRO<br />
| 2015<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=623373&hilit=Kelvin+the+frog Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=623373&hilit=Kelvin+the+frog Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3731642#p3731642 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3731642#p3731642 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 10/12'''<br />
| joey8189681<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h624714p3741743 Initial Discussion]<br />
| [https://www.dropbox.com/s/1c8hhl6yt2awpix/Mock%20AMC%2010.pdf?dl=0 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h624714p3754593 Answers]<br />
| [http://www.artofproblemsolving.com/community/q2h626092p3756574 Results]<br />
|-<br />
! scope="row" | '''May Mock AMC 10 Contest'''<br />
| azmath333<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1082684_mock_amc_1012_contest Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684_mock_amc_1012_contest Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684p4812575 Answers] [http://www.artofproblemsolving.com/community/c5h1082684p4825662 Solutions]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684p4812575 Results / Discussion] <br />
|-<br />
! scope="row" | '''2015 Mock AMC 10*'''<br />
| droid347<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p4893513 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p4893513 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p5051006 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p5045295 Results / Discussion]<br />
|-<br />
! scope="row" | '''July Mock AMC 10 Contest'''<br />
| akshaygowrish<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1104125_july_mock_amc_10_contest Initial Discussion]<br />
| [https://docs.google.com/document/d/12OXd-mmS_T7SyMcqw1hfvykNlcj-4TR4mMXlRJ09uBg/edit?usp=sharing Problems]<br />
| [https://docs.google.com/document/d/1-Q_w5XNKcRaffvpCLSdoJ51TpRpcDAgYLmV9OlczBCs/edit?usp=sharing Answer Key]<br />
| [http://artofproblemsolving.com/community/c5h1104125p5154283 Results / Discussion]<br />
|-<br />
! scope = "row" |'''August Mock AMC 10'''<br />
| azmath333<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1115462_august_mock_amc_10 Initial Discussion]<br />
| [http://latex.artofproblemsolving.com/miscpdf/augustmockamc10.pdf Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1115462p5270430 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1115462p5270430 Results] / [http://www.artofproblemsolving.com/community/c121880_august_mock_amc_10_discussion_forum Discussion]<br />
|-<br />
! scope = "row" | '''September Mock AMC 10'''<br />
| cpma213<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1137447p5320386 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1137447p5320386 Problems]<br />
| n/a<br />
| [http://artofproblemsolving.com/community/c5h1137447p5479954 Results / Discussion]<br />
|-<br />
! scope = "row" | '''New Year's Mock AMC10*'''<br />
| checkmatetang<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1171366p5627439 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5627439 Problems]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5711384 Answers]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5711384 Results] / [http://artofproblemsolving.com/community/c202656_new_years_mock_amc10_discussion Discussion]<br />
|-<br />
! scope = "row" | '''2015-2016 Mock AMC 10*'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Problems]<br />
| [http://artofproblemsolving.com/community/c147536h1182005_mock_amc10_wrapup Answers]<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 10 2015-2016*'''<br />
| AlcumusGuy<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1177413p5687990 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1177413_mock_amc_10_20152016_released Problems]<br />
| [http://artofproblemsolving.com/community/c212844_mock_amc_10_20152016 Solutions]<br />
| [http://artofproblemsolving.com/community/c5h1177413p5769839 Results / Discussion]<br />
|-<br />
! scope = "row" | '''January 2016 Mock AMC 10*'''<br />
| atmchallenge<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5700377 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5700377 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5838468 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5838468 Results/Discussion]<br />
|-<br />
! scope = "row" | '''2015-2016 Mock AMC 10* #2'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1188467 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1188467 Problems]<br />
| [http://artofproblemsolving.com/community/c147536h1175930 Solutions]<br />
| [http://artofproblemsolving.com/community/c5h1188467 Results / Discussion]<br />
|-<br />
<br />
! scope="row" | '''MeepyMeepMeep Mock AMC 10'''<br />
| MeepyMeepMeep, speck<br />
| 2016<br />
| [http://artofproblemsolving.com/community/c5h1195432p5852002 Initial Discussion]<br />
| [https://www.dropbox.com/s/uw0herhuqk8zbp5/Mock%20AMC%2010.pdf?dl=0 Problems]<br />
| n/a<br />
| n/a<br />
|- <br />
<br />
!scope="row" | eisirrational's Mock AMC 10<br />
| eisirrational, illogical_21, whatshisbucket<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1372991_eisirrationals_mock_amc_10 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c5h1372991_eisirrationals_mock_amc_10 Problems]<br />
| [http://artofproblemsolving.com/community/c418591h1392426p7811150 Answer Key]<br />
| [https://artofproblemsolving.com/community/c418591_mock_amc_10_discussion Discussion]<br />
|-<br />
<br />
!scope="row" | Summer Mock AMC 10<br />
| Rowechen, OmicronGamma, FedeX333X, KenV, kvedula2004, ItzVineeth<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1471834_summer_mock_amc_series Initial Discussion]<br />
| [https://drive.google.com/file/d/0B3M-fxa6QG0_ODNpSnJZcEt3djQ/view Problems]<br />
| [http://latex.artofproblemsolving.com/miscpdf/hehdrwpi.pdf?t=1500270651030 Answers]<br />
| [https://artofproblemsolving.com/community/c481237_2017_summer_mock_amc_10_discussion_forum Statistics / Discussion]<br />
|-<br />
<br />
!scope="row" | scrabbler94's Mock AMC 10<br />
| scrabbler94<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Problems]<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Answers]<br />
| [http://artofproblemsolving.com/community/c5h1569848p9704902 Results] / [https://artofproblemsolving.com/community/c593716_scrabbler94s_mock_amc_10_discussion Discussion]<br />
|-<br />
! scope="row" | '''2018 Mock AMC 10'''<br />
| blue8931<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c594864h1606066 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c594864h1606066 Problems]<br />
| Coming Soon<br />
| Coming Soon<br />
|-<br />
<br />
|}<br />
<br />
=== Mock AMC 8 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" width=80 | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| mathfanatic<br />
| 2004<br />
| [http://www.artofproblemsolving.com/community/c5h15878p111575 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15878 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=114070#p114070 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h15878p114404 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| 13375P34K43V312<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=107507 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=108455 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=630802#p630802 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h108455p623522 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| ahaanomegas<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h459346p2577870 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2598111#p2598111 Problems]<br />
| n/a<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| utahjazz<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h485041p2717878 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2728186#p2728186 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2731391#p2731391 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| iNomOnCountdown<br />
| 2014<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&hilit=iNomonCountdown%27s+mock+amc+8 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&hilit=iNomonCountdown%27s+mock+amc+8 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&start=0 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&start=0 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8'''<br />
| Tan<br />
| 2014<br />
| [http://www.artofproblemsolving.com/community/c5h613297p3648226 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h613297p3648227 Problems]<br />
| [https://docs.google.com/spreadsheets/d/1U1QJ9r4r2xFbRByk9gXOhEVV48ScjoLWZp4IFanbKF0/edit#gid=1475864782 Answers]<br />
| [https://docs.google.com/spreadsheets/d/1U1QJ9r4r2xFbRByk9gXOhEVV48ScjoLWZp4IFanbKF0/edit#gid=1475864782 Results / Discussion]<br />
|-<br />
! scope = "row" | '''2015 Hard Mock AMC 8*'''<br />
| Not_a_Username, 8invalid8<br />
| 2015<br />
| [http://artofproblemsolving.com/community/q1h1128391p5227860 Initial Discussion]<br />
| [http://latex.artofproblemsolving.com/miscpdf/kashimyo.pdf Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1128391p5423312 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1128391p5423312 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c3h1152332p5457736 Initial Discussion]<br />
| [http://artofproblemsolving.com/downloads/printable_post_collections/163667 Problems]<br />
| [http://artofproblemsolving.com/community/category-admin/165328 Forum]<br />
| [http://artofproblemsolving.com/community/c165328h1155882p5484131 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8 #2'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c3h1167425p5586244 Initial Discussion]<br />
| [http://artofproblemsolving.com/downloads/printable_post_collections/165838 Problems]<br />
| [http://artofproblemsolving.com/community/c147536_the_mock_amc_8_forum Forum]<br />
| [http://artofproblemsolving.com/community/c3h1167425p5586244 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8 2015'''<br />
| Alberty44<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c194276_discusssion Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1168822p5674003 Problems]<br />
| n/a<br />
| [http://artofproblemsolving.com/community/c194276h1175928p5673996 Results/Discussion]<br />
|-<br />
! scope = "row" | '''Christmas AMC 8'''<br />
| Mudkipswims42<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1177489p5688588 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1177489p5688588 Problems]<br />
| [http://www.artofproblemsolving.com/community/c229455_christmas_amc8_discussion_forum Forum]<br />
| [http://artofproblemsolving.com/community/c5h1177489p5880200 Results/Discussion]<br />
|- <br />
<br />
! scope = "row" | '''Mock AMC 8!'''<br />
| eisirrational, pretzel, AOPS12142015, Th3Numb3rThr33, e_power_pi_times_i<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1526187_mock_amc_8 Initial Discussion]<br />
| [http://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvYi84LzFkNzUyMWYwZTViOTQ1MzRmZmU3ODE0NmI2MzIzMGUxNjA2MTcwLnBkZg==&rn=TW9jayBBTUMgOCB2Ny5wZGY= Problems]<br />
| [http://artofproblemsolving.com/community/c3h1545004p9368333 Answer Key/Solutions]<br />
| [https://artofproblemsolving.com/community/c561318_mock_amc_8_2017_discussion Discussion]<br />
|}<br />
<br />
----<br />
<br />
== See also ==<br />
* [[American Mathematics Competitions]]<br />
* [[Math books]]<br />
* [[Mathematics competitions]]<br />
* [[Mock AIME]]<br />
* [[Mock MathCounts]]<br />
* [[Mock USAMO]]<br />
* [[Mock USAJMO]]<br />
* [[Resources for mathematics competitions]]<br />
* [[AoPS Past Contests]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AMC&diff=93275
Mock AMC
2018-03-16T01:56:04Z
<p>Blue8931: /* Mock AMC 10 */</p>
<hr />
<div>A '''Mock AMC''' is a contest intended to mimic an actual [[AMC]] exam. A number of '''Mock AMC''' competitions have been hosted on the [[Art of Problem Solving]] message boards. They are generally made by one community member and then administered for any of the other community members to take. Sometimes, the administrator may ask other people to sign up to write problems for the contest.<br />
<br />
Mock AMC's are usually very popular in the months leading up to the actual [[AMC]] competition. There is no guarantee that community members will make Mock AMC's in any given year, but it's usually a good bet that someone will.<br />
<br />
Feel free to remove mock tests which are not of good quality, or recommend others.<br />
<br />
== Tips for Writing a Mock AMC ==<br />
Anyone can write a Mock AMC and administer it. If you are interested in writing one, here are some tips:<br />
<br />
* Look at past [[AMC]]/[[AHSME]] tests to get a feel for what kind of problems you should write and what difficulty level they should be.<br />
* Look at famous theorems and formulas and see if there's any way you can make a good problem out of them.<br />
* If you're running out of creative juice and decide to pull problems from contests, try using problems from obscure contests first, if possible. This way, even the more experienced test takers will hopefully find problems that they do not already know how to do.<br />
* Pair up with another user on AoPS and write it together. Two minds are much better than one. With just one person, the problems might be biased toward one subject, but with two people, the chances of this happening are smaller.<br />
<br />
== Past Mock AMCs ==<br />
<br />
Listed below are the [higher-quality] Mock AMCs which have been hosted over AoPS in the past. Feel free to add, remove, or recommend.<br />
<br />
Note that the "level" column represents the originally intended difficulty. In other words, if a person makes a mock [[AMC 12]], the level would be "12", even if the problems themselves are much easier. Recommended mock tests are starred.<br />
<br />
=== Mock AMC 12 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" width=80 | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC #1'''<br />
| mathfanatic<br />
| 2003<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9321 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9353 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9572 1-5]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9573 6-10]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9574 11-15]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9575 16-20]<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9576 21-25]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=9365 Results]<br />
|-<br />
! scope="row" | '''Mock AMC #2'''<br />
| mathfanatic<br />
| 2004<br />
| [http://www.artofproblemsolving.com/community/c5h10497p67837 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10497 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=10497 Solutions]<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| JSRosen3<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14138 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14361 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=102483#p102483 Answers] [http://www.artofproblemsolving.com/community/c5h14516 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14489 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC B'''<br />
| beta<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14735 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14764 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=14894 Answers] [http://www.artofproblemsolving.com/community/c5h14884 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=105741#p105741 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC C'''<br />
| JGeneson<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15001 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15134 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15251 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15251 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC D'''<br />
| joml88<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=16886 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17888 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17891 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17891 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC E'''<br />
| Silverfalcon<br />
| 2004<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=21997 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22141 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22344 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22344 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC F'''<br />
| joml88<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=22049 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23163 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23177 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=23177 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC G'''<br />
| Lucky707<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=24355 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=24974 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=25087 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h25087p157983 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC H'''<br />
| Silverfalcon<br />
| 2005<br />
| [http://www.artofproblemsolving.com/community/c5h24437p154514 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h24437p154514 Problems]<br />
| throughout thread<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC I'''<br />
| white_horse_king88<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=21280 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=25181 Problems]<br />
| n/a<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC J'''<br />
| Silverfalcon<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=47625 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=48129 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=304246#p304246 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=48132 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC K'''<br />
| amirhtlusa<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=49958 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=50515 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=321102#p321102 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=321102#p321102 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC L'''<br />
| amirhtlusa<br />
| 2005<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=61330 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63041 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63258 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63258 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC M'''<br />
| Silverfalcon<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=63542 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=78982 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=79749 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=79749 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC N'''<br />
| chess64<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=98894 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99307 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99344 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99344 Results] / [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=99566 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC O'''<br />
| mustafa<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=121312 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=122126 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126071 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126071 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC P'''<br />
| Anirudh<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125029 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=709655#p709655 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=716240#p716240 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=716262#p716262 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125029 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC Q'''<br />
| calc rulz<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125194 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=125886 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128102 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128102 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC R'''<br />
| rnwang2<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=126107 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=715597#p715597 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127421 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127421 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC S'''<br />
| mysmartmouth<br />
| 2007<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127221 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=128689 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131403 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131403 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC T'''<br />
| paladin8<br />
| 2007<br />
| [http://www.artofproblemsolving.com/community/c5h127979p726003 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=127979 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=129159 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC U'''<br />
| Silverfalcon<br />
| 2008<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=184067 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185233 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185238 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185236 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=185238 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC V'''<br />
| gfour84<br />
| 2009<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=298452 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1634175#p1634175 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1637429#p1637429 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1637006#p1637006 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=302030 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 12'''<br />
| MathTwo<br />
| 2010<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=319184 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1759276#p1759276 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1778080#p1778080 Results]/[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=328510 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 2/11'''<br />
| Caelestor<br />
| 2011<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=390907 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2183293#p2183293 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=390907 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 1/12'''<br />
| Lord.of.AMC<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h456321p2563731 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2605537#p2605537 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2610048#p2610048 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2610048#p2610048 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 12'''<br />
| Diehard<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459149 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459710 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2580327#p2580327 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=459710 Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 12 2012'''<br />
| python123<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=456256 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2576205#p2576205 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h456256p2580610 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h456256p2580610 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC A'''<br />
| Binomial-theorem<br />
| 2012<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=473867 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2692082#p2692082 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2717578#p2717578 Solutions]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2707954#p2707954 Results]<br />
|-<br />
! scope = "row" | '''Almost 2016 Mock AMC 11.5'''<br />
| whatshisbucket<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Problems]<br />
| [http://artofproblemsolving.com/community/c209194_almost_2016_mock_amc_11.5 Solutions]<br />
| [http://www.artofproblemsolving.com/community/c5h1175087p5665743 Results / Discussion]<br />
|-<br />
! scope = "row" | '''December 2015 Mock AMC 1^3*(3+7)'''<br />
| mathisawesome2169<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5647504 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5647504 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/community/c5h1173465p5707101 Results / Discussion]<br />
|-<br />
! scope="row" | '''hnkevin42 Mock AMC 12'''<br />
| hnkevin42<br />
| 2016<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5913294 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1187484p5778754 Results/Discussion]<br />
|-<br />
! scope="row" | '''Last-Minute Mock AMC 12'''<br />
| CountofMC<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Problems]<br />
| [https://artofproblemsolving.com/community/c594864h1582044_lastminute_mock_amc_12 Answers]<br />
| [https://artofproblemsolving.com/community/c4t334444f4_lastminute_mock_amc_12 Results/Discussion]<br />
|}<br />
<br />
=== Mock AMC 10 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 10'''<br />
| #H34N1<br />
| 2008<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=212730 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=214081 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=213727 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=213732 Results/Discussion]<br />
|-<br />
! scope="row" | '''agent's Mock AMC 10'''<br />
| agentcx<br />
| 2009<br />
| [http://www.artofproblemsolving.com/community/c5h331823p1775678 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1781208#p1781208 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/community/c5h331823p1782769 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10 Set'''<br />
| AwesomeToad<br />
| 2010<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=311120 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1762829#p1762829 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1778740#p1778740 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 10/12'''<br />
| djmathman<br />
| 2013<br />
| [http://www.artofproblemsolving.com/community/c5h556673s1_first_mock_amcs_of_the_20132014_season Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3294854 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3324794 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h556673p3324794 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 10 2014-2015*'''<br />
| AlcumusGuy<br />
| 2014<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=618080&hilit=AlcumusGuy%27s+mock+amc+10 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=618080&hilit=AlcumusGuy%27s+mock+amc+10 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h618080p3710795 Answers/Results]<br />
| [http://artofproblemsolving.com/community/c56018 Problem Discussion]<br />
|-<br />
! scope="row" | '''Kelvin the Frog v2015'''<br />
| BOGTRO<br />
| 2015<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=623373&hilit=Kelvin+the+frog Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=623373&hilit=Kelvin+the+frog Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3731642#p3731642 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3731642#p3731642 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 10/12'''<br />
| joey8189681<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h624714p3741743 Initial Discussion]<br />
| [https://www.dropbox.com/s/1c8hhl6yt2awpix/Mock%20AMC%2010.pdf?dl=0 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h624714p3754593 Answers]<br />
| [http://www.artofproblemsolving.com/community/q2h626092p3756574 Results]<br />
|-<br />
! scope="row" | '''May Mock AMC 10 Contest'''<br />
| azmath333<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1082684_mock_amc_1012_contest Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684_mock_amc_1012_contest Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684p4812575 Answers] [http://www.artofproblemsolving.com/community/c5h1082684p4825662 Solutions]<br />
| [http://www.artofproblemsolving.com/community/c5h1082684p4812575 Results / Discussion] <br />
|-<br />
! scope="row" | '''2015 Mock AMC 10*'''<br />
| droid347<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p4893513 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p4893513 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p5051006 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1094505p5045295 Results / Discussion]<br />
|-<br />
! scope="row" | '''July Mock AMC 10 Contest'''<br />
| akshaygowrish<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1104125_july_mock_amc_10_contest Initial Discussion]<br />
| [https://docs.google.com/document/d/12OXd-mmS_T7SyMcqw1hfvykNlcj-4TR4mMXlRJ09uBg/edit?usp=sharing Problems]<br />
| [https://docs.google.com/document/d/1-Q_w5XNKcRaffvpCLSdoJ51TpRpcDAgYLmV9OlczBCs/edit?usp=sharing Answer Key]<br />
| [http://artofproblemsolving.com/community/c5h1104125p5154283 Results / Discussion]<br />
|-<br />
! scope = "row" |'''August Mock AMC 10'''<br />
| azmath333<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1115462_august_mock_amc_10 Initial Discussion]<br />
| [http://latex.artofproblemsolving.com/miscpdf/augustmockamc10.pdf Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1115462p5270430 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1115462p5270430 Results] / [http://www.artofproblemsolving.com/community/c121880_august_mock_amc_10_discussion_forum Discussion]<br />
|-<br />
! scope = "row" | '''September Mock AMC 10'''<br />
| cpma213<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1137447p5320386 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1137447p5320386 Problems]<br />
| n/a<br />
| [http://artofproblemsolving.com/community/c5h1137447p5479954 Results / Discussion]<br />
|-<br />
! scope = "row" | '''New Year's Mock AMC10*'''<br />
| checkmatetang<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1171366p5627439 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5627439 Problems]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5711384 Answers]<br />
| [http://artofproblemsolving.com/community/c5h1171366p5711384 Results] / [http://artofproblemsolving.com/community/c202656_new_years_mock_amc10_discussion Discussion]<br />
|-<br />
! scope = "row" | '''2015-2016 Mock AMC 10*'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Problems]<br />
| [http://artofproblemsolving.com/community/c147536h1182005_mock_amc10_wrapup Answers]<br />
| [http://artofproblemsolving.com/community/c5h1168398p5595105 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 10 2015-2016*'''<br />
| AlcumusGuy<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1177413p5687990 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1177413_mock_amc_10_20152016_released Problems]<br />
| [http://artofproblemsolving.com/community/c212844_mock_amc_10_20152016 Solutions]<br />
| [http://artofproblemsolving.com/community/c5h1177413p5769839 Results / Discussion]<br />
|-<br />
! scope = "row" | '''January 2016 Mock AMC 10*'''<br />
| atmchallenge<br />
| 2015<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5700377 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5700377 Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5838468 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1178971p5838468 Results/Discussion]<br />
|-<br />
! scope = "row" | '''2015-2016 Mock AMC 10* #2'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1188467 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1188467 Problems]<br />
| [http://artofproblemsolving.com/community/c147536h1175930 Solutions]<br />
| [http://artofproblemsolving.com/community/c5h1188467 Results / Discussion]<br />
|-<br />
<br />
! scope="row" | '''MeepyMeepMeep Mock AMC 10'''<br />
| MeepyMeepMeep, speck<br />
| 2016<br />
| [http://artofproblemsolving.com/community/c5h1195432p5852002 Initial Discussion]<br />
| [https://www.dropbox.com/s/uw0herhuqk8zbp5/Mock%20AMC%2010.pdf?dl=0 Problems]<br />
| n/a<br />
| n/a<br />
|- <br />
<br />
!scope="row" | eisirrational's Mock AMC 10<br />
| eisirrational, illogical_21, whatshisbucket<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1372991_eisirrationals_mock_amc_10 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c5h1372991_eisirrationals_mock_amc_10 Problems]<br />
| [http://artofproblemsolving.com/community/c418591h1392426p7811150 Answer Key]<br />
| [https://artofproblemsolving.com/community/c418591_mock_amc_10_discussion Discussion]<br />
|-<br />
<br />
!scope="row" | Summer Mock AMC 10<br />
| Rowechen, OmicronGamma, FedeX333X, KenV, kvedula2004, ItzVineeth<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1471834_summer_mock_amc_series Initial Discussion]<br />
| [https://drive.google.com/file/d/0B3M-fxa6QG0_ODNpSnJZcEt3djQ/view Problems]<br />
| [http://latex.artofproblemsolving.com/miscpdf/hehdrwpi.pdf?t=1500270651030 Answers]<br />
| [https://artofproblemsolving.com/community/c481237_2017_summer_mock_amc_10_discussion_forum Statistics / Discussion]<br />
|-<br />
<br />
!scope="row" | scrabbler94's Mock AMC 10<br />
| scrabbler94<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Initial Discussion]<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Problems]<br />
| [https://artofproblemsolving.com/community/c5h1569848_mock_2018_amc_10_test_scrabbler94 Answers]<br />
| [http://artofproblemsolving.com/community/c5h1569848p9704902 Results] / [https://artofproblemsolving.com/community/c593716_scrabbler94s_mock_amc_10_discussion Discussion]<br />
|-<br />
! scope="row" | '''2018 Mock AMC 10'''<br />
| blue8931<br />
| 2018<br />
| [https://artofproblemsolving.com/community/c594864h1606066 Initial Discussion]<br />
| Coming Soon<br />
| Coming Soon<br />
| Coming Soon<br />
|-<br />
<br />
|}<br />
<br />
=== Mock AMC 8 ===<br />
<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Author'''<br />
! scope="col" | '''Year'''<br />
! scope="col" | '''Initial Discussion'''<br />
! scope="col" | '''Problems'''<br />
! scope="col" width=80 | '''Answers'''<br />
! scope="col" | '''Results/Discussion'''<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| mathfanatic<br />
| 2004<br />
| [http://www.artofproblemsolving.com/community/c5h15878p111575 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=15878 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=114070#p114070 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h15878p114404 Results / Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| 13375P34K43V312<br />
| 2006<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=107507 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=108455 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=630802#p630802 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h108455p623522 Results/Discussion]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| ahaanomegas<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h459346p2577870 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2598111#p2598111 Problems]<br />
| n/a<br />
| n/a<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| utahjazz<br />
| 2012<br />
| [http://www.artofproblemsolving.com/community/c5h485041p2717878 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2728186#p2728186 Problems]<br />
| n/a<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2731391#p2731391 Results]<br />
|-<br />
! scope="row" | '''Mock AMC 8'''<br />
| iNomOnCountdown<br />
| 2014<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&hilit=iNomonCountdown%27s+mock+amc+8 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&hilit=iNomonCountdown%27s+mock+amc+8 Problems]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&start=0 Answers]<br />
| [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=132&t=590451&start=0 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8'''<br />
| Tan<br />
| 2014<br />
| [http://www.artofproblemsolving.com/community/c5h613297p3648226 Initial Discussion]<br />
| [http://www.artofproblemsolving.com/community/c5h613297p3648227 Problems]<br />
| [https://docs.google.com/spreadsheets/d/1U1QJ9r4r2xFbRByk9gXOhEVV48ScjoLWZp4IFanbKF0/edit#gid=1475864782 Answers]<br />
| [https://docs.google.com/spreadsheets/d/1U1QJ9r4r2xFbRByk9gXOhEVV48ScjoLWZp4IFanbKF0/edit#gid=1475864782 Results / Discussion]<br />
|-<br />
! scope = "row" | '''2015 Hard Mock AMC 8*'''<br />
| Not_a_Username, 8invalid8<br />
| 2015<br />
| [http://artofproblemsolving.com/community/q1h1128391p5227860 Initial Discussion]<br />
| [http://latex.artofproblemsolving.com/miscpdf/kashimyo.pdf Problems]<br />
| [http://www.artofproblemsolving.com/community/c5h1128391p5423312 Answers]<br />
| [http://www.artofproblemsolving.com/community/c5h1128391p5423312 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c3h1152332p5457736 Initial Discussion]<br />
| [http://artofproblemsolving.com/downloads/printable_post_collections/163667 Problems]<br />
| [http://artofproblemsolving.com/community/category-admin/165328 Forum]<br />
| [http://artofproblemsolving.com/community/c165328h1155882p5484131 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8 #2'''<br />
| PersonPsychopath<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c3h1167425p5586244 Initial Discussion]<br />
| [http://artofproblemsolving.com/downloads/printable_post_collections/165838 Problems]<br />
| [http://artofproblemsolving.com/community/c147536_the_mock_amc_8_forum Forum]<br />
| [http://artofproblemsolving.com/community/c3h1167425p5586244 Results / Discussion]<br />
|-<br />
! scope = "row" | '''Mock AMC 8 2015'''<br />
| Alberty44<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c194276_discusssion Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1168822p5674003 Problems]<br />
| n/a<br />
| [http://artofproblemsolving.com/community/c194276h1175928p5673996 Results/Discussion]<br />
|-<br />
! scope = "row" | '''Christmas AMC 8'''<br />
| Mudkipswims42<br />
| 2015<br />
| [http://artofproblemsolving.com/community/c5h1177489p5688588 Initial Discussion]<br />
| [http://artofproblemsolving.com/community/c5h1177489p5688588 Problems]<br />
| [http://www.artofproblemsolving.com/community/c229455_christmas_amc8_discussion_forum Forum]<br />
| [http://artofproblemsolving.com/community/c5h1177489p5880200 Results/Discussion]<br />
|- <br />
<br />
! scope = "row" | '''Mock AMC 8!'''<br />
| eisirrational, pretzel, AOPS12142015, Th3Numb3rThr33, e_power_pi_times_i<br />
| 2017<br />
| [https://artofproblemsolving.com/community/c5h1526187_mock_amc_8 Initial Discussion]<br />
| [http://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvYi84LzFkNzUyMWYwZTViOTQ1MzRmZmU3ODE0NmI2MzIzMGUxNjA2MTcwLnBkZg==&rn=TW9jayBBTUMgOCB2Ny5wZGY= Problems]<br />
| [http://artofproblemsolving.com/community/c3h1545004p9368333 Answer Key/Solutions]<br />
| [https://artofproblemsolving.com/community/c561318_mock_amc_8_2017_discussion Discussion]<br />
|}<br />
<br />
----<br />
<br />
== See also ==<br />
* [[American Mathematics Competitions]]<br />
* [[Math books]]<br />
* [[Mathematics competitions]]<br />
* [[Mock AIME]]<br />
* [[Mock MathCounts]]<br />
* [[Mock USAMO]]<br />
* [[Mock USAJMO]]<br />
* [[Resources for mathematics competitions]]<br />
* [[AoPS Past Contests]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=2013_AMC_12B_Problems/Problem_24&diff=85394
2013 AMC 12B Problems/Problem 24
2017-04-23T04:10:50Z
<p>Blue8931: </p>
<hr />
<div>==Problem==<br />
Let <math>ABC</math> be a triangle where <math>M</math> is the midpoint of <math>\overline{AC}</math>, and <math>\overline{CN}</math> is the angle bisector of <math>\angle{ACB}</math> with <math>N</math> on <math>\overline{AB}</math>. Let <math>X</math> be the intersection of the median <math>\overline{BM}</math> and the bisector <math>\overline{CN}</math>. In addition <math>\triangle BXN</math> is equilateral with <math>AC=2</math>. What is <math>BN^2</math>?<br />
<br />
<math>\textbf{(A)}\ \frac{10-6\sqrt{2}}{7} \qquad \textbf{(B)}\ \frac{2}{9} \qquad \textbf{(C)}\ \frac{5\sqrt{2}-3\sqrt{3}}{8} \qquad \textbf{(D)}\ \frac{\sqrt{2}}{6} \qquad \textbf{(E)}\ \frac{3\sqrt{3}-4}{5}</math><br />
<br />
==Solution==<br />
Let <math>BN=x</math> and <math>NA=y</math>. From the conditions, let's deduct some convenient conditions that seem sufficient to solve the problem.<br />
<br />
<br />
<br />
'''<math>M</math> is the midpoint of side <math>AC</math>.'''<br />
<br />
This implies that <math>[ABX]=[CBX]</math>. Given that angle <math>ABX</math> is <math>60</math> degrees and angle <math>BXC</math> is <math>120</math> degrees, we can use the area formula to get<br />
<br />
<cmath>\frac{1}{2}(x+y)x \frac{\sqrt{3}}{2} = \frac{1}{2} x \cdot CX \frac{\sqrt{3}}{2}</cmath><br />
<br />
So, <math>x+y=CX</math> .....(1)<br />
<br />
<br />
<br />
'''<math>CN</math> is angle bisector.'''<br />
<br />
In the triangle <math>ABC</math>, one has <math>BC/AC=x/y</math>, therefore <math>BC=2x/y</math>.....(2)<br />
<br />
Furthermore, triangle <math>BCN</math> is similar to triangle <math>MCX</math>, so <math>BC/CM=CN/CX</math>, therefore <math>BC = (CX+x)/CX = (2x+y)/(x+y)</math>....(3)<br />
<br />
By (2) and (3) and the subtraction law of ratios, we get <br />
<br />
<cmath>BC=2x/y = (2x+y)/(y+x) = y/x</cmath><br />
<br />
Therefore <math>2x^2=y^2</math>, or <math>y=\sqrt{2}x</math>. So <math>BC = 2x/(\sqrt{2}x) = \sqrt{2}</math>.<br />
<br />
Finally, using the law of cosine for triangle <math>BCN</math>, we get<br />
<br />
<cmath>2 = BC^2 = x^2 + (2x+y)^2 - x(2x+y) = 3x^2 + 3xy + y^2 = \left(5+3\sqrt{2}\right)x^2</cmath><br />
<br />
<cmath>x^2 = \frac{2}{5+3\sqrt{2}} = \boxed{\textbf{(A) }\frac{10-6\sqrt{2}}{7}}.</cmath><br />
<br />
==Solution 2 (Analytic)==<br />
<center>[[File:2013 AMC 12B 24.jpg]]</center><br />
<br />
<br />
Let us dilate triangle <math>ABC</math> so that the sides of equilateral triangle <math>BXN</math> are all equal to <math>2.</math> The purpose of this is to ease the calculations we make in the problem. Given this, we aim to find the length of segment <math>AM</math> so that we can un-dilate triangle <math>ABC</math> by dividing each of its sides by <math>AM</math>. Doing so will make it so that <math>AM = 1</math>, as desired, and doing so will allow us to get the length of <math>BN</math>, whose square is our final answer. <br />
<br />
Let <math>O</math> the foot of the altitude from <math>B</math> to <math>NX.</math> On the coordinate plane, position <math>O</math> at <math>(0, 0)</math>, and make <math>NX</math> lie on the x-axis. Since points <math>N</math>, <math>X</math>, and <math>C</math>, are collinear, <math>C</math> must also lie on the x-axis. Additionally, since <math>NX = 2</math>, <math>OB = \sqrt{3}</math>, meaning that we can position point <math>B</math> at <math>(0, \sqrt{3})</math>. Now, notice that line <math>\overline{AB}</math> has the equation <math>y = \sqrt{3}x + \sqrt{3}</math> and that line <math>\overline{BM}</math> has the equation <math>y = -\sqrt{3}x + \sqrt{3}</math> because angles <math>BNX</math> and <math>BXN</math> are both <math>60^{\circ}</math>. We can then position <math>A</math> at point <math>(n, \sqrt{3}(n + 1))</math> and <math>C</math> at point <math>(p, 0)</math>. Quickly note that, because <math>CN</math> is an angle bisector, <math>AC</math> must pass through the point <math>(0, -\sqrt{3})</math>.<br />
<br />
We proceed to construct a system of equations. First observe that the midpoint <math>M</math> of <math>AC</math> must lie on <math>BM</math>, with the equation <math>y = -\sqrt{3}x + \sqrt{3}</math>. The coordinates of <math>M</math> are <math>\left(\frac{p + n}{2}, \frac{\sqrt{3}}{2}(n + 1)\right)</math>, and we can plug in these coordinates into the equation of line <math>BM</math>, yielding that <cmath>\frac{\sqrt{3}}{2}(n + 1) = -\sqrt{3}(\frac{p + n}{2}) + \sqrt{3} \implies n + 1 = -p - n + 2 \implies p = -2n + 1.</cmath> For our second equation, notice that line <math>AC</math> has equation <math>y = \frac{\sqrt{3}}{p}x - \sqrt{3}</math>. Midpoint <math>M</math> must also lie on this line, and we can substitute coordinates again to get <cmath>\frac{\sqrt{3}}{2}(n + 1) = \frac{\sqrt{3}}{p}(\frac{p + n}{2}) - \sqrt{3} \implies n + 1 = \frac{p + n}{p} - 2 \implies n + 1 = \frac{n}{p} - 1</cmath> <cmath>\implies p = \frac{n}{n + 2}.</cmath><br />
<br />
Setting both equations equal to each other and multiplying both sides by <math>(n + 2)</math>, we have that <math>-2n^2 - 4n + n + 2 = n \implies -2n^2 - 4n + 2 = 0</math>, which in turn simplifies into <math>0 = n^2 + 2n - 1</math> when dividing the entire equation by <math>-2.</math> Using the quadratic formula, we have that <cmath>n = \frac{-2 \pm \sqrt{4 + 4}}{2} = -1 - \sqrt{2}.</cmath> Here, we discard the positive root since <math>A</math> must lie to the left of the y-axis. Then, the coordinates of <math>C</math> are <math>(3 + 2\sqrt{2}, 0)</math>, and the coordinates of <math>A</math> are <math>(-1 - \sqrt{2}, -\sqrt{6}).</math> Seeing that segment <math>AM</math> has half the length of side <math>AC</math>, we have that the length of <math>AM</math> is <cmath>\frac{\sqrt{(3 + 2\sqrt{2} - (-1 - \sqrt{2}))^2 + (\sqrt{6})^2}}{2} = \frac{\sqrt{16 + 24\sqrt{2} + 18 + 6}}{2} = \sqrt{10 + 6\sqrt{2}}.</cmath><br />
<br />
Now, we divide each side length of <math>\triangle ABC</math> by <math>AM</math>, and from this, <math>BN^2</math> will equal <math>\left(\frac{2}{\sqrt{10 + 6\sqrt{2}}}\right)^2 = \frac{2}{5+3\sqrt{2}} = \boxed{\textbf{(A) }\frac{10-6\sqrt{2}}{7}.}</math><br />
<br />
==Solution 3 ==<br />
<br />
By some angle-chasing, we find that <math>\triangle ANC \sim \triangle BXC</math>. From here, construct a point <math>D</math> on <math>AC</math> such that <math>\triangle DXC \sim \triangle ANC</math>. Now, let <math>BC = a</math>, which means that <math>DM = a - 1</math> and <math>AD = 2 - a</math>, and let <math>BN = BX = XN = XD = DN = b</math>. Note that we want to compute <math>b^2</math>. Because <math>\triangle AND \sim \triangle DXM</math>, we have:<br />
<br />
<cmath>\frac{AN}{2-a} = \frac{b}{a-1} \implies AN = \frac{b(2-a)}{(a-1)}</cmath><br />
<br />
However, we have more similar triangles. In fact, going back to our original pair of similar triangles - <math>\triangle ANC</math> and <math>\triangle BXC</math> - gives us more similarity ratios:<br />
<br />
<cmath>\frac{AN}{AC} = \frac{BX}{BC} \implies \frac{\frac{b(2-a)}{(a-1)}}{2} = \frac{b}{a} \implies a = \sqrt{2}</cmath><br />
<br />
Since we constructed point <math>D</math> such that <math>DX</math> is parallel to <math>AB</math>, we now examine trapezoid <math>ABXD</math>. From the variables that we already set up, we know that <math>AB = b + b\sqrt{2}, BX = XD = b</math>, and <math>DA = 2 - \sqrt{2}</math>. Let <math>X'</math> denote the foot of the perpendicular from <math>X</math> to base <math>AB</math> and define <math>D'</math> similarly. <br />
<br />
Because <math>\triangle BXX'</math> is a <math>30, 60, 90</math> triangle, <math>XX' = \frac{b\sqrt{3}}{2}</math> and <math>BX' = \frac{b}{2}</math>. Thus, <math>D'A = b\sqrt{2} - \frac{b}{2}</math> and <math>DD' = XX' = \frac{b\sqrt{3}}{2}</math>. By the Pythagorean Theorem on <math>\triangle ADD'</math>,<br />
<br />
<cmath>\left (b\sqrt{2} - \frac{b}{2} \right)^2 + \left(\frac{b\sqrt{3}}{2} \right)^2 = \left(2 - \sqrt{2} \right)^2 \implies b^2 = \boxed{\textbf{(A) } \frac{10-6\sqrt{2}}{7}}</cmath>.<br />
<br />
== See also ==<br />
{{AMC12 box|year=2013|ab=B|num-b=23|num-a=25}}<br />
<br />
[[Category:Introductory Geometry Problems]]<br />
{{MAA Notice}}</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=2013_AMC_12B_Problems/Problem_24&diff=85393
2013 AMC 12B Problems/Problem 24
2017-04-23T04:09:47Z
<p>Blue8931: </p>
<hr />
<div>==Problem==<br />
Let <math>ABC</math> be a triangle where <math>M</math> is the midpoint of <math>\overline{AC}</math>, and <math>\overline{CN}</math> is the angle bisector of <math>\angle{ACB}</math> with <math>N</math> on <math>\overline{AB}</math>. Let <math>X</math> be the intersection of the median <math>\overline{BM}</math> and the bisector <math>\overline{CN}</math>. In addition <math>\triangle BXN</math> is equilateral with <math>AC=2</math>. What is <math>BN^2</math>?<br />
<br />
<math>\textbf{(A)}\ \frac{10-6\sqrt{2}}{7} \qquad \textbf{(B)}\ \frac{2}{9} \qquad \textbf{(C)}\ \frac{5\sqrt{2}-3\sqrt{3}}{8} \qquad \textbf{(D)}\ \frac{\sqrt{2}}{6} \qquad \textbf{(E)}\ \frac{3\sqrt{3}-4}{5}</math><br />
<br />
==Solution==<br />
Let <math>BN=x</math> and <math>NA=y</math>. From the conditions, let's deduct some convenient conditions that seem sufficient to solve the problem.<br />
<br />
<br />
<br />
'''<math>M</math> is the midpoint of side <math>AC</math>.'''<br />
<br />
This implies that <math>[ABX]=[CBX]</math>. Given that angle <math>ABX</math> is <math>60</math> degrees and angle <math>BXC</math> is <math>120</math> degrees, we can use the area formula to get<br />
<br />
<cmath>\frac{1}{2}(x+y)x \frac{\sqrt{3}}{2} = \frac{1}{2} x \cdot CX \frac{\sqrt{3}}{2}</cmath><br />
<br />
So, <math>x+y=CX</math> .....(1)<br />
<br />
<br />
<br />
'''<math>CN</math> is angle bisector.'''<br />
<br />
In the triangle <math>ABC</math>, one has <math>BC/AC=x/y</math>, therefore <math>BC=2x/y</math>.....(2)<br />
<br />
Furthermore, triangle <math>BCN</math> is similar to triangle <math>MCX</math>, so <math>BC/CM=CN/CX</math>, therefore <math>BC = (CX+x)/CX = (2x+y)/(x+y)</math>....(3)<br />
<br />
By (2) and (3) and the subtraction law of ratios, we get <br />
<br />
<cmath>BC=2x/y = (2x+y)/(y+x) = y/x</cmath><br />
<br />
Therefore <math>2x^2=y^2</math>, or <math>y=\sqrt{2}x</math>. So <math>BC = 2x/(\sqrt{2}x) = \sqrt{2}</math>.<br />
<br />
Finally, using the law of cosine for triangle <math>BCN</math>, we get<br />
<br />
<cmath>2 = BC^2 = x^2 + (2x+y)^2 - x(2x+y) = 3x^2 + 3xy + y^2 = \left(5+3\sqrt{2}\right)x^2</cmath><br />
<br />
<cmath>x^2 = \frac{2}{5+3\sqrt{2}} = \boxed{\textbf{(A) }\frac{10-6\sqrt{2}}{7}}.</cmath><br />
<br />
==Solution 2 (Analytic)==<br />
<center>[[File:2013 AMC 12B 24.jpg]]</center><br />
<br />
<br />
Let us dilate triangle <math>ABC</math> so that the sides of equilateral triangle <math>BXN</math> are all equal to <math>2.</math> The purpose of this is to ease the calculations we make in the problem. Given this, we aim to find the length of segment <math>AM</math> so that we can un-dilate triangle <math>ABC</math> by dividing each of its sides by <math>AM</math>. Doing so will make it so that <math>AM = 1</math>, as desired, and doing so will allow us to get the length of <math>BN</math>, whose square is our final answer. <br />
<br />
Let <math>O</math> the foot of the altitude from <math>B</math> to <math>NX.</math> On the coordinate plane, position <math>O</math> at <math>(0, 0)</math>, and make <math>NX</math> lie on the x-axis. Since points <math>N</math>, <math>X</math>, and <math>C</math>, are collinear, <math>C</math> must also lie on the x-axis. Additionally, since <math>NX = 2</math>, <math>OB = \sqrt{3}</math>, meaning that we can position point <math>B</math> at <math>(0, \sqrt{3})</math>. Now, notice that line <math>\overline{AB}</math> has the equation <math>y = \sqrt{3}x + \sqrt{3}</math> and that line <math>\overline{BM}</math> has the equation <math>y = -\sqrt{3}x + \sqrt{3}</math> because angles <math>BNX</math> and <math>BXN</math> are both <math>60^{\circ}</math>. We can then position <math>A</math> at point <math>(n, \sqrt{3}(n + 1))</math> and <math>C</math> at point <math>(p, 0)</math>. Quickly note that, because <math>CN</math> is an angle bisector, <math>AC</math> must pass through the point <math>(0, -\sqrt{3})</math>.<br />
<br />
We proceed to construct a system of equations. First observe that the midpoint <math>M</math> of <math>AC</math> must lie on <math>BM</math>, with the equation <math>y = -\sqrt{3}x + \sqrt{3}</math>. The coordinates of <math>M</math> are <math>\left(\frac{p + n}{2}, \frac{\sqrt{3}}{2}(n + 1)\right)</math>, and we can plug in these coordinates into the equation of line <math>BM</math>, yielding that <cmath>\frac{\sqrt{3}}{2}(n + 1) = -\sqrt{3}(\frac{p + n}{2}) + \sqrt{3} \implies n + 1 = -p - n + 2 \implies p = -2n + 1.</cmath> For our second equation, notice that line <math>AC</math> has equation <math>y = \frac{\sqrt{3}}{p}x - \sqrt{3}</math>. Midpoint <math>M</math> must also lie on this line, and we can substitute coordinates again to get <cmath>\frac{\sqrt{3}}{2}(n + 1) = \frac{\sqrt{3}}{p}(\frac{p + n}{2}) - \sqrt{3} \implies n + 1 = \frac{p + n}{p} - 2 \implies n + 1 = \frac{n}{p} - 1</cmath> <cmath>\implies p = \frac{n}{n + 2}.</cmath><br />
<br />
Setting both equations equal to each other and multiplying both sides by <math>(n + 2)</math>, we have that <math>-2n^2 - 4n + n + 2 = n \implies -2n^2 - 4n + 2 = 0</math>, which in turn simplifies into <math>0 = n^2 + 2n - 1</math> when dividing the entire equation by <math>-2.</math> Using the quadratic formula, we have that <cmath>n = \frac{-2 \pm \sqrt{4 + 4}}{2} = -1 - \sqrt{2}.</cmath> Here, we discard the positive root since <math>A</math> must lie to the left of the y-axis. Then, the coordinates of <math>C</math> are <math>(3 + 2\sqrt{2}, 0)</math>, and the coordinates of <math>A</math> are <math>(-1 - \sqrt{2}, -\sqrt{6}).</math> Seeing that segment <math>AM</math> has half the length of side <math>AC</math>, we have that the length of <math>AM</math> is <cmath>\frac{\sqrt{(3 + 2\sqrt{2} - (-1 - \sqrt{2}))^2 + (\sqrt{6})^2}}{2} = \frac{\sqrt{16 + 24\sqrt{2} + 18 + 6}}{2} = \sqrt{10 + 6\sqrt{2}}.</cmath><br />
<br />
Now, we divide each side length of <math>\triangle ABC</math> by <math>AM</math>, and from this, <math>BN^2</math> will equal <math>\left(\frac{2}{\sqrt{10 + 6\sqrt{2}}}\right)^2 = \frac{2}{5+3\sqrt{2}} = \boxed{\textbf{(A) }\frac{10-6\sqrt{2}}{7}.}</math><br />
<br />
==Solution 3 ==<br />
<br />
By some angle-chasing, we find that <math>\triangle ANC \sim \triangle BXC</math>. From here, construct a point <math>D</math> on <math>AC</math> such that <math>\triangle DXC \sim \triangle ANC</math>. Now, let <math>BC = a</math>, which means that <math>DM = a - 1</math> and <math>AD = 2 - a</math>, and let <math>BN = BX = XN = XD = DN = b</math>. Note that we want to compute <math>b^2</math>. Because <math>\triangle AND \sim \triangle DXM</math>, we have:<br />
<br />
<cmath>\frac{AN}{2-a} = \frac{b}{a-1} \implies AN = \frac{b(2-a)}{(a-1)}</cmath><br />
<br />
However, we have more similar triangles. In fact, going back to our original pair of similar triangles - <math>\triangle ANC</math> and <math>\triangle BXC</math> - gives us more similarity ratios:<br />
<br />
<cmath>\frac{AN}{AC} = \frac{BX}{BC} \implies \frac{\frac{b(2-a)}{(a-1)}}{2} = \frac{b}{a} \implies a = \sqrt{2}</cmath><br />
<br />
Since we constructed point <math>D</math> such that <math>DX</math> is parallel to <math>AB</math>, we now examine trapezoid <math>ABXD</math>. From the variables that we already set up, we know that <math>AB = b + b\sqrt{2}, BX = XD = b</math>, and <math>DA = 2 - \sqrt{2}</math>. Let <math>X'</math> denote the foot of the perpendicular from <math>X</math> to base <math>AB</math> and define <math>D'</math> similarly. <br />
<br />
Because <math>\triangle BXX'</math> is a <math>30, 60, 90</math> triangle, <math>XX' = \frac{b\sqrt{3}}{2}</math> and <math>BX' = \frac{b}{2}</math>. Thus, <math>D'A = b\sqrt{2} - \frac{b}{2}</math> and <math>DD' = XX' = \frac{b\sqrt{3}}{2}</math>. By the Pythagorean Theorem on <math>\triangle ADD'</math>,<br />
<br />
<cmath>\left (b\sqrt{2} - \frac{b}{2} \right)^2 + \left(\frac{b\sqrt{3}}{2} \right)^2 = \left(2 - \sqrt{2} \right)^2 \implies b^2 = \boxed{\frac{10-6\sqrt{2}}{7}}</cmath>.<br />
<br />
== See also ==<br />
{{AMC12 box|year=2013|ab=B|num-b=23|num-a=25}}<br />
<br />
[[Category:Introductory Geometry Problems]]<br />
{{MAA Notice}}</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_I_2015_Problems/Problem_11&diff=83490
Mock AIME I 2015 Problems/Problem 11
2017-02-12T18:52:55Z
<p>Blue8931: /*Solution*/</p>
<hr />
<div>==Solution==<br />
<br />
For convenience, let's use <math>a, b, c</math> instead of <math>\alpha, \beta, \gamma</math>. Define a polynomial <math>P(x)</math> such that <math>P(x) = (x-a)(x-b)(x-c) = x^3 - (a+b+c)x^2 + (ab+ac+bc)x - abc</math>. Let <math>j = ab + ac + bc</math> and <math>k = -abc</math>. Then, our polynomial becomes <math>P(x) = x^3 - (a+b+c)x^2 + jx + k</math>. <br />
Note that we want to compute <math>-\frac{j}{k}</math>. <br />
<br />
<br />
From the given information, we know that the coefficient of the <math>x^2</math> term is <math>6</math>, and we also know that <math>P(-1) = -33</math>, or in other words, <math>-j + k = -26</math>. By Newton's Sums (since we are given <math>a^3 + b^3 + c^3</math>), we also find that <math>6j + k = 43</math>. Solving this system, we find that <math>(j, k) \in (\frac{69}{7}, -\frac{113}{7})</math>. Thus, <math>\frac{j}{-k} = \frac{69}{113}</math>, so our final answer is <math>69 + 113 = \boxed{182}</math>.</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_I_2015_Problems/Problem_10&diff=83489
Mock AIME I 2015 Problems/Problem 10
2017-02-12T18:51:19Z
<p>Blue8931: Blanked the page</p>
<hr />
<div></div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_I_2015_Problems/Problem_11&diff=83488
Mock AIME I 2015 Problems/Problem 11
2017-02-12T18:49:20Z
<p>Blue8931: Solution</p>
<hr />
<div>For convenience, let's use <math>a, b, c</math> instead of <math>\alpha, \beta, \gamma</math>. Define a polynomial <math>P(x)</math> such that <math>P(x) = (x-a)(x-b)(x-c) = x^3 - (a+b+c)x^2 + (ab+ac+bc)x - abc</math>. Let <math>j = ab + ac + bc</math> and <math>k = -abc</math>. Then, our polynomial becomes <math>P(x) = x^3 - (a+b+c)x^2 + jx + k</math>. <br />
Note that we want to compute <math>-\frac{j}{k}</math>. <br />
<br />
From the given information, we know that the coefficient of the <math>x^2</math> term is <math>6</math>, and we also know that <math>P(-1) = -33</math>, or in other words, <math>-j + k = -26</math>. By Newton's Sums (since we are given <math>a^3 + b^3 + c^3</math>), we also find that <math>6j + k = 43</math>. Solving this system, we find that <math>(j, k) \in (\frac{69}{7}, -\frac{113}{7})</math>. Thus, <math>\frac{j}{-k} = \frac{69}{113}</math>, so our final answer is <math>69 + 113 = \boxed{182}</math>.</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_I_2015_Problems&diff=83487
Mock AIME I 2015 Problems
2017-02-12T18:48:58Z
<p>Blue8931: /* Problem 11 */</p>
<hr />
<div>== Problem 1 ==<br />
David, Justin, Richard, and Palmer are demonstrating a "math magic" concept in front of an audience. There are four boxes, labeled A, B, C, and D, and each one contains a different number. First, David pulls out the numbers in boxes A and B and reports that their product is <math>14</math>. Justin then claims that the product of the numbers in boxes B and C is <math>16</math>, and Richard states the product of the numbers in boxes C and D to be <math>18</math>. Finally, Palmer announces the product of the numbers in boxes D and A. If <math>k</math> is the number that Palmer says, what is <math>20k</math>?<br />
<br />
[[Mock AIME I 2015 Problems/Problem 1|Solution]]<br />
<br />
== Problem 2 ==<br />
Suppose that <math>x</math> and <math>y</math> are real numbers such that <math>\log_x 3y = \tfrac{20}{13}</math> and <math>\log_{3x}y=\tfrac23</math>. The value of <math>\log_{3x}3y</math> can be expressed in the form <math>\tfrac ab</math> where <math>a</math> and <math>b</math> are positive relatively prime integers. Find <math>a+b</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 2|Solution]]<br />
<br />
== Problem 3 ==<br />
Let <math>A,B,C</math> be points in the plane such that <math>AB=25</math>, <math>AC=29</math>, and <math>\angle BAC<90^\circ</math>. Semicircles with diameters <math>\overline{AB}</math> and <math>\overline{AC}</math> intersect at a point <math>P</math> with <math>AP=20</math>. Find the length of line segment <math>\overline{BC}</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 3|Solution]]<br />
<br />
== Problem 4 ==<br />
At the AoPS Carnival, there is a "Weighted Dice" game show. This game features two identical looking weighted 6 sided dice. For each integer <math>1\leq i\leq 6</math>, Die A has <math>\tfrac{i}{21}</math> probability of rolling the number <math>i</math>, while Die B has a <math>\tfrac{7-i}{21}</math> probability of rolling <math>i</math>. During one session, the host randomly chooses a die, rolls it twice, and announces that the sum of the numbers on the two rolls is <math>10</math>. Let <math>P</math> be the probability that the die chosen was Die A. When <math>P</math> is written as a fraction in lowest terms, find the sum of the numerator and denominator.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 4|Solution]]<br />
<br />
== Problem 5 ==<br />
In an urn there are a certain number (at least two) of black marbles and a certain number of white marbles. Steven blindfolds himself and chooses two marbles from the urn at random. Suppose the probability that the two marbles are of opposite color is <math>\tfrac12</math>. Let <math>k_1<k_2<\cdots<k_{100}</math> be the <math>100</math> smallest possible values for the total number of marbles in the urn. Compute the remainder when <cmath>k_1+k_2+k_3+\cdots+k_{100}</cmath> is divided by <math>1000</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 5|Solution]]<br />
<br />
== Problem 6 ==<br />
Find the number of <math>5</math> digit numbers using only the digits <math>1,2,3,4,5,6,7,8</math> such that every pair of adjacent digits is no more than <math>1</math> apart. For instance, <math>12345</math> and <math>33234</math> are acceptable numbers, while <math>13333</math> and <math>56789</math> are not.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 6|Solution]]<br />
<br />
== Problem 7 ==<br />
For all points <math>P</math> in the coordinate plane, let <math>P'</math> denote the reflection of <math>P</math> across the line <math>y=x</math>. For example, if <math>P=(3,1)</math>, then <math>P'=(1,3)</math>. Define a function <math>f</math> such that for all points <math>P</math>, <math>f(P)</math> denotes the area of the triangle with vertices <math>(0,0)</math>, <math>P</math>, and <math>P'</math>. Determine the number of lattice points <math>Q</math> in the first quadrant such that <math>f(Q)=8!</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 7|Solution]]<br />
<br />
== Problem 8 ==<br />
Let <math>a,b,c</math> be consecutive terms (in that order) in an arithmetic sequence with common difference <math>d</math>. Suppose <math>\cos b</math> and <math>\cos d</math> are roots of a monic quadratic <math>p(x)</math> with <math>p(-\tfrac{1}{2})=\tfrac1{2014}</math>. Then <cmath>|\cos a+\cos b+\cos c+\cos d\,|=\frac pq</cmath> for positive relatively prime integers <math>p</math> and <math>q</math>. Find the remainder when <math>p+q</math> is divided by <math>1000</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 8|Solution]]<br />
<br />
== Problem 9 ==<br />
Compute the number of positive integer triplets <math>(a,b,c)</math> with <math>1\le a,b,c\le 500</math> that satisfy the following properties: <br />
<br />
(a) <math>abc</math> is a perfect square,<br />
<br />
(b) <math>(a+7b)c</math> is a power of <math>2</math>,<br />
<br />
(c) <math>a</math> is a multiple of <math>b</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 9|Solution]]<br />
<br />
== Problem 10 ==<br />
Let <math>f</math> be a function defined along the rational numbers such that <math>f(\tfrac mn)=\tfrac1n</math> for all relatively prime positive integers <math>m</math> and <math>n</math>. The product of all rational numbers <math>0<x<1</math> such that <cmath>f\left(\dfrac{x-f(x)}{1-f(x)}\right)=f(x)+\dfrac9{52}</cmath> can be written in the form <math>\tfrac pq</math> for positive relatively prime integers <math>p</math> and <math>q</math>. Find <math>p+q</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 10|Solution]]<br />
<br />
== Problem 11 ==<br />
Suppose <math>\alpha</math>, <math>\beta</math>, and <math>\gamma</math> are complex numbers that satisfy the system of equations <cmath>\begin{align*}\alpha+\beta+\gamma&=6,\\\alpha^3+\beta^3+\gamma^3&=87,\\(\alpha+1)(\beta+1)(\gamma+1)&=33.\end{align*}</cmath> If <math>\frac1\alpha+\frac1\beta+\frac1\gamma=\tfrac mn</math> for positive relatively prime integers <math>m</math> and <math>n</math>, find <math>m+n</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 11|Solution]]<br />
<br />
== Problem 12 ==<br />
Alpha and Beta play a game on the number line below.<br />
<br />
<asy><br />
import olympiad;<br />
size(140);<br />
dot(origin); real t = .2; draw((-3,0)--(3,0), Arrows(6)); for(int i=-2; i<3; i=i+1) { draw((i,t)--(i,-t)); label(string(i), (i,-t), dir(270), fontsize(8));}<br />
</asy><br />
Both players start at <math>0</math>. Each turn, Alpha has an equal chance of moving <math>1</math> unit in either the positive or negative directions while Beta has a <math>\tfrac{2}{3}</math> chance of moving <math>1</math> unit in the positive direction and a <math>\tfrac{1}{3}</math> chance of moving <math>1</math> unit in the negative direction. The two alternate turns with Alpha going first. If a player reaches <math>2</math> at any point in the game, he wins; however, if a player reaches <math>-2</math>, he loses and the other player wins. If <math>\tfrac pq</math> is the probability that Alpha beats Beta, where <math>p</math> and <math>q</math> are relatively prime positive integers, find <math>p+q</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 12|Solution]]<br />
<br />
== Problem 13 ==<br />
Let <math>A_1A_2A_3A_4A_5A_6</math> be a hexagon inscribed inside a circle of radius <math>r</math>. Furthermore, for each positive integer <math>1\leq i\leq 6</math> let <math>M_i</math> be the midpoint of the segment <math>\overline{A_iA_{i+1}}</math>, where <math>A_7\equiv A_1</math>. Suppose that hexagon <math>M_1M_2M_3M_4M_5M_6</math> can also be inscribed inside a circle. If <math>A_1A_2=A_3A_4=5</math> and <math>A_5A_6=23</math>, then <math>r^2</math> can be written in the form <math>\tfrac mn</math> where <math>m</math> and <math>n</math> are positive relatively prime integers. Find <math>m+n</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 13|Solution]]<br />
<br />
== Problem 14 ==<br />
Consider a set of <math>\tfrac{n(n+1)}{2}</math> pennies laid out in the formation of an equilateral triangle with "side length" <math>n</math>. You wish to move some of the pennies so that the triangle is flipped upside down. For example, with <math>n=2</math>, you could take the top penny and move it to the bottom to accomplish this task, as shown:<br />
<br />
<asy><br />
size(180);<br />
defaultpen(linewidth(0.8));<br />
filldraw(circle((-2,0),1)^^circle((2,0),1)^^circle((0,2*sqrt(3)),1)^^circle((10,0),1)^^circle((14,0),1)^^circle((12,-2*sqrt(3)),1),grey);<br />
draw((-1.25,2*sqrt(3))..(-4.5,0)..(-1.25,-2*sqrt(3)),linetype("4 4"),EndArrow);<br />
draw(circle((0,-2*sqrt(3)),1),linetype("4 4"));<br />
</asy><br />
<br />
Let <math>S_n</math> be the minimum number of pennies for which this can be done in terms of <math>n</math>. Find <math>S_{50}</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 14|Solution]]<br />
<br />
== Problem 15 ==<br />
Let <math>\triangle ABC</math> be a triangle with <math>AB=13</math>, <math>BC=14</math>, and <math>CA=15</math>. Let <math>O</math> denote its circumcenter and <math>H</math> its orthocenter. The circumcircle of <math>\triangle AOH</math> intersects <math>AB</math> and <math>AC</math> at <math>D</math> and <math>E</math> respectively. Suppose <math>\tfrac{AD}{AE}=\tfrac mn</math> where <math>m</math> and <math>n</math> are positive relatively prime integers. Find <math>m-n</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 15|Solution]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_I_2015_Problems/Problem_10&diff=83486
Mock AIME I 2015 Problems/Problem 10
2017-02-12T18:48:33Z
<p>Blue8931: Created page with "For convenience, let's use <math>a, b, c</math> instead of <math>\alpha, \beta, \gamma</math>. Define a polynomial <math>P(x)</math> such that <math>P(x) = (x-a)(x-b)(x-c) = x..."</p>
<hr />
<div>For convenience, let's use <math>a, b, c</math> instead of <math>\alpha, \beta, \gamma</math>. Define a polynomial <math>P(x)</math> such that <math>P(x) = (x-a)(x-b)(x-c) = x^3 - (a+b+c)x^2 + (ab+ac+bc)x - abc</math>. Let <math>j = ab + ac + bc</math> and <math>k = -abc</math>. Then, our polynomial becomes <math>P(x) = x^3 - (a+b+c)x^2 + jx + k</math>. <br />
Note that we want to compute <math>-\frac{j}{k}</math>. <br />
<br />
From the given information, we know that the coefficient of the <math>x^2</math> term is <math>6</math>, and we also know that <math>P(-1) = -33</math>, or in other words, <math>-j + k = -26</math>. By Newton's Sums (since we are given <math>a^3 + b^3 + c^3</math>), we also find that <math>6j + k = 43</math>. Solving this system, we find that <math>(j, k) \in (\frac{69}{7}, -\frac{113}{7})</math>. Thus, <math>\frac{j}{-k} = \frac{69}{113}</math>, so our final answer is <math>69 + 113 = \boxed{182}</math>.</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_I_2015_Problems&diff=83485
Mock AIME I 2015 Problems
2017-02-12T18:47:40Z
<p>Blue8931: /* Problem 11 */</p>
<hr />
<div>== Problem 1 ==<br />
David, Justin, Richard, and Palmer are demonstrating a "math magic" concept in front of an audience. There are four boxes, labeled A, B, C, and D, and each one contains a different number. First, David pulls out the numbers in boxes A and B and reports that their product is <math>14</math>. Justin then claims that the product of the numbers in boxes B and C is <math>16</math>, and Richard states the product of the numbers in boxes C and D to be <math>18</math>. Finally, Palmer announces the product of the numbers in boxes D and A. If <math>k</math> is the number that Palmer says, what is <math>20k</math>?<br />
<br />
[[Mock AIME I 2015 Problems/Problem 1|Solution]]<br />
<br />
== Problem 2 ==<br />
Suppose that <math>x</math> and <math>y</math> are real numbers such that <math>\log_x 3y = \tfrac{20}{13}</math> and <math>\log_{3x}y=\tfrac23</math>. The value of <math>\log_{3x}3y</math> can be expressed in the form <math>\tfrac ab</math> where <math>a</math> and <math>b</math> are positive relatively prime integers. Find <math>a+b</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 2|Solution]]<br />
<br />
== Problem 3 ==<br />
Let <math>A,B,C</math> be points in the plane such that <math>AB=25</math>, <math>AC=29</math>, and <math>\angle BAC<90^\circ</math>. Semicircles with diameters <math>\overline{AB}</math> and <math>\overline{AC}</math> intersect at a point <math>P</math> with <math>AP=20</math>. Find the length of line segment <math>\overline{BC}</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 3|Solution]]<br />
<br />
== Problem 4 ==<br />
At the AoPS Carnival, there is a "Weighted Dice" game show. This game features two identical looking weighted 6 sided dice. For each integer <math>1\leq i\leq 6</math>, Die A has <math>\tfrac{i}{21}</math> probability of rolling the number <math>i</math>, while Die B has a <math>\tfrac{7-i}{21}</math> probability of rolling <math>i</math>. During one session, the host randomly chooses a die, rolls it twice, and announces that the sum of the numbers on the two rolls is <math>10</math>. Let <math>P</math> be the probability that the die chosen was Die A. When <math>P</math> is written as a fraction in lowest terms, find the sum of the numerator and denominator.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 4|Solution]]<br />
<br />
== Problem 5 ==<br />
In an urn there are a certain number (at least two) of black marbles and a certain number of white marbles. Steven blindfolds himself and chooses two marbles from the urn at random. Suppose the probability that the two marbles are of opposite color is <math>\tfrac12</math>. Let <math>k_1<k_2<\cdots<k_{100}</math> be the <math>100</math> smallest possible values for the total number of marbles in the urn. Compute the remainder when <cmath>k_1+k_2+k_3+\cdots+k_{100}</cmath> is divided by <math>1000</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 5|Solution]]<br />
<br />
== Problem 6 ==<br />
Find the number of <math>5</math> digit numbers using only the digits <math>1,2,3,4,5,6,7,8</math> such that every pair of adjacent digits is no more than <math>1</math> apart. For instance, <math>12345</math> and <math>33234</math> are acceptable numbers, while <math>13333</math> and <math>56789</math> are not.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 6|Solution]]<br />
<br />
== Problem 7 ==<br />
For all points <math>P</math> in the coordinate plane, let <math>P'</math> denote the reflection of <math>P</math> across the line <math>y=x</math>. For example, if <math>P=(3,1)</math>, then <math>P'=(1,3)</math>. Define a function <math>f</math> such that for all points <math>P</math>, <math>f(P)</math> denotes the area of the triangle with vertices <math>(0,0)</math>, <math>P</math>, and <math>P'</math>. Determine the number of lattice points <math>Q</math> in the first quadrant such that <math>f(Q)=8!</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 7|Solution]]<br />
<br />
== Problem 8 ==<br />
Let <math>a,b,c</math> be consecutive terms (in that order) in an arithmetic sequence with common difference <math>d</math>. Suppose <math>\cos b</math> and <math>\cos d</math> are roots of a monic quadratic <math>p(x)</math> with <math>p(-\tfrac{1}{2})=\tfrac1{2014}</math>. Then <cmath>|\cos a+\cos b+\cos c+\cos d\,|=\frac pq</cmath> for positive relatively prime integers <math>p</math> and <math>q</math>. Find the remainder when <math>p+q</math> is divided by <math>1000</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 8|Solution]]<br />
<br />
== Problem 9 ==<br />
Compute the number of positive integer triplets <math>(a,b,c)</math> with <math>1\le a,b,c\le 500</math> that satisfy the following properties: <br />
<br />
(a) <math>abc</math> is a perfect square,<br />
<br />
(b) <math>(a+7b)c</math> is a power of <math>2</math>,<br />
<br />
(c) <math>a</math> is a multiple of <math>b</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 9|Solution]]<br />
<br />
== Problem 10 ==<br />
Let <math>f</math> be a function defined along the rational numbers such that <math>f(\tfrac mn)=\tfrac1n</math> for all relatively prime positive integers <math>m</math> and <math>n</math>. The product of all rational numbers <math>0<x<1</math> such that <cmath>f\left(\dfrac{x-f(x)}{1-f(x)}\right)=f(x)+\dfrac9{52}</cmath> can be written in the form <math>\tfrac pq</math> for positive relatively prime integers <math>p</math> and <math>q</math>. Find <math>p+q</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 10|Solution]]<br />
<br />
== Problem 11 ==<br />
Suppose <math>\alpha</math>, <math>\beta</math>, and <math>\gamma</math> are complex numbers that satisfy the system of equations <cmath>\begin{align*}\alpha+\beta+\gamma&=6,\\\alpha^3+\beta^3+\gamma^3&=87,\\(\alpha+1)(\beta+1)(\gamma+1)&=33.\end{align*}</cmath> If <math>\frac1\alpha+\frac1\beta+\frac1\gamma=\tfrac mn</math> for positive relatively prime integers <math>m</math> and <math>n</math>, find <math>m+n</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 11|Solution]]<br />
<br />
For convenience, let's use <math>a, b, c</math> instead of <math>\alpha, \beta, \gamma</math>. Define a polynomial <math>P(x)</math> such that <math>P(x) = (x-a)(x-b)(x-c) = x^3 - (a+b+c)x^2 + (ab+ac+bc)x - abc</math>. Let <math>j = ab + ac + bc</math> and <math>k = -abc</math>. Then, our polynomial becomes <math>P(x) = x^3 - (a+b+c)x^2 + jx + k</math>. <br />
Note that we want to compute <math>-\frac{j}{k}</math>. <br />
<br />
From the given information, we know that the coefficient of the <math>x^2</math> term is <math>6</math>, and we also know that <math>P(-1) = -33</math>, or in other words, <math>-j + k = -26</math>. By Newton's Sums (since we are given <math>a^3 + b^3 + c^3</math>), we also find that <math>6j + k = 43</math>. Solving this system, we find that <math>(j, k) \in (\frac{69}{7}, -\frac{113}{7})</math>. Thus, <math>\frac{j}{-k} = \frac{69}{113}</math>, so our final answer is <math>69 + 113 = \boxed{182}</math>.<br />
<br />
== Problem 12 ==<br />
Alpha and Beta play a game on the number line below.<br />
<br />
<asy><br />
import olympiad;<br />
size(140);<br />
dot(origin); real t = .2; draw((-3,0)--(3,0), Arrows(6)); for(int i=-2; i<3; i=i+1) { draw((i,t)--(i,-t)); label(string(i), (i,-t), dir(270), fontsize(8));}<br />
</asy><br />
Both players start at <math>0</math>. Each turn, Alpha has an equal chance of moving <math>1</math> unit in either the positive or negative directions while Beta has a <math>\tfrac{2}{3}</math> chance of moving <math>1</math> unit in the positive direction and a <math>\tfrac{1}{3}</math> chance of moving <math>1</math> unit in the negative direction. The two alternate turns with Alpha going first. If a player reaches <math>2</math> at any point in the game, he wins; however, if a player reaches <math>-2</math>, he loses and the other player wins. If <math>\tfrac pq</math> is the probability that Alpha beats Beta, where <math>p</math> and <math>q</math> are relatively prime positive integers, find <math>p+q</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 12|Solution]]<br />
<br />
== Problem 13 ==<br />
Let <math>A_1A_2A_3A_4A_5A_6</math> be a hexagon inscribed inside a circle of radius <math>r</math>. Furthermore, for each positive integer <math>1\leq i\leq 6</math> let <math>M_i</math> be the midpoint of the segment <math>\overline{A_iA_{i+1}}</math>, where <math>A_7\equiv A_1</math>. Suppose that hexagon <math>M_1M_2M_3M_4M_5M_6</math> can also be inscribed inside a circle. If <math>A_1A_2=A_3A_4=5</math> and <math>A_5A_6=23</math>, then <math>r^2</math> can be written in the form <math>\tfrac mn</math> where <math>m</math> and <math>n</math> are positive relatively prime integers. Find <math>m+n</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 13|Solution]]<br />
<br />
== Problem 14 ==<br />
Consider a set of <math>\tfrac{n(n+1)}{2}</math> pennies laid out in the formation of an equilateral triangle with "side length" <math>n</math>. You wish to move some of the pennies so that the triangle is flipped upside down. For example, with <math>n=2</math>, you could take the top penny and move it to the bottom to accomplish this task, as shown:<br />
<br />
<asy><br />
size(180);<br />
defaultpen(linewidth(0.8));<br />
filldraw(circle((-2,0),1)^^circle((2,0),1)^^circle((0,2*sqrt(3)),1)^^circle((10,0),1)^^circle((14,0),1)^^circle((12,-2*sqrt(3)),1),grey);<br />
draw((-1.25,2*sqrt(3))..(-4.5,0)..(-1.25,-2*sqrt(3)),linetype("4 4"),EndArrow);<br />
draw(circle((0,-2*sqrt(3)),1),linetype("4 4"));<br />
</asy><br />
<br />
Let <math>S_n</math> be the minimum number of pennies for which this can be done in terms of <math>n</math>. Find <math>S_{50}</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 14|Solution]]<br />
<br />
== Problem 15 ==<br />
Let <math>\triangle ABC</math> be a triangle with <math>AB=13</math>, <math>BC=14</math>, and <math>CA=15</math>. Let <math>O</math> denote its circumcenter and <math>H</math> its orthocenter. The circumcircle of <math>\triangle AOH</math> intersects <math>AB</math> and <math>AC</math> at <math>D</math> and <math>E</math> respectively. Suppose <math>\tfrac{AD}{AE}=\tfrac mn</math> where <math>m</math> and <math>n</math> are positive relatively prime integers. Find <math>m-n</math>.<br />
<br />
[[Mock AIME I 2015 Problems/Problem 15|Solution]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_4_2006-2007_Problems/Problem_11&diff=83381
Mock AIME 4 2006-2007 Problems/Problem 11
2017-02-09T23:33:51Z
<p>Blue8931: /* Solution */</p>
<hr />
<div>==Problem==<br />
Let <math>\triangle ABC</math> be an equilateral triangle. Two points <math>D</math> and <math>E</math> are chosen on <math>\overline{AB}</math> and <math>\overline{AC}</math>, respectively, such that <math>AD = CE</math>. Let <math>F</math> be the intersection of <math>\overline{BE}</math> and <math>\overline{CD}</math>. The area of <math>\triangle ABC</math> is 13 and the area of <math>\triangle ACF</math> is 3. If <math>\frac{CE}{EA}=\frac{p+\sqrt{q}}{r}</math>, where <math>p</math>, <math>q</math>, and <math>r</math> are relatively prime positive integers, compute <math>p+q+r</math>.<br />
<br />
==Solution==<br />
<br />
Let <math>AD = CE = a</math>, and <math>EA = DB = b</math>. Note that we want to compute the ratio <math>\frac{a}{b}</math>. <br />
<br />
Assign a mass of <math>a</math> to point <math>A</math>. This gives point <math>C</math> a mass of <math>b</math> and point <math>D</math> a mass of <math>a + \frac{a^2}{b}</math>. Thus, <math>\frac{CF}{FD} = \frac{a+\frac{a^2}{b}}{b}</math>. <br />
<br />
Since the ratio of areas of triangles that share an altitude is simply the ratio of their bases, we have that:<br />
<br />
<math>13 \cdot \frac{a}{a+b} \cdot \frac{a+\frac{a^2}{b}}{a+\frac{a^2}{b} + b} = 3<br />
\newline<br />
\newline<br />
\newline<br />
13 \cdot \frac{a}{a+b} \cdot \frac{ab + a^2}{ab + a^2 + b^2} = 3<br />
\newline<br />
\newline<br />
\newline<br />
13 \cdot \frac{a^2}{ab+a^2+b^2} = 3<br />
\newline<br />
\newline<br />
\newline<br />
\frac{a^2}{ab+a^2+b^2} = \frac{3}{13}<br />
\newline<br />
\newline<br />
\newline<br />
\frac{b^2 + a^2 + ab}{a^2} = \frac{13}{3}<br />
\newline <br />
\newline<br />
\newline<br />
(\frac{b}{a})^2 + \frac{b}{a} = \frac{10}{3}</math>.<br />
<br />
By the quadratic formula, we find that <math>\frac{b}{a} = \frac{\sqrt{129}-3}{6}</math>, so <math>\frac{a}{b} = \frac{6}{\sqrt{129}-3} = \frac{3 + \sqrt{129}}{20}</math>.<br />
<br />
Thus, our final answer is <math>3 + 129 + 20 = \boxed{152}</math>. <br />
<br />
<br />
<br />
----<br />
<br />
*[[Mock AIME 4 2006-2007 Problems/Problem 12| Next Problem]]<br />
*[[Mock AIME 4 2006-2007 Problems/Problem 10| Previous Problem]]<br />
*[[Mock AIME 4 2006-2007 Problems]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_4_2006-2007_Problems/Problem_11&diff=83380
Mock AIME 4 2006-2007 Problems/Problem 11
2017-02-09T23:30:31Z
<p>Blue8931: /* Solution */</p>
<hr />
<div>==Problem==<br />
Let <math>\triangle ABC</math> be an equilateral triangle. Two points <math>D</math> and <math>E</math> are chosen on <math>\overline{AB}</math> and <math>\overline{AC}</math>, respectively, such that <math>AD = CE</math>. Let <math>F</math> be the intersection of <math>\overline{BE}</math> and <math>\overline{CD}</math>. The area of <math>\triangle ABC</math> is 13 and the area of <math>\triangle ACF</math> is 3. If <math>\frac{CE}{EA}=\frac{p+\sqrt{q}}{r}</math>, where <math>p</math>, <math>q</math>, and <math>r</math> are relatively prime positive integers, compute <math>p+q+r</math>.<br />
<br />
==Solution==<br />
<br />
{{solution}}<br />
<br />
Let <math>AD = CE = a</math>, and <math>EA = DB = b</math>. Note that we want to compute the ratio <math>\frac{a}{b}</math>. <br />
<br />
Assign a mass of <math>a</math> to point <math>A</math>. This gives point <math>C</math> a mass of <math>b</math> and point <math>D</math> a mass of <math>a + \frac{a^2}{b}</math>. Thus, <math>\frac{CF}{FD} = \frac{a+\frac{a^2}{b}}{b}</math>. <br />
<br />
Since the ratio of areas of triangles that share an altitude is simply the ratio of their bases, we have that:<br />
<br />
<math>13 \cdot \frac{a}{a+b} \cdot \frac{a+\frac{a^2}{b}}{a+\frac{a^2}{b} + b} = 3<br />
\newline<br />
\newline<br />
\newline<br />
13 \cdot \frac{a}{a+b} \cdot \frac{ab + a^2}{ab + a^2 + b^2} = 3<br />
\newline<br />
\newline<br />
\newline<br />
13 \cdot \frac{a^2}{ab+a^2+b^2} = 3<br />
\newline<br />
\newline<br />
\newline<br />
\frac{a^2}{ab+a^2+b^2} = \frac{3}{13}<br />
\newline<br />
\newline<br />
\newline<br />
\frac{b^2 + a^2 + ab}{a^2} = \frac{13}{3}<br />
\newline <br />
\newline<br />
\newline<br />
(\frac{b}{a})^2 + \frac{b}{a} = \frac{10}{3}</math>.<br />
<br />
By the quadratic formula, we find that <math>\frac{b}{a} = \frac{\sqrt{129}-3}{6}</math>, so <math>\frac{a}{b} = \frac{6}{\sqrt{129}-3} = \frac{3 + \sqrt{129}}{20}</math>.<br />
<br />
Thus, our final answer is <math>3 + 129 + 20 = \boxed{152}</math>. <br />
<br />
<br />
<br />
----<br />
<br />
*[[Mock AIME 4 2006-2007 Problems/Problem 12| Next Problem]]<br />
*[[Mock AIME 4 2006-2007 Problems/Problem 10| Previous Problem]]<br />
*[[Mock AIME 4 2006-2007 Problems]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_4_2006-2007_Problems/Problem_11&diff=83379
Mock AIME 4 2006-2007 Problems/Problem 11
2017-02-09T23:30:05Z
<p>Blue8931: /* Solution */</p>
<hr />
<div>==Problem==<br />
Let <math>\triangle ABC</math> be an equilateral triangle. Two points <math>D</math> and <math>E</math> are chosen on <math>\overline{AB}</math> and <math>\overline{AC}</math>, respectively, such that <math>AD = CE</math>. Let <math>F</math> be the intersection of <math>\overline{BE}</math> and <math>\overline{CD}</math>. The area of <math>\triangle ABC</math> is 13 and the area of <math>\triangle ACF</math> is 3. If <math>\frac{CE}{EA}=\frac{p+\sqrt{q}}{r}</math>, where <math>p</math>, <math>q</math>, and <math>r</math> are relatively prime positive integers, compute <math>p+q+r</math>.<br />
<br />
==Solution==<br />
<br />
{{solution}}<br />
<br />
Let <math>AD = CE = a</math>, and <math>EA = DB = b</math>. Note that we want to compute the ratio <math>\frac{a}{b}</math>. <br />
<br />
Assign a mass of <math>a</math> to point <math>A</math>. This gives point <math>C</math> a mass of <math>b</math> and point <math>D</math> a mass of <math>a + \frac{a^2}{b}</math>. Thus, <math>\frac{CF}{FD} = \frac{a+\frac{a^2}{b}}{b}</math>. <br />
<br />
Since the ratio of areas of triangles that share an altitude is simply the ratio of their bases, we have that:<br />
<br />
<math>13 \cdot \frac{a}{a+b} \cdot \frac{a+\frac{a^2}{b}}{a+\frac{a^2}{b} + b} = 3<br />
\newline<br />
\newline<br />
13 \cdot \frac{a}{a+b} \cdot \frac{ab + a^2}{ab + a^2 + b^2} = 3<br />
\newline<br />
\newline<br />
13 \cdot \frac{a^2}{ab+a^2+b^2} = 3<br />
\newline<br />
\newline<br />
\frac{a^2}{ab+a^2+b^2} = \frac{3}{13}<br />
\newline<br />
\newline<br />
\frac{b^2 + a^2 + ab}{a^2} = \frac{13}{3}<br />
\newline <br />
\newline<br />
(\frac{b}{a})^2 + \frac{b}{a} = \frac{10}{3}</math>.<br />
<br />
By the quadratic formula, we find that <math>\frac{b}{a} = \frac{\sqrt{129}-3}{6}</math>, so <math>\frac{a}{b} = \frac{6}{\sqrt{129}-3} = \frac{3 + \sqrt{129}}{20}</math>.<br />
<br />
Thus, our final answer is <math>3 + 129 + 20 = \boxed{152}</math>. <br />
<br />
<br />
<br />
----<br />
<br />
*[[Mock AIME 4 2006-2007 Problems/Problem 12| Next Problem]]<br />
*[[Mock AIME 4 2006-2007 Problems/Problem 10| Previous Problem]]<br />
*[[Mock AIME 4 2006-2007 Problems]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_4_2006-2007_Problems/Problem_11&diff=83378
Mock AIME 4 2006-2007 Problems/Problem 11
2017-02-09T23:29:15Z
<p>Blue8931: /* Solution */</p>
<hr />
<div>==Problem==<br />
Let <math>\triangle ABC</math> be an equilateral triangle. Two points <math>D</math> and <math>E</math> are chosen on <math>\overline{AB}</math> and <math>\overline{AC}</math>, respectively, such that <math>AD = CE</math>. Let <math>F</math> be the intersection of <math>\overline{BE}</math> and <math>\overline{CD}</math>. The area of <math>\triangle ABC</math> is 13 and the area of <math>\triangle ACF</math> is 3. If <math>\frac{CE}{EA}=\frac{p+\sqrt{q}}{r}</math>, where <math>p</math>, <math>q</math>, and <math>r</math> are relatively prime positive integers, compute <math>p+q+r</math>.<br />
<br />
==Solution==<br />
<br />
{{solution}}<br />
<br />
Let <math>AD = CE = a</math>, and <math>EA = DB = b</math>. Note that we want to compute the ratio <math>\frac{a}{b}</math>. <br />
<br />
Assign a mass of <math>a</math> to point <math>A</math>. This gives point <math>C</math> a mass of <math>b</math> and point <math>D</math> a mass of <math>a + \frac{a^2}{b}</math>. Thus, <math>\frac{CF}{FD} = \frac{a+\frac{a^2}{b}}{b}</math>. <br />
<br />
Since the ratio of areas of triangles that share an altitude is simply the ratio of their bases, we have that:<br />
<br />
<math>13 \cdot \frac{a}{a+b} \cdot \frac{a+\frac{a^2}{b}}{a+\frac{a^2}{b} + b} = 3<br />
\newline<br />
13 \cdot \frac{a}{a+b} \cdot \frac{ab + a^2}{ab + a^2 + b^2} = 3<br />
\newline<br />
13 \cdot \frac{a^2}{ab+a^2+b^2} = 3<br />
\newline<br />
\frac{a^2}{ab+a^2+b^2} = \frac{3}{13}<br />
\newline<br />
\frac{b^2 + a^2 + ab}{a^2} = \frac{13}{3}<br />
\newline <br />
(\frac{b}{a})^2 + \frac{b}{a} = \frac{10}{3}</math>.<br />
<br />
By the quadratic formula, we find that <math>\frac{b}{a} = \frac{\sqrt{129}-3}{6}</math>, so <math>\frac{a}{b} = \frac{6}{\sqrt{129}-3} = \frac{3 + \sqrt{129}}{20}</math>.<br />
<br />
Thus, our final answer is <math>3 + 129 + 20 = \boxed{152}</math>. <br />
<br />
<br />
<br />
----<br />
<br />
*[[Mock AIME 4 2006-2007 Problems/Problem 12| Next Problem]]<br />
*[[Mock AIME 4 2006-2007 Problems/Problem 10| Previous Problem]]<br />
*[[Mock AIME 4 2006-2007 Problems]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=1983_AIME_Problems/Problem_13&diff=82647
1983 AIME Problems/Problem 13
2017-02-01T02:08:02Z
<p>Blue8931: /* Solution 3 */</p>
<hr />
<div>== Problem ==<br />
<!-- don't remove the following tag, for PoTW on the Wiki front page--><onlyinclude>For <math>\{1, 2, 3, \ldots, n\}</math> and each of its non-empty subsets, an alternating sum is defined as follows. Arrange the number in the subset in decreasing order and then, beginning with the largest, alternately add and subtract successive numbers. For example, the alternating sum for <math>\{1, 2, 4, 6,9\}</math> is <math>9-6+4-2+1=6</math> and for <math>\{5\}</math> it is simply <math>5</math>. Find the sum of all such alternating sums for <math>n=7</math>.<!-- don't remove the following tag, for PoTW on the Wiki front page--></onlyinclude><br />
<br />
== Solution 1==<br />
Let <math>S</math> be a non-[[empty set | empty]] [[subset]] of <math>\{1,2,3,4,5,6\}</math>. <br />
<br />
Then the alternating sum of <math>S</math> plus the alternating sum of <math>S</math> with 7 included is 7. In mathematical terms, <math>S+ (S\cup 7)=7</math>. This is true because when we take an alternating sum, each term of <math>S</math> has the opposite sign of each corresponding term of <math>S\cup 7</math>.<br />
<br />
Because there are <math>63</math> of these pairs, the sum of all possible subsets of our given set is <math>63*7</math>. However, we forgot to include the subset that only contains <math>7</math>, so our answer is <math>64\cdot 7=\boxed{448}</math>.<br />
<br />
== Solution 2==<br />
<br />
Consider a given subset <math>T</math> of <math>S</math> that contains 7; then there is a subset <math>T'</math> which contains all the elements of <math>T</math> except for 7, and only those. Since each element of <math>T'</math> has one element fewer preceding it than it does in <math>T</math>, their signs are opposite; so the sum of the alternating sums of <math>T</math> and <math>T'</math> is equal to 7. There are <math>2^6</math> subsets containing 7, so our answer is <math>7 * 2^6 = \boxed{448}</math>.<br />
<br />
==Solution 3==<br />
<br />
Denote the desired total of alternating sums of an <math>n</math> element set with <math>S_n</math>. We are looking for <math>S_7</math>. Note that all alternating sums of an <math>n</math> element set are also alternating sums of an <math>n+1</math> element set. However, when we go from an <math>n</math> to <math>n+1</math> element set, for each subset with the new element, we are adding the new element and subtracting one of the alternating sums of the <math>n</math> element set. There are <math>2^n</math> subsets of an <math>n+1</math> element set that includes the new element, giving us the following relationship.<br />
<br />
<math>S_{n+1} = S_n + 2^n(n+1) - S_n = 2^n(n+1)</math>. <br />
<br />
For <math>n = 6</math>, this becomes <math>S_ 7 = 2^6(7) = \boxed{448}</math>.<br />
<br />
== See Also ==<br />
{{AIME box|year=1983|num-b=12|num-a=14}}<br />
<br />
[[Category:Intermediate Combinatorics Problems]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=1983_AIME_Problems/Problem_13&diff=82646
1983 AIME Problems/Problem 13
2017-02-01T01:58:34Z
<p>Blue8931: </p>
<hr />
<div>== Problem ==<br />
<!-- don't remove the following tag, for PoTW on the Wiki front page--><onlyinclude>For <math>\{1, 2, 3, \ldots, n\}</math> and each of its non-empty subsets, an alternating sum is defined as follows. Arrange the number in the subset in decreasing order and then, beginning with the largest, alternately add and subtract successive numbers. For example, the alternating sum for <math>\{1, 2, 4, 6,9\}</math> is <math>9-6+4-2+1=6</math> and for <math>\{5\}</math> it is simply <math>5</math>. Find the sum of all such alternating sums for <math>n=7</math>.<!-- don't remove the following tag, for PoTW on the Wiki front page--></onlyinclude><br />
<br />
== Solution 1==<br />
Let <math>S</math> be a non-[[empty set | empty]] [[subset]] of <math>\{1,2,3,4,5,6\}</math>. <br />
<br />
Then the alternating sum of <math>S</math> plus the alternating sum of <math>S</math> with 7 included is 7. In mathematical terms, <math>S+ (S\cup 7)=7</math>. This is true because when we take an alternating sum, each term of <math>S</math> has the opposite sign of each corresponding term of <math>S\cup 7</math>.<br />
<br />
Because there are <math>63</math> of these pairs, the sum of all possible subsets of our given set is <math>63*7</math>. However, we forgot to include the subset that only contains <math>7</math>, so our answer is <math>64\cdot 7=\boxed{448}</math>.<br />
<br />
== Solution 2==<br />
<br />
Consider a given subset <math>T</math> of <math>S</math> that contains 7; then there is a subset <math>T'</math> which contains all the elements of <math>T</math> except for 7, and only those. Since each element of <math>T'</math> has one element fewer preceding it than it does in <math>T</math>, their signs are opposite; so the sum of the alternating sums of <math>T</math> and <math>T'</math> is equal to 7. There are <math>2^6</math> subsets containing 7, so our answer is <math>7 * 2^6 = \boxed{448}</math>.<br />
<br />
==Solution 3==<br />
<br />
Denote the desired total of alternating sums of an <math>n</math> element set with <math>S_n</math>. We are looking for <math>S_7</math>. Note that all alternating sums of an <math>n</math> element set are also alternating sums of an <math>n+1</math> element set. However, when we go from an <math>n</math> to <math>n+1</math> element set, for each subset with the new element, we are adding the new element and subtracting one of the alternating sums of the <math>n</math> element set. There are <math>2^n</math> subsets of an <math>n+1</math> element set that includes the new element, giving us the following relationship.<br />
<br />
<math>S_{n+1} = S_n + 2^n(n+1) - S^n = 2^n(n+1)</math>. <br />
<br />
For <math>n = 6</math>, this becomes <math>S_ 7 = 2^6(7) = \boxed{448}</math>. <br />
<br />
== See Also ==<br />
{{AIME box|year=1983|num-b=12|num-a=14}}<br />
<br />
[[Category:Intermediate Combinatorics Problems]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_1_Pre_2005_Problems/Problem_12&diff=82030
Mock AIME 1 Pre 2005 Problems/Problem 12
2016-12-27T02:41:06Z
<p>Blue8931: /* Solution */</p>
<hr />
<div>== Problem ==<br />
<math>ABCD</math> is a rectangular sheet of paper. <math>E</math> and <math>F</math> are points on <math>AB</math> and <math>CD</math> respectively such that <math>BE < CF</math>. If <math>BCFE</math> is folded over <math>EF</math>, <math>C</math> maps to <math>C'</math> on <math>AD</math> and <math>B</math> maps to <math>B'</math> such that <math>\angle{AB'C'} \cong \angle{B'EA}</math>. If <math>AB' = 5</math> and <math>BE = 23</math>, then the area of <math>ABCD</math> can be expressed as <math>a + b\sqrt{c}</math> square units, where <math>a, b,</math> and <math>c</math> are integers and <math>c</math> is not divisible by the square of any prime. Compute <math>a + b + c</math>.<br />
<br />
== Solution ==<br />
Let <math>\angle{AB'C'} = \theta</math>. By some angle chasing in <math>\triangle{AB'E}</math>, we find that <math>\angle{EAB'} = 90^{\circ} - 2 \theta</math>. Before we apply the law of sines, we're going to want to get everything in terms of <math>\sin \theta</math>, so note that <math>\sin \angle{EAB'} = \sin(90^{\circ} - 2 \theta) = \cos 2 \theta = 1 - 2 \sin^2 \theta</math>. Now, we use law of sines, which gives us the following:<br />
<br />
<math>\frac{\sin \theta}{5}=\frac{1 - 2 \sin^2 \theta}{23} \implies \sin \theta = \frac{-23 \pm 27}{20}</math>, <br />
but since <math>\theta < 180^{\circ}</math>, we go with the positive solution. Thus, <math>\sin \theta = \frac15</math>.<br />
<br />
Denote the intersection of <math>B'C'</math> and <math>AE</math> with <math>G</math>. By another application of the law of sines, <math>B'G = \frac{23}{\sqrt{24}}</math> and <math>AE = 10\sqrt{6}</math>. Since <math>\sin \theta = \frac15, GE = \frac{115}{\sqrt{24}}</math>, and <math>AG = AE - GE = 10\sqrt{6} - \frac{115}{\sqrt{24}} = \frac{5}{\sqrt{24}}</math>. Note that <math>\triangle{EB'G} \sim \triangle{C'AG}</math>, so <math>\frac{EG}{B'G}=\frac{C'G}{AG} \implies C'G = \frac{25}{\sqrt{24}}</math>.<br />
<br />
Now we have that <math>AB = AE + EB = 10\sqrt{6} + 23</math>, and <math>B'C' = BC = B'G + C'G = \frac{23}{\sqrt{24}} + \frac{25}{\sqrt{24}} = \frac{48}{\sqrt{24}}=4\sqrt{6}</math>. Thus, the area of <math>ABCD</math> is <math>(10\sqrt{6} + 23)(4\sqrt{6}) = 92\sqrt{6} + 240</math>, and our final answer is <math>92 + 6 + 240 = \boxed{338}</math>.<br />
<br />
== See also ==<br />
{{Mock AIME box|year=Pre 2005|n=1|num-b=11|num-a=13|source=14769}}<br />
<br />
<br />
[[Category:Intermediate Geometry Problems]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=Mock_AIME_1_Pre_2005_Problems/Problem_12&diff=82029
Mock AIME 1 Pre 2005 Problems/Problem 12
2016-12-27T02:39:05Z
<p>Blue8931: /* Solution */</p>
<hr />
<div>== Problem ==<br />
<math>ABCD</math> is a rectangular sheet of paper. <math>E</math> and <math>F</math> are points on <math>AB</math> and <math>CD</math> respectively such that <math>BE < CF</math>. If <math>BCFE</math> is folded over <math>EF</math>, <math>C</math> maps to <math>C'</math> on <math>AD</math> and <math>B</math> maps to <math>B'</math> such that <math>\angle{AB'C'} \cong \angle{B'EA}</math>. If <math>AB' = 5</math> and <math>BE = 23</math>, then the area of <math>ABCD</math> can be expressed as <math>a + b\sqrt{c}</math> square units, where <math>a, b,</math> and <math>c</math> are integers and <math>c</math> is not divisible by the square of any prime. Compute <math>a + b + c</math>.<br />
<br />
== Solution ==<br />
Let <math>\angle{AB'C'} = \theta</math>. By some angle chasing in <math>\triangle{AB'E}</math>, we find that <math>\angle{EAB'} = 90^{\circ} - 2 \theta</math>. Before we apply the law of sines, we're going to want to get everything in terms of <math>\sin \theta</math>, so note that <math>\sin \angle{EAB'} = \sin(90^{\circ} - 2 \theta) = \cos 2 \theta = 1 - 2 \sin^2 \theta</math>. Now, we use law of sines, which gives us the following:<br />
<br />
<math>\frac{\sin \theta}{5}=\frac{1 - 2 \sin^2 \theta}{23} \implies \sin \theta = \frac{-23 \pm 27}{20}</math>, <br />
but since <math>\theta < 180^{\circ}</math>, we go with the positive solution. Thus, <math>\sin \theta = \frac15</math>.<br />
<br />
Denote the intersection of <math>B'C'</math> and <math>AE</math> with <math>G</math>. By another application of the law of sines, <math>B'G = \frac{23}{\sqrt{24}}</math> and <math>AE = 10\sqrt{6}</math>. Since <math>\sin \theta = \frac15, GE = \frac{115}{\sqrt{24}}</math>, and <math>AG = AE - GE = 10\sqrt{6} - \frac{115}{\sqrt{24}} = \frac{5}{\sqrt{24}}</math>. Note that <math>\triangle{EB'G} \sim \triangle{C'AG}</math>, so <math>\frac{EG}{B'G}=\frac{C'G}{AG} \implies C'G = \frac{25}{\sqrt{24}}</math>.<br />
<br />
Now we have that <math>AB = AE + EB = 10\sqrt{6} + 23</math>, and <math>B'C' = BC = B'G + C'G = \frac{23}{\sqrt{24}} + \frac{25}{\sqrt{24}} = \frac{48}{\sqrt{24}}=4\sqrt{6}</math>. Thus, the area of <math>ABCD</math> is <math>(10\sqrt{6} + 23)(4\sqrt{6}) = 92\sqrt{6} + 240</math>, and our final answer is <math>92 + 6 + 240 = \boxed{338}</math>.<br />
<br />
[i]Solution by blue8931[/i]<br />
<br />
== See also ==<br />
{{Mock AIME box|year=Pre 2005|n=1|num-b=11|num-a=13|source=14769}}<br />
<br />
<br />
[[Category:Intermediate Geometry Problems]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=North_Suburban_Mathematics_League&diff=82024
North Suburban Mathematics League
2016-12-26T16:42:20Z
<p>Blue8931: /* 2016-2017 Topics */</p>
<hr />
<div>The North Suburban Math League is a group of schools in the Chicago area that compete in five math competitions throughout the school year.<br />
<br />
== 2016-2017 Meet Dates ==<br />
*Meet #1: Thursday, September 29, 2016<br />
*Meet #2: Wednesday, November 16, 2016<br />
*Meet #3: Thursday, December 8, 2016<br />
*Meet #4: Wednesday, February 1, 2017<br />
*Meet #5: Wednesday, March 8, 2017 (Conference Meet)<br />
<br />
== 2016-2017 Topics ==<br />
Meets 3 and 4 are NO CALCULATOR.<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Meet 1'''<br />
! scope="col" | '''Meet 1'''<br />
! scope="col" | '''Meet 3'''<br />
! scope="col" | '''Meet 4'''<br />
|-<br />
! scope="row" | '''Freshmen'''<br />
| Ratios, Proportions, and Percent<br />
| Counting Basics and Simple Probability<br />
| Quadratics<br />
| Number Bases<br />
|-<br />
! scope="row" | '''Sophomores'''<br />
| Coordinate Geometry with Applications<br />
| Geometric Probability<br />
| Similarity<br />
| Advanced Geometry Topics<br />
|-<br />
! scope="row" | '''Juniors'''<br />
| Algebraic Coordinate Geometry<br />
| Probability<br />
| Modular Arithmetic<br />
| Sequences and Series<br />
|-<br />
! scope="row" | '''Seniors'''<br />
| Triangle Trigonometry with Applications<br />
| Probability<br />
| Diophantine Equations<br />
| Vector Analytic Graphing<br />
|-<br />
! scope="row" | '''Orals'''<br />
| Divisibility<br />
| Markov Chains<br />
| Linear Programming<br />
| The Algebra of Logic<br />
|-<br />
|}<br />
<br />
== Rules and Information ==<br />
''This is only a summary of the rules. To see the complete rules, please see the [http://nsml.org/current/rules/ NSML website].''<br />
=== Written Events ===<br />
*Each team enters 5 contestants and 5 alternates at each event. If a team wants to bring more than 5 alternates for any event, they must get permission from the host school in advance. No alternates are allowed at meet 5 (the conference meet). <br />
<br />
*The team's score for an event is the sum of the top three contestants' scores. Alternates' scores will only be counted towards their individual records, not towards the team's total.<br />
<br />
*There will be four written tests at each meet, one at each grade level. Each test will consist of five short-answer questions, worth a total of 25 points. Questions 1 and 2 will each be worth 4 points, question 3 will be worth 5 points, and questions 4 and 5 will be worth 6 points each.<br />
<br />
*Each test will be exactly thirty minutes in length.<br />
<br />
*The only materials students may use during the contest are: pens or pencils, erasers, calculators, and extra batteries. A student may use at most three calculators. Any battery (or solar) powered calculator that does not do symbolic manipulation is allowed. Freshmen and sophomores may not use an HP48 series calculator. In some cases, symbolic manipulators may be expected. These contests will be designated as CAS topics. Likewise, some contests may be designated as no calculator contests. Contests with special calculator exceptions will be identified as such on the schedule and on the topics list.<br />
<br />
*Students may compete in more than one event at each meet. They may compete above their grade level but not below it. The freshman and junior competitions begin at 6:15; the sophomore and senior competitions begin at 7:00. No one may compete as a contestant in both the oral and written events at a given meet.<br />
<br />
*A student who is not yet in the ninth grade may not compete as a contestant. Any student may compete as an alternate.<br />
<br />
=== Oral Events ===<br />
*There will be three questions, each on a different sheet of paper. Fifteen minutes are allowed for preparation, and ten minutes for presenting. The student may bring print or written materials and a calculator into the preparation room. For meets 1-3, the student must work alone; for meet 4, up to two students may work together in the preparation room, but only one may present. There is no oral event at the conference meet (meet 5).<br />
<br />
*Scoring - each judge will award points according to the following criteria:<br />
**Question #1 - 10 points for correctness<br />
**Question #2 - 12 points for correctness<br />
**Question #3 - 13 points for correctness<br />
**Presentation - 15 points<br />
<br />
==See Also==<br />
*[http://nsml.org NSML Website]<br />
*[[Illinois mathematics competitions]]</div>
Blue8931
https://artofproblemsolving.com/wiki/index.php?title=North_Suburban_Mathematics_League&diff=82022
North Suburban Mathematics League
2016-12-26T16:39:34Z
<p>Blue8931: /* 2015-2016 Meet Dates */</p>
<hr />
<div>The North Suburban Math League is a group of schools in the Chicago area that compete in five math competitions throughout the school year.<br />
<br />
== 2016-2017 Meet Dates ==<br />
*Meet #1: Thursday, September 29, 2016<br />
*Meet #2: Wednesday, November 16, 2016<br />
*Meet #3: Thursday, December 8, 2016<br />
*Meet #4: Wednesday, February 1, 2017<br />
*Meet #5: Wednesday, March 8, 2017 (Conference Meet)<br />
<br />
== 2015-2016 Topics ==<br />
Meets 3 and 4 are NO CALCULATOR.<br />
{| class="wikitable" style="text-align:center;width:100%"<br />
|-<br />
|<br />
! scope="col" | '''Meet 1'''<br />
! scope="col" | '''Meet 1'''<br />
! scope="col" | '''Meet 3'''<br />
! scope="col" | '''Meet 4'''<br />
|-<br />
! scope="row" | '''Freshmen'''<br />
| Ratios, Proportions, and Percent<br />
| Counting Basics and Simple Probability<br />
| Number Theory and Divisibility<br />
| Applications of Systems of Linear Equations and Inequalities<br />
|-<br />
! scope="row" | '''Sophomores'''<br />
| Perimeter, Area, and Surface Area<br />
| Geometric Probability<br />
| Circles<br />
| Advanced Geometry Topics<br />
|-<br />
! scope="row" | '''Juniors'''<br />
| Systems of Linear Equations and Inequalities with Applications<br />
| Probability<br />
| Logs and Exponents<br />
| Functions and Relations<br />
|-<br />
! scope="row" | '''Seniors'''<br />
| Triangle Trigonometry with Applications<br />
| Probability<br />
| Algebra of Complex Numbers<br />
| Sequences and Series<br />
|-<br />
! scope="row" | '''Orals'''<br />
| Taxicab Geometry<br />
| Fair Cake Division<br />
| Planning and Scheduling<br />
| Congruence and Similarity Transformations<br />
|-<br />
|}<br />
<br />
== Rules and Information ==<br />
''This is only a summary of the rules. To see the complete rules, please see the [http://nsml.org/current/rules/ NSML website].''<br />
=== Written Events ===<br />
*Each team enters 5 contestants and 5 alternates at each event. If a team wants to bring more than 5 alternates for any event, they must get permission from the host school in advance. No alternates are allowed at meet 5 (the conference meet). <br />
<br />
*The team's score for an event is the sum of the top three contestants' scores. Alternates' scores will only be counted towards their individual records, not towards the team's total.<br />
<br />
*There will be four written tests at each meet, one at each grade level. Each test will consist of five short-answer questions, worth a total of 25 points. Questions 1 and 2 will each be worth 4 points, question 3 will be worth 5 points, and questions 4 and 5 will be worth 6 points each.<br />
<br />
*Each test will be exactly thirty minutes in length.<br />
<br />
*The only materials students may use during the contest are: pens or pencils, erasers, calculators, and extra batteries. A student may use at most three calculators. Any battery (or solar) powered calculator that does not do symbolic manipulation is allowed. Freshmen and sophomores may not use an HP48 series calculator. In some cases, symbolic manipulators may be expected. These contests will be designated as CAS topics. Likewise, some contests may be designated as no calculator contests. Contests with special calculator exceptions will be identified as such on the schedule and on the topics list.<br />
<br />
*Students may compete in more than one event at each meet. They may compete above their grade level but not below it. The freshman and junior competitions begin at 6:15; the sophomore and senior competitions begin at 7:00. No one may compete as a contestant in both the oral and written events at a given meet.<br />
<br />
*A student who is not yet in the ninth grade may not compete as a contestant. Any student may compete as an alternate.<br />
<br />
=== Oral Events ===<br />
*There will be three questions, each on a different sheet of paper. Fifteen minutes are allowed for preparation, and ten minutes for presenting. The student may bring print or written materials and a calculator into the preparation room. For meets 1-3, the student must work alone; for meet 4, up to two students may work together in the preparation room, but only one may present. There is no oral event at the conference meet (meet 5).<br />
<br />
*Scoring - each judge will award points according to the following criteria:<br />
**Question #1 - 10 points for correctness<br />
**Question #2 - 12 points for correctness<br />
**Question #3 - 13 points for correctness<br />
**Presentation - 15 points<br />
<br />
==See Also==<br />
*[http://nsml.org NSML Website]<br />
*[[Illinois mathematics competitions]]</div>
Blue8931