Wednesday, February 3, 2016

AMC 8, 10, and 12: Multiple choice math competitions that are just the beginning


The Mathematical Association of America runs a number of competitions for middle and high schools students, which are usually administered in schools, and are the most well known and widely taken math competitions in the US.  However, the high school competitions are actually the first step of many in the selection process for the US International Mathematical Olympiad (IMO).  There are a lot of acronyms in this post, so I included a cheat sheet and a flow chart at the bottom.

AMC 8:
  • Anyone in grades 8 and below can participate
  • Students have 40 minutes to answer 25 multiple choice questions
  • Takes place in November
  • Students are not penalized for incorrect answers
AMC 10/12
  • Anyone in grades 10 and below (AMC 10) or 12 and below (AMC 12) can participate
  • Students have 75 minutes to answer 25 multiple choice questions 
  • Draws on material up through algebra and geometry (AMC 10) or precalculus (AMC 12)
  • Offered twice in February (A and B version)
  • Students are penalized for incorrect answers
  • 150 is perfect score
For the top scorers, the AMC 10/12 is just the beginning! 
  • High scorers (usually 120+ on AMC 10 or 100+ on AMC 12) are invited to take the AIME.
  • The AIME consists of 15 questions of increasing difficulty where each answer in an integer between 0 and 999 inclusive. 
  • A combination of AMC and AIME score is used to determine qualification for the USAMO (for students who took AMC 12) and USAJMO (for students who took AMC 10)
  • The USAMO and USAJMO are proof based exams and are spread over two days.  During each day, students are given four and a half hours to answer 3 questions. 
  • Top scorers on the USAMO and USAJMO (who are US residents) are invited to MOSP and considered for the US IMO team. 
  • MOSP is an intensive summer program meant to select and train the US IMO team held at Carnegie Mellon University.
  • From MOSP, 6 students are invited to represent the United States in the IMO. 
  • The IMO is proof based and spread over two days.  During each day, students have four and a half hours to answer 3 questions. 
My thoughts: 

I think that all middle and high school students who like math should take the appropriate AMC.  As I've gotten older, I've appreciated the quality of the problems more and more.  For students who are serious about math competitions, it's worth practicing with old exams, which you can find here.  

It also should be noted that students can take more than one of these exams per year, and can chose to take one that is higher than their grade level.  For example, a middle schooler can take (AMC 8) and (AMC 10A or AMC 12A) and (AMC 10B or AMC 12B).  A 9th or 10th grader can take (AMC 10A or AMC 12A) and (AMC 10B or AMC 12B).  An 11th or 12th grader can take (AMC 12A) and (AMC 12B).  This kind of thing mainly makes sense for students who want to improve their chances of advancing to the AIME and beyond.  If you want to take more than just the AMC 8 as a middle schooler or the AMC 10/12 A as a high schooler, you will likely have to be more proactive with your school (or look for an enrichment center or university that offers the exams).  

Acronym Cheat Sheet:
  • AMC = American Mathematics Competitions
  • AIME = American Invitational mathematics Examination
  • USAMO = United States of America Mathematical Olympiad
  • USAJMO = United States of America Junior Mathematical Olympiad
  • MOSP = Mathematical Olympiad Summer Program (sometimes abbreviated MOP)
  • IMO = International Mathematical Olympiad


Note: Between MOSP and IMO, there's also a Team Selection Test Selection Test and a Team Selection Test, but if you're at that level, I am no longer qualified to give you any guidance.


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