Hello everybody! I know some of you participate in math team, and if you do, you're probably going to take the AMC 8 this Tuesday, November 12.
First, an introduction. AMC (American Mathematics Competition) is an extremely well-known competition series. A good score on an AMC is a ticket into some amazing summer programs and opportunities, and in a couple of years, good AMC scores will help with applying to college as well.
The AMC series begins with the AMC 8 which middle schoolers typically take. It has 25 multiple-choice questions and it is scored out of 25. Anyone in 10th grade or below can also take the AMC 10, and anyone in 12th grade or below can also take the AMC 12. Both of these have 25 multiple-choice questions.
Here's what makes the AMC super cool: If you work your way up, you're invited to represent USA on the international stage of math! If you do well on the AMC 10 or the AMC 12, you can take an invitational competition called the AIME (American Invitational Math Exam), which has only 15 questions for 3 hours! (They're pretty hard questions, hence the amount of time you get, but it's a lot of fun.) If you do well on the AIME, you get to participate in USAMO (USA Math Olympiad), which has even harder questions that require proofs and it gives you even less questions in even more time (because they're so hard) for an even higher stake. From there, a super high score sends you to MOSP (Mathematical Olympiad Summer Program), and the top students there are selected to represent the US at the International Math Olympiad.
Only six students ever make it that far, but it is incredibly neat that the possibility exists for anyone taking this test nationwide, so I highly encourage all middle schoolers to also take the AMC 10 to get a taste of the wider world of AMCs.
My personal experience with the AMC has culminated in the AIME so far, which I was able to make in 8th grade and every year since. To put that in perspective, only 2.5% of all the people - mostly high schoolers - who take the AMC 10 ever make the AIME. (For USAMO, only about five people ever make it in Georgia, and that's an aspiration of many of us on the state math team.)
But back to the real point of this blog post! I want to give you guys some strategies for the AMC 8. Some of these come from artofproblemsolving.com which I always highly recommend, and some of these come from my personal experience.
1. Do lots of practice problems! I know it's only a couple of days before the exam, but just glancing through and trying an AMC always helps! You can find some here. You can also check out this forum to discuss and collaborate with others on how to solve some problems! Try mixing it up and doing some problems on the fly but taking others under the real 40-minute time pressure. Always make sure you read the solutions afterward for those you miss and those you get right but spend too much time on because often there's a faster way of solving the problem.
2. Check out these facts and formulas! This link is Coach Monks's MathCounts Playbook, and it's geared towards MathCounts, but it also really helps for AMC 8.
3. Know what to bring. Typically, number 2 pencils and erasers are enough, but you're also allowed to have rulers, protractors, scratch paper, and graph paper, so ask your teacher/proctor if they have any you can use for the test or bring in your own!
4. Manage your time. It's 40 minutes! Keep an eye on the clock, and leave the last couple minutes to check and review and just make sure you bubbled everything correctly.
5. Organize your scratch paper into sections. One thing that really helps on AMCs is dividing your paper up into four boxes on each side. Label each box with a question number and keep your work for that question in there, so if you want to review something, it's easy to find!
6. Avoid careless errors! This is easier said than done, but keeping your work organized on your scratch paper and slowing down are two great ways to avoid accidentally multiplying incorrectly or the like. Just stay careful and attentive and your score could go way up! Here's a great article about learning to avoid stupid mistakes.
7. Read, read and read! This goes right along with avoiding careless errors. Make sure you're interpreting the problem correctly. Some of the highest scorers recommend reading the problem once to get the gist of it and immediately reading it a second time, paying more attention to details. Then, after you've solved the problem, read it one more time to make sure you're actually answering what they're asking. Also, read the answer choices to see if you can rule anything out immediately.
8. Don't be afraid to guess. There's no guessing penalty on the AMC 8, so go ahead and guess! And if you can narrow it down to a range (if you know it's greater than 20 or that's it's a square number for example), that makes guessing even easier.
9. Dive in! Some problems are easier than they seem (especially geometry), so just go ahead and try it out. Often, if there's a long equation that looks pretty complicated, there's a pretty easy way to go around it if you just think about it for a bit. Test writers put these problems later in the test because they look hard not because they're actually hard, so they tend to be easier than you think they'll be. This is one of my most crucial tips because it's so important you don't end up just sitting and staring. Gravitating towards problems you know you can do is a great way to get a good score, but cycle back around and at least try as many as you can!
10. The standard tips: I might as well tell you to get a good night's sleep and eat a healthy breakfast. Cliche, but it honestly helps so much!
Here are the awards you can get for doing exceptionally well on the AMC along with the scores you probably need to get to get them!
Top 2%: Certificate of Distinction (around 22-25)
Top 5%: Honor Roll Certificate of Distinction (around 18-21)
Top 15% (6th graders and younger only): Certificate of Merit (around 15-25)
Schools can also give out first, second and third place awards within their school.
If you're even more serious about improving your AMC 8 scores (or 10/12 down the road), check out these resources:
- Art of Problem Solving's Volume 1 on competition math is probably the best resource for both AMC 8 and 10. You can find it on their website or on Amazon.
-Some other great books include The Three-Year MathCounts Marathon by Karen Ge and Art and Craft of Problem Solving by Paul Zeitz, and feel free to ask in the comments for even more book recommendations!
-Ardent Academy's video is a great description of AMC 8 strategies that I referenced while writing this blog post, so watch that for even more detail.
-Doing practice problems and learning concepts on cheat sheets, like the MathCounts playbook I mentioned earlier, is a great way to learn for AMCs for free. (I have some cheat sheets up in the high school resources section that also work for middle schoolers looking to learn more.)
A quick disclaimer: Math competitions are amazing opportunities to show the math you can do and to learn and expose yourself to new math topics, like number theory and combinatorics that show up on AMCs but not in math class. They've been incredible for me, but they're also not for everybody. There are some people I know that are incredible at math (and other fields like programming and physics), but they don't do well under pressure at math competitions or simply don't like them, and that's totally okay. You can enjoy math in other ways as well, such as reading my blog posts, reading math books, or investigating math on your own or with others. Emory Math Circle in Atlanta does a great job of exposing students to the last part, and there are math circles everywhere, so if you're from somewhere else, find one near you! I'm always willing to recommend options for anybody, so tell me a little bit about yourself and I can give you some advice!
Thanks so much for reading this week's blog post, and if you have any questions about the AMC 8 or AMCs or math competitions in general, just let me know in the comments! I've done quite a few competitions in my life, so I'm always willing to answer any questions or suggestions!