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How to Study for the Math Olympiad: AMC 10/AMC 12


Have you ever wondered what it would take to represent America at the International Math Olympiad? Or maybe you're a strong math student who is wondering what opportunities are available to you outside the classroom?

In this article, we'll answer all your Math Olympiad questions! We'll explain what it takes to qualify for the International Math Olympiad and how to ace the qualifying tests—the AMC 10 and AMC 12.


How Do You Qualify for Math Olympiad?

In this section we discuss the three key steps to qualifying for Math Olympiad.


Step 1: Take the AMC 10 or AMC 12

The AMC 10 and AMC 12 are nationwide tests administered by the Mathematical Association of America that qualify you for the American Invitational Mathematics Exam (AIME). Only those with top scores will be invited to take the AIME. The MAA recommends 9th and 10th graders take the AMC 10, and 11th and 12th graders take the AMC 12. You can take the AMC 10 and/or 12 multiple times.

The AMC 10 and AMC 12 each have 25 questions. You have 75 minutes for the entire exam. Each correct answer is worth 6 points (for a maximum score of 150) and each unanswered question is worth 1.5 points. There is no deduction for wrong answers.

Note that you don't need to get all of the questions right to get a qualifying score. You just have to do better than most of the other students taking the exam! Keep that in mind as you come up with a strategy for the test.

You need to be in the top 5% of scorers on the AMC 12 or the top 2.5% of scorers on the AMC 10 to qualify, so the vast majority of people who take the AMC exams don't qualify. But, if you do qualify, you can take the American Invitation Mathematics Examination, or AIME.


Step 2: Take the AIME

The AIME is a 15-question, three-hour exam, and each answer is an integer between 0 and 999, inclusive. Regardless of whether you took the AMC 10 or AMC 12, everyone takes the same AIME. It's offered once a year (with an alternate test date available for those who can't make the official exam date) in the spring.

Unlike the AMC 10 and the AMC 12, you can only take the AIME once per qualification. So while you can take the AMC 10 or AMC 12 multiple times to qualify, once you qualify, you've only got one shot at the AIME. That means you want to make sure you do your best on it.

After you take the AIME, your AIME score is multiplied by ten and added to your AMC score to determine if you qualify for Math Olympiad. The cutoff score for qualifying changes yearly, but it's set so about 260-270 students qualify for Math Olympiad each year.


Step 3: Qualify for and Compete in Math Olympiad

If you do well on the AIME, you can qualify for the US Mathematical Olympiad. The top scorers from that competition then have the opportunity to train to be on the US team that competes at the International Math Olympiad. (You can find more info on this process over at the Mathematical Association of American website.)

If you took the AMC 10, you'll compete in the USA Junior Mathematical Olympiad (USAJMO). Students who took the AMC 12 will compete in the USA Mathematical Olympiad (USAMO).

It's a long process to get to the IMO, and very few students make it that far. But even just taking the AIME can set you apart in the college admissions process, especially if you are interested in engineering programs. Along with a high GPA and strong SAT/ACT scores, taking the AIME is a way to signal to colleges you have superior math and problem-solving skills.


How Can You Learn Math Olympiad Content?

Math through pre-calculus covers most topics tested on the AMC 10 and 12 and the AIME, but math competition problems will be trickier than what you see on your usual math homework assignments.

If you're not up to pre-calculus in school yet, your first task will be learning the content before focusing on how to solve problems that the AMC 10 and 12 tend to ask.

See if there is a teacher or peer who is willing to tutor you if you haven't taken pre-calculus. You could also see if it's possible to take the course over the summer to get caught up quickly. There may also be private tutoring available in your area that can help get your precalculus skills up to speed!

In the meantime, you can explore parts of your own math textbook you haven't gotten to yet, or ask to borrow textbooks from teachers at your school if you want to brush up on a topic not covered in the math class you're taking this year.

Also check out these online content resources from the MAA to help you study (you'll need to create an online account).


How Can You Learn Problem-Solving Skills?

The key to doing well on AMC is not just knowing math and being able to do rote problems, but to know concepts inside and out and be able to use them to solve tricky problems.



Think outside the textbook.


The website Art of Problem Solving is a hub for math competition resources and problems, and has been mentioned by many former AMC-takers as a top resource. They have pages on learning to solve certain types of problems, advice on the best prep books, and forums where you can talk to other AIME hopefuls about studying and strategy.

This page provides links to practice problems and prep books and is a great place to get started.

Our advice to study for the AMC is to do lots of practice problems, and then correct them. Carefully analyze your weaknesses. Don't just notice what you did wrong, get inside your head and figure out why you got a problem wrong and how you will work to get it correct the next time.

To improve your problem-solving ability, you can also consider borrowing or purchasing books specifically about solving math problems. Try How To Solve It by George Polya, Problem-Solving Strategies by Arthur Engel, or Challenging Problems in Algebra by Alfred Posamentier and Charles Salkind. These books will give you skills not typically taught in your math classes.


How to Prepare for Math Olympiad

Studying is more than just putting the time in. You want to make sure you are using the best practice problems and really analyzing your weak points to get your math skills to where they need to be.

Read on to learn the six tips you need to follow to study like a pro.


#1: Use Quality Practice Problems

Use practice problems from past AMCs when possible. You want to prepare for the format and type of questions on the AMC. Any problem-solving practice you get will be helpful, but if you're set on qualifying the AIME, you should spend the majority of your time prepping for AMC-type questions.

If you're unclear on how to solve a problem, ask your math teacher, a math team friend, or an online forum like the one at Art of Problem Solving. The better you understand each AMC problem you encounter, the more likely you are to be prepared for the real thing.


#2: Don't Lounge Around

Quality practice time is key! Make sure to time yourself and simulate real test-taking conditions when doing practice problems—find a quiet room, don't use outside resources while you test, and sit at a proper table or desk (don't lounge in bed!). As you review problems, bring in your outside resources, from websites to problem-solving books, but remember to stay alert and focused.



Don't let study time turn into naptime!


#3: Focus on Your Weak Areas

When studying, spend the most time focusing on your weak areas. As you work through practice problems, keep track of problems you didn't know how to solve or concepts you're shaky on. You can log your mistakes into a journal or notebook to help focus your studying.

And don't just log your mistakes and move on, figure out why you made those mistakes—what didn't you know, what you assumed—and make a plan to get similar problems right in the future.


#4: Beware of Tiny Mistakes

Be very, very careful about small mistakes—like forgetting a negative sign, accidentally moving a decimal point, or making a basic arithmetic error. You could get the meat of a problem correct but still answer a problem wrong if you make a tiny mistake. Get in the habit of being hyper-vigilant and careful when you practice, so you don't make these mistakes when you take the exam for real. Never assume you're too smart for a silly mistake!


#5: Schedule Regular Study Time

Finally, set aside dedicated time each week for studying. By practicing at least once a week, you will retain all of the skills you learn and continue to build on your knowledge. Build studying into your schedule like it's another class or extracurricular. If you don't, your studying could fall by the wayside and you'll lose out on getting the amount of practice you need.


#6: Attend Other Math Competitions

If there is a math team or club at your school, join for the practice! Doing smaller competitions can help you learn to deal with nerves and will give you more opportunities to practice. It will also help you find a community of students with similar interests who you can study with.

Also, the earlier you can start, the better. Some middle schools and even elementary schools have math clubs that expose you to tricky problem-solving questions in a way your standard math classes will not.


What Should You Do the Night Before a Competition?

After all your preparation, you don't want to trip at the finish line and ruin all your hard work right before the competition. Don't do tons of studying the night before you take the AMC. By that point, you will have done all of the work you can. Focus on relaxing and getting in the right mindset for the exam.

Also, make sure you get enough sleep the night before, and follow our other tips for the night before a test. Don't waste all of your hard work studying by staying up late the night before!

Finally, make sure you are set to go in the morning with transportation and directions to where you are taking the test. You don't want to deal with a morning-of crisis! Plan to get to the exam center early in case you hit traffic or any other last-minute snags.


What's Next?

Curious about the math scores it takes to get into top tech schools like MIT and CalTech? Read more about admission to engineering schools.

Going for a perfect math SAT or ACT score? Get tips from our full-scorer on how to get to a perfect 800 on SAT math or a perfect 36 on ACT math.

Wondering about paying for college? Check out automatic scholarships available for high ACT and SAT scores.



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Halle Edwards
About the Author

Halle Edwards graduated from Stanford University with honors. In high school, she earned 99th percentile ACT scores as well as 99th percentile scores on SAT subject tests. She also took nine AP classes, earning a perfect score of 5 on seven AP tests. As a graduate of a large public high school who tackled the college admission process largely on her own, she is passionate about helping high school students from different backgrounds get the knowledge they need to be successful in the college admissions process.

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