AMC
Everything you need to know to ace every level of the AMC competition.
The American Mathematics Competition, better known as the AMC, is the first step to becoming America’s best mathlete and going all the way to the Math Olympiad. But the AMC is so much more than just the pathway to winning the title of America’s greatest high school mathematician. Even for academic mortals, the AMC’s 75 minutes of pure problem-solving fun is likely one of the most enjoyable tests you’ll ever take.
So, whether you’re aiming for the lofty heights of the Olympiad, or you just want to test your chops and see if you can get a perfect score, this complete guide will help you prepare for the AMC-8, the AMC-10, and the AMC 12.
Love math? Great! Then keep reading. We’ll explain everything you need to know, from the AMC scoring system to the skills you need to succeed.
Can you improve your problem-solving skills?
Even if the AMC problem above melted your brain, you can still excel at the competition. Many researchers have looked closely at what skills lead to dominating at board games, logic puzzles (like Sudoku), or these types of AMC problems. The science is unambiguous: if you enjoy learning and have a growth mindset you can definitely become a master problem-solver.
What precisely does it take to shine at these kinds of problems? you’ll use your deliberate practice sessions to master these core skills:
Working backward
Working systematically
Looking for patterns
Visualizing
Iterating on an initial best guess
Reasoning logically
Once you have learned these strategies, you’ll be a pro at mathematical reasoning. You’ll be able to summon all of your mathematical knowledge and creativity and be on your way to a top score!
Why all the numbers? What does the 8,10, and 12 Mean?
The AMC has three levels: AMC-8, AMC-10, and AMC-12. The number represents the target grade. For example, the Mathematical Association of America calibrates the AMC-8 for 8th graders. But that doesn’t mean you can’t take a higher level than your current grade.
Some 6th graders (even sometimes some 5th graders) take the AMC-8. Some 7th graders take the AMC-8, but others decide to take the AMC-10. As long as you haven’t graduated from the grade the competition is for, and you haven’t aged out, you are eligible to compete. Whether you are an American student in elementary school or doing secondary school mathematics in Australia, there is an AMC competition right for you. Here are the age and grade limits for each level:
AMC-8
Currently 8th grade or lower
14.5 years old or younger
AMC-10
Currently 10th grade or lower
17.5 years old or younger
AMC-12
Currently 12th grade or lower
19.5 years old or younger
How do I get to the Math Olympiad from the AMC?
You don’t have to aspire to be an elite mathlete to take the AMC, but it is the first step to getting on the US International Mathematical Olympiad (IMO) team. How many steps are there between a great AMC score and the IMO team? Here’s how it works.
Being a top scorer on the AMC-8 gives you bragging rights. A high score on either the AMC-10 (top 2.5%) or AMC-12 (top 5%) gives you the chance to compete again on a test known as the AIME, the American Invitational Mathematics Examination.
Crushed the AIME? Yeah! Depending on whether you made the selection cut-off with an AMC-10 score or an AMC-12 score, you’ll be invited to either the USA Junior Mathematical Olympiad (USAJMO) or the United States of America Mathematical Olympiad (USAMO). And yes, you can qualify for both! While it can vary a bit year-to-year, in general, about 500 kids reach these lofty heights.
From there, you’ll get invited to the Mathematical Olympiad Summer program. Finally, the top six students who have beaten these levels will win one of the six coveted spots on the US Olympiad team—called the USIMO—that competes each year against 100 other countries. It’s pretty amazing to think that all these different teams of six mathletes at the world competition represent 90% of the planet’s population.
What Kind of Problems does the Olympiad Team Do?
Even though you’re here to learn all about how to ace the AMC, it’s never too early to dream of becoming one of the most elite mathletes in the world. The Olympiad problems (like the AMC and the AIME problems) require deep problem-solving skills. While it’s OK to use calculus in the Olympiad (and might even be useful), it’s never needed to solve any AMC, AIME, or Olympiad question.
A founding principle of these competitions is that winning should reward mathematical reasoning and creativity, not the number of years you’ve been grinding through common core classes. The Olympiad level will hit you with advanced Algebra and Precalculus concepts and problems, but the competition explores a lot of other interesting topics too, like:
Combinatorics
Projective Geometry
Complex Geometry
Functional Equations
Number Theory
The essential facts you need to know about the AMC.
How many problems are on the AMC-8, and how much time will I get?
There is a bit of time pressure, and you must perform with the clock ticking. Here is the lowdown on how many questions there are and exactly how fast you must be:
AMC-8
25 Questions
40 Minutes
90 Seconds per question
AMC-10
25 Questions
75 Minutes
3 Minutes per question
AMC-12
25 Questions
75 Minutes
3 Minutes per question
How is the AMC-8 Scored? Is it better to guess or leave a problem blank?
Good news if you are taking the AMC-8: there is no penalty for wrong answers. Every question is worth the same number of points, so if a problem has you stumped, or you know it will take you a long time, skip it and come back after you’ve tackled easier problems.
Even if this took a long time, don’t worry about it. Analytical thinking is something you can improve with practice and instruction. And if you figured it out quickly? Great! We’ll have more sample problems for you in the next section.
How are the AMC-10 and the AMC-12 Scored? Guess or skip hard problems?
When you get to the AMC-10 and AMC-12, the scoring system changes. There are still 25 questions, and all correct problems are worth an equal number of points, six per answer.
Can you compete at the same AMC level multiple times in one year?
The AMC-8 competition occurs only once per year, so it would be impossible to take it multiple times in a single year, but it is possible to take either the 10 twice in the same year or take the 12 twice in the same year.
The 10 and 12 each have two versions, the “A” and then the “B.” That makes five total competition events per year: 8, 10A, 10B, 12A, and 12B.
Why is there is an “A” and “B” version of the AMC-10 and 12?
The AMC-10 and the AMC-12 are each offered twice in a single year. The MAA designates the first test date of the year “A” and the second, “B.” The “A” version of the test and the “B” version of the tests are entirely different.
The 10A and 12A always take place on the same day. Later in the year (also on the same day), the 10B and 12B happen. Notably, the 10A and 12A share several of the same problems. Likewise, the 10B and 12B share a few problems. It might seem odd that the 10th-grade competition and the 12th-grade one have a few questions that are the same, but it is true. A consensus among AMC competitors is that both the AMC-10 and the AMC-12 start at about the same level of difficulty, and each test gets progressively more demanding. The difference is that the 12 ramps up to more challenging questions faster. So while it’s true that a few questions overlap, the 12 is still quite a bit harder than the 10!
It is strictly forbidden for a student to take the 10 and 12 on the same day, but it is fine to take them both in the same year. How? The mathlete could take the 10A and 12B or flip the sequence and take the 12A and the 10B.
Enabling students who want to try both (the 10 and the 12) in the same year is one reason the MAA has these two distinct versions of the test. If the Olympiad is your goal, one more interesting fact is that taking both AMC 10 and AMC 12 gives you a shot at qualifying for the USAMO and USAJMO separately.