If you love taking high-level math courses and think that the SAT and ACT math is too easy, then you may be interested in taking up the ultimate math challenge for high schoolers – the AMC 10 and 12.
As one of the most well-known math-focused competitions in the world, the AMC tests are an excellent way to exhibit your problem-solving and analytical skills, along with providing a gateway into more exclusive and prestigious opportunities. If you are interested in excelling in the AMC, read this article to learn more!
What is the AMC 10/12? Is it prestigious?
The American Mathematics Competitions (AMC) are hosted by the MAA yearly, and the program is dedicated to fostering the next generation of mathematical thinkers. Starting in 1950, it first reached to 200 schools and tested 6,000 students in the New York area, but now, it has grown immensely to reach 300,000 students in over 4,000 schools.
Because of its reputation and mission, the AMC is highly prestigious and students who perform well on the assessment are recognized to be highly skilled in math. Those who make the cutoff scores in AMC 10/12 are invited to take part in the American Invitational Mathematics Exam (AIME). Those who do well on the AIME are then allowed to compete in the USA Junior Mathematical Olympiad (USAJMO) for AMC 10, or US Mathematical Olympiad (USAMO) for AMC 12.
Finally, the top 12 USAMO scorers are invited to the Mathematical Summer Olympiad Program (MOSP). For three to four weeks, students work intensely daily, practicing various math problems. A 4.5 hour test, including 3 essay problems, determines which six students get to compete in the International Math Olympiad (IMO).
Who is eligible for the AMC 10/12? Can you take both?
Students with a passion for problem-solving who are in grade 10 or below and under 17.5 years of age on the day of the contest can take the AMC 10. Meanwhile, students in grade 12 or below and under 19.5 years of age on the day of the contest can take the AMC 12.
You are allowed to register for both tests in the AMC 10 or 12 yearly. For example, as a 10th grader, you are allowed to register for both dates and take AMC 10 A and B separately. Same rules apply for the AMC 12.
You are allowed to take AMC 10 and 12 if you are eligible for both. However, you can only take one exam on the competition date, and there is a significant difference in difficulty between the two exams.
How is the AMC 10/12 structured?
Both the AMC 10 and 12 have 25 questions and are administered over the course of 75 minutes. All questions are in multiple choice.
While the overall structure of two exams are very similar, they differ in content. AMC 10 covers material that is expected for 9th and 10th graders to know, such as elementary algebra; basic geometry knowledge (Pythagorean Theorem, area and volume formulas), elementary number theory, and elementary probability. On the other hand, AMC 12 is more difficult and includes subjects in trigonometry, advanced algebra, and advanced geometry in addition to AMC 10 material. Test takers are not expected to know calculus.
On the day of the exam, students will be required to go to a selected location at a certain time, such as a specific classroom after the school day ends. They will be provided the exam booklet, multiple choice answer sheet, and scratch paper. Exam content in the booklet will differ for different testing dates – for example, the earlier date will be for AMC 10/12 A and the later date will be for AMC 10/12 B. While only the answer sheet will be graded, all test-related materials will need to be submitted to the proctor. Calculators are not permitted.
How is the AMC 10/12 scored?
The maximum score that a participant can receive from the AMC 10/12 is a score of 150. A correct answer is worth 6 points, an unanswered question is worth 1.5 points, and a wrong answer is worth 0 points. Therefore, students are discouraged from randomly guessing on the exam.
What is the score I need to pass the AMC 10/12?
There is no yearly, pre-set score cutoff in the AMC 10/12 to qualify for the AIME. Instead, the 2.5% of scorers in the AMC 10 are invited to move to the next step. All students who received a score of 100 or more, or 5% of scorers in the AMC 12 qualify.
Thus, score cutoffs will change annually based on the performance of the year’s cohort of students. The qualifying score range for the AMC 10 will generally lie within the 90-115 range, and the qualifying score range for the AMC 12 will be roughly between 80-95. The most recent test in 2022 had the following cutoff scores:
In addition, the AMC 10/12 provides multiple types of awards and certificates. Those who score in the 1% of participants receive Distinguished Honor Roll, while Distinction is awarded to those with scores in the top 5% of the AMC 10/12. Regional-based certificates may be awarded to those who perform well in their particular district.
How do I study for the AMC 10/12?
Tip #1: Build a math framework through your schoolwork or sign up for a structured course.
First, it is recommended that you prepare a firm foundation in mathematics in your schoolwork. Because AMC 10/12 tests students on high school math material, it is imperative that you pursue rigorous math classes in your academics. While it’s possible to self-study, being able to learn math concepts in the classroom with a teacher may allow you to fully understand them. In no particular order, some important math classes to consider are: Algebra I and II, Geometry, Trigonometry, Statistics, and Pre-calculus. High school math curriculum may differ from school to school, but take the rigorous math classes expected for your grade.
Tip #2: Take the practice exams.
One of the best resources you can take advantage of is the Art of Problem Solving Online. On their website, you can see and download all past exams. They not only provide answer keys for the problems, but also multiple detailed solutions. Often, problems have different approaches to reach the answer, some being substantially easier than the others. AoPS has written and video solutions that provide many ways to excel in the exams and save you time. The link for the AMC 10 Problems and Solutions and AMC 12 Problems and Solutions are provided.
The best way to take the exams is to recreate the actual testing environment – find a quiet place, set a timer for 75 minutes, and try your best to finish the exam to the best of your ability. Afterwards, check your answers and compare your score to the cutoff of that year. If you find yourself consistently scoring above the cutoff, great! If not, identify which problems are causing you the most trouble and get extra practice in that area. For example, if you find yourself constantly stuck on the trigonometry problems in the AMC 12, then ask to meet with your geometry or trigonometry teacher to help you with the difficult concepts.
Tip #3: Retake the practice exams.
Taking the exams once is helpful, but in order for you to truly learn, retaking the exams will help you better understand the problems and enhance your memory. Studies have shown that repetition leads your brain to retain more information effectively, increase recall speed, and improve test results.
Therefore, after going through the exams the first time, go back a second time and make note of any questions you repeatedly get wrong. Refresh yourself on past concepts you’ve learned and thoroughly study the solutions. Then, retake the exams as many times as you need – even until you get that full 150 score!
Tip #4: Read math books.
If you have enough time and commitment, there are physical resources available. For example, the AoPS published their own book series Art of Problem Solving Volume 1: The Basics and Art of Problem Solving Volume 2: and Beyond, with corresponding solution materials as well. These provide information and practice problems that go beyond the practice exams on their website, so if you are looking for more variety, these are very helpful.
Another good book to keep in mind is the Three-Year MATHCOUNTS Marathon by Karen Ge. While MATHCOUNTS is a separate competition from the AMC, they test on similar math knowledge that go beyond middle school. The book has informative, concise explanations that can provide a deeper look into math questions.
Tip #5: Check out formula lists and cheat sheets.
Online you can find many helpful resources on topics and formulas that are good to know during the exam. If you know the formula, you can sometimes skip the entire calculation process and find the answer directly.
I recommend checking out Eashan Gandotra's Formulas for Pre-Olympiad Math. While you don’t need to know all of it and should not force yourself to memorize it, review the beginnings of each section to remind yourself of what you know. It can also provide helpful tidbits that can come in handy during the exam.
Others good cheat sheets include Coach Monk's High School Playbook and the outline All of Math in Three Pages. You can also check out Jim Sukha's ARML Handbook and Tom Davis's Contest Geometry Handbook. They are all good references that help you learn fascinating math concepts and can get you ready for the exam!
Tip #6: During the exam…
Finally, after months of extensive preparation, you are in the exam room and about to submit a real exam. What should you do?
First, you should relax and take a deep breath – no matter how ready or not ready you may feel, you’ve put in the work and effort to be there, so be confident no matter what. Being nervous or anxious won’t help your performance, so keep your head up high regardless of what score you think you’ll receive.
Over the next 75 minutes, you should be aware of your pacing by keeping an eye on the clock or your watch. If you find yourself stuck on a problem, it’s more strategic for you to skip it and come back to it later – you’ll score more points on the problems that you know. Leave the last five to ten minutes to check your answers and most importantly, ensure that you bubbled in the right spots on your answer sheet.
When checking your answers, be sure to avoid careless errors. While this may be hard to do in the heat of the moment, keep your work organized and slow down. Being messy and thinking too fast can cause logical jumps and errors. Annotating the questions, such as underlining keywords and making quick notes, can also help you from reading the problems too fast. In addition, read – and I mean read – the problems. Are you sure you interpreted the question properly? Did any questions feel suspiciously easy, like they’re hiding a tricky component?
If you ultimately can’t find a solution to the problem, don’t carelessly guess, because you are losing out on 1.5 points on leaving the answer blank. If you have enough time, you can even use the multiple choice answers to solve your problem, or plug them into your calculations. In the instance you eliminate the answer choices to 3, you should guess because the odds will be in your favor.
With these tips in mind, you’re now ready to embark on your journey to excel in the AMC 10/12 exams. No matter your score on the actual competition, you’re definitely going to improve your math and problem-solving skills. Good luck!
Lydia is currently a sophomore at Harvard University, studying Molecular and Cellular Biology. During high school, she pursued engineering activities like attending the Governor's School of Engineering and Technology. In her spare time, she likes to create digital art while listening to music.
Image source: MAA