How to Prepare for the AMC 10: A Comprehensive Guide

What is the AMC 10 Contest
The AMC 10 is a math contest organized by the Mathematical Association of America (MAA). The AMC 10 contest contains 25 multiple choice questions that must be completed within 75 minutes. You get 1.5 points for every question that is left blank, so remember to not guess blindly.

The top 2.5% (approximately) students on the AMC 10 are invited to take the American Invitational Mathematics Examination (AIME).

Who can take the AMC 10
Students in grade 10 or below and under 17.5 years of age on the day of the contest can take the AMC 10. Note that even students in elementary schools are eligible to take the contest.

Where can you take the AMC 10
Many middle/high schools host the contest in their school. If your school doesn't offer the contest, you can try requesting your math teachers or principal to consider becoming a hosting site. You can also search for nearby locations hosting the contest using this zip code search.

The Mathematical Association of America also requests its member institutions of higher learning to consider offering the AMC 10 to students whose schools will not be offering the contest. You can find a list of alternate locations in your area here.

If you are in a school that does not host the contest, you can also reach out to math teachers in nearby high schools and check if any of them will allow outside students to take the contest.

How to score high on the AMC 10
So, how can you score well on the AMC 10? Here are four key things to focus on:

• Understanding all the content: The problems go beyond the school curriculum, so if you're new to competition math you will need to learn a variety of concepts from Algebra, Number Theory, Combinatorics, and Geometry.
• Being able to apply concepts to tricky problems: AMC 10 problems are not straightforward like in school math, so the problems require creative thinking, and that's something that can only be achieved with significant practice.
• Solving the problems accurately: You need to simulate test conditions to learn how to avoid common mistakes like calculation errors, silly mistakes, misreading the questions, etc.
• Working quickly: You need to finish 25 problems in 75 minutes, and you need to learn good time management so you can attempt most of the questions without getting stuck.

How to prepare for the AMC 10 contest

Step 1: Reviewing the Basics
If you are new to competition math or taking the AMC 10 for the first or second time, you need to ensure that you have a good understanding of the fundamental mathematical concepts. You can use the following resources to get started:

• Free Mastering AMC 8 Book: If you are new to competition math, then this free book can help you get started. This is a 400+ page hybrid book with video lectures for every topic and hundreds of practice problems.
• Free AMC 10/12 Fundamentals Course: A free course that covers the most basic concepts for the AMC 10/12 like Expected Value, Modular Arithmetic, Diophantine Equations, Power of a Point, etc.
• Volume 1: The Basics by AoPS Volume 1: The Basics essentially provides a summary of the Introduction Series by AoPS, covering many important concepts.

Step 2 (If Time): Build Strong Fundamentals
If you are really serious about AMC 10 preparation, it is highly recommended that you work through the AoPS Introductory series books. They are quite comprehensive, but they take a long time to complete. If you are just starting your preparation less than 2 months before the contest, I recommend you skip to Step 3.

Introduction Series books by AoPS

• Introduction to Algebra
• Introduction to Counting & Probability
• Introduction to Geometry
• Introduction to Number Theory

You can also use Alcumus for extra practice along with these books.

In addition, you can also check out paid classes from Alphastar Academy, Art of Problem Solving, Outschool, International Chess Academy, and many other organizations.

Step 3: Mastering AMC 10 Concepts
In the last 1-2 months before the contest, it is important to review and refresh all the concepts that are important for the AMC 10 test. Moreover, the AoPS Introduction books do not cover some of the topics that have come up in recent AMC 10 tests, which need to be studied from other sources.

• Mastering AMC 10/12: Chapters 1 - 40: This free book will help you learn and practice advanced concepts useful for AMC 10 problems such as Linearity of Expectation, Markov Chains, Cyclic Quadrilaterals, etc.

Step 4: Practice Contests & Mocks
In order to practice speed and accuracy, it's important to take full AMC 10 tests.

Some tips when mocking AMC 10's:

• Don't brush off silly mistakes: Rather than treating a silly mistake as something that's not a big deal, analyze why you made that silly mistake and what you will do to avoid making that mistake again. Here is a video with tips to avoid sillies.
• Peek but not read: For problems that you are not able to solve, don't just "read the solution". Rather, try to look at a few lines of the solution and then solve the rest of the problem on your own.
• Build speed gradually: At first, try to work at a pace that you can achieve high accuracy with. Then, try to gradually increase your speed while still maintaining high accuracy. Never rush or work carelessly to increase speed as this will only reduce your accuracy significantly.

List of Mock Contests

• Official AMC 10 from previous years with solutions: Use these tests with a 75-minute timer to simulate test-taking situations. The AMC's are increasing in difficulty every year, so only AMC 10 contests from 2021 Fall and after are representative of the difficulty of recent AMC 10.
• AoPS Created AMC Contests: High-quality mock contests created by Art of Problem Solving problem writers.
• AoPS Created AMC 10 Mock Contest These mock contests are created by users on the AoPS forums and are of varying quality and difficulty levels. Still, they are good practice if you have completed all the previous year’s AMC 10 contests.
• AlphaStar AMC 10 Practice Tests Book: A book with some high-quality mock contests created by the problem writing team at AlphaStar Academy.

Problem Trainers
For even more practice, there are some useful websites that help you practice specific topics and improve problem-solving speed.

• Alcumus: Free resource by AoPS to practice problems from specific topics.
• AMC Trivial: This site generates problems from past contests. You can even make custom mocks from older questions and it can give problems from specific topics or difficulty levels.
• MAA Tester: This site makes it easy to search for problems related to any topic from various contests.
• For the Win! Practice speed and accuracy by playing head to head against other players to answer questions quickly.

By using these resources and practicing regularly, you can improve your skills and increase your chances of success on the AMC 10.

Videos:

• How to Prepare for AMC 10/12, and qualify for AIME and USA(J)MO
• Ultimate AMC 10 Crash Course - Combinatorics, Algebra, Number Theory, Geometry

Crucial Tips for Improving on the AMC 10

• Bring colored pencils/pens. For Geometry problems, sometimes it may help to use colors to mark different regions or draw similar triangles. Colors can help you visualize things better and make geometric observations.
• Double-check what the question is asking for. When you finish solving a problem, take a quick glance at the last sentence in the question to confirm that you are marking what the question is asking for. For example: You solve a complex Geometry problem and correctly calculate the side length of a square, mark that answer, and move on… but the question was asking for the area of the square. You don’t want to make that mistake.
• Double-check the bubbled answers. Towards the end, don’t forget to double-check the answer sheet to make sure that the answers you have bubbled match up to the answer you have marked in the question paper.
  
  One time, pi_is_3.14, a contributor to this blog, actually forgot that he had skipped a problem and then for all the subsequent problems, the answers were shifted up by one so all of those problems got marked wrong. Here is an important tip to check the answers - don’t just check it as “A, C, D, B”. Always try to associate the question with its number like, “15 A, 16 C, 17 D, 18 D, etc.”
  
  Also, don’t leave this task to the last second, as you may be in the middle of solving a problem and won’t like to waste time checking. Try to double-check a few minutes before the end, maybe around the 65-70 minute mark. Most test centers will announce a time warning a few minutes before the end, so plan to check things at that time.
• Don’t get stuck on any question. All questions have equal points, so your goal is to solve as many questions as possible. The questions are usually in increasing order of difficulty, but some questions can be misplaced. Don’t get stuck on any question. If you are not making progress or the problem looks too complicated, then just mark it and skip it during the first pass. You should come back to it later. You should not have the mindset that “oh, it's number five; I should be able to solve it, but I’m not able to solve it.”
• Don’t be intimidated by the questions at the end. There are 25 questions and 75 minutes to finish the test, so you have an average of 3 minutes per question, which is not a lot of time. So make sure you budget your time wisely and leave enough time for the end questions, which are typically harder. But some of them may be misplaced or from one of your stronger subjects, so depending on how much time you have left, try to solve the ones that are from your strong subjects or that look doable.
• Sleep well, eat healthy, stay calm. This seems like common sense, but it is important to emphasize it again. Don’t try to cram till 4am on the day before the contest. A good night’s sleep and a relaxed mind can be more helpful in making sure that you don’t make silly mistakes.
  
  One simple meditation trick that is worth trying just before the test: Just close your eyes and take 5 deep breaths, and it will help calm your nerves.
  
  Some people recommend eating dark chocolate before the test as it is considered a mood enhancer.
• Don’t guess blindly. Remember you get 1.5 points for any question left blank, so don’t guess blindly as the chances of getting it right are only 20%. But you can use meta-solving techniques to improve your chances of finding answers to problems without actually solving them.
• Timed Test Practice. Since only a few days are remaining for the AMC 10, try to take at least one timed test - either previous year’s AMC 10 contest or a mock test, and remember to keep a 75-minute timer to simulate real test conditions. And try to apply the tips mentioned here during that practice test. This will help you get used to handling the stress of the test and help you with learning the time management that works best for you.
• Review, Revise, Refresh. On the day before the test, try not to stress and don’t start learning new topics. Just review concepts and formulas for topics that you already know.

Good Luck on the AMC 10!