amc 12 2021 art of problem solving

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Information overview, what is the amc 10/12.

The AMC 10 and AMC 12 are both 25-question, 75-minute, multiple-choice examinations in high school mathematics designed to promote the development and enhancement of problem-solving skills.

The AMC 10 is for students in 10th grade and below and covers the high school curriculum up to 10th grade. Students in grade 10 or below and under 17.5 years of age on the day of the contest can take the AMC 10. The AMC 12 covers the entire high school curriculum, including trigonometry, advanced algebra, and advanced geometry, but excluding calculus. Students in grade 12 or below and under 19.5 years of age on the day of the contest can take the AMC 12.

The AMC 10/12 provides an opportunity for high school students to develop positive attitudes towards analytical thinking and mathematics that can assist in future careers. The AMC 10/12 is the first in a series of competitions that eventually lead all the way to the International Mathematical Olympiad (see Invitational Competitions ).

The AMC 10/12 is also available in braille in print administration only and large print in online administration only.

Registration Deadlines and Competition Date

• AMC 10/12 A Early Bird Registration Deadline: Aug 18 - Sept 18, 2023
• AMC 10/12 A Regular Registration Deadline: Sept 19 - Oct 26, 2023
• AMC 10/12 A Late Registration Deadline: Oct 27 - Nov 3, 2023
• AMC 10/12 A Competition Date: November 8, 2023 from 8:00 am ET to 11:59 pm ET
• AMC 10/12 B Early Bird Registration Deadline: Aug 18 - Sept 25, 2023
• AMC 10/12 B Regular Registration Deadline: Sept 26 - Nov 2, 2023
• AMC 10/12 B Late Registration Deadline: Nov 3 - Nov 9, 2023
• AMC 10/12 B Competition Date: November 14, 2023 from 8:00 am ET to 11:59 pm ET

What is the difference between the A and B versions of the examinations?

Both the A and the B versions of the AMC 10 and the AMC 12 have the same number of questions, the same scoring, and the same rules for administration. The only differences are the competition dates and that each version has a distinct set of questions, although the two examinations are designed to be equal in difficulty and distribution of topics. Schools can order one or both versions of the tests, so long as they pay the appropriate registration fee for each competition date and purchase the competition bundles for each date.

Resources for Hosting the AMC 10/12 

This section includes all of the resources you need to host a successful AMC 10 and AMC 12 in your school. Download and read the AMC 10 and AMC 12 Teacher’s Manual for more details about how to host an AMC 10 and AMC 12 competition .

   2023-2024 AMC 10/12 A Teacher's Manual (PDF)   

   2023-2024 AMC 10/12 B Teacher's Manual (PDF)   

Administration Resources

Competition Managers can find all additional forms needed below.

• Registration and Administration Deadlines
• Hosting MAA Competitions Guide : Expands on the Teacher's Manual for Competition Managers who desire additional details.
• AMC 10/12 Registration Form 
• AMC 10/12 Additional Bundles Order Form : Used by Competition Managers who need to add competition bundle orders to an order that they have already placed. 
• Letter to Parents

STATISTICS FOR THE AMC 10/12

We are hosting our statistics through our new platform. Find the reports for the AMC 10/12 A & B below. Please note that we have amended the information we publicly provide in these statistics for student privacy.

   SUMMARY STATISTICS    

Preparing Your Students for the AMC 10/12

These resources will help you prepare your students for the types of questions found on the AMC 10/12 exam.

• AMC 10/12 Practice Questions
• Curriculum Inspirations Videos and essays for your classroom
• AMC Preparation Materials for Purchase

FAQs for the AMC 10/12

Q. What material is covered on the AMC 10 and 12?

A.  The AMC 10 covers mathematics normally associated with grades 9 and 10. The AMC 10 assumes knowledge of elementary algebra; basic geometry knowledge including the Pythagorean Theorem, area and volume formulas; elementary number theory; and elementary probability. What are excluded are trigonometry, advanced algebra, and advanced geometry. The AMC 12 covers the entire high school mathematics curriculum, including the above, as well as trigonometry, advanced algebra, and advanced geometry, but excludes calculus.

Q. Who is eligible to take the AMC 10 and the AMC 12?

A.  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. Students in grade 12 or below and under 19.5 years of age on the day of the contest can take the AMC 12.

Q. Who can proctor the competition?

A.  Only competition manager proctoring is allowed. Parents or guardians cannot proctor students. Starting 2022-2023, their competition manager will proctored students in person. Competition Managers will be contacted if there is any suspicion of cheating or unapproved resources.  View Disqualification and Cheating policies here . For further questions on AMC 8 proctoring policy, contact the MAA AMC at  [email protected]

Q. Can the AMC 10/12 competition be proctored to different math classes during various time slots on the official administration date(s), or do all the students have to take the competition at the same time?

A. Competition managers must administer competitions during their valid competition window . The valid competition window for this cycle is 8:00 AM to 11:59 PM Eastern Standard time (GMT +5) on the official USA competition dates. See competition dates . Competition managers may choose to administer the competition at separate times to different sections of students; however, for competition integrity and security, the MAA AMC strongly encourages competition managers to administer the competition to all participating students at the same time.

Q. How do I request a rescore of my answer forms?     

A. Use the  AMC 10/12 Rescoring Request Form to request a rescore. There is a $35 charge for each participant's answer form that is rescored. The official answers will be the ones blackened on the answer form. All participant answer forms returned for grading will be recycled 80 days after the AMC 10/12 competition date.

Q. Can I order more bundles even if I’ve already registered my school for the AMC 10/12?

A .  Yes , you can use the  Additional Bundles Order Form  to order more. Orders for additional bundles will be accepted until the deadline for participating domestic institutions located within the United States and Canada. 

Q. Can a student take both competitions?

A.  Yes, as long as a student is eligible to take the appropriate competitions. That is, a 10th grader or below can take both AMC 10 A and the AMC 10 B, the AMC 12 A and the AMC 12 B, etc., and an 11th or 12th grader can take the AMC 12 A and the AMC 12 B. However, the school must register for both dates and order bundles for each competition.

Q. What if a school registers for one date and then wants to change the registration to another?

A.  Although we discourage a change in date because of potential confusion, a date change is permitted under certain circumstances. If the competition materials have not been shipped and time permits according to the registration schedule, a school can pay the corresponding change in registration fee (plus any change in bundles) to change contest dates. Credit cards must pay additional fees when a date change is requested to expedite changes. Please email [email protected] to process this change.

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2021 Fall AMC 12B Problems/Problem 23

• 2 Solution 1
• 3 Solution 2
• 4 Solution 3 (casework bash)
• 5 Solution 4
• 6 Solution 5
• 7 Video Solution by OmegaLearn
• 8 Video Solution
• 9 Video Solution by The Power Of Logic
• 10 See Also

Solution 3 (casework bash)

-fidgetboss_4000

~Steven Chen (www.professorchenedu.com)

Video Solution by OmegaLearn

https://youtu.be/EE-TtptBHeI?t=541

~ pi_is_3.14

Video Solution

https://youtu.be/OH5H-ic8Pgw

~MathProblemSolvingSkills.com

Video Solution by The Power Of Logic

https://youtu.be/hgsPW2sM1GQ

• Intermediate Combinatorics Problems

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Your chance of acceptance, your chancing factors, extracurriculars, amc 10 prep advice.

Hello, I'm looking to participate in the upcoming AMC 10 competition. I feel like I'm decent at math, but I want to excel. Any tips or resources I should use to prepare for it? I'd appreciate any help!

Hello! It's great that you're interested in participating in the AMC 10 competition. Excelling in this contest requires practice and understanding of various mathematical concepts. Here are some tips and resources to help you prepare:

1. Understanding the syllabus: Familiarize yourself with the topics and concepts covered on the AMC 10. The primary subjects include algebra, geometry, number theory, and combinatorics. Getting a solid grasp of these topics will allow you to tackle a wide range of problems.

2. Official materials: Start by reviewing AMC 10 past papers and solutions available on the MAA website. This will give you exposure to the format, types of problems, and difficulty level of the test. Additionally, you can try the free online math resources that MAA offers, such as videos and articles.

3. Books: Numerous books are targeted towards AMC 10 preparation, such as "The Art of Problem Solving" series by Richard Rusczyk, which is quite popular among students preparing for math contests. The series covers topics in a comprehensive manner and includes numerous problems to solve.

4. Practice problems: One of the most effective ways to prepare is by solving a variety of problems regularly. Websites like AoPS (Art of Problem Solving) and Brilliant offer a wealth of problems and solutions in their algebra, geometry, number theory, and combinatorics sections. Participate in their forums and engage in discussions to learn and share knowledge with fellow students.

5. Time management: Develop your time management skills by setting time limits while practicing. Each problem on the AMC 10 is allotted roughly 2.5 minutes, so try to solve problems within that time frame. This'll help you manage time effectively during the actual test.

6. Mock tests: Periodically take simulated tests under exam-like conditions. This will help you gauge your progress, identify areas of improvement, and get used to the time constraints.

7. Learn from your mistakes: After solving practice problems or taking a mock test, review the solutions and pinpoint areas where you struggled. Not only understand how to solve the problem correctly but also analyze what went wrong in your initial attempt. This reflection process will help you improve as you progress in your preparation.

8. Maintain balance: While preparing for AMC 10, don't neglect your regular school work and other commitments. Create a study schedule that allows you to balance your extracurricular activities, academics, and AMC 10 preparation.

Remember, the key to success in AMC 10 is consistent practice, active engagement with various mathematical concepts, and learning from your mistakes. Good luck with your preparation!

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