**Scroll to view full description**- The AMC 10 and AMC 12 math competitions are 25-question, 75-minute, multiple-choice examinations in high school mathematics designed to promote problem-solving and critical thinking.
- It is the first contest in a series run by the Mathematical Association of America (MAA) and provides an opportunity to qualify and compete in prestigious mathematical Olympiads such as the United States of America Junior Mathematical Olympiad (USAJMO) and the International Mathematical Olympiad (IMO).
- The AMC 10 is open to students in grades 10 and below. The AMC 12 evaluates all students in grades 12 and below and more difficult concepts, and the two tests have on average an overlap of 10-15 problems. Thus, students cannot take both the AMC 10 and the AMC 12 at the same time.
- Both provide two different tests administered a week apart, the AMC 10/12 A and the AMC 10/12 B, giving students an additional opportunity to qualify for the next round, the American Invitational Mathematics Exam (AIME). The top 5% of AMC 12 test-takers and the top 2.5% of AMC 10 test-takers qualify for the AIME.
- High-scoring AMC 10 test takers qualify for USAJMO and high-scoring AMC 12 test takers qualify for the USAMO.
- A correct answer will receive 6 points, while a blank one receives 1.5 points, and an incorrect one receives 0 points. Therefore, the maximum score is 150 points. AIME cutoffs are selected for the AMC 10/12 A/B, and students exceeding the cutoff qualify for the next level of competition, AIME. This score will, later on, be used in conjunction with the AIME score to determine a USAJMO index, which determines USAJMO qualification.
- The AMC 10/12 provides an opportunity for high school students across the U.S. to develop positive attitudes towards analytical thinking and mathematics that can assist in future careers. Students apply classroom skills to unique problem-solving challenges in a low-stress and friendly environment.

AMC 10A 2022 Answers

AMC 10A 2022 Solutions

AMC 10B 2022 Problems and Solutions

AMC 12B 2022 Problems and Solutions

AMC 10/12 Information

- The AMC 10 and AMC 12 math competitions are 25-question, 75-minute, multiple-choice examinations in high school mathematics designed to promote problem-solving and critical thinking.
- It is the first contest in a series run by the Mathematical Association of America (MAA) and provides an opportunity to qualify and compete in prestigious mathematical Olympiads such as the United States of America Junior Mathematical Olympiad (USAJMO) and the International Mathematical Olympiad (IMO).
- The AMC 10 is open to students in grades 10 and below. The AMC 12 evaluates all students in grades 12 and below and more difficult concepts, and the two tests have on average an overlap of 10-15 problems. Thus, students cannot take both the AMC 10 and the AMC 12 at the same time.
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syllabus

- The material covered on the AMC 10/12 test includes topics from an advanced high school mathematics curriculum.
- Possible topics to appear in the math competition include but are not limited to:
- - Arithmetic and Logic

- Functions and Polynomials

- Sequences and Series

- Word Problems

-Number Theory

-Counting and probability

-Euclidean geometry

-Coordinates and graphs - In addition, some of the later questions in AMC 12 may involve trigonometry, complex numbers, and other topics traditionally covered in an Algebra II course.

Schedule

- The AMC 10/12 is usually administered in the second and third weeks of November. There is a 1-day window for students to take the test.
- In Fall 2021, the tests were administered on Wednesday, November 10, and Tuesday, November 16. Both tests were administered at Random Math.
- Random Math will administer the 2022 AMC 10/12 math competitions in November. Registration will open from September to October 2022.

The AMC 10/12 tests are 25-problem exams open to high schoolers in the U.S. Students are given 75 minutes to solve all problems, which increase in difficulty as students progress through the math tournament.

There are no prerequisites to participate in this math competition. As this is a competition primarily geared toward high schooler students, students interested in applying for the AMC 10 must be from Grade 10 or below and under 17.5 years to be able to take the exam, and those applying for the AMC 12 must be from Grade 12 or below and under 19.5 years.

Students must also be U.S. residents.

Students must also be U.S. residents.

The AMC 10/12 test are 25-problem exams that students need to solve in 75 minutes. It is a middle to fast-paced multiple-choice test where problems increase in difficulty as the test progresses.

Correct answers are each awarded 6 points, blank answers are each worth 1.5 points, and incorrect answers are each worth 0 points, with a total score of 150. The time limit allocates approximately 3 minutes per problem.

The problems are designed to challenge students and offer problem-solving experiences beyond those provided in most high school mathematics classes.

To help with competitive math training, visit our archive to view and practice previous AMC 10 and AMC 12 tests.

Correct answers are each awarded 6 points, blank answers are each worth 1.5 points, and incorrect answers are each worth 0 points, with a total score of 150. The time limit allocates approximately 3 minutes per problem.

The problems are designed to challenge students and offer problem-solving experiences beyond those provided in most high school mathematics classes.

To help with competitive math training, visit our archive to view and practice previous AMC 10 and AMC 12 tests.

75 Minutes

There are 75 minutes given in the exam.

*Generally, this is considered to be an easier but fast-paced test as compared to some of the other tests in the series.*

The AMC 10 (generally ranked levels 1-3 in difficulty) is easier than the AMC 12 (difficulty levels 2-4). The AMC 10/12 math competitions are significantly easier than the AIME (difficulty levels 3-6) and USAJMO (difficulty levels 6-7) and are accessible to most high school students.

The AMC 10/12 are 25-question, 75-minute multiple-choice examinations in high school mathematics designed to promote problem-solving and critical thinking skills.

Our AMC math competition training helps middle school students achieve excellent results at the AMC 10 and AMC 12 competitions, but more importantly, it helps develop problem-solving and critical-thinking skills that benefit all fields. Learn more about our AMC 10/12 math results below.

- Out of the 125 students who took the competition at Random Math, 115 —or 92% — won an award at the AMC 10/12. Approximately 86% of students qualified for the AIME.
- 84 Random Math students were recognized in the Honor Roll, the top 5 percentile of AMC 10/12 participants, and 48 students were recognized in the Distinguished Honor Roll, the top 1 percentile of AMC 10/12 participants.
- Additionally, 42 Random Math middle schoolers were recognized in the Achievement Roll, an award that rewards the top middle school performance on the AMC 10/12 in the nation.

108

AIME

Qualifiers

Qualifiers

24

DIstinguished honor roll

84

HONOR

Roll

Roll

42

Achievement

award

award

Random Math prepares students for the AMC 10/12 competition in a year-round system that maximizes the improvement students obtain during the spring, summer, and fall/winter. In the two months before the competitions, students go through a series of mock tests and review sessions, where they are guided through difficult concepts students need to master for the math competition.

Random Math’s Competitive Program allows students to work on challenging problems to stretch their problem-solving skills with other students at their levels over a year. By working with peers near their level, students can learn new ways to approach tough problems from their coaches and classmates. Random Math’s classrooms encourage students to speak out, ask questions, and share their thoughts to help everyone improve their math proficiency to a new level.

Through the Accelerator Program, students’ progress is consistently tracked and their workload — consisting of the unique set of topics and concepts, types of problems, and types of competitive math skills that each individual needs to improve on — is continuously updated to ensure students are on track to reaching their goals. Each week, students take a mock test tailored by our coaches to fit the specific level’s needs.

Our math problems are divided into four units over the school year and cover all topics tested in AMC 10/12 math: Algebra, Number Theory, Geometry, and Combinatorics. Once students have mastered these four units, they will excel at the AMC 10/12. Random Math closely monitors students’ progress by tracking their scores on mock tests, analyzing every individual’s weakness, and teaching appropriate concepts to help each student overcome their weakness and achieve mastery.

Over 80% of Random Math students have continuously placed among the top 5-10% of the AMC 10/12 math competitions, and that statistic has been increasing by approximately 30 students every year since 2019. Those who place in the honor roll, which comprises the top 2.5-percentile scorers, and the distinguished honor roll, which comprises the top 1-percentile scorers, have continued to perform well in the AIME.

In Fall 2021, 108 out of 125 students who took the competition at Random Math --- 86% --- qualified for the AIME. 48 students were recognized in the Distinguished Honor Roll, the top 1-percentile of all AMC 10/12 competitors, and 84 students were recognized in the Honor Roll, the top 5-percentile of all AMC 10/12 participants.

For more information about our results, please see the page: https://www.randommath.com/tournaments/amc-10-12.

The Random Math curriculum prepares students for the AMC 10/12 competition on a year-round basis, allowing students to build up their mathematical proficiency and critical thinking skills for optimal achievement in the contests.

However, elite students choose to optimize their time in the summer to leapfrog their mathematical skill levels.

Random Math’s various Summer Programs ensure that students make the most of their time by placing students in small groups of peers with similar mathematical proficiency levels and guiding them through intense lecture sessions, mock tests, and challenging problems from prestigious national and international math contests to stretch their problem-solving skills.

The Competitive Summer curriculum at Random Math is a compact but similar version of its Competitive curriculum that runs over an entire year. Students are placed in levels 3 to 7 based on their mathematical skill level and goals for the upcoming school year, and the summer is divided into four camps, each focusing on a topic fundamental to AMC 10/12 and other high-school level math competitions: Number Theory, Algebra, Geometry, and Counting and Probability.

For more information on the topics covered by level and other details, please visit our page: https://www.randommath.com/summer-camps.

The AMC 10/12 are among the largest high school-level math competitions in the U.S. Both are taken individually, but several high school tournaments have both individual and team rounds.

The Harvard-MIT Math Tournament (HMMT), open to students grade 12 and below, is among the most prestigious high school level tournaments drawing close to 1000 contestants around the globe. High school tournaments like the HMMT provide insight into what a future in math may look like for students. It includes an individual round, a team round, and the guts round, where students work together to solve questions on an assortment of subjects. In 2022, the Random Math Team placed 2nd in the Guts Round, 4th in the Overall Sweepstakes, and Top 7 in the Team Round. One Random Math student placed 1st overall. For more information about HMMT, please see our page: https://www.randommath.com/tournaments/hmmt.

The Berkeley Math Tournament (BMT) is another well-known high-school mathematics competition. It takes place over two days and consists of one individual round, three team rounds, and a tiebreaker round. In 2021, 7 Random Math students placed in the top 10 individual awards, and 13 students placed in the Distinguished Honor Roll, the top 20 percentile of all competitors. Two Random Math Teams placed in the top 4 for team awards, and Random Math took home 1st place in Team Overall. For more information about BMT, please see our page: https://www.randommath.com/tournaments/bmt.

Other popular high school level math competitions include the Stanford Math Tournament, Caltech Harvey Mudd Math Competition, Carnegie Mellon Informatics and Mathematics Competition, Princeton University Mathematics Competition, and Math Majors of America Tournament for High Schools, hosted by Yale University.

For a complete list of middle school math tournaments, please see our page: https://www.randommath.com/tournaments/high-school-tournaments.