American Mathematics Competitions (AMC10)

In 1950, the first American Mathematics Competition sponsored by the Mathematics Association of America (MAA) took place. Today, the challenge has become the most influential youth math challenge with over 300,000 students participating annually in over 6,000 schools from 30 countries and regions. AMC hosts a series of challenges such as AMC8 held in January for grade 8 or below, AMC10/12 held in November for students at/below grade 10/12. AIME held in March for high scoring AMC10/12 participants for promotion, and USAMO / USAJMO is for excellent AMC10/12 participants of qualification trial of AMC national team.

	AMC 8	AMC 10	AMC 12	AIME
Qualification	In grade 8 or below and also under 14.5 years of age on the day of the challenge	In grade 10 or below and also under 17.5 years of age on the day of the challenge	In grade 12 or below and also under 19.5 years of age on the day of the challenge	In grade 12 or below
Range	AMC 8 covers from a middle school mathematics curriculum. Possible topics include but are not limited to: counting and probability, estimation, proportional reasoning, elementary geometry including the Pythagorean Theorem, spatial visualization, everyday applications, and reading and interpreting graphs and tables. Some of the later questions may involve linear or quadratic functions and equations, coordinate geometry, and other topics traditionally covered in a beginning algebra course.	Usually covers mathematics syllabus in Grade 9 and Grade 10, including elementary algebra, basic geometry (Pythagorean theorem, area and volume formulas, etc.), elementary number theory and probability. Trigonometry, advanced algebra and advanced geometry will not be included.	AMC12 covers all mathematics knowledge learned in high school, including trigonometry, advanced algebra, advanced algebra and part of calculus.	Students who get great results in AMC 10/12 will be invited to participate in AIME. More difficult than AMC 10/12.
Form	Individual, 25 multiple choice questions	Individual, 25 multiple choice questions	Individual, 25 multiple choice questions	Individual, 15 questions
Time	40 minutes	75 minutes	75 minutes	180 minutes
Scoring Criteria	25 points in total 1 point for 1 correct answer 0 points for 1 blank answer or 1 wrong answer	150 points in total 6 points for 1 correct answer 1.5 points for 1 blank answer 0 points for 1 wrong answer	150 points in total 6 points for 1 correct answer 1.5 points for 1 blank answer 0 points for 1 wrong answer	15 points in total 1 point for 1 correct answer 0 points for 1 blank answer or 1 wrong answer

The cutoff score of USA(J)MO in 2022

	USAJMO cutoff scores		USAMO cutoff scores
	AMC 10 A	AMC 10 B	AMC 12 A	AMC 12 B
AIME I	203.5	190.5	222	227.5
AIME II	196.5	182	208.5	203

1.Qualification of USA(J)MO in 2022:
Candidates whose scores meet the USA(J) MO advancement cutoff score for the 2022 USA(J)MO.U.S. citizens and students studying in the United States and Canada (with qualifying scores) are eligible to take the USAMO and USAJMO.
2.Exam Time of USA(J)MO in 2022:
March 22-23, 2022 (American Eastern Standard Time)
(*Details may vary depending on the policy of the year)

From the overall distribution of the graph, the distribution curve of the scores is positively skewed, the highest point is the mode of the scores. The mode of Version A is 48, which means that the largest number of students answered 8 questions correctly (25 questions in total, disregarding the case of non-response). The mode of Version B is 42, which means that the largest number of students answered 7 questions correctly. Meanwhile, the mean of Version A is 59.40 and the mean of Version B is 56.32, which means that the students' scores are at the middle to lower level and the questions have a certain difficulty.

From the graphical characteristics, all obvious prominent straight bars in the bar graph are multiples of 6, which indicates that students are more inclined to answer questions to get high scores, rather than not answering to get 1.5 points; the standard deviation of Version A is 23.28 points, and the standard deviation of Version B is 24.23 points, which indicates that there is a large gap between students' levels and the paper has a certain selectivity, on the other hand, the standard deviation values of paper A and B are similar, which indicates that there is no significant difference between the difficulty of Version A and Version B.