Math contests

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The Mathematical Association of America has run annual high school and college (Putnam) math contests for decades. A summary of the contest information is here:

In high school, there are two levels for the multiple choice exam. There is a tenth grade level (10A and 10B) and a twelfth grade level (12A and 12B). There are two exam dates in February of each year, and "A" reflects the first exam date while "B" reflects the second exam date. The exams are different on the two dates, but at the same levels. A 10th grader can arrange to take both the 10th and 12th grade exams.

The exam consists of 25 questions to be completed in 75 minutes. 6 points are awarded for each correct answer, 2 points for each blank answer, and 0 points for each incorrect answer. In other words, it does hurt to guess wrong.

The highest scorers on these exams are then invited to participate in the AIME (American Invitational Mathematics Examination). To qualify, all students who achieved a score of 100 or more out of a possible 150 on the AMC12 are invited to take the AIME. All students who scored of 120 or were in the top 1% of the AMC10 are invited to take the AIME. The AIME is given in March of each year.

The top 250 scores on the AIME are then invited to take the USAMO (United States of American Math Olympiad). Top students may then be invited to participate in a summer camp that trains them for the International Math Olympiad:

Very few can score over 120 on the AMC12 exam. In 2005, fewer than 150 girls scored at least 120/150 out of a total of about 50,000 (boys and girls) who took that exam. Only about 900 boys could attain that score.

Some gaps in pre-calculus backgrounds that require attention for this exam are: