AMC 10/12 Exam Strategy

How many questions should you answer on AMC 10 and AMC 12 to get the best chances of qualifying for AIME? The optimal strategy is to answer 21 questions on AMC 10 (if you make two mistakes, you still qualify with a score of 120) and 18 questions on AMC 12 (if you make three mistakes, you still qualify with a score of 100.5).

AMC 10/12 and AIME

AMC 10 and AMC 12 are two qualifing exams for American Invitational Mathematics Examination (AIME). All students who take the AMC 12 and achieved a score of 100 or in the top 5% are invited to take the AIME. All students who take the AMC 10 and achieved a score of 120 or in the top 2.5% are also invoted to take the AIME. Annually, about 10,000 students take the AIME.

AMC 10/12 Scoring Method

In AMC 10 and AMC 12, there are 25 questions. You have 75 minutes to complete the exam. Each correct answer is worth 6 points and each unanswerd question is worth 1.5 points. There is no points deducted for guessing. The maximum score is 150.

For example, if you answered all 25 questions, but answered 6 of them wrong in AMC 10, your score will be 19*6 = 114. You will not qualify for AIME unless 114 is in the top 2.5%. If you spent time on all 25 questions, you may not have enough time to check the answer. Therefore, increasing the chances to make mistakes. Therefore, if your goal is to qualify for AIME, you don't need to answer all the questions. What is the optimal strategy for the exam?

AMC 10 Strategy

The optimal strategy is to answer 21 questions and leave 4 questions blank. You can afford to make two mistakes and still achieve a qualifying score of 120 (19x6 + 4x1.5 = 120). This strategy allows you to spend about 3.5 minutes on each of the 21 questions you will answer and skip the four most difficulty questions (usually question #22 - #25).

AMC 12 Strategy

The optimal strategy is to answer 18 questions and get 15 of them correct and 7 questions unanswered. You can afford to make three mistakes and still achieve a qualifying score of 100.5 (15x6 + 7x1.5 = 100.5). This strategy allows you to spend more than 4 minutes on each questions and skip the 7 most difficulty questions.

AMC 10 or AMC 12

If you are not a Junior or Senior in high school and your goal is to qualify for AIME, you should take AMC 12 if you have completed pre-calculus. Here is why:

Each year, there are about 7 questions that appear on both AMC 10 and AMC 12. If you take AMC 10, you need to answer another 12 questions to achieve a qualifying score but if you take AMC 12, you only need to answer 9 additional questions. If you have completed pre-calculus, you have all the math knowledge to answer AMC 12 questions.

Life After AIME

However, if you are an able math students, you should work hard and try to qualify for USAJMO and USAMO. The qualification is based on the USAMO Index, which is your AMC score plus 10 times of your AIME score. For example, if you score 126 on AMC 10 and 8 on the AIME, your USAMO Index will be 206 (126 + 8x10 = 206). Therefore, a higher AMC10 or AMC12 score will reduce the number of correct AIME answers in qualifying for USAJMO and USAMO.

USAJMO or USAMO

USAJMO is designed for students in grade 10 or less. The top 12 students will be invited to attend the pretigious United States Math Olympiad Summer Program (MOP). Only students who take AMC10 can qualify for USAJMO and only students who take AMC12 can qualify for USAMO. If you take both, for example AMC10A and AMC12B, and qualified for both USAJMO and USAMO, you will be an USAMO qualifer and take the USAMO exam. Generally speaking, a younger student have less competition to qualifying MOP via USAJMO than USAMO. Therefore, if your goal is MOP, take USAJMO. Otherwise, USAMO is a more prestigous exam.

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