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 1% 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 2.5 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 1%.  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 the 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

If you don't make any mistake on AMC 10, you need to answer 17 questions correct and leave the other 8 questions unanswered.  You will have a qualifying score of 122 (17x6 + 8x2.5 = 122).  However, the chances are that you will make mistakes.  So, the strategy of answering just 17 questions is very risky.

The optimal strategy is to answer 20 questions and leave 5 questions blank.  You can afford to make two mistakes and still achieve a qualifying score of 120.5 (18x6 + 5x2.5 = 120.5).  This strategy allows you to spend about 3.5 minutes on each of the twenty questions you will answer and skip the five most difficulty questions (usually question #21 - #25).

AMC 12 Strategy

Use the same method for AMC 10, we find that if you answer 11 questions correct and leave 14 questions unanswered, you will achieve a qualifying score of 101 (11x6 + 14x2.5 = 101).   However, this strategy is risky.

The optimal strategy is to answer 16 questions and get 13 of them correct and 9 questions unanswered.  You can afford to make three mistakes and still achieve a qualifying score of 100.5 (16x6 + 9x2.5 = 100.5).  This strategy allows you to spend more than 4 minutes on each questions and skip the 9 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 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, if you have a high probability of qualifying for AIME you should take the AMC 10 to increase your USAMO Index.  The USAMO Index is used to select the top 375 students from the 10,000 AIME contesters.