Advantages of Taking AMC 12 Instead of AMC 10 for Students Who Are Eligible for AMC 10

 

1. AMC 12 Is NOT Much Harder to Prepare for Than AMC 10

The additional topics tested in AMC 12 but not in AMC 10 include: logarithmic functions, complex numbers, trigonometric functions, general polynomial functions, trigonometric approaches to solving geometric problems, and advanced two-dimensional geometry.

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It is true that a student who plans to take AMC 10 has a lighter learning burden because they do not need to study these materials. However, this is not necessarily a good strategy for preparing for AMC 10. The reasons are as follows.

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(1) Although these additional materials are not directly tested in AMC 10, they are quite useful for solving AMC 10 problems.

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For instance, in some AMC 10 geometry problems, it is necessary to add auxiliary lines to facilitate analysis. However, adding auxiliary lines is generally non-trivial and requires significant creative thinking. No student can guarantee that they will always find appropriate auxiliary lines during an AMC 10 contest within a very limited amount of time.

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However, many such problems can be solved much more straightforwardly using trigonometry without adding any auxiliary lines. Therefore, learning these additional materials equips students with more powerful tools to solve some AMC 10 problems that would otherwise be challenging.

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(2) These materials are not difficult to learn.

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A student can learn these materials relatively quickly and easily.

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2. It May NOT Be Easier to Advance to AIME by Taking AMC 10 Compared to Taking AMC 12

 

(1) The percentage of AMC 10 examinees who advance to AIME is only half of that of AMC 12 examinees.

This percentage is approximately 2.5% for AMC 10, while it is about 5% for AMC 12.

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(2) The cutoff score required to qualify for AIME through AMC 10 is often about 20% higher than the cutoff score for AMC 12.

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It is relatively easier to reach the AMC 12 cutoff score than the AMC 10 cutoff score when considering the following facts:

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• AMC 10 and AMC 12 share approximately 40%–60% overlapping questions (equivalently, about 10–15 questions).

• The majority of these overlapping questions are easy or medium in difficulty.

 

For example, in 2020 AMC Version A, the cutoff score for AMC 10 was 103.5, which was 19% higher than the AMC 12 cutoff score of 87.

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Suppose a student answers every attempted question correctly.

• If the student takes AMC 10, they must answer 15 out of 25 questions correctly to qualify for AIME.

• If the student takes AMC 12, they need only 11 correct answers out of 25 questions to qualify.

 

Since AMC 10 and AMC 12 typically share 10–15 overlapping questions, and most of these are easy or medium difficulty, a student taking AMC 12 needs to correctly answer only a small number of non-overlapping questions beyond the shared ones. In contrast, a student taking AMC 10 must answer significantly more additional questions correctly.

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3. If a Student Aims to Advance to AIME and Achieve a Good Score, Taking AMC 12 Is More Efficient and Effective

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(1) The additional topics covered in AMC 12 but not AMC 10 may appear in AIME.

For example, in 2019 AIME I, 4 out of 15 problems (27%) involved these additional topics:

• Problem 7 involved logarithmic functions

• Problem 8 involved trigonometric functions

• Problem 10 involved complex numbers and polynomial functions

• Problem 12 involved complex numbers

 

Note that the time between AMC 10/12 and AIME is only about one month. Therefore, it can be very rushed to learn these additional topics within such a short time.

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If a student aims to perform well in AIME (for example, to strengthen a college application or to qualify for USAMO), a good strategy is to learn these topics well before AMC and register directly for AMC 12.

 

(2) The increase in difficulty from AMC 10 to AIME is much steeper than from AMC 12 to AIME.

Approximately 20% of AIME problems (Problems 13–15) are more difficult than all AMC 12 problems.

However, approximately 67% of AIME problems (Problems 6–15) are more difficult than all AMC 10 problems.

Therefore:

• If a student is comfortable solving the most difficult AMC 12 problems, they are already prepared for most AIME problems.

• If a student is only comfortable solving the most difficult AMC 10 problems but not AMC 12 problems, they still have a long way to go before being ready for AIME.

 

4. AMC 12 Is More Valuable for a Student’s College Application Than AMC 10

 

(1) College admissions committees generally place more weight on AMC 12 scores than AMC 10 scores.

There are two main reasons.

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First, AMC 12 covers the entire high school mathematics curriculum (except calculus), whereas AMC 10 covers only part of it.

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Second, AMC 12 has a higher level of difficulty.

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(2) Performing well in AMC 10 but poorly in AMC 12 may weaken a student’s college application.

When admissions committees review an application, they consider not only past performance but also the applicant’s future potential.

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Suppose a student performs exceptionally well in AMC 10 (for example, receiving Distinguished Honor Roll and qualifying for AIME) but performs significantly worse in AMC 12 two years later (for example, scoring well below the AIME cutoff). This may signal to colleges that the student struggles with more advanced mathematical topics and may have limited potential in mathematics or other quantitative fields.

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(3) Taking AMC 12 earlier gives students more opportunities to achieve a strong AMC 12 score.

AMC 10/12 competitions are held in January–February, while many college application deadlines occur before that. Therefore, AMC 12 scores obtained in Grade 12 typically provide little benefit for college applications.

Students usually rely on their AMC 12 scores from Grade 11 or earlier.

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If a student takes AMC 12 only when they are no longer eligible for AMC 10 (typically Grade 11), they will have only two opportunities to take AMC 12 before applying to college (since AMC 12 is offered twice per year).

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However, if the student begins taking AMC 12 as early as Grade 9—when they are still eligible for AMC 10—they may have six opportunities to take AMC 12 before applying to college. This represents a 200% increase in opportunities, which provides several advantages.

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First, each time a student takes AMC 12, they gain valuable contest experience. This experience improves their ability to perform well in future attempts.

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Second, the difficult problems in different years or versions of AMC 12 may emphasize different topics. Suppose a student is relatively weak in a particular topic, such as geometry. If the student takes AMC 12 only once and most of the difficult problems happen to focus on geometry, they may perform poorly.

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However, if the student takes AMC 12 multiple times, it is very likely that at least one test will emphasize topics where the student is stronger. As a result, the student will have a better chance of achieving a strong score.