It Is Easier to Qualify for the AIME Through the AMC 12 Than Through the AMC 10

(1) The percent of AMC 10 contestants to qualify for the AIME is only half of the percent of AMC 12 contestants.

The curve for the AMC 12 is much more generous. In fact, for AMC 10, invitations for taking the AIME are issued to the top 2.5% of all scorers. For AMC 12, invitations for taking the AIME are issued to the top 5% of all scorers.

(2) The cutoff scores for AMC 10 contestants eligible to qualify for the AIME are approximately 14% to 24% higher than that for AMC 12 contestants.

It is easier to achieve the AMC 12 cutoff scores than the AMC 10 cutoff scores. The AMC 10 and the AMC 12 contests have about 10 to 15 questions in common. Two contests have 40% to 60% overlapping questions, and the difficulty levels of a majority of these questions are easy.

The following are cutoff scores for AIME qualification from 2019 to 2021.

Year AMC 10A AMC 10B AMC 12A AMC 12B
2021 Fall 96 96  91.5 84
2021 Spring 103.5 102 93 91.5
2020 103.5 102 87 87
2019 103.5 108 84 94.5
Average 101.6 102 88.9 89.2

In fall 2022, the AMC 10A and AMC 12A had 12 overlapping questions, and the AMC 10B and AMC 12B had 11 overlapping questions, as shown in The 2021 Fall AMC 10 and AMC 12 Have 11 to 12 Questions in Common.

For instance, in 2022 Fall version B tests, the AIME floor for the AMC 10 was 96, 14.3% higher than the floor for AMC 12, 84. Even if the AMC 12 problems are more difficult, the difference in 12 points is just from two problems. To qualify for AIME through the AMC 10, the minimum correct answers needed are 15 to 16. For the AMC 12, however, you only need at least 13 correct answers.

Furthermore, the AMC 12 questions have about at least 9 questions out of the first 15 that are the same as the AMC 10’s and they do not get significantly harder until after Question 16. In fact, the difficulty level of most of these overlapping questions are easy or medium. This entails that beyond correctly answering most of their overlapping questions, a student taking the AMC 12 only needs to correctly answer very few nonoverlapping questions. By contrast, a student taking the AMC 10 needs to correctly answer much more than that.

Hence, it is easier to qualify for the AIME through the AMC 12 than the AMC 10.

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