AMC 10 vs. AMC 12
If the student has already studied PreCalculus, regardless of their grade level, it is recommended to prepare directly for the AMC 12. The difference between AMC 10 and AMC 12 is not very significant.
The AMC 12 exam covers a few additional topics compared to the AMC 10, including complex numbers, logarithms, trigonometric functions, the Law of Sines, the Law of Cosines, analytic geometry, various triangle centers, polynomial forms and rational roots, some concepts in probability, and several theorems in number theory. These topics are all very interesting and useful and can be very helpful for AMC 10 problems as well. For example, in AMC 10 2023 A Problem 13, the Law of Sines solves the problem directly without needing additional lines.
Each year's AMC 12 has a lot of overlap with the AMC 10, with fewer simple questions, so students can more easily focus on slightly more challenging problems, reducing the potential loss of points from mistakes on simpler questions. For example, AMC 12 2023B has 11 problems that are exactly the same as those in AMC 10 2023B. The specific comparison is:
10 vs 12: 1/1, 2/2, 3/3, 4/4, 10/5, 12/6, 13/9, 17/13, 18/15, 21/19, 25/25
To qualify for the AIME, the AMC 12 takes the top 10-15%, while the AMC 10 takes the top 5-8%. The qualifying score for AMC 12 is generally about 15-20% lower than that for AMC 10. Since the AMC 12 covers all high school mathematics knowledge, universities generally place more emphasis on AMC 12 scores.
Dr. Xue
Nov. 22, 2023
AMC 10 vs. AMC 12
如果孩子们已经学过PreCalculus的话，不管几年级，建议直接准备AMC 12。AMC 10和12的区别不是很大。
AMC 12考试内容比AMC 10多如下几项，复数, 对数, 三角函数, 正弦定理, 余弦定理, 解析几何, 三角形的各种心, 多项式形式和有理根, 概率里的一些概念, 数论里的几个定理。这些内容都非常有趣和有用，对AMC 10的题目也非常有帮助。举例说明：AMC 10 2023 A Problem 13 用正弦定理一下就出来了，不需要添加辅助线。
每年的AMC 12跟AMC 10有很大重复，简单题目更少一些，所以学生更容易集中精力挑战稍微难一些的题目，减小在简单题目上犯错误的损失。举例说明：AMC 12 2023B 有11题跟 AMC 10 2023B一模一样。具体对照表：
10 vs 12：1/1，2/2，3/3，4/4，10/5，12/6，13/9，17/13，18/15，21/19，25/25
AMC 12晋级AIME取前10-15%，AMC 10取5-8%。AMC 12晋级的分数线一般比AMC 10低15-20%左右。因为AMC12涵盖了高中所有数学知识，所以大学一般更看重AMC12的成绩。
薛老师
2023年11月22日