# The AMC 8/10/12 Contests are Getting Harder

Henry Wan, Ph.D.

We have developed a comprehensive, integrated, non-redundant, well-annotated database “CMP” consisting of various competitive math problems, including all previous problems on the AMC 8/10/12, AIME, MATHCOUNTSMath Kangaroo ContestMath Olympiads for Elementary and Middle Schools (MOEMS), ARML, HMMT, Math League, PUMaC, Stanford Math Tournament (SMT). The CPM is an invaluable “big data” system we use for our research and development, and is a golden resource for our students, who are the ultimate beneficiaries.

We have also devised a data mining and predictive analytics tool for math problem similarity searching. Using this powerful tool, we can align query math problems against those present in the target database “CPM,” and then detect those similar problems in the CMP database.

1.  The scope of the AMC is greatly expanded

Transformation geometry

Recursive sequences

Equations involving the floor and ceiling functions

Equations involving gcd and lcm

Geometric probability

Infinite geometric series with probability

2.  The difficulty of the AMC is increased

For those hard problems on the 2017 AMC 10A/12A, according to the database searching, we have found:

• The 2017 AMC 10A Problem 18 (also known as Problem 15 on the 2017 AMC 12A) is the same as the following 3 problems:
• 2015 AMC 12B Problem 9
• 2016 AMC 12B Problem 19
• 1981 AHSME Problem 26
• The first part of the 2017 AMC 10A Problem 21 (also known as Problem 19 on the 2017 AMC 12A) is exactly the same as  the 2007 AMC 10B Problem 21

Click HERE to see my detailed solutions of the hard problems on the 2017 AMC 10A/12A.

In my AMC 10/12 Prep Class, I ever used Problem #19 on the 2016 AMC 12B, as a typical example, to efficiently solve discrete probability problems on the AMC10/12, including the complementary probabilities. Thus, when my students attended the 2017 AMC 10A/12A, they already knew how to solve the AMC 10A Problem 18/AMC 12A Problem 15 and its answer. So they took one second to bubble the correct answer and then got 6 points very easily!

Conclusions
The AMC changes every single year and even undergoes a huge change every five years. Thus, it is extremely important to study materials that are relevant to the current AMC, not just the past AMC, which the Ivy League Education Center prioritize.

All problems from past AMC 10/12 exams (2000-2017) and AHSME (1950–1999) form our “big data” system. The AHSME (American High School Mathematics Examination) was the former name of the AMC, before 2000. We have used data mining and predictive analytics to extensively examine the types and the frequencies of questions in all these materials, and then completely “decoded” the AMC 10/12. We always show all the “secret code” cracked from the above big data to students, and teach them to totally grasp and “control” the AMC. For all questions on the recent AMC contests, we can find their “ancestors” and “roots” from the old AMC problems. Therefore, the best way to prepare for the contest is to practice by solving old AMC problems.

References

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