The Hardest Problems on the 2018 AMC 8 are Nearly Identical to Former Problems on the AMC 8, 10, 12, and MathCounts

The detailed article is in pdf format and can be viewed and downloaded HERE.

We created 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, MATHCOUNTS, Math Kangaroo Contest, Math Olympiads for Elementary and Middle Schools (MOEMS), ARML, USAMTS, Mandelbrot, Math League, Harvard–MIT Mathematics Tournament (HMMT), Princeton University Mathematics Competition (PUMaC), Stanford Math Tournament (SMT), Berkeley Math Tournament (BmMT), the Caltech Harvey Mudd Math Competition (CHMMC), the Rice Math Tournament, the Carnegie Mellon Informatics and Mathematics Competition (CMIMC), the Australian Mathematics Competition, and the United Kingdom Mathematics Trust (UKMT) . 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.

Based on artificial intelligence (AI), machine learning, and deep learning, we also developed a data mining and predictive analytics tool for math problem similarity searching. Using this powerful tool, we can align a set of query math problems against all in the database “CPM,” and then detect those similar problems in the CMP database.

amc8 The AMC 8 is a 25-question, 40-minute, multiple choice examination in middle school mathematics designed to promote the development and enhancement of problem solving skills. The problems generally increase in difficulty as the exam progresses. Usually the last 5 problems are the hardest ones.

Among the final 5 problems on the 2018 AMC 8 contest, there are 3 discrete math problems (which contains number theory and counting): Problems 21, 23, and 25; and there are 2 geometry problems: Problems 22 and 24.

For those hardest problems on the 2018 AMC 8, we found:

2018 AMC 8 Problem 21 is very similar to the following 9 problems:
- 1985 Australian Mathematics Competition Junior #23
- 2004 AMC 8 Problem 19
- 2012 AMC 8 Problem 15
- 2006 AMC 8 Problem 23
- 1951 AHSME #37
- 2010 Mathcounts State Sprint #8
- 2009 Mathcounts National Countdown #77
- 2009 Mathcounts School Sprint #19
- 2011-2012 MathCounts School Handbook #266

2018 AMC 8 Problem 22 is very similar to the following 3 problems:
- 2016 AMC 10A Problem 19
- 1991AHSME Problem 23
- 2010MathCounts State Team Problem 10

2018 AMC 8 Problem 23 is exactly the same as 2012 MathCounts State Sprint Problem 3, and very similar to the following 4 problems:
- 2017 MathCounts Chapter Countdown #49
- 2016 MathCounts National Sprint #11
- 2016 – 2017 MathCounts School Handbook Problems #195
- 2011 MathCounts State Countdown #22

2018 AMC 8 Problem 24 is completely identical to the following 2 problems:
- 2008 AMC 10A Problem 21
- 2002 Mathcounts National Team Problem 10

2018 AMC 8 Problem 25 is very similarly to the following 5 problems:
- 2013 Michigan Mathematics Prize Competition #1
- 2007 MathCounts State print #8
- 2007 MathCounts State Countdown #52
- 2009 MathCounts State Countdown #3
- 2010–2011 MathCounts School Handbook Workout 1 #5

We can see that every problem has strong similarities to previous problems. Particularly, 2018 AMC 8 Problem 23 is exactly the same as 2012 MathCounts State Sprint Problem 3, and 2018 AMC 8 Problem 24 is completely identical to 2008 AMC 10A Problem 21.

In my AMC 8/MathCounts Prep Class, I ever used Problem 3 on the 2012 MathCounts State Sprint, as a typical example, to elegantly solve discrete probability problems. In my AMC 10/12 Prep Class which there were 25 students at grades 4 to 8 to attend, I ever took Problem 21 on the 2008 AMC 10A, as a classic example, to show the art of solving 3-D geometry problems. When my students attended the AMC 8 on Nov. 13, 2018, they already knew how to solve Problems 23 and 24 and their answers. So they took two seconds to bubble the correct answers and then got 2 points easily!

AMC 8-New

This year’s AMC 8 was much more difficult than the last year’s AMC 8. Some hard problems were even at the AMC 10 level. For example, Problems 21, 22, and 24 on the 2018 AMC 8 are three typical hard level AMC 10 problems.

15a98df8551bb48d483c6ae893622e34 (1) Because the AMC 8 problems are getting harder, we have to practice not only previous AMC 8 problems but also easy, medium, and even high difficulty level problems from previous AMC 10/12 to do well on the AMC 8.