**Henry Wan**,** Ph.D.**

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.

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!

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.

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.

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

More details can be found at:

**AMC 8 Historical Results from 2010 to 2016**- 2016 AMC 8 Results Announced — Eleven Students Received Perfect Scores
- 20 Sets of AMC 8 Mock Test with Detailed Solutions
**Premier National Mathematics Competition — AMC 8**- AMC 8/10/12/AIME Problems and Answers
**The Big Value of Middle School Math Competitions****Great Benefits of Math Competitions****A Little Competition Can Inspire Math Students to Greater Achievement****Small-sized Class Instruction-focused Model****Homework Correction is very Important — We Give an Extensive Correction of the Incorrect Answers of All Homework****Homework assignments are a fundamental part of our courses****Mathematics competitions are NOT mysterious, and every student can attend them! — 数学竞赛绝非神秘，每个学生都可参加！****Girls should attend math competitions — 女生更应参加数学竞赛**- Why Math Competitions are so Important to Girls?
**2015 AMC 8 Results Announced****2014 AMC 8 Winners for the U.S. Ivy League Education Center****Why Discrete Math is very Important**

Click ** HERE** find out more about Math Competitions!

Click ** HERE** to find out more about SAT Prep!

**Copyright Dr. Henry Wan. All rights reserved****. **