The 2020 AMC 12A contest was held on Jan. 30, 2020. We posted the 2020 AMC 12A Problems and Answers at 12 a.m. (EST) midnight on January 30, 2020. You can click the following to download them:

We have a long history of close collaboration with the MAA‘s American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO). There are many math competitions in the United States. Of those, only AMC → AIME → USAMO sequence would take you to the IMO (International Math Olympiad), the highest level math competition for high school students in the world. We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national and math competitions. We have collected all AMC8/10/12 and AIME Official Problems and Official Solutions as shown in the article ” American Mathematics Competitions (AMC) Materials,” which have formed our “big data” system, a golden resource for our students, who are the ultimate beneficiaries.

The 2020 AMC 10A contest was held on Jan. 30, 2020. We posted the 2020 AMC 10A Problems and Answers at 12 a.m. (EST) midnight on January 30, 2020. You can click the following to download them:

We record all of our lessons so that our students can watch them after class for review and self-study.

We will help students gain a deeper understanding of the fundamental math concepts, build a solid foundation in math, and develop the critical thinking and problem-solving skills different from those in the school classes, motivation, and perseverance for reaching their full potential.

We will focus on efficient tricks, shortcuts, and strategies to solve competitive math problems as well as test-taking tactics.

The emphasis of this class will be on geometry, discrete math, and comprehensive problem-solving, which are very common in competitive math, but is not included in school curriculum. See: Why Discrete Math is very Important

You are very welcome to sign up for our online course which offers a quick, efficient way for students to interact with teachers over long distance. We use the Google Meet to video chat and easily connect with students to teach them our tricks and shortcuts to getting an amazing score on their contests, as well as offer them our guidance and support. Students can ask questions face-to-face, and can complete problems with the supervision of our teachers/coaches. Click HERE to see detailed instruction.

A commitmentto the whole coursecan maximize the benefit of learning all the math ideas, methods, strategies, tactics, skills, and techniques.

Contact Information: Ivy League Education Center
Tel: 301-922-9508
Email: chiefmathtutor@gmail.com

Specific Goal of the AMC 8:
To become part of the top 5% of scorers on the 2018 AMC 8, and then receive National Honor Roll Certificates.

Specific Goal of the AMC 10:
To earn a score of90or more out of 150 on the 2019 AMC 10, and then receiveNational Achievement Honor RollCertificates.

Specific Goal of the MathCounts:
To become one of thetop winnersin the individual competitionat the chapter level and thenadvance to the state competition.

There are many math competitions in the United States. Of those,only AMC → AIME → USAMO sequence would take you to the IMO (International Math Olympiad), the highest level math competition for high school students in the world!

Description: Our curriculum focuses on advancing the mathematical skills of 5th-8th graders to prepare them for math competitions, such as Mathcounts, AMC 8, Math Olympiads for Elementary and Middle Schools (MOEMS), Math Kangaroo, and Math League. A variety of contest questions are used to teach students strategies to solve problems and help students prepare for the competitions. These problems stimulate their interest and enthusiasm for critical thinking and problem solving, broaden their mathematical intuition, and develop their brainpower. The topics taught in this class are not covered in regular school math classes, allowing our students to stay one step ahead.

Benefits:

12 tutorial handouts (480 pages) developed by Dr. Henry Wan and 500 new problems similar to AMC 8 level from the licensed AMC Database

4 FREE mock tests, each of which has 25 questions taken from the licensed AMC Database. Mock tests are calibrated to be at the same difficulty level as the real AMC 8. These simulated tests will help students assess their level of preparation for the Math Competitions. After attempting the test, students get answers, explanations, and a detailed score report and wise performance summary.

Class Outline:
In AMC 8/Mathcounts Prep Class, we will focus on efficient tricks, shortcuts, and strategies to solve competitive math problems as well as test-taking tactics. The emphasis of this class will be on problem-solving which is the most important to competitive math.

Spring Session I

Class

Date

Topic

1

6/29, Sat

Sets and Venn Diagrams, Basic Counting Techniques: Casework, Complementary Counting, Constructive Counting, Counting with Restrictions

2

6/30, Sun

Factorials, Permutations, and Combinations

3

7/6, Sat

Binomial Formula, Pascal’s Triangle, Pascal Patterns, Hockey Sticks

4

7/7, Sun

Counting Paths on a Grid, Counting Triangles on a Grid, Counting Geometric Figures

5

7/13, Sat

Counting Divisors, Odd Divisors, Even Divisors, Perfect Square Divisors, And Perfect Cubic Divisors

6

7/14, Sun

Counting Techniques in Probability Problems, Coin & Dice Probability, Probability with Marbles, Balls, or Games

Spring Session II

Class

Date

Topic

1

7/20, Sat

Divisibility, Number Bases, and Primes

2

7/21, Sun

Testing Primality

3

7/27, Sat

Modular Arithmetic

4

7/28, Sun

Patters of the Last Two Digits

5

8/3, Sat

Integer Divisions, Integer Equations, And Diophantine Equations

6

8/4, Sun

The Stars And Bars Method

Homework:

The focus will be on the final 15 problems on the AMC 8, and the first 10 problems on the AMC 10, as well as those Those medium and hard-level difficulty questions on the MathCounts. We will provide students with 500 brand new problems, extracted from the licensed AMC Database, having similar difficulty and style as the hard real AMC 8 problems.

On average, at least6 hours per week, as described in the article: Homework assignments are a fundamental part of our courses. We will carefully review and check students’ homework, and correct any mistakes. Based on the student work, we will provide him/her with individualized help and support.

Click HERE to see a typical homework sample we developed.

We have to face the simple truth that to do well on these grueling contests, we will need to practice. Just like it is for sports and music, the key to success is repetition and practice. We strongly believe in effort and the malleability of intelligence. Intelligence can be enhanced through effort. People can develop impressive levels of expertise through hard work and practice. Effort and persistence are the keys to success. Hard work always pays off: practice makes perfect!

All problems from past AMC 8 exams (1985-2018) and MathCounts (1990–2019) form our “big data” system. Based on artificial intelligence (AI), machine learning, and deep learning, we devised a data mining and predictive analytics tool for math problem similarity searching. Using this powerful tool, we examined the types, styles, frequencies, characteristics, and traits of questions in all these materials, and then completely “decoded” the AMC 8 and MathCounts. We always completely show all the “secret code” cracked from the above big data to our students, and teach them to totally grasp and “control” the AMC and MathCounts. For all questions on the recent AMC/MathCounts contests, we can find their “ancestors” and “roots” from the old AMC/MathCounts problems. Therefore, the best way to prepare for the contest is to practice by solving old AMC/MathCounts problems.

Main Purpose: Our main purpose is to help our students gain deeper understanding of the fundamental math concepts, build a solid foundation in math, and develop the critical thinking and problem-solving skills that are so valuable to success in any career. We are big believers in the FUNDAMENTALS! Our students will receive the LIFELONG BENEFITS from learning math.

Regardless of his/her math level, each student will have the opportunity to learn math in a fun, friendly, cooperative, supportive learning environment. The most important thing is to have fun.

Our Students

In 2019, we had 4 Students Qualified for the USAMO and 4 Students for the USAJMO.

Of the 280 USA Math Olympiad national qualifiers, 4 are our students: Luke C., Zipeng L., Sameer P.,and Peter P.

Of the 235 USA Junior Math Olympiad national qualifiers, 4 are our students: Michael H., Noah W., Holden W., and Isabella Z.

In 2019, we had 76 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 22 Perfect Scorers worldwide on the AMC 10A: Noah W.and one of our students were among the 10 Perfect Scorers worldwide on the AMC 12B: Kenneth W. Very impressively, 32 middle schoolers and 7 elementary schoolers qualified for the AIME!

In 2018, we had 64 students who obtained top scores on the AMC 8 contest!

3 of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.

40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.

21 students received National Honor Roll Certificates awarded to top 5% test takers.

64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

In 2018, we had 73 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students were among the 35 Perfect Scorers worldwide on the AMC 10A: Austen M. and Jason W. and two of our students were among the 21 Perfect Scorers worldwide on the AMC 12B: Kaan D. and Edward W. Remarkably, 11 middle schoolers and 2 elementary schoolers qualified for the AIME!

In 2017, we had 63 students who earned top scores on the AMC 8 contest!

7 of our students were among the top 75 National Winners (Perfect Scorers).

34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.

22 students received National Honor Roll Certificates awarded to top 5% test takers.

63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

In 2017, we had 61 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 28 Perfect Scorers worldwide on the AMC 10A: Austen M., and two of our students were among the 65 Perfect Scorers worldwide on the AMC 10B: Ashwin A. and Brad Z. Remarkably, eight middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Very impressively, Bryan Z., a 6th grader, gained a score of 132 out of 150 on the AMC 10B.Read more at: 2017 AIME Qualifiers Announced — 61 Students Qualified for the AIME

In 2016, we had 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23 Perfect Scorers worldwide on the AMC 10A: Joel (Junyao) T. Particularly, seven middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Pravalika P., a 6th grader, got a 115.5 out of 150 on the AMC10B, which is very impressive. Read more at: 2016 AIME Qualifiers Announced — 36 Students Qualified for AIME

2011 – 2015: In total, 37 students scored above 120 on the American Mathematics Contest 10 (AMC 10) and qualified for the American Invitational Mathematics Examination (AIME); 26 students scored above 100 on the American Mathematics Contest 12 (AMC 12) and qualified for the American Invitational Mathematics Examination (AIME); 3 students qualified for the USA Mathematical Olympiad (USAMO), the highest level of math competition for high school students in the USA

2011 – 2015: In total, 23 students achieved perfect scores of 28 on the AMC 8

We have a long history of close collaboration with the MAA‘s American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO).

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national and math competitions.

We have extracted 5,000 brand new problems at the level of the AMC 8 from the licensed AMC Database. In addition, we have also collected all AMC8/10/12 and AIME Official Solutions as shown in the article “American Mathematics Competitions (AMC) Materials.” All these materials have formed a golden resource for our students, who are the ultimate beneficiaries.

We record all of our lessons as a big bonus so that our students can watch class videosafter class for review and self-study.

There are many math competitions in the United States. Of those, only

AMC → AIME → USAMO sequence

would take you to the IMO (International Math Olympiad), the highest level math competition for high school students in the world!

Featured Math Instructors

All of our sessions are taught by highly qualified instructors who are excellent experts on preparing students for the exam. We distinguish ourselves by the high quality of our instructors. Finding top-quality instructors is no easy task. We’ve hand-picked some of the best, including graduates of Ivy League institutions.

Our instructors are dedicated to teaching and student success. They are very knowledgeable, patient, available, and willing to help our students. Our students receive a quality education that goes beyond the classroom.

In 2019, we had 76 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 22 Perfect Scorers worldwide on the AMC 10A: Noah W.and one of our students were among the 10 Perfect Scorers worldwide on the AMC 12B: Kenneth W. Very impressively, 32 middle schoolers and 7 elementary schoolers qualified for the AIME!

In 2018, we had 64 students who obtained top scores on the AMC 8 contest!

3 of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.

40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.

21 students received National Honor Roll Certificates awarded to top 5% test takers.

64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

In 2018, we had 73 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students were among the 35 Perfect Scorers worldwide on the AMC 10A: Austen M. and Jason W. and two of our students were among the 21 Perfect Scorers worldwide on the AMC 12B: Kaan D. and Edward W. Remarkably, 11 middle schoolers and 2 elementary schoolers qualified for the AIME!

In 2017, we had 63 students who earned top scores on the AMC 8 contest!

7 of our students were among the top 75 National Winners (Perfect Scorers).

34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.

22 students received National Honor Roll Certificates awarded to top 5% test takers.

63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

In 2017, we had 61 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 28 Perfect Scorers worldwide on the AMC 10A: Austen M., and two of our students were among the 65 Perfect Scorers worldwide on the AMC 10B: Ashwin A. and Brad Z. Remarkably, eight middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Very impressively, Bryan Z., a 6th grader, gained a score of 132 out of 150 on the AMC 10B.Read more at: 2017 AIME Qualifiers Announced — 61 Students Qualified for the AIME

In 2016, we had 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23 Perfect Scorers worldwide on the AMC 10A: Joel (Junyao) T. Particularly, seven middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Pravalika P., a 6th grader, got a 115.5 out of 150 on the AMC10B, which is very impressive. Read more at: 2016 AIME Qualifiers Announced — 36 Students Qualified for AIME

2011 – 2015: In total, 37 students scored above 120 on the American Mathematics Contest 10 (AMC 10) and qualified for the American Invitational Mathematics Examination (AIME); 26 students scored above 100 on the American Mathematics Contest 12 (AMC 12) and qualified for the American Invitational Mathematics Examination (AIME); 3 students qualified for the USA Mathematical Olympiad (USAMO), the highest level of math competition for high school students in the USA

2011 – 2015: In total, 23 students achieved perfect scores of 28 on the AMC 8

We have a long history of close collaboration with the MAA‘s American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO).

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national math competitions.

Great Benefits of Math Competitions

In an increasingly competitive college application pool, the process of mastering math skills through our courses and participating in the American Math Competitions will help students strengthen and diversify their extracurricular activities. These contests can motivate students’ interest and passion in math, and they can discover their talent through solving challenging problems different from those in the school classes. Many top colleges also request AMC scores as part of the college application process. Both MIT and Caltech have entry blanks on their official admission application forms for the applicant to enter their best AMC and AIME scores. Ivy League Colleges and Stanford ask for to the AMC and AIME scores in their Supplement to the Common Application Forms. Your children deserve the chance to list these scores on their applications! Good AMC scores will greatly enhance admission opportunities for students to elite colleges.

This program has been carefully designed for the students have higher expectation for their American Invitational Mathematics Examination (AIME) scores. While enriching their resume through the school classes, honing the test skill for AIME becomes even more critical.

The AIME is used to determine qualification for the United States of America Mathematical Olympiad (USAMO). There are many math competitions in the United States. Of those, only

AMC → AIME → USAMO sequence

would take you to the IMO (International Math Olympiad), the highest level math competition for high school students in the world!

Contact Information: Ivy League Education Center
Tel: 301-922-9508 Email: chiefmathtutor@gmail.com

Objectives

Improve student scores by working on both fundamental theorems and ideas

Develop and foster creative problem solving strategies

Make the USA(J)MO!!!

For Whom?
This AIME course is aimed at those students with AMC 10/12 scores of 100+ to students who have scored around 4 on the AIME.

What?
This class will focus mostly on building strong basics in the five main pillars of Combinatorics, Number Theory, Geometry, Algebra, and Probability. The goal is for students to obtain the mental agility required to tackle these complex problems and hopefully get them within and past range of qualification for the USAMO and USAJMO, or around 9 problems.

How?
Focus on basic concepts and essential knowledge before moving on developing the skills and intuition to find and pursue good lines of attack for complex problems.

Class Outline:
In AMIE Prep Class, we will focus on efficient tricks, shortcuts, and strategies to solve AIME problems as well as test-taking tactics.

This is a live class, not a pre-recorded one. Instructors will ask students questions, and students can also ask questions during the class or email their questions to instructors after class.

We record all of our lessons as a big bonus so that our students can watch class videosafter class for review and self-study.

Class Outline:
In AMIE Prep Class, we will focus on efficient tricks, shortcuts, and strategies to solve AIME problems as well as test-taking tactics.

Class

Date

Topic

1

2/9, Sun

Advanced Geometry: Plane Geometry, Spatial Geometry, and Analytic Geometry

2

2/16, Sun

Using the Advanced Algebra Toolkit to Solve the AIME Problems

3

2/23, Sun

The Comprehensive Art of Problem-solving in Number Theory

4

3/1, Sun

The Art and Craft for Solving AIME Counting and Combinatorics Problems

5

3/8, Fri

Tricks and Shortcuts for Solving AIME Probability Problems

Benefits:

5 tutorial handouts (>250 pages) developed by Dr. Henry Wan and 100 new problems at the AIME level from the licensed AMC Database

2 FREE mock tests that are intended to mimic an actual math competition exam, each of which has 15 questions similar to the AIME level taken from the licensed AMC Database. These simulated tests help students assess their level of preparation for the Math Competitions.

Homework: At least 3 hour of homework per class. Students are expected to complete the first eight problems of all previous AIME contests in the past 10 years. Our instructors are open to questions on any previous AIMEs.

All problems from all of the previous 54 AIME contests (1983-2019) form our “big data” system. We have used data mining and predictive analytics to examine the types and the frequencies of questions in all these materials, and then completely “decoded” the AIME. We will show all the “secret code” cracked from the above big data to students, and teach them to totally grasp and “control” the AIME. For all questions on the recent AIME contests, we can find their “ancestors” and “roots” from the old AIME problems. Therefore, the best way to prepare for the contest is to practice by solving old AIME problems.

Our Students

In 2019, we had 4 students qualified for the USAMO and 4 Students for the USAJMO.

Of the 280 USA Math Olympiad national qualifiers, 4 are our students: Luke C., Zipeng L., Sameer P., and Peter P.

Of the 235 USA Junior Math Olympiad national qualifiers, 4 are our students: Michael H., Noah W., Holden W., and Isabella Z.

In 2019, we had 76 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 22 Perfect Scorers worldwide on the AMC 10A: Noah W., and one of our students was among the 10 Perfect Scorers worldwide on the AMC 12B: Kenneth W. Very impressively, 32 middle schoolers and 7 elementary schoolers qualified for the AIME!

In 2018, we had 64 students who obtained top scores on the AMC 8 contest!

3 of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.

40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.

21 students received National Honor Roll Certificates awarded to top 5% test takers.

64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

In 2018, we had 73 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students were among the 35 Perfect Scorers worldwide on the AMC 10A: Austen M. and Jason W. and two of our students were among the 21 Perfect Scorers worldwide on the AMC 12B: Kaan D. and Edward W. Remarkably, 11 middle schoolers and 2 elementary schoolers qualified for the AIME!

In 2017, we had 63 students who earned top scores on the AMC 8 contest!

7 of our students were among the top 75 National Winners (Perfect Scorers).

34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.

22 students received National Honor Roll Certificates awarded to top 5% test takers.

63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

In 2017, we had 61 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 28 Perfect Scorers worldwide on the AMC 10A: Austen M., and two of our students were among the 65 Perfect Scorers worldwide on the AMC 10B: Ashwin A. and Brad Z. Remarkably, eight middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Very impressively, Bryan Z., a 6th grader, gained a score of 132 out of 150 on the AMC 10B.Read more at: 2017 AIME Qualifiers Announced — 61 Students Qualified for the AIME

In 2016, we had 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23 Perfect Scorers worldwide on the AMC 10A: Joel (Junyao) T. Particularly, seven middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Pravalika P., a 6th grader, got a 115.5 out of 150 on the AMC10B, which is very impressive. Read more at: 2016 AIME Qualifiers Announced — 36 Students Qualified for AIME

2011 – 2015: In total, 37 students scored above 120 on the American Mathematics Contest 10 (AMC 10) and qualified for the American Invitational Mathematics Examination (AIME); 26 students scored above 100 on the American Mathematics Contest 12 (AMC 12) and qualified for the American Invitational Mathematics Examination (AIME); 3 students qualified for the USA Mathematical Olympiad (USAMO), the highest level of math competition for high school students in the USA

2011 – 2015: In total, 23 students achieved perfect scores of 28 on the AMC 8

We have a long history of close collaboration with the MAA‘s American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO).

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national math competitions.

Great Benefits of Math Competitions

In an increasingly competitive college application pool, the process of mastering math skills through our courses and participating in the American Math Competitions will help students strengthen and diversify their extracurricular activities. These contests can motivate students’ interest and passion in math, and they can discover their talent through solving challenging problems different from those in the school classes. Many top colleges also request AMC scores as part of the college application process. Both MIT and Caltech have entry blanks on their official admission application forms for the applicant to enter their best AMC and AIME scores. Ivy League Colleges and Stanford ask for to the AMC and AIME scores in their Supplement to the Common Application Forms. Your children deserve the chance to list these scores on their applications! Good AMC scores will greatly enhance admission opportunities for students to elite colleges.

From time to time, a student will write to us asking for advice on studying, rather than on math itself. As either successful students, or teachers, or (quite often) as adults who recall overcoming difficulties in the past, we have some good advice to offer. Today, I want to look at three answers, by three Math Doctors, over a span of more than a decade, all answering the basic question, How can I stop making these careless mistakes? In each case, the answer is long and I will only summarize the main points; to get the full benefit, you will have to read the whole answers.

How to avoid careless mistakes? I have tried do as many problems as possible, but mistakes are constantly made just because of carelessness!

Doctor Ian makes three main points, each illustrated by detailed examples that I will omit:

1. Realize how important it is

Once I became convinced of the importance of what he calls ‘the habit of correctness and precision’, I found that I started adopting it quite naturally, without much effort at all.

2. Don’t do too much in your head

Write more steps than you think you need to, so that you can see what you’ve done. (My personal version of this is: Until you write something, you can’t tell whether it’s wrong; writing clarifies what you are thinking.)

Having said that, it seems to me that many, if not most, of the careless mistakes that we see here at Ask Dr. Math are caused by trying to do too many steps at once. …

A good rule to keep in mind that you can’t make mistakes fast enough to get a correct answer. :^D

3. Always check your answer

(That is, make sure it really does what you were asked to do.)

I also make it a point _always_ to check my answer, after I think I’ve found it. At first this is something you have to remember to do, but after a while it becomes natural.

In addition, doing a check with actual numbers sometimes clarifies what you should have done with variables.

4. Translate “word problems” into equations in small steps

A second kind of careless error, which sort of falls into the same category, is caused by translating story problems too quickly into equations. …

5. But there’s a trade-off:

The less you write, the more easily you can make a mistake, but the more you write, the more places there are to make a mistake! (I just said this to a student yesterday!)

On the one hand, working ‘in place’ is an easy way to get sucked into making careless mistakes; but on the other hand, the more times you copy something, the greater the error that you’re going to copy it incorrectly. With a computer, you can simply copy the old line and change it, which is what I’ve done here. Without a computer, you have to use your judgment about whether working in place or copying is more likely to cause a problem. To make that judgment, you have to have some idea about the kinds of mistakes that you tend to make, and how often you make them.

6. Keep a record of the kinds of mistakes you make

Which leads to my final recommendation, which is that you might want to keep a notebook of the careless mistakes you make. Keeping track of them would allow you to observe patterns, and figuring out what you’re doing is the first step towards changing _any_ kind of behavior.

Develop routines

The second answer was written by Doctor Rick to a different student just a few days later:

No matter how hard I try it’s not good enough. I understand the material – it’s the other stuff, like when it asked me for the range, domain, and inverse of ordered pairs, I just put the inverse because I misread the question. Or like when I had the right answer on scrap paper but I left off part of the answer when I wrote it on the answer sheet. It makes me feel really stupid.

I’ve had this problem with careless mistakes since 6th grade, but it’s getting worse. Proofreading my work helps very little and sometimes I don’t have time when I’m done with the test. What do I do?

Doctor Rick has two main suggestions for this student, who clearly is a diligent student with good observations of his own.

1. Learn from your mistakes

(I ask my own students to rework any problems they get wrong on a test and turn it in for partial extra credit; you should do this yourself even if there is no external reward.)

You have observed some specific kinds of mistakes you make, and that’s a great way to start. One step in problem solving that many people forget about – even after checking your work, which is easy enough to forget – is to look back on what you’ve done and see what you can learn from it. Sometimes you see something positive that you’ll be able to use again – a trick that worked, or a pattern you saw (“when I see this, I can try that”). Other times, as in your case, you see something to avoid next time. The question is, how can you avoid these sorts of mistakes?

2. Make a habit of writing what you are asked to find

(I commonly list the “givens” and the “goals”, with blanks next to the latter; I may also underline these things in the original problem.)

You say that you misread a question, so you didn’t give all the answers that you should have. This is a reminder that another important step in problem solving – the first, and sometimes the most important – is to ask, “What am I supposed to find?” Try making a ritual of starting a problem by listing exactly what you are supposed to find. Then when you finish your work, write each answer next to the list, or at least check off your list as you copy the answers. This will also solve your other observation: that you forgot to copy all the answer from your scratch paper.

Develop a growth mindset

Finally, in 2016, Doctor Floor gave a very helpful answer to a long and thoughtful question:

Our son, a high school junior, is currently taking Advanced Placement BC Calculus. He has always excelled in math (and all other subjects), and never had to study much, because he easily understands concepts. He has, however, always had a tendency of making careless mistakes.

This year this tendency has become a particular problem, with his grades suffering for the first time. Part of his tests are multiple choice — no calculator allowed. Here, he does not have to show any work. But this part needs to be turned in prior to starting on the next section, one where calculators are allowed. On the calculator section, he does need to show his work; and the brevity of the short answers often belies the many intermediary steps they required. …

My son’s teacher says all his mistakes have been careless ones, not conceptual ones: he makes simple calculation errors, or misreads questions, or omits units, or runs out of time, depriving him the opportunity to check his work.

Doctor Floor lists three observations:

1. Smart kids often have surprisingly poor strategies

Smart kids often have learning strategies that seem lazy or careless, due to the fact that they haven’t been really challenged in younger years. Because of this lack of challenge, there has never been any motivation to develop learning strategies or solving strategies. Easy tasks pave the way for good grades, and the cycle reinforces itself.

But at some point in a school career, relying on talent alone turns out to be not enough. Even worse, teachers often think that by high school, high-performing kids must have good strategies. …

So the key is in his homework. Do not only complete homework, but *review it.* Learn from your mistakes. Even when you do it correctly, wonder if you could have done it smarter, or quicker. If you encounter a trick or novel thought, make a note. Be concentrated and targeted in your review.

2. Too much stress holds you back

People cope with this very differently, so consider these as only the most general of observations:

Be confident. If you know you are well-prepared, there is no need to be stressed. …

At the same time, be realistic about what to expect. This is particularly important if the test turns out to be more difficult than you thought, or time pressure is higher than you thought.

Force yourself not to think of any consequences while taking the test. Just take your test, and stick with taking the test. Other thoughts will only break your concentration. Prepare ahead of time so that if you do lose concentration, you already have a way to re-focus and get back on track. …

If you can show your abilities in a test, that is the best you can do.

3. Mindset matters

Quite a few kids have a mindset that holds them back. It is called fixed mindset, and comes with the thought, “It doesn’t really matter if I do the homework or not; either I will understand it or I won’t.” Often kids who are labeled as “smart” or “intelligent” develop such a mindset. These kids think their intelligence is fixed, learning is understanding, and that developing intelligence does not exist (e.g., by homework).

By contrast, a “growth mindset” posits that developing intelligence is possible. Research shows that there is indeed a correlation between mindset and intellectual development.

The parent responded:

We can’t thank you enough for your response! It was spot-on!

I feel all your points are excellent and will be very useful. I can’t wait to share your response with our son (he came home with the flu yesterday), because I think he will now understand the underlying issues, make the adjustments needed, and as a result cope better. The difficulty will be for him to accept that he needs more practice even if he already “understands” concepts, and to figure out how to change his habits.

While we were familiar with “smart kid” issues and the danger of not being challenged, we had not anticipated that this would become THE instant when everything would back-fire.

As you can see, there are a wide variety of ways in which careless errors can arise; each of us has to be aware of our own personal issues, and make a strategy. I hope these three discussions will help others.

I’ll add something I’ve been telling students recently, which summarizes many of the points made above: In order to solve a problem well, you have to

This program has been carefully designed for the students have higher expectation for their American Invitational Mathematics Examination (AIME) scores. While enriching their resume through the school classes, honing the test skill for AIME becomes even more critical.

The AIME is used to determine qualification for the United States of America Mathematical Olympiad (USAMO). There are many math competitions in the United States. Of those, only

AMC → AIME → USAMO sequence

would take you to the IMO (International Math Olympiad), the highest level math competition for high school students in the world!

You are very welcome to sign up for our online course which offers a quick, efficient way for students to interact with teachers over long distance. We use Google Meet to video chat and easily connect with students to teach them our tricks and shortcuts to getting an amazing score on their contests, as well as offer them our guidance and support. Students can ask questions face-to-face, and can complete problems with the supervision of our teachers/coaches. Click HERE to see detailed instruction.

Contact Information: Ivy League Education Center
Tel: 301-922-9508 Email: chiefmathtutor@gmail.com

Objectives

Improve student scores by working on both fundamental theorems and ideas

Develop and foster creative problem solving strategies

Make the USA(J)MO!!!

For Whom?
This AIME course is aimed at those students with AMC 10/12 scores of 100+ to students who have scored around 4 on the AIME.

What?
This class will focus mostly on building strong basics in the five main pillars of Combinatorics, Number Theory, Geometry, Algebra, and Probability. The goal is for students to obtain the mental agility required to tackle these complex problems and hopefully get them within and past range of qualification for the USAMO and USAJMO, or around 9 problems.

How?
Focus on basic concepts and essential knowledge before moving on developing the skills and intuition to find and pursue good lines of attack for complex problems.

Class Outline:
In AMIE Prep Class, we will focus on efficient tricks, shortcuts, and strategies to solve AIME problems as well as test-taking tactics.

This is a live class, not a pre-recorded one. Instructors will ask students questions, and students can also ask questions during the class or email their questions to instructors after class.

We record all of our lessons as a big bonus so that our students can watch class videosafter class for review and self-study.

Class Outline:
In AMIE Prep Class, we will focus on efficient tricks, shortcuts, and strategies to solve AIME problems as well as test-taking tactics.

Class

Date

Topic

1

2/9, Sun

Advanced Geometry: Plane Geometry, Spatial Geometry, and Analytic Geometry

2

2/16, Sun

Using the Advanced Algebra Toolkit to Solve the AIME Problems

3

2/23, Sun

The Comprehensive Art of Problem-solving in Number Theory

4

3/1, Sun

The Art and Craft for Solving AIME Counting and Combinatorics Problems

5

3/8, Fri

Tricks and Shortcuts for Solving AIME Probability Problems

Benefits:

5 tutorial handouts (>250 pages) developed by Dr. Henry Wan and 100 new problems at the AIME level from the licensed AMC Database

2 FREE mock tests that are intended to mimic an actual math competition exam, each of which has 15 questions similar to the AIME level taken from the licensed AMC Database. These simulated tests help students assess their level of preparation for the Math Competitions.

Homework: At least 3 hour of homework per class. Students are expected to complete the first eight problems of all previous AIME contests in the past 10 years. Our instructors are open to questions on any previous AIMEs.

All problems from all of the previous 54 AIME contests (1983-2019) form our “big data” system. We have used data mining and predictive analytics to examine the types and the frequencies of questions in all these materials, and then completely “decoded” the AIME. We will show all the “secret code” cracked from the above big data to students, and teach them to totally grasp and “control” the AIME. For all questions on the recent AIME contests, we can find their “ancestors” and “roots” from the old AIME problems. Therefore, the best way to prepare for the contest is to practice by solving old AIME problems.

Our Students

In 2019, we had 4 students qualified for the USAMO and 4 Students for the USAJMO.

Of the 280 USA Math Olympiad national qualifiers, 4 are our students: Luke C., Zipeng L., Sameer P., and Peter P.

Of the 235 USA Junior Math Olympiad national qualifiers, 4 are our students: Michael H., Noah W., Holden W., and Isabella Z.

In 2019, we had 76 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 22 Perfect Scorers worldwide on the AMC 10A: Noah W., and one of our students was among the 10 Perfect Scorers worldwide on the AMC 12B: Kenneth W. Very impressively, 32 middle schoolers and 7 elementary schoolers qualified for the AIME!

In 2018, we had 64 students who obtained top scores on the AMC 8 contest!

3 of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.

40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.

21 students received National Honor Roll Certificates awarded to top 5% test takers.

64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

In 2018, we had 73 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students were among the 35 Perfect Scorers worldwide on the AMC 10A: Austen M. and Jason W. and two of our students were among the 21 Perfect Scorers worldwide on the AMC 12B: Kaan D. and Edward W. Remarkably, 11 middle schoolers and 2 elementary schoolers qualified for the AIME!

In 2017, we had 63 students who earned top scores on the AMC 8 contest!

7 of our students were among the top 75 National Winners (Perfect Scorers).

34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.

22 students received National Honor Roll Certificates awarded to top 5% test takers.

63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

In 2017, we had 61 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. One of our students was among the 28 Perfect Scorers worldwide on the AMC 10A: Austen M., and two of our students were among the 65 Perfect Scorers worldwide on the AMC 10B: Ashwin A. and Brad Z. Remarkably, eight middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Very impressively, Bryan Z., a 6th grader, gained a score of 132 out of 150 on the AMC 10B.Read more at: 2017 AIME Qualifiers Announced — 61 Students Qualified for the AIME

In 2016, we had 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23 Perfect Scorers worldwide on the AMC 10A: Joel (Junyao) T. Particularly, seven middle schoolers and one elementary schooler qualified for the AIME, which is geared toward high school students. Pravalika P., a 6th grader, got a 115.5 out of 150 on the AMC10B, which is very impressive. Read more at: 2016 AIME Qualifiers Announced — 36 Students Qualified for AIME

2011 – 2015: In total, 37 students scored above 120 on the American Mathematics Contest 10 (AMC 10) and qualified for the American Invitational Mathematics Examination (AIME); 26 students scored above 100 on the American Mathematics Contest 12 (AMC 12) and qualified for the American Invitational Mathematics Examination (AIME); 3 students qualified for the USA Mathematical Olympiad (USAMO), the highest level of math competition for high school students in the USA

2011 – 2015: In total, 23 students achieved perfect scores of 28 on the AMC 8

We have a long history of close collaboration with the MAA‘s American Mathematics Competitions (AMC), which are dedicated to strengthening the mathematical capabilities of our nation’s youth, and are the first of a series of competitions in high school mathematics that determine the United States team for the International Mathematical Olympiad (IMO).

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national math competitions.

Great Benefits of Math Competitions

In an increasingly competitive college application pool, the process of mastering math skills through our courses and participating in the American Math Competitions will help students strengthen and diversify their extracurricular activities. These contests can motivate students’ interest and passion in math, and they can discover their talent through solving challenging problems different from those in the school classes. Many top colleges also request AMC scores as part of the college application process. Both MIT and Caltech have entry blanks on their official admission application forms for the applicant to enter their best AMC and AIME scores. Ivy League Colleges and Stanford ask for to the AMC and AIME scores in their Supplement to the Common Application Forms. Your children deserve the chance to list these scores on their applications! Good AMC scores will greatly enhance admission opportunities for students to elite colleges.