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Online Intensive AMC 8/Mathcounts Prep (for Rising 4th to 8th Graders) Summer Weekend (Discrete Math) Course Starting June 8

Posted on 2024-04-05 | Leave a comment

Summer is the golden time to prepare for the American Math Competitions!

The period of time between 4th-8th grade is most critical to the development of students’ mathematical fascinations, interests, and skills!

How to Prepare for the AMC 8
2024 AMC 8: 10 perfect scorers. 54 students got the DHR. 29 students got the HR.
2023 AMC/AIME: 99 AIME qualifiers. 1 AMC 10 perfect scorer. 1 AMC 12 perfect scorer.
2023 JMO/AMO: 8 USAMO Awardees and 7 USAJMO Awardees
- 1 USAMO Gold Award, 1 USAMO Silver Award, 4 USAMO Bronze Awards, and 2 USAMO Honorable Mention Awards.
- 1 USAJMO Top Winner, 1 USAJMO Winner, and 5 USAJMO Honorable Mention Awards.
2023 MOP: 4 MOP winners.

Summer Session I (Counting and Probability)
8 Classes (Eastern Time: 1:00 – 4:00 pm), Total: 24 Hours
6/8, 6/9, 6/15, 6/16, 6/22, 6/23, 6/29, 6/30 (Mock Exam/Review)

Summer Session II (Number Theory)
8 Classes (Eastern Time: 1:00 – 4:00 pm), Total: 24 Hours
7/6, 7/7, 7/13, 7/14, 7/20, 7/21, 7/27, 7/28 (Mock Exam/Review)

Course Outline

Class Handout Sample

Online Registration is now open! Click HERE to register and pay.

Tuition (including all materials)
Session I (24 Hours)
New Student:	Via Zelle: $840 (Phone: 240-406-3402) Please include your child’s name and “AMC 8 Summer I” in the “Memo” box.
	Via PayPal: $870
Returning Student:	Via Zelle: $825 (Phone: 240-406-3402) Please include your child’s name “AMC 8 Summer I” in the “Memo” box.
	Via PayPal: $855
Session II (24 Hours)
New Student:	Via Zelle: $840 (Phone: 240-406-3402) Please include your child’s name “AMC 8 Summer II” in the “Memo” box.
	Via PayPal: $870
Returning Student:	Via Zelle: $825 (Phone: 240-406-3402) Please include your child’s name “AMC 8 Summer II” in the “Memo” box.
	Via PayPal: $855
Sessions I & II (48 Hours)
New Student:	Via Zelle: $1,655 (Phone: 240-406-3402) Please include your child’s name and “AMC 8 Summer I and II” in the “Memo” box.
	Via PayPal: $1,715
Returning Student:	Via Zelle: $1,635 (Phone: 240-406-3402) Please include your child’s name and “AMC 8 Summer I and II” in the “Memo” box.
	Via PayPal: $1,695
Click HERE to see payment and refund policy.

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 videos after class for review and self-study.

This year’s AMC 8 contest contains 5 number theory problems and 6 counting & probability problems. In last year’s AMC 8/MathCounts Prep Summer Weekend Course about Discrete Math (Number Theory, Counting, and Probability), what we comprehensively presented fully covered all the geometry topics that appeared in the 2024 AMC 8 test. All Discrete Math problems on the 2024 AMC 8 are the same as or very similar to the typical examples demonstrated in our Summer Course so that our students can become very familiar with them and fully master those powerful methods to solve them. This is how our course can greatly help our students to get a high score on the AMC 8 contest!

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 via Google meet, and can complete problems with the supervision of our teachers/coaches. Click HERE to see detailed instruction.

A commitment to the whole course can maximize the benefit of learning all the math ideas, methods, strategies, tactics, skills, and techniques. Click HERE to see attendance/absence/aancellation/makeup lesson policy

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 comprehensive problem-solving in discrete math (number theory, counting, and probability), which is very common in competitive math, but is not included in school curriculum. See more at: Why Discrete Math is very Important
We will utilize a highly effective teaching model as described in the article: Small-sized Class Instruction-focused Model.

Instructor: Dr. Henry Wan

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Purpose: To prepare for math competitions, such as

AMC 8 — January 22 – 28, 2025.
MATHCOUNTS
Math Kangaroo Contest
Math Olympiads for Elementary and Middle Schools (MOEMS)

Contact Information:
Ivy League Education Center
Tel: 240-300-4380
Email: chiefmathtutor@gmail.com

$Math-Competitions$

Specific Goal of the 2025 AMC 8:

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

Specific Goal of the 2024 AMC 10:

To earn a score of 90 or more out of 150 on the AMC 10, and then receive National Achievement Honor Roll Certificates.

Specific Goal of the MathCounts:

To become one of the top winners in the individual competition at the chapter level and then advance to the state competition.

AMC-General

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!

Click here to read more!

Description:
Our curriculum focuses on advancing the mathematical skills of 5th-8th graders to prepare them for math competitions, such as AMC 8, AMC 10, Mathcounts, Math Olympiads for Elementary and Middle Schools (MOEMS), Math Kangaroo, and Math League. A variety of contest questions, including all past official AMC 8 problems, the first 15 problems on each old AMC 10 tests, and MathCounts Competition problems at the school, chapter, state, and national level, 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:

16 tutorial handouts (640 pages) developed by Dr. Henry Wan and 500 new problems similar to AMC 8 level from the licensed AMC Database. Click HERE to see a typical class handout sample we developed.
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. Surprisingly, some problems in our previous mock tests appeared in the recent official AMC 8 tests, as shown at:
- Problem 23 on the 2023 AMC 8 is Exactly the Same as a Problem on Our 2022 AMC 8 Mock Test
- Two Problems on the 2020 AMC 8 are Exactly the Same as Two Problems on Our Sample 2017 AMC 8 Mock Test
FREE registration for the AMC 8 Contest on January 16, 2025. Please see: The Online AMC 8 Contest at the Ivy League Center on January 16, 2025
FREE registration for the AMC 10A — November 10, 2024 and AMC 10B — November 16, 2024. Please see: The AMC 10/12 Contests on November 10, 2024, and November 16, 2024

Grade Levels: Rising Grades 4-8

Class Outline:

This class focuses 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 comprehensively problem-solving in discrete math (number theory, counting, and probability), which is the most important to competitive math. We reserve the right to adjust the teaching content and pace according to the actual performance of students .

Session I (Counting and Probability)

Class	Date	Topic
1	6/8, Sat	Counting with Sets and Venn Diagrams
2	6/9, Sun	Counting with Factorials, Permutations, and Combinations
3	6/15, Sat	Counting with Pascal’s Triangle, Pascal Patterns, and Hockey Sticks
4	6/16, Sun	Counting Paths on a Graph
5	6/22, Sat	Casework Counting
6	6/23, Sun	Stars and Bars Method, and Integer Equations
7	6/29, Sat	Counting Techniques in Probability
8	6/30, Sun	Counting with Patterns

Session II (Number Theory)

Class	Date	Topic
1	7/6, Sat	Divisibility Rules
2	7/7, Sun	Factor Trees and Prime Factorization
3	7/13, Sat	Counting Divisors
4	7/14, Sun	Greatest Common Divisors, and Least Common Multiples
5	7/20, Sat	Units Digits in Arithmetic
6	7/21, Sun	Patterns in the Last Two Digits of a Power
7	7/27, Sat	Base Numbers, Base Number Digits, and Converting Integers Between Bases
8	7/28, Sun	Modular Arithmetic and Linear Congruences

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.

Our Students

In 2024, we had 90 students who obtained top scores on the AMC 8 contest!

10 of our students were among the top 116 worldwide winners (Perfect Scorers).
54 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 697 worldwide winners.
29 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,683 worldwide winners.
93 out of our 96 students (96.9%) received National Awards for the AMC 8 from the Mathematical Association of America

In 2023, we had 99 students who qualified for the AIME either through the AMC 10A/12A or the AMC 10B/12B. One of our students was among the 11 Perfect Scorers worldwide on the AMC 10B: Ali R. and one of our students was among the 13 Perfect Scorers worldwide on the AMC 12B: Yaoyun X. Read more at: 99 Students Qualified for the 2024 AIME and 2 Students Received Perfect Scores on the 2023 AMC 10/12

In 2023, we had 8 students who won USAMO awards and 7 students who won USAJMO awards.

1 USAMO Gold Award, 1 USAMO Silver Award, 4 USAMO Bronze Awards, and 2 USAMO Honorable Mention Awards.
1 USAJMO Top Winner, 1 USAJMO Winner, and 5 USAJMO Honorable Mention Awards.

In 2023, we had 90 students who obtained top scores on the AMC 8 contest!

8 of our students were among the top 81 worldwide winners (Perfect Scorers).
51 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 697 worldwide winners.
31 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,571 worldwide winners.
90 out of our 93 students (96.8%) received National Awards for the AMC 8 from the Mathematical Association of America.

In 2022, we had 96 students who qualified for the AIME either through the AMC 10A/12A or the AMC 10B/12B. One of our students was among the 6 Perfect Scorers worldwide on the AMC 10A: Justin W. and one of our students was among the 3 Perfect Scorers worldwide on the AMC 12B: Ming Y. Read more at: 96 Students Qualified for the 2023 AIME and 2 Students Received Perfect Scores on the 2023 Fall AMC 10/12

In 2022, we had 3 students qualified for the Math Olympiad Summer Program. Read more at: Brendon J., Kyle S., and Isabella Z. Qualified for the 2022 Math Olympiad Summer Program

In 2022, we had 1 student Competes in International Girls’ Math Olympiad. Read more at: sabella Z. Competes in International Girls’ Math Olympiad

In 2022, we had 7 students qualified for the USAMO and 7 students for the USAJMO. Read more at: 2022 USAMO and USAJMO Qualifiers Announced — Seven Students Qualified for the USAMO and Seven Students for the USAJMO.

In 2022, we had 88 students who obtained top scores on the AMC 8 contest!

10 of our students were among the top 131 worldwide winners (Perfect Scorers), as shown in Table 1. Click Here see a full list of the 131 worldwide winners.
52 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 1,010 worldwide winners. Click HERE see a full list.
26 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,449 worldwide winners. Click HERE see a full list.
88 out of our 91 students (96.7%)received National Awards for the AMC 8 from the Mathematical Association of America

In Fall 2021, we had 93 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 5 Perfect Scorers worldwide on the AMC 10A: Nina L. and one of our students was among the 2 Perfect Scorers worldwide on the AMC 10B: Ming Y. Read more at: 93 Students Qualified for the 2021 Fall AIME and 2 Students Received Perfect Scores on the 2021 Fall AMC 10/12

In 2021, we had 6 students qualified for the USAMO and 6 students for the USAJMO. Read more at: 2021 USAMO and USAJMO Qualifiers Announced — Six Students Qualified for the USAMO and Six Students for the USAJMO

In Spring 2021, we had 91 students who are qualified to take the AIME either through the AMC 10A/12A or AMC 10B/12B. Two of our students was among the 17 Perfect Scorers worldwide on the AMC 12A: Evan L. and Suraj O. and one of our students was among the 27 Perfect Scorers worldwide on the AMC 10A: Xinchen L. Read more at: 91 Students Qualified for the 2021 AIME and 3 Students Received Perfect Scores on the 2021 AMC 10/12

In 2021, we had 8 students who got into the MathCounts state-level top 10. Yunyi L. won 9th Place in the 2021 MathCounts National Competition!

In 2020, we had 79 students who obtained top scores on the AMC 8 contest!

5 of our students were among the top 57 worldwide winners (Perfect Scorers).
49 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
25 students received National Honor Roll Certificates awarded to top 5% test takers.
79 out of our 81 students (97.5%) received National Awards for the AMC 8 from the Mathematical Association of America.

In 2020, we had 82 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 11 Perfect Scorers worldwide on the AMC 12A: Yiyang X, and one of our students was among the 13 Perfect Scorers worldwide on the AMC 10A: Jason W.. 43 middle schoolers and 9 elementary schoolers qualified for the AIME!

In 2019, we had 71 students who obtained top scores on the AMC 8 contest!

8 of our students were among the top 151 National Winners (Perfect Scorers), including 2 sixth graders.
36 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers, as shown in Table 2.
27 students received National Honor Roll Certificates awarded to top 5% test takers, as shown in Table 3.
71 out of our 73 students (97.3%) received National Awards for the AMC 8 from the Mathematical Association of America

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

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

Read more at: Notable Achievements of Our Students

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Our Uniqueness

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.

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.

Read more at::

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Click HERE find out more about Math Competitions!

Click HERE to find out more about SAT Prep!

AMC 8-New

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Over-Reliance on Calculators: A Heavy Burden on Fundamental Education

Posted on 2024-03-12 | Leave a comment

Henry Wan, Ph.D.

The widespread use of calculators has introduced significant challenges to mathematics education. In primary and middle schools, excessive dependence on these devices is eroding students’ foundational mathematical abilities.

Mathematics education is not merely about performing calculations — it is about cultivating logical thinking and problem-solving skills. When students become accustomed to obtaining answers by simply pressing buttons, they lose the valuable process of reasoning through problems. A simple arithmetic operation, when solved mentally, requires an understanding of the order of operations, carrying and borrowing rules, and number relationships. These seemingly basic processes are, in fact, the cornerstone of mathematical thinking and cognitive development.

The Consequences of Over-Reliance on Calculators

Excessive use of calculators leads to a decline in students’ mathematical abilities. Research shows that students who rely heavily on calculators tend to have significantly weaker mental calculation skills than their peers who use them sparingly. This weakness is not just in calculation speed but also in number sense and conceptual understanding. When students lose their intuition for numbers, they struggle to solve complex mathematical problems that require deeper reasoning.

The premature introduction of calculators in primary and middle school creates a dependency that can be difficult to break. What begins as a reliance on calculators for basic arithmetic gradually turns into an inability to perform even the simplest calculations without them. Many students lose confidence in their ability to compute manually, feeling the need to verify even basic sums with a calculator. In extreme cases, this over-reliance cripples their fundamental calculation skills, leaving them unable to perform mental or written arithmetic efficiently.

A Phased Approach to Calculator Use

To address this issue, we advocate for a phased approach to calculator use in education:

Primary school students should be completely prohibited from using calculators to ensure they develop a solid foundation in arithmetic.
Middle school students may use calculators moderately under strict limitations, ensuring that they do not become over-reliant.
High school students can be allowed unrestricted use of calculators, as they transition to more advanced mathematical concepts that involve real-world applications.

During the critical years of mathematical development, students should be guided to establish a strong foundation through mental and written calculations. Developing mental arithmetic skills is not just about improving speed; it is about enhancing logical thinking and problem-solving ability. Primary school should be the stage where students solidify their number sense, while middle school should focus on further strengthening these skills before gradually introducing calculators in a controlled manner.

The Impact of Banning Calculators in Math Competitions

As is well known, prior to 2008, the American Mathematics Competitions (AMC) allowed students to use calculators. However, after our persistent appeals and protests, the Mathematical Association of America (MAA) implemented a landmark policy change prohibiting calculator use in AMC starting in 2008. This decision forced students to develop stronger mental and rapid calculation skills, significantly improving their overall mathematical abilities.

The ban was based on the realization that calculators were hindering the development of fundamental arithmetic skills. By removing this crutch, students were compelled to engage more deeply with numerical concepts, developing stronger intuition for numbers and a deeper understanding of mathematical principles. As a result, students not only became more proficient in calculations but also sharpened their problem-solving and logical reasoning skills — essential abilities for success in mathematics and beyond.

Training Students for Mental and Quick Calculation

To support this transition and further enhance students’ mathematical skills, we have introduced specialized training programs. Every summer, we offer intensive courses designed to help students improve their mental and rapid calculation abilities. More details can be found at Online Intensive Mental Math Course (Summer Session). These programs provide a structured environment where students refine their skills through a series of progressive exercises and challenges.

The impact of these initiatives has been profound. Students who participate in our summer programs consistently demonstrate remarkable improvements in their mathematical performance. They develop a greater appreciation for the beauty and logic of mathematics and gain the confidence to tackle complex problems without relying on calculators. By fostering a generation of students proficient in mental calculations, we are not only boosting their academic achievements but also preparing them for future success in fields that demand strong analytical and quantitative skills.

Conclusion

Mathematics education is fundamentally about nurturing thinking skills, and over-reliance on calculators is a major obstacle to achieving this goal. The prohibition of calculators in math competitions, along with structured training programs, has played a pivotal role in enhancing students’ mathematical abilities. These efforts reaffirm our commitment to building a generation of mathematically proficient individuals, equipped to excel in an increasingly competitive and data-driven world.

By reducing dependence on calculators and reinforcing mental arithmetic, we can ensure that students develop deep mathematical intuition, problem-solving abilities, and logical reasoning skills — qualities that will benefit them not only in academics but throughout their lives. Let us safeguard the integrity of basic education and lay a strong mathematical foundation for future generations.

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Tagged ai, american-mathematics-contest, artificial-intelligence, calculator, education, learning, math, math-competition, math-contest, math-education, mathematics, mental-math, teachers, teaching

The Golden Rule of Learning Mathematics: Transitioning from Memorization to Deep Understanding and Creative Thinking

Posted on 2024-03-06 | Leave a comment

Henry Wan, Ph.D.

The true key to mastering mathematics lies in transforming knowledge from something external — merely memorized — into an internalized skillset that becomes second nature. To achieve this, students must go beyond rote learning and actively engage in a process of deep comprehension and creative exploration.

Step 1: Recall — Testing Your Understanding

After attending a math class, immediately review the concepts covered without referring to any materials. Try to recall the key points discussed by the teacher, including formulas, theorems, and their derivations. The ability to reconstruct this information from memory is the best test of how effectively you absorbed the material during class. If you struggle to recall certain details, it signals areas that require further review.

Step 2: Derivation — Reinforcing Knowledge Through Independent Thought

Take out a notebook and write down the important formulas and theorems from memory. However, do not stop at simply writing them down — challenge yourself to re-derive the formulas and prove the theorems using your own thought process. This independent thinking exercise helps pinpoint gaps in your understanding and solidifies your grasp of mathematical principles. The process of struggling through a derivation on your own is invaluable, as it forces you to connect different pieces of knowledge logically rather than just memorizing results.

Step 3: Comparison — Evaluating and Refining Methods

After completing your derivations, open your textbook and class notes to compare your approach with those presented in the materials or by the teacher. This comparison often leads to valuable insights: perhaps your method is more intuitive, or maybe the textbook’s approach is more elegant and universally applicable. By analyzing the strengths and weaknesses of different methods, you develop a more profound and flexible understanding of mathematical concepts.

Step 4: Generalization — Expanding Mathematical Thinking

True mastery of mathematics extends far beyond simply deriving formulas, proving theorems, or solving problems. It involves questioning assumptions, identifying patterns, and generalizing principles to uncover deeper insights. Consider the Pythagorean Theorem as an example. Memorizing, deriving, proving, and applying the Pythagorean formula for right triangles is just the starting point. To truly grasp its significance, challenge yourself with these thought-provoking questions:

Why does the theorem specifically apply to right triangles?
How does the relationship change if the triangle is acute? (Hint: The equation transforms into an inequality.)
How does the relationship change if the triangle is obtuse? (Hint: The equation also transforms into an inequality.)
How does the theorem evolve when extended from two dimensions to three, four, or eve n-dimensional space?
What happens when we move from Euclidean space to spherical geometry? (On a sphere, the classical Pythagorean Theorem no longer holds, and an entirely new geometric relationship emerges.)

By exploring these deeper questions, you shift from merely using mathematical tools to truly understanding their foundations, limitations, and broader implications. This approach nurtures creativity, critical thinking, innovation, and problem-solving skills — hallmarks of true mathematical mastery.

A Real Example: From Competitive Math to Cutting-Edge Research

One of our students, inspired by this approach, successfully extended the Pythagorean theorem and the Law of Cosines to higher-dimensional spaces and eventually to spherical geometry. Under our guidance, the student refined this work into a rigorous mathematical paper, which we helped recommend for publication in a prestigious journal of the Mathematical Association of America. This outstanding academic achievement became a key stepping stone, ultimately securing the student’s admission to MIT.

Why This Method Works: From Passive Learning to Active Discovery

This structured learning approach — Recall, Derivation, Comparison, and Generalization — transforms passive reception into active engagement. Rather than simply memorizing formulas, you develop a deep contextual understanding and an independent problem-solving mindset. These habits not only enhance academic performance but also cultivate the ability to think critically, explore new ideas, and innovate — skills that extend far beyond the classroom.

Mathematics is not just about solving problems — it’s about discovering patterns, questioning assumptions, and pushing the boundaries of what you know. By following this learning strategy, you will not only excel in math but also develop a lifelong ability to think deeply and creatively.

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The Learning Trifecta: Preview, Note-taking, and Review

Posted on 2024-03-05 | Leave a comment

Henry Wan, Ph.D.

Learning effectively requires a structured approach. A good study habit includes three essential steps: previewing before class, taking notes during class, and reviewing after class. These are three interconnected and essential steps in the learning process, forming a complete learning cycle. When executed effectively, can significantly enhance your understanding and retention of knowledge.

Previewing Before Class

Before attending a class, students should take time to go through the relevant materials. Previewing helps them get a basic understanding of the topic, identify key points, and formulate any questions they may have.. This preparation not only makes it easier to follow the teacher’s explanations but also enables students to engage more actively in class discussions and absorb new knowledge more effectively.

Taking Notes During Class

During the lesson, taking clear and organized notes is essential. This skill helps students stay focused and systematically organize information. Well-taken notes capture key concepts, important formulas, and explanations that may not be found in textbooks. Writing information in one’s own words enhances understanding and retention, making it easier to review later. Additionally, structured notes serve as a valuable resource for reinforcing learning and preparing for exams.

Reviewing After Class

After class, reviewing the material is crucial for reinforcing what has been learned. Students should go through their notes, clarify any unclear points, and consolidate their knowledge by recalling key concepts and main ideas without referring to their materials. Regular review helps prevent forgetting and promotes a deeper understanding of the subject. Additionally, completing homework assignments and engaging in discussions with classmates can further strengthen their grasp of the material.

Conclusion

These three steps are interconnected and essential for effective learning. Previewing lays the groundwork for understanding new material, note-taking captures key points during the lesson, and reviewing reinforces and solidifies knowledge. By consistently following this cycle, students can enhance their comprehension, retain information more effectively, and improve their academic performance.

Developing this habit not only leads to greater academic success but also cultivates a lifelong ability to learn efficiently. Remember, learning is a continuous journey, not just a destination. By embracing this structured approach and integrating it into your study routine, you can unlock your full potential and achieve your academic goals.

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How To Use A Solutions Manual Correctly?

Posted on 2024-03-05 | Leave a comment

Henry Wan, Ph.D.

We have meticulously developed the Solutions Manual to provide detailed, step-by-step solutions for all homework problems. Each problem includes at least one solution, all of which were derived without the use of a calculator to encourage students for developing mathematical reasoning, problem-solving abilities, and creative thinking skills.

In cases where multiple solutions are presented, they are included to highlight key contrasts in problem-solving approaches. These alternative methods help students develop a deeper understanding of mathematical concepts by exploring different perspectives, such as:

Algebraic vs. Geometric — Solving problems through symbolic manipulation versus visual or spatial reasoning.
Elementary vs. Advanced — Approaching problems using fundamental techniques versus more sophisticated methods.
Computational vs. Conceptual — Focusing on numerical calculations versus underlying theoretical principles.
Explicit vs. Implicit — Directly solving for unknowns versus deriving solutions through indirect reasoning.
Analytic vs. Discrete — Using continuous methods versus discrete, step-by-step reasoning.
Forward-Solving vs. Back-Solving — Progressing logically from given information versus working backward from the desired outcome.

Understanding these different approaches helps students become more flexible and adaptable problem solvers, equipping them with the skills necessary for success in mathematical competitions and beyond.

To ensure students use the Solutions Manual as a tool for learning rather than a shortcut to answers, we have written this article, “How to Use a Solutions Manual Correctly?” This guide provides strategies to maximize the manual’s benefits while reinforcing independent problem-solving skills, ultimately fostering deeper comprehension and mathematical growth.

Many of the problems you encounter are subtle or complex, requiring careful thought — and time! — before a clear solution method emerges. The best way to learn is by attempting to solve a problem on your own, even if you don’t succeed at first. This process of grappling with challenges is crucial for deepening your understanding.

Learning mathematics requires a certain amount of “healthy frustration,” which is a natural part of developing problem-solving skills. You may need to try different approaches (some of which may lead nowhere or a dead end) until you find a viable solution. While this process can be time-consuming, it is important to persist without immediately relying on outside help. If you turn to the solutions manual too quickly, you risk missing out on the critical thinking and problem-solving skills that are key to success, particularly in competitive settings like math contests. Simply understanding the solutions provided in the manual does not mean you’ve truly mastered the material!

The solutions manual can be a helpful learning tool if used correctly, but it can also subtly hinder your progress if relied upon too heavily. How you use the manual can significantly affect your learning experience. If you use it prematurely or excessively, you may end up undermining your own efforts to master the material and perform well on contests.

The most important principle to remember is this: Do not consult the solutions manual until you have made a genuine attempt to solve the problem yourself. Ideally, you should use the manual primarily to confirm your answer. In many cases, your solution will align with the one in the manual, but occasionally, you may discover a different approach that is equally correct — or even more efficient — than the one presented. If you find an alternative method, we would love to hear about it! Please send us your solution at mathteam@ivyleaguecenter.org.

If, after a substantial effort, you still can’t find the solution, then it’s appropriate to look at solution offered in the manual. Even then, start by reading only the beginning of the solution to see if you can continue on your own. The goal is not just to arrive at the answer but to fully engage with the process, which will ultimately deepen your understanding and develop your problem-solving.

The goal is not just to reach the answer but to immerse yourself in the process, enhancing your understanding, sharpening your problem-solving skills, and fostering your creative thinking.

By using the solutions manual in the right way, you will maximize your learning and enhance your ability to solve problems independently — skills that are invaluable in both academic settings and math competitions.

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Why Drawing a Good Diagram Is Important to Solve a Geometry Problem?

Posted on 2024-03-01 | Leave a comment

Henry Wan, Ph.D.

Geometry is a branch of mathematics that heavily relies on visualization. Unlike algebra, where equations and numbers dominate problem-solving, geometry problems often involve shapes, angles, measurements, and spatial relationships. One of the most effective tools for tackling geometry problems is a well-drawn diagram. A clear, accurate diagram not only helps in understanding the given information but also reveals hidden relationships that might not be immediately obvious. Below are several reasons why drawing a good diagram is essential when solving geometry problems.

Enhances Understanding of the Problem

A geometry problem often involves complex relationships between points, lines, angles, and shapes. Without a visual representation, these relationships can be difficult to grasp. Drawing a diagram translates abstract descriptions into concrete images, making it easier to grasp the given information and see how different elements interact. By sketching the diagram, you can identify key points, label known values, and ensure that you correctly interpret the problem statement. This step is especially useful for word problems that describe geometric figures verbally rather than presenting them visually.

Helps Identify Important Geometric Properties

When solving a geometry problem, identifying key values and conditions is essential for finding the solution. Drawing a diagram allows one to clearly label known angles, lengths, and relationships such as parallel lines, perpendicular bisectors, or congruent triangles. This visual representation helps organize information systematically, reducing the risk of overlooking important details. More importantly, a well-drawn diagram highlights crucial geometric properties such as symmetry, parallelism, congruence, and similarity, which often hold the key to an efficient solution. For example, a carefully constructed diagram might reveal that two triangles are similar, enabling the straightforward application of proportional reasoning.

Reduces Errors and Misinterpretations

Without a diagram, it is easy to misread a problem or overlook critical details, increasing the risk of misinterpreting given information or making calculation errors. A well-drawn diagram serves as a visual checkpoint, helping problem-solvers verify their steps and ensure their reasoning aligns with the actual figure. Incorrect assumptions can often be identified quickly by reviewing a clearly labeled diagram. Additionally, a diagram ensures that angles, side lengths, and relationships are accurately represented, minimizing the chances of computational or logical errors.

Facilitates the Application of Theorems and Formulas

Many geometric theorems, such as the Pythagorean Theorem, the Angle Bisector Theorem, the properties of similar triangles, the properties of circles, or the sum of interior angles in a polygon, become easier to apply when visualized in a diagram. A well-drawn figure highlights key elements like right angles, perpendicular bisectors, and tangent lines, guiding the solver to the correct approach.

Encourages Logical Thinking and Pattern Recognition

A diagram allows problem-solvers to explore different approaches and recognize patterns that may not be immediately apparent from the text alone. For example, extending a line, drawing an auxiliary shape, or marking equal segments and congruent angles can reveal insights that simplify the problem. Many competition-level geometry problems become significantly easier with a well-placed additional construction.

Additionally, a lot of geometry problems require logical reasoning, and a diagram serves as a structured visual aid to support step-by-step analysis. It helps track the flow of arguments, ensuring that conclusions logically follow from the given premises.

Saves Time in Problem Solving

In competitive math settings, time is a critical factor. A good diagram often leads to a quicker solution by allowing direct visualization of relationships rather than relying on lengthy calculations. Instead of writing out multiple equations, a simple observation in a well-drawn diagram might provide an instant shortcut to the answer.

How to Draw an Effective Diagram?

To maximize the benefits of a diagram, consider the following tips:

Use a ruler (if time allows) or draw neatly by hand. A clear, proportional diagram prevents misinterpretation.
Label key points, angles, and lengths. This helps keep track of known values and relationships.
Mark congruent or similar segments. Highlighting these properties can make important relationships stand out.
Add auxiliary lines if necessary. Sometimes, drawing an extra line, such as a perpendicular or a median, simplifies the problem significantly.
Avoid cluttering the diagram. Too many unnecessary details can lead to confusion rather than clarity.

Conclusion

Drawing a good diagram is a fundamental skill in solving geometry problems. It enhances understanding, organizes key information, reduces errors, reveals crucial properties, displays patterns, supports logical reasoning, and facilitates the application of theorems. Whether tackling a school assignment, preparing for math competitions, or solving complex geometric proofs, investing a few moments in creating an accurate and well-structured diagram can be the key to success. By developing strong diagram-drawing habits, students can approach geometry problems with confidence and efficiency.

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How to Prepare for the AMC 10

Posted on 2024-01-31 | Leave a comment

AMC 10-2017

The AMC 10 is one of the most prestigious high school Math competitions in the USA and the world. It provides a way for students interested in math to use their knowledge and skills to experience the joy of competiting against others.

The best way to prepare for the AMC 10 is to attend our AMC 10/12 training program. This is a comprehensive one-year program offering an entire course to cover all the topics that will be tested on the AMC 10/12. Students who participate in our training program will have free access to video recordings of every single class. Students who are not able to attend our training program can also purchase our course materials and recordings, including tutorial handouts, recorded videos, detailed solutions of homework problems, and mock tests, to learn all our course content. Starting each November just after the AMC 10/12 contests, we offer these sessions in sequence, as shown below.

Sessions	Topics	Course Outlines
Winter Session	Arithmetic and Algebra	Course Outline
Spring Session	Geometry	Course Outline
Summer Session	Number Theory, and Counting and Probability	Course Outline
Fall Session	Comprehensive Problem Reasoning and Solving for AMC 10/12	Course Outline

It imust be stressed that in each session, no old material is repeated. Each session contains new, unique material, as well as a brand new comprehensive art of problem solving. We strongly believe that learning should be a long-term process of acquiring new material, information, and knowledge.

The easiest way to prepare is to practice solving previous official AMC 10 problems. Click the links below to visit our Practice Page for:

Archived Exams: A full archive of every year’s AMC 10 A and B tests. Students can take a practice exam that includes the real questions, timing, and scoring of each exam.
Mock Tests: Practice exams are also available for purchase. Our team developed 20 different sets of AMC 10 mock tests for students to practice with. They are intended to mimic the actual AMC 10 exam with 25 brand new questions all calibrated to be at the same style and difficulty level as the real AMC 10. In particular, they are peer-reviewed by at least two experts in math education outside our center. These simulated tests are extremely helpful for assessing students’ level of preparation for the AMC 10. Our team also devised detailed solutions to all 25 problems on our 20 sets of AMC 10 mock tests. All these mock tests and their detailed solutions are a golden fountain of knowledge for our students, who are the ultimate beneficiaries. Surprisingly, some problems in our previous mock tests appeared in the recent official AMC 10 tests, as shown at:

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How to Prepare for the AMC 12

Posted on 2024-01-30 | Leave a comment

AMC 12-New

The AMC 12 is one of the most prestigious high school Math competitions in the USA and the world. It is a great way for younger students to gain valuable experience with math competitions and develop powerful problem solving skills.

The best way to prepare for the AMC 12 is to attend our AMC 10/12 training program. This is a well developed, comprehensive, systematic one-year program offering an entire course to cover all the topics that will be tested on the AMC 12. Students who participate in our training program will have free access to video recordings of every single class. Students who are not able to attend our training program can also purchase our course materials and recordings, including tutorial handouts, recorded videos, detailed solutions of homework problems, and mock tests, to learn all our course content. Starting each November just after the AMC 12 contests, we offer these sessions in sequence, as shown below.

Sessions	Topics	Course Outlines
Winter Session	Arithmetic and Algebra	Course Outline
Spring Session	Geometry	Course Outline
Summer Session	Number Theory, and Counting and Probability	Course Outline
Special Summer Session	Precalculus	Course Outline
Fall Session	Comprehensive Problem Reasoning and Solving for AMC 10/12	Course Outline

It is very worth emphasizing that in each session, no old material is repeated. Each session contains new, unique material, as well as a brand new comprehensive art of problem solving. We strongly believe that learning should be a long-term process of acquiring new material, information, and knowledge.

The easiest way to prepare is to practice solving previous official AMC 12 problems. Click the links below to visit our Practice Page for:

Archived Exams: A full archive of every year’s AMC 12 A and B tests. Students can take a practice exam that includes the real questions, timing, and scoring of each exam.
AMC 12 Mock Tests: Practice exams are also available for purchase. Our team developed 20 different sets of AMC 12 mock tests for students to practice with. They are intended to mimic the actual AMC 12 exam with 25 brand new questions all calibrated to be at the same style and difficulty level as the real AMC 12. In particular, they are peer-reviewed by at least two experts in math education outside our center. These simulated tests are extremely helpful for assessing students’ level of preparation for the AMC 12. Our team also devised detailed solutions to all 25 problems on our 20 sets of AMC 12 mock tests. All these mock tests and their detailed solutions are a golden fountain of knowledge for our students, who are the ultimate beneficiaries. Surprisingly, some problems in our previous mock tests appeared in the recent official AMC 12 tests, as shown at:

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How to Prepare for the AIME

Posted on 2024-01-29 | Leave a comment

aime2

The AIME is a prestigious math competition whose successful completion provides a path towards the International Mathematics Olympiad (IMO), the most premier international high school level problem solving contest. It provides the exceptional students who are invited to take it with yet another opportunity to challenge their mathematical abilities, and means towards furthering mathematical development and interest.

The best way to prepare for the AIME is to attend our AIME training program. This is a well developed, comprehensive, systematic one-year program offering an entire course to cover all the topics that will be tested on the AIME. The course is thoughtfully structured to delve into advanced mathematical concepts and hone problem-solving strategies and arts, with a particular emphasis on the kinds of challenges commonly encountered in questions 5-12 of the AIME, which are renowned for their moderate level of difficulty.

Students who participate in our training program will have free access to video recordings of every single class. Students who are not able to attend our training program can also purchase our course materials and recordings, including tutorial handouts, recorded videos, detailed solutions of homework problems, and mock tests, to learn all our course content. Starting each February just after the AIME contest, we offer these sessions in sequence, as shown below.

Sessions	Topics	Course Outlines
Spring Session	Advanced Algebra	Course Outline
Summer Session	Combinatorics and Number Theory	Course Outline
Fall Session	Advanced Geometry	Course Outline
Winter Session	Comprehensive Problem Reasoning and Solving for AIME	Course Outline

It must be pointed out that in each session, no old material is repeated. Each session contains new, unique material, as well as a brand new comprehensive art of problem solving. We strongly believe that learning should be a long-term process of acquiring new material, information, and knowledge.

The easiest way to prepare is to practice solving previous official AIME problems. Click the links below to visit our Practice Page for:

Archived Exams: A full archive of every year’s AIME I and II tests. Students can take a practice exam that includes the real questions, timing, and scoring of each exam.
AIME Mock Tests: Practice exams are also available for purchase. Our team developed 20 different sets of AIME mock tests for students to practice with. They are intended to mimic the actual AIME exam with 15 brand new questions all calibrated to be at the same style and difficulty level as the real AIME. In particular, they are peer-reviewed by at least two experts in math education outside our center. These simulated tests are extremely helpful for assessing students’ level of preparation for the AIME. Our team also devised detailed solutions to all 15 problems on our 20 sets of AIME mock tests. All these mock tests and their detailed solutions are a golden fountain of knowledge for our students, who are the ultimate beneficiaries. Surprisingly, some problems in our previous mock tests appeared in the recent official AIME tests.

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!

AMC-AIME-USAMO-IMO AMC-General

Featured Math Instructors

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Online Intensive AMC 8/Mathcounts Prep (for 4th to 8th Graders) Special Spring Session (Advanced Geometry) Starting March 30

Posted on 2024-01-17 | Leave a comment

Spring is the crucial time to prepare for the AMC 8 and Mathcounts!

The period of time between 4th-8th grade is most critical to the development of students’ mathematical fascinations, interests, and skills!

2024 AMC 8: 10 perfect scorers. 54 students got the DHR. 29 students got the HR.
2023 AMC/AIME: 99 AIME qualifiers. 1 AMC 10 perfect scorer. 1 AMC 12 perfect scorer.
2023 JMO/AMO: 8 USAMO Awardees and 7 USAJMO Awardees
- 1 USAMO Gold Award, 1 USAMO Silver Award, 4 USAMO Bronze Awards, and 2 USAMO Honorable Mention Awards.
- 1 USAJMO Top Winner, 1 USAJMO Winner, and 5 USAJMO Honorable Mention Awards.
2023 MOP: 4 MOP winners.
How to Prepare for the AMC 8

Special Spring Session (Circle Geometry and Advanced Topics)
10 Weekends (EASTERN Time: 6:00 – 8:00 pm), Total: 20 Hours
3/30, 4/6, 4/13, 4/20, 4/27, 5/4, 5/11, 5/18, 5/25, 6/1

Course Outline

Class Handout Sample

Online Registration is now open! Click HERE to register and pay.

Tuition (including all materials)
Special Session (20 Hours)
New Student:	Via Zelle: $700 (Phone: 240-300-4380) Please include your child’s name “AMC 8 Spring II” in the “Memo” box.
	Via PayPal: $725
Returning Student:	Via Zelle: $685 (Phone: 240-300-4380) Please include your child’s name “AMC 8 Spring II” in the “Memo” box.
	Via PayPal: $710
Click HERE to see payment and refund policy.

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 so that our students can watch them after class for review and self-study.

In last year’s AMC 8/Mathcounts Prep Spring Session, what we comprehensively presented fully covered all the geometry topics that appeared in the 2023 AMC 8 test. All geometry problems on the 2023 AMC 8 are the same as or similar to the typical examples demonstrated in our spring session. This is how our course can greatly help our students to get a high score on the AMC 8 contest!

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 commitment to the whole course can maximize the benefit of learning all the math ideas, methods, strategies, tactics, skills, and techniques.

We will help students gain a deep 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 utilize a highly effective teaching model as described in the article: Small-sized Class Instruction-focused Model.

Instructors: Dr. Henry Wan

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Purpose: To prepare for math competitions, such as

AMC 8 — Thursday, January 16, 2025.
MATHCOUNTS
Math Kangaroo Contest
Math Olympiads for Elementary and Middle Schools (MOEMS)

Contact Information:
Ivy League Education Center
Tel: 240-300-4380
Email: chiefmathtutor@gmail.com

$Math-Competitions$

Specific Goal of the 2025 AMC 8:

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

Specific Goal of the 2024 AMC 10:

To earn a score of 90 or more out of 150 on the AMC 10, and then receive National Achievement Honor Roll Certificates.

Specific Goal of the MathCounts:

To become one of the top winners in the individual competition at the chapter level and then advance to the state competition.

AMC-General

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!

amc8

Although the last round of this year’s AMC 8 will be coming at a close on January 18, 2024, we must prepare in advance for the 2025 AMC 8 contest. As the great scientist Louis Pasteur said, “Chance favors only the prepared mind.” Those who strive to prepare early, and work hard are the ones who achieve the best results. The AMC is a complex math competition that requires dedication and focus. Therefore, the earlier our students start preparing, the better their scores will be.

Click here to read more!

Benefits:

20 tutorial handouts (800 pages) developed by Dr. Henry Wan and 500 new problems similar to AMC 8 level from the licensed AMC Database. Click HERE to see a typical class handout sample we developed.
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. Surprisingly, some problems in our previous mock tests appeared in the recent official AMC 8 tests, as shown at:
- Problem 23 on the 2023 AMC 8 is Exactly the Same as a Problem on Our 2022 AMC 8 Mock Test
- Two Problems on the 2020 AMC 8 are Exactly the Same as Two Problems on Our Sample 2017 AMC 8 Mock Test
FREE registration for the AMC 8 Contest on January 16, 2025. Please see: The Online AMC 8 Contest at the Ivy League Center on January 16, 2025
FREE registration for the AMC 10A — November 10, 2024 and AMC 10B — November 16, 2024. Please see: The AMC 10/12 Contests on November 10, 2024, and November 16, 2024

Grade Levels: Grades 4-8

Class Outline:

This class focuses 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 comprehensively problem-solving in geometry, which is the most important to competitive math. In particular, we will help students use mental math for accurately and quickly solving contest questions in their heads. We reserve the right to adjust the teaching content and pace according to the actual performance of students.

Spring Session I

Class	Date	Topic
1	1/20, Sat	Angles, Parallel and Perpendicular Lines
2	1/27, Sat	Pythagorean Theorem, Pythagorean Triplets, Side-based Special Right Triangles
3	2/3, Sat	Areas of Triangles
4	2/10, Sat	Squares and 45^o-45^o-90^oTriangles
5	2/17, Sat	Equilateral Triangles and 30^o-60^o-90^o Triangles
6	2/24, Sat	Similar Triangles
7	3/2, Sat	Proportions in Triangles
8	3/9, Sat	Perimeters and Areas of Similar Triangles
9	3/16, Sat	Comparing the Areas of Triangles
10	3/23, Sat	Quadrilaterals

Spring Session II (Continuation of Session I)

1	3/30, Sat	Fundamental Properties of Polygons
2	4/6, Sat	Areas of Polygons
3	4/13, Sat	Circles: Basic Properties, Areas, and Circumferences
4	4/20, Sat	Circles: Arcs, Angles, Chord, Tangent, and Secant Segments
5	4/27, Sat	Right Triangles and Circles
6	5/4, Sat	Incircles of Triangles
7	5/11, Sat	Circumcircles of Rectangles and Triangles
8	5/18, Sat	Solid Geometry
9	5/25, Sat	Fundamental Coordinate Geometry
10	6/1, Sat	More on Coordinate Geometry

Homework:

The focus will be on the final 15 problems on the AMC 8, and the first 15 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.

Our Students

In 2023, we had 8 students who won USAMO awards and 7 students who won USAJMO awards.

1 USAMO Gold Award, 1 USAMO Silver Award, 4 USAMO Bronze Awards, and 2 USAMO Honorable Mention Awards.
1 USAJMO Top Winner, 1 USAJMO Winner, and 5 USAJMO Honorable Mention Awards.

In 2023, we had 90 students who obtained top scores on the AMC 8 contest!

8 of our students were among the top 81 worldwide winners (Perfect Scorers).
51 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 697 worldwide winners.
31 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,571 worldwide winners.
90 out of our 93 students (96.8%) received National Awards for the AMC 8 from the Mathematical Association of America.

In 2022, we had 3 students qualified for the Math Olympiad Summer Program. Read more at: Brendon J., Kyle S., and Isabella Z. Qualified for the 2022 Math Olympiad Summer Program

In 2022, we had 1 student Competes in International Girls’ Math Olympiad. Read more at: sabella Z. Competes in International Girls’ Math Olympiad

In 2022, we had 88 students who obtained top scores on the AMC 8 contest!

10 of our students were among the top 131 worldwide winners (Perfect Scorers), as shown in Table 1. Click Here see a full list of the 131 worldwide winners.
52 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers. They were among the 1,010 worldwide winners. Click HERE see a full list.
26 students received National Honor Roll Certificates awarded to top 5% test takers. They were among the 2,449 worldwide winners. Click HERE see a full list.
88 out of our 91 students (96.7%)received National Awards for the AMC 8 from the Mathematical Association of America

In 2021, we had 8 students who got into the MathCounts state-level top 10. Yunyi L. won 9th Place in the 2021 MathCounts National Competition!

In 2020, we had 79 students who obtained top scores on the AMC 8 contest!

5 of our students were among the top 57 worldwide winners (Perfect Scorers).
49 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
25 students received National Honor Roll Certificates awarded to top 5% test takers.
79 out of our 81 students (97.5%) received National Awards for the AMC 8 from the Mathematical Association of America.

In 2020, we have 2 students, Isabella Z. and Sameer P., who were among the 61 students selected nationwide to attend. Read more at: Warmest congratulations to Isabella Z. and Sameer P. for being accepted into the Math Olympiad Program!

In 2019, we had 71 students who obtained top scores on the AMC 8 contest!

8 of our students were among the top 151 National Winners (Perfect Scorers), including 2 sixth graders.
36 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers, as shown in Table 2.
27 students received National Honor Roll Certificates awarded to top 5% test takers, as shown in Table 3.
71 out of our 73 students (97.3%) received National Awards for the AMC 8 from the Mathematical Association of America

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

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 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 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

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

Read more at: Notable Achievements of Our Students

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Great Benefits of Math Competitions

Read more at::

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Click HERE find out more about Math Competitions!

Click HERE to find out more about SAT Prep!

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Online Intensive AMC 8/Mathcounts Prep (for Rising 4th to 8th Graders) Summer Weekend (Discrete Math) Course Starting June 8

How to Prepare for the AMC 8

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Over-Reliance on Calculators: A Heavy Burden on Fundamental Education

The Golden Rule of Learning Mathematics: Transitioning from Memorization to Deep Understanding and Creative Thinking

The Learning Trifecta: Preview, Note-taking, and Review

How To Use A Solutions Manual Correctly?

Why Drawing a Good Diagram Is Important to Solve a Geometry Problem?

How to Prepare for the AMC 10

How to Prepare for the AMC 12

How to Prepare for the AIME

AMC → AIME → USAMO sequence

Online Intensive AMC 8/Mathcounts Prep (for 4th to 8th Graders) Special Spring Session (Advanced Geometry) Starting March 30

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