How To Use A Solutions Manual Correctly?

Posted on 2024-03-05 | Leave a comment

copyright-small 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.

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

copyright-small 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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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2024 USAMO and USAJMO Qualifying Thresholds

Posted on 2024-03-01 | Leave a comment

The 2024 USA(J)MO will be held on March 19th and 20th, 2024. Students qualify for the USA(J)MO based on their USA(J)MO Indices, as shown below.

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Selection to the USAMO is based on the USAMO index which is defined as AMC 12 Score plus 10 times AIME Score.

Selection to the USAJMO is based on the USAJMO index which is defined as AMC 10 Score plus 10 times AIME Score.

USA(J)MO Indices from 2010 to 2024 can be found at: USAMO and USAJMO Qualification Indices from 2010 to 2024

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2024 Special Spring Session – Competitive Math Courses

Posted on 2024-02-20 | 1 comment

Spring is the best time to develop students’ math skills and to prepare for the American Mathematics Competitions!

Only undertake what you can do in an excellence fashion. There are no prizes for average performance.

  • 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.

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Competitive Math Program — 2004 Special Spring Session Schedule

Class Day/Time Grade
Online Intensive AMC 8/Mathcounts Prep Special Spring Session: Circle Geometry and Advanced Topics

10 Weekends (EASTERN Time: 6:00 – 8:00 pm), Total: 22 Hours
3/30,  4/6,  4/13,  4/20,  4/27,  5/4,  5/11,  5/18,  5/25,  6/1

Class Handout Sample
View Course Outline

 4-8
Online Intensive AMC 10/12/ARML Prep Special Spring Session: Circles and Advanced Geometry

9 Weekends (EASTERN Time: 6:00 – 8:00 pm), Total: 18 Hours

4/14,  4/21,  4/28,  5/5,  5/12,  5/19, 5/26, 6/2,  6/9 (Final Mock Exam/Review)

Class Handout Sample
View Course Outline

 6-11
Online Intensive AIME Prep Special Spring Session:  Advanced Algebra

9 Classes  (EASTERN Time: 3:00 – 4:30 pm), Total: 13.5 Hours

4/14,  4/21,  4/28,  5/5,  5/12,  5/19, 5/26, 6/2,  6/9 (Final Mock Exam/Review)

Class Handout Sample
View Course Outline

 6-12

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.

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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!

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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.

Meet some of them here:

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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.

Read more at: 2023 USAMO and USAJMO Awardees Announced — Congratulations to Eight USAMO Awardees and Seven USAJMO Awardees

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.

Read more at: 2023 AMC 8 Results Just Announced — Eight Students Received Perfect Scores

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

Read more at: 2022 AMC 8 Results Just Announced — Ten Students Received Perfect Scores

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.

Read more at: 2020 AMC 8 Results Just Announced — Five Students Received Perfect Scores

In 2020, we had 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 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!

Read more at: 2020 AIME Qualifiers Announced — 82 Students 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

Read more at: 2019 AMC 8 Results Just Announced — Eight Students Received Perfect Scores

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.

Read more at: 2019 USAMO and USAJMO Qualifiers Announced — Four Students Qualified for the USAMO and Four Students for the USAJMO

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!

Read more at: 2019 AIME Qualifiers Announced — 76 Students 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

Read more at: 2018 AMC 8 Results Just Announced — Three Students Received Perfect Scores

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!

Read more at: 2018 AIME Qualifiers Announced — 73 Students 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

Read more at: 2017 AMC 8 Results Just Announced — Seven Students Received Perfect Scores

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 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, Caltech, 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:

Contact Information:

Ivy League Education Center
Tel:  240-300-4380     or     240-406-3402（中文专线）
Email:  chiefmathtutor@gmail.com

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2024 AMC 8 Results Just Announced — Ten Students Received Perfect Scores

Posted on 2024-02-19 | Leave a comment

HEARTFELT CONGRATULATIONS TO THE STUDENTS WHO EARNED TOP SCORES ON THE 2024 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

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The 2024 AMC 8 (American Mathematics Competitions 8) was held on January 18, 2024 through January 24, 2024. The AMC 8 is the most rigorous nationwide mathematics competition at the middle school level, dedicated to the goal of strengthening the mathematical capabilities of our nation’s youth. The AMC 8 has a total score of 25. Ten of our students were among the 116 Worldwide Winners (Perfect Scorers).

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In 2024, there were 96 students in grades 4-8 who attended our AMC 8 Prep, AMC 10/12 Prep, and AIME Prep Classes, including One-on-One Private Coaching and Small Group (4-10 students) Classes. All of them attended the AMC 8 contest on January 18, 2024 through January 24, 2024, and their average score is 20.6. Particularly, 93 students received National Awards for the AMC 8 from the Mathematical Association of America. Furthermore, 37 students in grade 6 or under received National Awards.

All our students who achieved the top scores on the AMC 8 actually attended our high level AMC 10/12/AIME classes, not our standard level AMC 8 classes. They know that in order to get a top score, they must aim even higher!shoot-for-the-mooneven-if-you-missyoull-land-among-the-stars-inspirational-quote

There was a total of 272,0359 students worldwide participated in the 2024 AMC 8 contest from over 2,000 schools. In the USA, 231,478 students participated, and the overall national average score is 10.54 out of a maximum of 25. All our students achieved an average score of 22.8 that is much higher than the overall national average score.

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Top scorers and statistics can be found at http://amc-reg.maa.org/reports/generalreports.aspx

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2024 AMC 8 Honor Roll and Honor Roll of Distinction Cut-off Scores

Posted on 2024-02-19 | Leave a comment

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  • Honor Roll of Distinction (Top 1%): Score of 22
  • Honor Roll of Certificate (Top 5%): Score of 18
  • Achievement Honor Roll (6th Grade and below): Score of 15.

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This year’s contest is of intermediate difficulty compared to the contests in the last 5 years. For more details, please see:

MAA AMC 8

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Read more at:

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Click HERE to find out more about SAT Prep!

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路透社大放厥词：中国空气污染减少，太清洁导致气温升高

Posted on 2024-02-11 | Leave a comment

来源：微信公众号“前HR随笔”

来了，果然来了：路透社，中国空气污染减少，太清洁导致气温升高，印度不能学！

路透社说，所谓6位西方著名气候专家表示，研究中国长达十年、高效的“污染战争”结果，由于除去散射和反射太阳辐射的、由污染物构成有毒屏障，中国的平均气温自2014年以来上升了0.7摄氏度，引发了更为剧烈的热浪。对此，西方科学家们表示，过去10年，空气污染的消除——科学家们称之为“揭开面纱”——对中国一些工业城市气温的影响，可能比温室气体本身造成的变暖更大。

专家们警告称，如果印度和中东等世界其它高污染地区效仿中国，清洁天空中的二氧化硫及其形成的污染性气溶胶，那么气候变暖将出现类似的跃升。你看看这些烂货，中国治理污染导致气温提升都来了，他们眼里中国做什么都不对，这暗戳戳带节奏中国要对全球气温提升负责了。

实际上，欧美媒体，尤其盎格鲁萨克逊团伙媒体经常自打脸。中国上世纪沙漠化严重，他们就说中国无序开发，导致沙漠化。中国本世纪人进沙退，绿化成为全球最好的，贡献了全球一半的新增森林面积。结果欧美说中国治沙是破坏生态的自然状态。

中国以前吃肉少，他们就鄙视中国蛋白质摄入量不够，是儿童不长高的根源。等中国可以吃肉喝奶了，他们就说中国吃一块牛肉亚马逊雨林就冒起一团火，意思是因为中国买巴西的大豆导致了巴西去烧森林。可是他们从来不反思欧美人均吃肉比中国高多了，中国饮食习惯虽然能奶肉了，但是还是荤素搭配比他们强多了。

所以，一些人说要和欧美友好，我们什么时候说过不和欧美友好了？问题是他们看不得我们过得好，认为我们过得好是挤占他们生存空间。奥巴马在澳大利亚演讲说如果中国生活达到发达国家水平需要4个地球，西方生活就无法维持了。你开车好好的不去撞人，可是有人要来撞你，你有什么办法呢？现在美国人就是在你走着路冲过来撞你的那个人。而美国人还通过舆论洗脑，说是你撞他们。

随着中国信息产业发展，美国人以前把信息产业说是人类之光，要免税，要提升人类的数字平权。现在中国超出他们，信息产品就是安全威胁了。类似绿色低碳产业，英国干不过中国了就说不能以牺牲英国人生活满足地球环保了。那以前他们为什么不对发展中国家这样说？

因此，看到欧美各种没有底线的双标，大家已经习惯成自然，上他们擂台，并把他们打下来，让他们在台下当小丑，这才是我们最好的逻辑。

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香港消散的優越感殘影（葉家興）

Posted on 2024-02-02 | Leave a comment
香港進出大陸的人流出現逆轉！海關數據顯示，2023年全年香港居民約有5300萬人次北上，遠超過大陸旅客約2600萬人次訪港。（shutterstock）
香港進出大陸的人流出現逆轉！海關數據顯示，2023年全年香港居民約有
5300萬人次北上，遠超過大陸旅客約2600萬人次訪港。

香港進出大陸的人流出現逆轉！海關數據顯示，2023年全年香港居民約有5300萬人次北上，遠超過大陸旅客約2600萬人次訪港。北上大陸的香港人也已超過2018年水平，反觀南下香港的大陸人，相較疫情前兩年平均6000萬人次的規模卻大幅縮減。

1月初英國廣播公司（BBC）中文版網站在一篇「香港經濟低迷，為什麼愈來愈多港人北上深圳跨境消費」報導中，引述政府數據，並以若干港人實例，極好地證明了港人心裡存在的優越感殘影逐漸消散。

例如，26歲的李承謙小時候曾陪媽媽到過羅湖商業城，但已經沒什麼記憶，對於深圳的印象一直都停留在「不太發達」的城市，故一直都沒有想要前往消費的慾望。直到2023年5月，他才重新申請回鄉證，開始了第一次的「北上消費」之旅。他坦言，去了第一次之後，翻轉了他過往對於深圳的印象，「我第一次是去萬象天地，看到很多高樓大廈。」此後每個月他都會到訪深圳一兩次，每次都嘗試一家不同的餐廳。

香港處處優越於大陸，是1840年鴉片戰爭導致香港割讓給英國後，近200年發展差距的積累。然而大陸改革開放後經濟高速增長，原本只是小漁村的深圳一躍成為科技與金融領域的中心，總體經濟規模也已在2017年超越香港。雖然只是一河之隔，但深、港發展翻轉的心理反應，大概需要幾年才得以改變。

從尖沙嘴香港西九龍高鐵站到深圳市中心的福田高鐵站，高鐵行程只有14分鐘，距離30公里，比北捷淡水信義線象山站到淡水站32公里（行程54分鐘）還近，但優越感的殘影作祟，短短十幾分鐘的物理距離，在「心理距離」的刻度上竟要費時數年！

同樣心理上的失落感，讓不少中老一代台灣人難以接受「落後不文明」的大陸比自己進步。優越感的殘影作用，使「中國高鐵沒有靠背」這種離譜的謠言有市場。伴隨大陸股市房市不振，各種「中國崩潰論」推陳出新。任何關於大陸真相的正面傳遞會被迅速貼上「認知作戰」的標籤。中老年一代自我屏蔽真實資訊的能力驚人，反而十幾歲的青少年沒有這種優越感的殘影，他們可以在抖音、小紅書等APP上客觀地追尋大陸的時尚流行資訊。

放大到世界格局上亦是如此。西方自工業革命之後已經遙遙領先東方長達數個世紀之久。高高在上的西方政客，早已習慣別人對他唯唯諾諾，當然很難接受「東升西降」的現實，很難接受非西方提出的各種國際倡議，諸如「一帶一路」倡議、金磚國家組織等等。心理上的失落感強烈，卻無法認真反思治理制度的缺失，只能用偏頗的輿論醜化對手來維持他們優越感的殘影。

優越感有殘影，自卑感也有殘影。二戰後美援時代成長的台灣人，以及改革開放後第一批發家的大陸人，就有不少人「欽慕」美國，想方設法傾家蕩產也要移民，或把子女送到美國。大陸電視劇《都挺好》裡面的「蘇大強」更是把這種「慕洋」情結刻畫得入木三分。他們對現今美國治理失調的各種危機視而不見，因為自卑感的殘影更難洗盡。

核武時代，超級大國間的競爭不太可能靠打仗來決一勝負。因此，意識形態的殘影需要更多的交流來消解。就像被反華媒體蒙蔽多年的港人一樣，他們一旦用雙眼與真心體會感受了事實，這種翻轉的印象猶未晚矣，可為更愉快的生活體驗增添驚喜。

殘影原本指的是顯示器面板的圖像殘留，或人眼的視覺暫停現象，但機械或肉眼的殘影構成不了大礙，反而善加利用可以創造新藝術類型，增添人類文化的光彩。但比物理殘影影響更大的是心理殘影，包括意識形態僵固造成的各種殘影，在信息繭房的演算法助攻下，更成了難以消散的心魔。所幸港人以實際行動證明，只要願意跳出認知的舒適圈，再頑固的殘影也有散去的一刻！

（作者為香港中文大學金融系副教授）

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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:

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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:

More articles about math competitions:

 maausasf

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