Tag Archives: learning

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

Posted on 2024-03-01 | Leave a comment

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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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.

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!

AMC-AIME-USAMO-IMO AMC-General

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.

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 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!

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 USAJMO.

Of the 280 USA Math Olympiad national qualifiers, 4 are our students: Luke C., Zipeng L., Sameer P., and Peter P.
Of the 235 USA Junior Math Olympiad national qualifiers, 4 are our students: Michael H., Noah W., Holden W., and Isabella Z.

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

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

3 of our students were among the top 44 National Winners (Perfect Scorers): Eric B., Kevin Y., and Isabella Z.
40 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
21 students received National Honor Roll Certificates awarded to top 5% test takers.
64 out of our 66 students (96.5%) received National Awards for the AMC 8 from the Mathematical Association of America

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

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

7 of our students were among the top 75 National Winners (Perfect Scorers).
34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.
22 students received National Honor Roll Certificates awarded to top 5% test takers.
63 out of our 65 students (97%) received National Awards for the AMC 8 from the Mathematical Association of America

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

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.

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.

Contact Information:

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

2014124135627709 Click HERE find out more about Math Competitions!Click HERE to find out more about SAT Prep! 1090007ad4f9061d818 %e6%95%b0%e5%ad%a6%e5%a4%a7%e6%9c%89%e4%bd%9c%e4%b8%ba AIME_RGB %e6%95%b0%e4%b8%ad%e8%87%aa%e6%9c%89%e9%bb%84%e9%87%91%e5%b1%8b AMC AMC_Airlines_logo_svg mathis_1 IMOLogo s-gudder-quote-the-essence-of-mathematics-is-not-to-make-simple-things

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How to Prepare for the AMC 10

Posted on 2024-01-31 | 1 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:

How to Prepare for the AMC 12

Posted on 2024-01-30 | 1 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:

How to Prepare for the AIME

Posted on 2024-01-29 | 3 comments

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

maausasf

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Posted in Math Competitions

Tagged aime, amc-12, american-invitational-mathematics-examination, american-mathematics-competitions, american-mathematics-contest, education, learning, math, math-competition, math-contest, mathematics, teaching

Tag Archives: learning

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

2024 Special Spring Session – Competitive Math Courses

AMC → AIME → USAMO sequence

How to Prepare for the AMC 10

How to Prepare for the AMC 12

How to Prepare for the AIME

AMC → AIME → USAMO sequence

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