Tag Archives: teaching

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

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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How to Prepare for the AMC 10

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:

More articles about math competitions:

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How to Prepare for the AMC 12

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

How to Prepare for the AIME

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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.

More articles about math competitions:

Ivy League Education Center | Education is not the filling of a pail, but  the lighting of a fire. Genius is 1% inspiration and 99% perspiration!

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-IMOAMC-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

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 810 perfect scorers. 54 students got the DHR. 29 students got the HR.
  • 2023 AMC/AIME99 AIME qualifiers. 1 AMC 10 perfect scorer. 1 AMC 12 perfect scorer.
  • 2023 JMO/AMO8 USAMO Awardees and 7 USAJMO Awardees
    • 1 USAMO Gold Award, 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 MOP4 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 Buy Now Button
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 Buy Now Button
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.

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

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!

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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:

Grade Levels: Grades 4-8

AMC Logo

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 45o-45o-90Triangles

5

2/17, Sat

Equilateral Triangles and 30o-60o-90o 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.

Read more at:

On average, at least 2 hours per week, as described in the article: Homework assignments are a fundamental part of our courses. Click HERE to see a typical homework sample we developed. Each week, we will carefully review and check 3 students’ homework, and correct any mistakes. The next week, we will check another 3 students’ homework, and this will continue on a rotational basis until all students have had their homework checked at least once and the cycle will start again. Based on the work of the 3 students that week, we will provide the those 3 students with individualized proposal and support. More details can be found in the article: Homework Correction is very Important — We Give an Extensive Correction of the Incorrect Answers of All Homework.

do-math

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

All problems from past AMC 8 exams (1985-2024),  AMC 10 exams (2000-2023), and MathCounts (1990–2024) form our “big data” system. Based on artificial intelligence (AI), machine learning, and deep learning, we devised a data mining and predictive analytics tool for math problem similarity searching. Using this powerful tool, we examined the types, styles, frequencies, characteristics, and traits of questions in all these materials, and then completely “decoded” the AMC, and MathCounts. We always completely show all the “secret code” cracked from the above big data to our students, and teach them to totally grasp and “control” the AMC and MathCounts. For all questions on the recent AMC/MathCounts contests, we can find their “ancestors” and “roots” from the old AMC/MathCounts problems. Therefore, the best way to prepare for the contest is to practice by solving old AMC/MathCounts problems.

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Main Purpose:

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

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

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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 ProgramRead 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 OlympiadRead more at: sabella Z. Competes in International Girls’ Math Olympiad

In 2022, we had 7 students qualified for the USAMO andstudents 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 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 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

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 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.

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 WVery 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!

  • 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!

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

  • 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’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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20 Sets of AIME Mock Test with Detailed Solutions

Click HERE to see a typical AIME Mock Test Sample.

Click HERE to see the detailed solution of the AIME Mock Test Sample.

About the AIME Mock Test Series

We have collected every problem from all past AIME exams (1983–present) to build a comprehensive “big data” system. Using artificial intelligence (AI), machine learning, and deep learning, we created an advanced math problem similarity and prediction tool.

Through this innovative system, we carefully analyzed the types, styles, and frequency patterns of AIME problems — effectively decoding the contest’s structure and logic.

Based on this “decoded” system, we developed 20 original AIME Mock Tests, each containing 15 brand-new problems. Every question is carefully calibrated for difficulty and style to match the official AIME exam.

These simulated exams are invaluable for assessing a student’s readiness for the AIME and building the mastery needed for top scores. Each mock test also comes with detailed step-by-step solutions explaining every problem clearly and rigorously.

Together, these 20 tests and solutions form a gold-standard resource for AIME preparation — a proven tool that has helped countless students strengthen their problem-solving skills and gain a competitive edge.


🌟 Quality You Can Trust

At Ivy League Education Center, quality is never an afterthought — it’s our foundation.

Every year, we meticulously analyze the thought processes and problem-design patterns of  10 AIME Test Creators, drawing insights from their published contest problems and mathematical research. Using this deep understanding — combined with the most recent official AIME questions and trends — we continuously refine our mock examinations so that they completely reflect the evolving style, structure, and rigor of the official contests.

Each new edition is peer-reviewed by two independent experts, ensuring every problem and solution meets the highest standards of accuracy, clarity, and educational value.

Our mock tests faithfully mirror the real MAA/AMC exams, giving students a realistic, reliable, and predictive measure of their readiness for competition.

Parents and students can have full confidence that they are preparing with the most authentic, data-driven, and expertly reviewed AMC resources available anywhere.

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Why Take Mock Tests?

Taking mock tests is one of the most effective ways to maximize learning and solidify mastery of the core concepts, strategies, and techniques required to excel on the AIME — and beyond.

“Practice isn’t just preparation — it’s prediction.”
Regular testing helps students internalize methods, identify weak points, and build the confidence needed for success in national and international math contests.

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Materials Price Sales Discounts
5 AIME Mock Tests plus Answer Keys $130 $130 0
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10 AIME Mock Tests plus Answer Keys $260 $230 $30
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15 AIME Mock Tests plus Answer Keys $390 $330 $60
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20 AIME Mock Tests plus Answer Keys $520 $430 $90
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5 AIME Mock Tests with Detailed Solutions $260 $230 $30
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10 AIME Mock Tests with Detailed Solutions $520 $430 $90
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15 AIME Mock Tests with Detailed Solutions $780 $630 $150
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20 AIME Mock Tests with Detailed Solutions $1040 $830 $210
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🚚Free Shipping (U.S. Orders)

We offer free USPS Priority Mail shipping for all domestic orders.
Standard international shipping rates apply for overseas purchases.

All items are shipped to a verified address that appears on the PayPal transaction, and most U.S. orders arrive within 2–7 business days after successful payment processing.

Refund and Return Policies

Please review your order carefully before purchase. Refunds and returns are accepted only when eligible items are returned using the proper method.

If your return is shipped after the designated timeframes, we regret that we cannot issue a refund.

General Return Policy

  • Items must be returned within 30 days of purchase in their original condition.
  • Damaged, marked, or incomplete materials cannot be refunded.
  • Refunds are processed within 5–10 business days after receipt.

Special Policy for Mock Test Papers

  • If mock test papers have been used (even partially), the purchase is not refundable.
  • Due to copyright restrictions, all mock tests are provided in hard copy by mail via USPS.
  • In rare exceptions, we may provide five or more electronic (PDF) mock tests via email to the verified email address associated with the PayPal transaction.
  • Payments for electronic versions are non-refundable.

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Customer Service

📧 Email: customer-service@ivyleaguecenter.org
📞 Phone: 240-406-3402 (Monday–Friday, 9 a.m.–5 p.m.)

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Google Meet Online Class Instruction

Ivy league Cnter-2017You are very welcome to sign up for our Online Course, which offers a quick and efficient way for students to interact with teachers over long distance. We use Google Meet to connect with students in real time, provide instruction, share problem-solving strategies, and offer guidance and support. Students can ask questions face-to-face and work through problems under the supervision of our teachers/coaches.

Please Note:

  • This is a live class, not a pre-recorded one. Instructors will ask students questions during class, and students are encouraged to ask questions as well.
  • 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.
  • These videos will only be available to view for 30 days after the class.

Please let us know ASAP what Gmail account your child will use for Google Meet to attend our online class! We have listed below several pointers you should follow to ensure that our Google Meet session goes as smoothly as possible:

  1. We will send out the Google Meet invite at exactly 5 minutes before the start of the class. Please make sure that you have your Gmail account screen ready at that time.
  2. Please use Google Chrome as your browser. This browser supports Google Hangout MOST efficiently.
  3. Before the class, please check your microphone and webcam to make sure you are wired for sound and picture. It is absolutely imperative that your computer’s audio and visual systems are working well.
  4. Shut down ALL OTHER unnecessary software programs and browser tabs.
  5. STUDENTS PLAESE PAY ATTENTION: please leave your Google Hangout window on during the whole duration of class time and DO NOT OPEN ANY OTHER TABS OR BROWSE IN ANY OTHER TABS! AND DO NOT TOUCH THE MOUSE! EVEN DURING BREAK TIME, it is NOT advised to touch the screen AT ALL. (Throughout these years of using Google Hangout, our main line has never ever dropped. Hence we firmly believe that the reason for dropping the line must be the result of the student accidentally clicking off the Hangout screen.
  6. Make sure your device is suitably charged. A lot of devices will lag if the battery is down to its last 10%.
  7. One account per student, single device at a time: Each registered account is for one student only—the student who is enrolled with us. Course access, including live online classes, recorded lessons, and handout materials, is provided exclusively to the registered student and is strictly prohibited from being shared with any other individual. Each registered account must be logged in on only one device at a time. Logging in on multiple devices simultaneously using the same account is not permitted. If multiple devices are detected during class, our administrator will randomly remove the extra devices and keep only one active device to avoid disruption.
  8. Recording, sharing, and redistribution policy:
    To protect the learning environment and our instructional content, all course contentincluding live classes, recorded lessons, and course materials, is the intellectual property of the instructors and the program owner and is provided for the personal educational use of the registered student only.
    Students and parents are not permitted to record, screenshot, share, distribute, repost, or resell any part of the course content. The instructors and program owner do not grant, and have never granted students any rights to sell, share, redistribute, or otherwise commercially exploit the course content under any circumstances.
  9. Please make sure your display name clearly shows the student’s name. If the account belongs to a parent or uses the parent’s name, that is acceptable as long as the instructor can clearly recognize which student is attending. This helps instructors address students directly and keeps the class organized.

  10. Please join the class 5 minutes early to allow time for technical checks and to ensure the class can start on time without delays.
  11. Important!! Please DO NOT sends us the invite if your line has dropped. You will have to call our assistant through the phone line (318-888-1168) to let us know. We will send out a new invite to the group.

We know for sure that if we follow ALL of these guidelines, we will always have very smooth Google Meet online sessions.