2017 AMC 8 Problems and Answers

amc-8-november-14-2017

The AMC 8 was administered from November 14, 2017 until November 21, 2017. According to the AMC policy, students, teachers, and coaches were not allowed to discuss the contest questions and solutions until after the end of the competition window, so we are only now able to post the 2017 AMC 8 Problems and Answers. You can click the following to download them:

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This year’s AMC 8 was more difficult than the last year’s AMC 8. Some hard problems were even AMC 10 level. For example, Problem 23 and Problem 24 on the 2017 AMC 8 are two typical AMC 10 hard problems.

Problem 23 is involved in detecting a sequence of four factors of 60 that forms an arithmetic progression with a common difference of 5.

2017 AMC 8 Problem 23

Problem 24 is equivalent to finding the number of integers among the first 365 positive integers that are not divisible by 3, 4, or 5. We should use the principle of inclusion and exclusion (for 3 sets) to solve this problem.

2017 AMC 8 Problem 24

We predict that this year’s AMC 8 Honor Roll and Distinguished Honor Roll cut-off scores will be: 17 and 20, respectively. Read more at: AMC 8 Historical Results from 2010 to 2016

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Because the AMC 8 problems are getting harder, we must practice not only previous AMC 8 problems but also easy, medium, and even high difficulty level problems from previous AMC 10 to do well on the AMC 8.

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More details can be found at:

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Click HERE to find out more about SAT Prep!

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20 Sets of AMC 12 Mock Test with Detailed Solutions

AMC 12-2017

Click HERE to see a typical AMC 12 Mock Test Sample.

Click HERE to see the detailed solution of the AMC 12 Mock Test Sample.

About the AMC 12 Mock Test Series

We have collected every problem from all past AMC 12 exams (2000–present) and AHSME (1950–1999) 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 AMC 12 problems — effectively decoding the contest’s structure and logic.

Based on this “decoded” system, we developed 20 original AMC 12 Mock Tests, each containing 25 brand-new problems. Every question is carefully calibrated for difficulty and style to match the real AMC 12 exam.

These simulated exams are invaluable for assessing a student’s readiness for the AMC 12 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 AMC 12 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 39 AMC 10 and 12 Test Creators, drawing insights from their published contest problems and mathematical research. Using this deep understanding — combined with the most recent AMC 10/12 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.


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 AMC 12 — 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.

Small MT

Materials Price Sales Discounts
5 AMC 12 Mock Tests plus Answer Keys $130 $130 0
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10 AMC 12 Mock Tests plus Answer Keys $260 $230 $30
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15 AMC 12 Mock Tests plus Answer Keys $390 $330 $60
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20 AMC 12 Mock Tests plus Answer Keys $520 $430 $90
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5 AMC 12 Mock Tests with Detailed Solutions $260 $230 $30
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10 AMC 12 Mock Tests with Detailed Solutions $520 $430 $90
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15 AMC 12 Mock Tests with Detailed Solutions $780 $630 $150
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20 AMC 12 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.
  • We can provide either the digital version or the paper version of the product, but not both. Unfortunately, we are unable to provide both formats at the same time.
  • 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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Click HERE find out more about Math Competitions!

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20 Sets of AMC 10 Mock Test with Detailed Solutions

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Click HERE to see a typical AMC 10 Mock Test Sample

Click HERE to see the detailed solution of the AMC 10 Mock Test Sample.

About the AMC 10 Mock Test Series

We have collected every problem from all past AMC 10 exams (2000–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 AMC 10 problems — effectively decoding the contest’s structure and logic.

Based on this “decoded” system, we developed 20 original AMC 10 Mock Tests, each containing 25 brand-new problems. Every question is carefully calibrated for difficulty and style to match the real AMC 10 exam.

These simulated exams are invaluable for assessing a student’s readiness for the AMC 10 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 AMC 10 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 39 AMC 10 and 12 Test Creators, drawing insights from their published contest problems and mathematical research. Using this deep understanding — combined with the most recent AMC 10/12 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.


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 AMC 10 — 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.

CA-Final-Mock-Test

Materials Price Sales Discounts
5 AMC 10 Mock Tests plus Answer Keys $120 $120 0
Buy Now Button
10 AMC 10 Mock Tests plus Answer Keys $240 $220 $20
 Buy Now Button
15 AMC 10 Mock Tests plus Answer Keys $360 $320 $40
 Buy Now Button
20 AMC 10 Mock Tests plus Answer Keys $480 $420 $60
 Buy Now Button
5 AMC 10 Mock Tests with Detailed Solutions $240 $220 $20
 Buy Now Button
10 AMC 10 Mock Tests with Detailed Solutions $480 $420 $60
 Buy Now Button
15 AMC 10 Mock Tests with Detailed Solutions $720 $620 $100
 Buy Now Button
20 AMC 10 Mock Tests with Detailed Solutions $960 $820 $140
 Buy Now Button

🚚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.
  • We can provide either the digital version or the paper version of the product, but not both. Unfortunately, we are unable to provide both formats at the same time.
  • Payments for electronic versions are NON-REFUNDABLE.

*********************************************************

Customer Service

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

*********************************************************

Click HERE find out more about Math Competitions!

AMC 10

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AMC 10 Picture

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Intensive AMC 10/12 Prep (for 7th to 12th Graders) Winter Weekend Course Starting December 3

Purpose: To prepare for the AMC 10/12 A — Tuesday, February 7, 2018 and/or AMC 10/12 B — Wednesday, February 15, 2018. Please see: 

BANNER_Top_Mathletics
Winter 2017-2018 Schedule
9 Weekends (Eastern Time: 6:00 – 8:30 pm)Total: 22.5 Hours
12/3,  12/10,  12/17 (Monthly Mock Test/Review)
1/7,  1/14,  1/21 (Monthly Mock Test/Review)
1/28, 2/4,  2/11 (Final Mock Test/Review)

  • We will focus on efficient tricks, shortcuts, and strategies to solve competitive math problems, especially those hard problems on the AMC 10/12 and easy problems on the AIME, as well as test-taking tactics.
  • The emphasis of this class will be on comprehensive problem-solving, which is very common in competitive math, but is not included in school curriculum.
  • We will utilize a highly effective teaching model as described in the article: Small-sized Class Instruction-focused Model.

Instructors:

Tuition: $900 (including all materials). We offer discounts of $30 for returning students.

Online Registration is now open! Click HERE to register.

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

Click HERE to see payment and refund policy.

Locations:
401 N Washington St, Rockville, MD 20850 (The class is FULL!)

18206 Endora Cir, Germantown, MD 20874 (Four spots are available!)

Contact Information:
Ivy League Education Center
Tel:  301-922-9508     or        240-406-3402
Email:  chiefmathtutor@gmail.com

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 10-12-New

Read more at:

math-olympiad-web

Specific Goal: 

To earn a score of 120 or more out of 150 on the American Mathematics Contest 10 (AMC 10), or a score of 100 or more out of 150 on the American Mathematics Contest 12 (AMC 12), and then qualify for the American Invitational Mathematics Examination (AIME), which is used to determine qualification for the United States of America Mathematical Olympiad (USAMO).

See for more details: Optimal Strategies to Solve Hard AMC Problems

imagesFX9CEY3L

Who should take this class: 

This class is very appropriate for 7th-12th grade students who are hoping to qualify for the AIME.

Benefits:

  • 9 tutorial handouts (>300 pages) developed by Dr. Henry Wan and 500 new problems similar to AMC 10/12 level from the licensed AMC Database.
  • 3 FREE mock tests that are intended to mimic an actual math competition exam. Each test has 25 questions taken from the licensed AMC Database. Mock tests are calibrated to be at the same difficulty level as the real AMC 10/12. These simulated tests help students assess their level of preparation for the Math Competitions. After attempting the test, students get answers, explanations, and a detailed score report and wise performance summary.
  • FREE registration for the AMC 10/12 A — Tuesday, February 7, 2018 and/or AMC 10/12 B — Wednesday, February 15, 2018. Please see: The AMC 10/12 Contests at Montgomery College on February 7, 2018, and February 15, 2018

Weekly Homework:

At least 3 hours per week. Problem sets include all problems from 36 past real AMC 10/12 test booklets, and 500 brand new problems having similar difficulty and style as the real AMC 10/12 problems, extracted from the licensed AMC Database.

The focus will on the final 10 problems on the AMC 10/12, and the first 5 problems on the AIME, as well as those hard problems on the ARML. Note that some hard problems on the recent AMC 10 and 12 are exactly the same as previous ARML Problems.

Each week, we will carefully review and check 2 students’ homework, and correct any mistakes. The next week, we will check another 2 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 2 students that week, we will provide the those 2 students with individualized proposal and support.

Qualifying AIME

Class Outline:

In the final sprint of AMC 10/12 preparation, we will focus on efficient tricks, shortcuts, and strategies to solve AMC problems as well as test-taking tactics. The emphasis of this class will be on comprehensive problem-solving, which are very common in competitive math. We will also help students develop quick problem solving strategies and effective time management skills.

Class Date Topic
1 12/3, Sun Functions, polynomials, equations, and Vieta’s formulas
2 12/10, Sun Comprehensive problem solving in inequalities, rationals, and quadratics
3 12/17, Sun Tricks and shortcuts for solving AMC counting and combinatorics problems
4 1/7, Sun The art and craft for solving AMC statistics and discrete probability problems
5 1/14, Sun Efficient strategies for testing primality and finding the prime factorization to solve AMC number theory problems
6 1/21, Sun Using area method and sophisticated algebra to solve geometry problems on the AMC
7 1/28, Sun  Mass Point Geometry and Barycentric Coordinates
8 2/4, Sun Most commonly used methods to draw auxiliary lines, and applying the ruler, protractor, and compass to solve geometry problems (See for more details: Optimal Strategies to Solve Hard AMC Geometry Problems)
9 2/11, Sun Number bases, modular arithmetic, integer divisions, and linear congruences at the heart of a great many AMC problems

AMC LogoSmall-sized Class Teaching Model:
We utilize the highly effective small-sized class teaching model. Smaller classes lead to pupils receiving more individual attention from teachers, and having more active interactions with them. We focus on every individual, not the whole class. Students will thrive from the smaller class sizes that allow them to reach their full potential. Particularly, students can benefit tremendously from high-frequent individualized student-teacher interactions leading to establishment of a stronger foundation for lifelong learning.

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.

IMG_2563_0

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.

Bronze_medal

Our Students

In 2017, we have 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 Scorersworldwide 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 have 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23Perfect 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

From 2011 to 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. Read more at: Notable Achievements of Our Students

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Our Uniqueness

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

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national and math competitions. We have collected 116 full-length real AMC 10/12 problems sets containing 2,960 problems, as described in the article “116 Full-length Real AMC Problems Sets are a Golden Resource to Our AMC 10/12 Prep Program.” Particularly, we have extracted additional 3,000 brand new problems at the level of the AMC 10/12, from the licensed AMC Database. In addition, we have also collected all AMC8/10/12 and AIME Official Solutions as shown in the article “American Mathematics Competitions (AMC) Materials.” All these materials have formed a golden resource for our students, who are the ultimate beneficiaries.

Click HERE find out more about Math Competitions!

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AIME_RGBAMC

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education priceless treasure

3

rosie_the_riveter_poster

Online Intensive AMC 10/12 Prep (for 7th to 12th Graders) Winter Weekend Course Starting December 3

Purpose: To prepare for the AMC 10/12 A — Tuesday, February 7, 2018 and/or AMC 10/12 B — Wednesday, February 15, 2018. Please see: 

BANNER_Top_Mathletics
Winter 2017-2018 Schedule
9 Weekends (Eastern Time: 6:00 – 8:30 pm), Total: 22.5 Hours
12/3,  12/10,  12/17 (Monthly Mock Test/Review)
1/7,  1/14,  1/21,  (Monthly Mock Test/Review)
1/28, 2/4,  2/11 (Final Mock Test/Review)

  • We will focus on efficient tricks, shortcuts, and strategies to solve competitive math problems, especially those hard problems on the AMC 10/12 and easy problems on the AIME, as well as test-taking tactics.
  • The emphasis of this class will be on comprehensive problem-solving, which is very common in competitive math, but is not included in school curriculum.
  • We will utilize a highly effective teaching model as described in the article: Small-sized Class Instruction-focused Model.

You are very welcome to sign up for our Online Intensive AMC 10/12 Prep Fall Weekend Course which offers a quick, efficient way for students to interact with teachers over long distance. We use Google Hangouts 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.

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

Tuition: $900 (including all materials). We offer discounts of $30 for returning students.

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

Click HERE to see payment and refund policy.

New students:

Buy Now Button

Returning students ($30 discount):

Buy Now Button

Instructors:

Contact Information:
Ivy League Education Center
Tel:  301-922-9508     or        240-406-3402
Email:  chiefmathtutor@gmail.com

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 10-12-New

Read more at:

math-olympiad-web

Specific Goal: To earn a score of 120 or more out of 150 on the American Mathematics Contest 10 (AMC 10), or a score of 100 or more out of 150 on the American Mathematics Contest 12 (AMC 12), and then qualify for the American Invitational Mathematics Examination (AIME), which is used to determine qualification for the United States of America Mathematical Olympiad (USAMO). See for more details: Optimal Strategies to Solve Hard AMC Problems

imagesFX9CEY3L

Who should take this class: This class is very appropriate for 7th-12th grade students who are hoping to qualify for the AIME.

Benefits:

  • 9 tutorial handouts (>300 pages) developed by Dr. Henry Wan and 500 new problems similar to AMC 10/12 level from the licensed AMC Database.
  • 3 FREE mock tests that are intended to mimic an actual math competition exam. Each test has 25 questions taken from the licensed AMC Database. Mock tests are calibrated to be at the same difficulty level as the real AMC 10/12. These simulated tests help students assess their level of preparation for the Math Competitions. After attempting the test, students get answers, explanations, and a detailed score report and wise performance summary.
  • FREE registration for the AMC 10/12 A — Tuesday, February 7, 2018 and/or AMC 10/12 B — Wednesday, February 15, 2018. Please see: The AMC 10/12 Contests at Montgomery College on February 7, 2018, and February 15, 2018

Weekly Homework:

At least 3 hours per week. Problem sets include all problems from 36 past real AMC 10/12 test booklets, and 500 brand new problems having similar difficulty and style as the real AMC 10/12 problems, extracted from the licensed AMC Database.

The focus will on the final 10 problems on the AMC 10/12, and the first 5 problems on the AIME, as well as those hard problems on the ARML. Note that some hard problems on the recent AMC 10 and 12 are exactly the same as previous ARML Problems.

Each week, we will carefully review and check 2 students’ homework, and correct any mistakes. The next week, we will check another 2 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 2 students that week, we will provide the those 2 students with individualized proposal and support.

Qualifying AIME

Class Outline:

In the final sprint of AMC 10/12 preparation, we will focus on efficient tricks, shortcuts, and strategies to solve AMC problems as well as test-taking tactics. The emphasis of this class will be on comprehensive problem-solving, which are very common in competitive math. We will also help students develop quick problem solving strategies and effective time management skills.

Class Date Topic
1 12/3, Sun Functions, polynomials, equations, and Vieta’s formulas
2 12/10, Sun Comprehensive problem solving in inequalities, rationals, and quadratics
3 12/17, Sun Tricks and shortcuts for solving AMC counting and combinatorics problems
4 1/7, Sun The art and craft for solving AMC statistics and discrete probability problems
5 1/14, Sun Efficient strategies for testing primality and finding the prime factorization to solve AMC number theory problems
6 1/21, Sun Using area method and sophisticated algebra to solve geometry problems on the AMC
7 1/28, Sun  Mass Point Geometry and Barycentric Coordinates
8 2/4, Sun Most commonly used methods to draw auxiliary lines, and applying the ruler, protractor, and compass to solve geometry problems (See for more details: Optimal Strategies to Solve Hard AMC Geometry Problems)
9 2/11, Sun Number bases, modular arithmetic, integer divisions, and linear congruences at the heart of a great many AMC problems

AMC LogoSmall-sized Class Teaching Model:
We utilize the highly effective small-sized class teaching model. Smaller classes lead to pupils receiving more individual attention from teachers, and having more active interactions with them. We focus on every individual, not the whole class. Students will thrive from the smaller class sizes that allow them to reach their full potential. Particularly, students can benefit tremendously from high-frequent individualized student-teacher interactions leading to establishment of a stronger foundation for lifelong learning.

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.

IMG_2563_0

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.

Bronze_medal

Our Students

In 2017, we have 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 Scorersworldwide 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 have 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23Perfect 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

From 2011 to 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. Read more at: Notable Achievements of Our Students

AAEAAQAAAAAAAAKeAAAAJDkzYTk2ZjE5LTk1YWQtNDBkNy1hZDhjLTVjOTA2YWQ2NmQ2Mw

Our Uniqueness

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

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national and math competitions. We have collected 116 full-length real AMC 10/12 problems sets containing 2,960 problems, as described in the article “116 Full-length Real AMC Problems Sets are a Golden Resource to Our AMC 10/12 Prep Program.” Particularly, we have extracted additional 3,000 brand new problems at the level of the AMC 10/12, from the licensed AMC Database. In addition, we have also collected all AMC8/10/12 and AIME Official Solutions as shown in the article “American Mathematics Competitions (AMC) Materials.” All these materials have formed a golden resource for our students, who are the ultimate beneficiaries.

Click HERE find out more about Math Competitions!

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1090007ad4f9061d818

AIME_RGBAMC

001YIeUmgy6X1ziaAW4d0&690

0AMC_Airlines_logo_svg

education priceless treasure

3

rosie_the_riveter_poster

Online AMC 10/Mathcounts Prep (for 5th to 9th Graders) Winter Weekend Course Starting December 2

Purpose: To prepare for math competitions, such as

mathequalsawesomelogo

Winter 2017-2018 Schedule
9 Weekends (Eastern Time: 6:00 – 8:00 pm), Total: 18 Hours
12/2,  12/9,  12/16 (Monthly Mock Test/Review)
1/6,  1/13,  1/20 (Monthly Mock Test/Review)
1/27, 2/3,  2/10 (Final Mock Test/Review)

  • We will help students gain a deeper understanding of the fundamental math concepts, build a solid foundation in math, and develop the critical thinking and problem-solving skills different from those in the school classes, motivation, and perseverance for reaching their full potential.
  • We will focus on efficient tricks, shortcuts, and strategies to solve competitive math problems as well as test-taking tactics.
  • The emphasis of this class will be on comprehensive problem-solving, which is very common in competitive math, but is not included in school curriculum.
  • We will utilize a highly effective teaching model as described in the article: Small-sized Class Instruction-focused Model.

Instructor: Dr. Henry Wan

You are very welcome to sign up for our online course which offers a quick, efficient way for students to interact with teachers over long distance. We use Google Hangouts 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/coachesClick HERE to see detailed instruction.

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

Tuition: $630 (including all materials). We offer discounts of $20 for returning students.

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

Click HERE to see payment and refund policy.

New students:

Buy Now Button

Returning students ($20 discount):

Buy Now Button

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

Specific Goal of the AMC 10:
To earn a score of 90 or more out of 150 on the 2018 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.

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

Description: 
Our curriculum focuses on advancing the mathematical skills of rising 5th-8th graders to prepare them for AMC 10 and MathCounts. A variety of contest questions, including the first 15 problems on the AMC 10, 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 and creative 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:

    • 9 tutorial handouts (200 pages) developed by Dr. Henry Wan and 500 new problems at the AMC 10 level taken from the licensed AMC Database
    • 40 past real MathCounts test booklets at the school, chapter, state, and national level from 2010–2017
    • 3 FREE mock tests, each of which has 25 questions taken from the licensed AMC Database. Mock tests are calibrated to be at the same difficulty level as the real AMC 10. 
    • FREE registration for the AMC 10/12 A — Tuesday, February 7, 2018 and/or AMC 10/12 B — Wednesday, February 15, 2018. Please see: The AMC 10/12 Contests at Montgomery College on February 7, 2018, and February 15, 2018

AMC LogoRead more at:

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

Class Date Topic
1 12/2, Sat Problem solving in algebra equations and Vieta’s formulas
2 12/9, Sat Newly defined functions and operations
3 12/16, Sat Finding the hundreds, tens, and units digits of a number
4 1/6, Sat Special Factoring Trick –– Completing the Rectangle
5 1/13, Sat Pythagorean Theorem and special right triangles (30o-60o-90o triangles, 45o-45o-90otriangles)
6 1/20, Sat Using the ruler, protractor, and compass to solve geometry problems (See for more details: Optimal Strategies to Solve Hard AMC Geometry Problems)
7 1/27, Sat Efficient strategies for testing primality
8 2/3, Sat Number bases, modular arithmetic, integer divisions, integer equations, and Diophantine equations
9 2/10, Sat Using the stars and bars method to solve AMC problems associated with number theory, counting, combinatorics, and probability

Mock Test:
Three simulated tests will help students assess their level of preparation for the Math Competitions. The test consists of 25 questions at the AMC 10 level from the licensed AMC Database, and is intended to mimic an actual math competition exam. After attempting the test, students get answers, explanations, and a detailed score report and wise performance summary.

Homework
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.

lets-do-the-math-1-728

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 10 exams (2000-2017) and MathCounts (1990–2017) form our “big data” system. We used data mining and predictive analytics to examine the types, styles,  and frequencies of questions in all these materials, and then completely “decoded” the AMC and MathCounts. We will show all the “secret code” cracked from the above big data to 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.

https___img_evbuc_com_https%253A%252F%252Fcdn_evbuc_com%252Fimages%252F14806251%252F149172474682%252F1%252Foriginal

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.

Bronze_medal

Our Students

In 2017, we have 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 Scorersworldwide 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 have 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23Perfect 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

From 2011 to 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. Read more at: Notable Achievements of Our Students

1591310027-we_are_all_unique-5604

Our Uniqueness

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

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national and math competitions. We have collected 116 full-length real AMC 10/12 problems sets containing 2,960 problems, as described in the article “116 Full-length Real AMC Problems Sets are a Golden Resource to Our AMC 10/12 Prep Program.” Particularly, we have extracted additional 3,000 brand new problems at the level of the AMC 10/12, from the licensed AMC Database. In addition, we have also collected all AMC8/10/12 and AIME Official Solutions as shown in the article “American Mathematics Competitions (AMC) Materials.” All these materials have formed a golden resource for our students, who are the ultimate beneficiaries.

Click HERE find out more about Math Competitions!

 

 

only-way-poster

mathis_1

AMCAMC_Airlines_logo_svg

Investing-in-Education

education priceless treasure

3.jpgMathCompetition4

61631996YouCanDoItPuppy

AMC 10/Mathcounts Prep (for 5th to 9th Graders) Winter Weekend Course Starting December 2

Purpose: To prepare for math competitions, such as

mathequalsawesomelogo

Winter 2017-2018 Schedule
9 Weekends (Eastern Time: 6:00 – 8:00 pm), Total: 18 Hours
12/2,  12/9,  12/16 (Monthly Mock Test/Review)
1/6,  1/13,  1/20 (Monthly Mock Test/Review)
1/27, 2/3,  2/10 (Final Mock Test/Review)

  • We will help students gain a deeper understanding of the fundamental math concepts, build a solid foundation in math, and develop the critical thinking and problem-solving skills different from those in the school classes, motivation, and perseverance for reaching their full potential.
  • We will focus on efficient tricks, shortcuts, and strategies to solve competitive math problems as well as test-taking tactics.
  • The emphasis of this class will be on comprehensive problem-solving, which is very common in competitive math, but is not included in school curriculum.
  • We will utilize a highly effective teaching model as described in the article: Small-sized Class Instruction-focused Model.

Instructor: Dr. Henry Wan

Online Registration is now open! Click HERE to register.

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

Tuition: $630 (including all materials). We offer discounts of $20 for returning students.

Click HERE to see payment and refund policy.

Location: 18206 Endora Cir, Germantown, MD 20841

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

Specific Goal of the AMC 10:
To earn a score of 90 or more out of 150 on the 2018 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.

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

Description: 
Our curriculum focuses on advancing the mathematical skills of rising 5th-8th graders to prepare them for AMC 10 and MathCounts. A variety of contest questions, including the first 15 problems on the AMC 10, 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 and creative 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:

    • 9 tutorial handouts (200 pages) developed by Dr. Henry Wan and 500 new problems at the AMC 10 level taken from the licensed AMC Database
    • 40 past real MathCounts test booklets at the school, chapter, state, and national level from 2010–2017
    • 3 FREE mock tests, each of which has 25 questions taken from the licensed AMC Database. Mock tests are calibrated to be at the same difficulty level as the real AMC 10. 
    • FREE registration for the AMC 10/12 A — Tuesday, February 7, 2018 and/or AMC 10/12 B — Wednesday, February 15, 2018. Please see: The AMC 10/12 Contests at Montgomery College on February 7, 2018, and February 15, 2018

AMC LogoRead more at:

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

Class Date Topic
1 12/2, Sat Problem solving in algebra equations and Vieta’s formulas
2 12/9, Sat Newly defined functions and operations
3 12/16, Sat Finding the hundreds, tens, and units digits of a number
4 1/6, Sat Special Factoring Trick –– Completing the Rectangle
5 1/13, Sat Pythagorean Theorem and special right triangles (30o-60o-90o triangles, 45o-45o-90otriangles)
6 1/20, Sat Using the ruler, protractor, and compass to solve geometry problems (See for more details: Optimal Strategies to Solve Hard AMC Geometry Problems)
7 1/27, Sat Efficient strategies for testing primality
8 2/3, Sat Number bases, modular arithmetic, integer divisions, integer equations, and Diophantine equations
9 2/10, Sat Using the stars and bars method to solve AMC problems associated with number theory, counting, combinatorics, and probability

Mock Test:
Three simulated tests will help students assess their level of preparation for the Math Competitions. The test consists of 25 questions at the AMC 10 level from the licensed AMC Database, and is intended to mimic an actual math competition exam. After attempting the test, students get answers, explanations, and a detailed score report and wise performance summary.

Homework
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.

lets-do-the-math-1-728

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 10 exams (2000-2017) and MathCounts (1990–2017) form our “big data” system. We used data mining and predictive analytics to examine the types, styles,  and frequencies of questions in all these materials, and then completely “decoded” the AMC and MathCounts. We will show all the “secret code” cracked from the above big data to 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.

https___img_evbuc_com_https%253A%252F%252Fcdn_evbuc_com%252Fimages%252F14806251%252F149172474682%252F1%252Foriginal

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.

Bronze_medal

Our Students

In 2017, we have 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 Scorersworldwide 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 have 36 students who are qualified to take AIME either through AMC 10A/12A or AMC 10B/12B. One of our students was among the 23Perfect 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

From 2011 to 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. Read more at: Notable Achievements of Our Students

1591310027-we_are_all_unique-5604

Our Uniqueness

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

We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our students have received top scores and awards at prestigious national and math competitions. We have collected 116 full-length real AMC 10/12 problems sets containing 2,960 problems, as described in the article “116 Full-length Real AMC Problems Sets are a Golden Resource to Our AMC 10/12 Prep Program.” Particularly, we have extracted additional 3,000 brand new problems at the level of the AMC 10/12, from the licensed AMC Database. In addition, we have also collected all AMC8/10/12 and AIME Official Solutions as shown in the article “American Mathematics Competitions (AMC) Materials.” All these materials have formed a golden resource for our students, who are the ultimate beneficiaries.

Click HERE find out more about Math Competitions!

 

 

only-way-poster

mathis_1

AMCAMC_Airlines_logo_svg

Investing-in-Education

education priceless treasure

3.jpgMathCompetition4

61631996YouCanDoItPuppy

35 Sets of Previous Official AMC 10 Tests with Answer Keys (PDF files)

AMC 10-2017
The best way to prepare for the AMC 10 is to do lots of practice problems either on your own or with a small group and then check your solutions with an answer key. For this reason, we provided all 35 sets of previous official AMC 10 contests (2000-2017) with answer keys and also developed 20 sets of AMC 10 mock test with detailed solutions to help you prepare for this premier contest.

AMC 10

AMC Logo.png

2010 AMC 10A

AMC 10 Picture

problemamc10_t

cof-10merit

 

35 Sets of Past Real AMC 12 Tests with Answer Keys (PDF files)

AMC 12-New
All problems from past AMC 12 (2000–2017) 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 past AMC 12 exams, and then completely “decoded” the AMC 12.

For all questions on the recent AMC 12 contests, we can find their “ancestors” and “roots” from the old AMC 12 problems. Therefore, the best way to prepare for the AMC 12 is to practice by solving old AMC 12 problems!

We provided 35 sets of past real AMC 12 tests (2000-2017) with answer keys and also developed 20 sets of AMC 12 mock test with detailed solutions to help students prepare for the AMC 12 contest.

AMC 12-2017
2010_AMC12_A

AMC 12 Logo

cof-12merit

MAA AMC 12

AMC 12 Picture

amc12

2015_AMC12_A.png

 

 

14 Sets of Previous Real AJHSME (AMC 8) Tests with Answer Keys

The American Junior High School Mathematics Examination (AJHSME) for students in grades 8 and below, begun in 1985, was the predecessor of the AMC 8, administered by the American Mathematics Competitions. Since 1999, the name has been changed into the American Mathematics Contest 8 (AMC 8).

https___cdn_evbuc_com_images_23502174_94898100017_1_original.gifAll problems from past AJHSME exams (1985-1998) and AMC 8 (1999–2016) form our “big data” system. We used data/text mining and predictive analytics to examine the types, styles, frequencies, and characteristics of questions in all these materials, and then completely “decoded” the AMC 8. For all questions on the recent AMC 8 contests, we can find their “ancestors” and “roots” from the old AMC problems. Therefore, the best way to prepare for the AMC 8 is to practice by solving old AMC problems!

We provided 14 sets of previous real AJHSME tests (1985-1999) with answer keys and also developed 20 sets of AMC 8 mock test with detailed solutions to help students prepare for the AMC 8 contest.

All past official AMC 8 problems (1999-2016) can be found at:

image001amc

AMC 8-New

amc-logo

pi-day-250

pattern-29872_960_720.png