The 2016 AMC 10A was held on Feb 2, 2016. Over 210,000 students from over 4,100 U.S. and international schools attended the 2016 AMC 10A contest and found it fun and rewarding. Top 10, well-known U.S. universities and colleges, including internationally recognized U.S. technical institutions, ask for AMC scores on their application forms. Your children deserve the chance to list these scores on their applications!
Now we can post the 2016 AMC 10A Problems and Answers below. You can click the following to download them:
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 was 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!
Our students earned top scores on the 2017 AMC 8 contest!
7 of our students were among the top 75 National Winners (Perfect Scorers).
34 students received National Distinguished Honor Roll Certificates awarded to top 1% test takers, as shown in Table 2.
22 students received National Honor Roll Certificates awarded to top 5% test takers, as shown in Table 3.
63 out of our 65 students(97%) received National Awards for the AMC 8 from the Mathematical Association of America
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 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
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
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.
The American Mathematics Contest 12 (AMC 12) is the first exam in the series of exams used to challenge bright students, grades 12 and below, on the path toward choosing the team that represents the United States at the International Mathematics Olympiad (IMO).
High scoring AMC 12 students are invited to take the more challenging American Invitational Mathematics Examination (AIME). The AMC 12 is administered by the American Mathematics Competitions (AMC). Two different versions of the contests are given on two dates, about two weeks apart, in February. All USA, USA embassy, Canadian, and foreign school students in grade 12 or below are eligible to participate as long as they are under 19.5 years of age on the day of the contest.
The AMC 12 is a 25 question, 75 minute multiple choice test. Problems generally increase in difficulty as the exam progresses. Ever since 2008, calculators have been banned from use during the test; however, calculators were never required to solve any problems, and students who do not use calculators were not disadvantaged.
The AMC 12 is scored in a way that penalizes guessing. Correct answers are worth 6 points, incorrect answers are worth 0 points, and unanswered questions are worth 1.5 points, to give a total score out of 150 points. From 2002 to 2006, the number of points for an unanswered question was 2.5 points and before 2002 it was 2 points. Students that score over 100 points or in the top 5% of the AMC 12 contest are invited to take the AIME.
Curriculum
The AMC 12 tests mathematical problem solving with arithmetic, algebra, counting, combinatorics, geometry, number theory, and probability and other secondary school math topics. Problems are designed to be solvable by students without any background in calculus. The AMC 12 is a 25-question, 75-minute, multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts.
B C的不少教授自身便是学界领袖，决定着学术的发展方向。这深深影响了学校的气氛和学生的心态，仿佛自己就处于世界中心未来也要争做主人翁一般。这固然有自大和可笑的一方面，但也意味着很多学生面对再难啃的学习上硬骨头都有“志在必得”“攻必克”的自信。而这种自信在中国国内的大学是非常缺乏的：我见过太多国内的聪明孩子不敢去学最难的学术文献。
这是纽约时报一篇长篇文章中强调的一个词。这篇文章主要讲的是：为什么 有很多爱好科学有志于学习理工科的孩子 到了大学学习两三年后纷纷转专业？—-因为理工科实在是太难了（so darn hard），特别是孩子们无法战胜低年级的数学科学死亡行军（math-science death march）。
But, it turns out, middle and high school students are having most of the fun,building their erector sets and dropping eggs into water to test the first lawof motion. The excitement quickly fades as students brush up against thereality of what David E. Goldberg, an emeritus engineering professor, calls “the math-science death march.” Freshmen incollege wade through a blizzard of calculus, physics and chemistry in lecturehalls with hundreds of other students. And then many wash out.
Tuition: $720 (including all materials and an extensive correction of the incorrect answers of all homework. Click HERE to see a sample)
Online Registration is now open! Click HEREto register.
Self-studying for AMC 8/10/12 Contests
Even if you cannot attend our classes, you can purchase the official AMC materials from our bookstore and, using our solutions, self-learn/study the tricks, shortcuts, tips, and strategies to solve AMC problems as well as test-taking tactics. VIEW ALL OFFICIAL AMC MATERIALS
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). 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. 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 all AMC8/10/12 and AIME Official Problems and Official Solutions as shown in the article ” American Mathematics Competitions (AMC) Materials,” which have formed our “big data” system, a golden resource for our students, who are the ultimate beneficiaries.
Featured Instructors
All of our sessions are taught by highly qualified instructors who are excellent experts on preparing students for the contests. We distinguish ourselves by the high quality of our instructors. Finding top-quality instructors is no easy task. We’ve hand-picked some of the best, including distinguished mathematicians. Meet some of them here:
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
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.
The AMC 10 is a 25-question, multiple choice contest. The questions are arranged from the easiest to the hardest. The scoring will be 6 points for a correct answer, 1.5 point for a blank answer, and 0 points for an incorrect answer. The key to doing well on the AMC 10 is not to get the most difficult questions (usually question #21 – #25) right; rather, it is to correctly answer the first 20 problems without error. However, the last five problems of the AMC 10 almost always contain at least two geometry problems that can be solved using a ruler, protractor and compass. Getting these two problems correct can give a student even more points, so they can get at least 120 points on the AMC 10 and advance to the next level, the AIME.
Although the rules of AMC state that no calculators are allowed, students are permitted to use scratch paper, graph paper, rulers, compass, protractors, and erasers. We must use these tools to our advantage. Even if you do not know to solve a problem mathematically, you can always use these tools to solve it. For example, 2014 AMC 10 Problem #22 is a very difficult problem to solve mathematically. But by simply using a ruler and a protractor, one can easily solve this problem.
2014 AMC 10A #22
In rectangle ABCD, AB = 20 and BC = 10. Let E be a point on CD such that . What is AE?
This program has been carefully designed for the students with higher expectation for their American Invitational Mathematics Examination (AIME) scores. While enriching their resume through the school classes, honing the test skill for AIME becomes even more critical.
The AIME is used to determine qualification for the United States of America Mathematical Olympiad (USAMO). 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.
Contact Information: Ivy League Education Center
Tel: 301-922-9508 or 240-780-8828
Email: chiefmathtutor@gmail.com
Purpose: To prepare for the AIME I — Thursday, March 3, 2016 or AIME II — Wednesday, March 16, 2016
Objectives
Improve student scores by working on both fundamental theorems and ideas
Develop and foster creative problem solving strategies
Make the USA(J)MO!!!
For Whom?
This AIME course is aimed at those students with AMC 10/12 scores of 100+ to students who have scored around 4 on the AIME.
What?
This class will focus mostly on building strong basics in the five main pillars of Combinatorics, Number Theory, Geometry, Algebra, and Probability. The goal is for students to obtain the mental agility required to tackle these complex problems and hopefully get them within and past range of qualification for the USAMO and USAJMO, or around 9 problems.
How?
Focus on basic concepts and essential knowledge before moving on developing the skills and intuition to find and pursue good lines of attack for complex problems.
Class Outline:
In AMIE Prep Class, we will focus on efficient tricks, shortcuts, and strategies to solve AIME problems as well as test-taking tactics.
Class
Date
Topic
Homework
Tutorial Handouts
1
1/10, Sun
Number Theory: Fundamental Theorem of Arithmetic, Greatest Common Divisor and Least Common Multiple, Modular Arithmetic, Divisibility Tests
AIME Problem Set on Number Theory
Yes
2
1/17, Sun
Combinatorics: Partitions and Bijections, Generating Functions, Combinatorial Identities, the Inclusion-Exclusion Principle, the pigeonhole principle
AIME Problem Set on Combinatorics
Yes
3
1/24, Sun
Probability: Properties of Probability Functions, Geometric probability, Algebraic Probability, Tournaments, Socks, and Dice
AIME Problem Set on Probability
Yes
4
1/31, Sun
Algebraic Equations: Distance-Rate-Time Problems, Systems of Nonlinear Equations
AIME Problem Set on Algebraic Equations
Yes
5
2/7, Sun
Diophantine Equations, Systems of Diophantine Equations, Quadratic Diophantine and Pell Equations, Special Factoring Trick –– Completing the Rectangle
AIME Problem Set on Diophantine and Pell Equations
Yes
6
2/14, Sun
Sequences and Series: Arithmetic Series, Geometric Series and the Telescope Tool, Tiling and the Fibonacci Recurrence, The Catalan Recurrence
AIME Problem Set on Sequences and Series
Yes
7
2/21, Sun
Logarithmic and Trigonometric Functions: Putting Logarithmic, Exponential, and Trigonometric Functions Together
AIME Problem Set on Logarithmic and Trigonometric Functions
Yes
8
2/28, Sun
Complex Numbers and Polynomials: The Algebra of Complex Numbers, The Geometry of Complex Numbers, Basic Definitions and Facts about Polynomials, Polynomials with Complex Roots
AIME Problem Set on Complex Numbers and Polynomials
Yes
9
3/6, Sun
Plane Geometry: Triangle Geometry, Circle Geometry, Geometrical Concepts in the Complex Plane
AIME Problem Set on Plane Geometry
Yes
10
3/13, Sun
Spatial Geometry: Rectangular Boxes, Cylinders, Cones, Spheres, Tetrahedra and Pyramids
AIME Problem Set on Spatial Geometry
Yes
Two FREE textbooks:
Paul Zeitz: The Art and Craft of Problem Solving, 2nd Edition
Richard Rusczyk and Sandor Lehoczky: The Art of Problem Solving, Vol. 2: And Beyond, 7th Edition
Homework: At least 5 hours per week. Students are expected to complete all of the previous AIME contests in the past 10 years, which is over 60 hours of practice. Our instructors are open to questions on any previous AIMEs.
All problems from all of the previous 49 AIME contests (1983-2015) form our “big data” system. We have used data mining and predictive analytics to examine the types and the frequencies of questions in all these materials, and then completely “decoded” the AIME. 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. For all questions on the recent AIME contests, we can find their “ancestors” and “roots” from the old AIME problems. Therefore, the best way to prepare for the contest is to practice by solving old AIME problems.
Our Students
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.
Contact Information: Ivy League Education Center Tel: 301-922-9508 or 240-780-8828 Email: chiefmathtutor@gmail.com
Purpose: To prepare for the AMC 10/12 A — Tuesday, February 2, 2016 and/or AMC 10/12 B — Wednesday, February 17, 2016.
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 Geometry Problems
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.
Who should take this class: This class is very appropriate for 7th-12th grade students who are hoping to qualify for the AIME.
Mock Tests: Two simulated tests help students assess their level of preparation for the Math Competitions. The test consists of 25 questions similar to AMC 10/12 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.
Weekly Homework: At least 3 hours per week. 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.
The only way to learn mathematics is by doing mathematics. Homework assignments are a fundamental part of a mathematics course. Homework is also seen as a welcome challenge and an opportunity for further learning. Homework given prior to a lesson can aid in understanding later during class. Homework also provides opportunities for reinforcement of the material learned in class.
We have to face the simple truth that to do well on this grueling contest, 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 10/12 exams (2000-2015) and AHSME (1973–1999) form our “big data” system. The AHSME (American High School Mathematics Examination) was the former name of the AMC, before 2000. We have used data mining and predictive analytics to examine the types and the frequencies of questions in all these materials, and then completely “decoded” the AMC 10/12. 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. For all questions on the recent AMC contests, we can find their “ancestors” and “roots” from the old AMC problems. Therefore, the best way to prepare for the contest is to practice by solving old AMC problems.
Our Students
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.
Small-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.
Benefits:
8 tutorial handouts (>160 pages) developed by Dr. Henry Wan and 400 new problems similar to AMC 10/12 level from the licensed AMC Database
2 FREE mock tests, each of which has 25 questions taken from the licensed AMC Database
This course is designed to extend skills in problem solving and critical thinking, to foster mathematical creativity, and to introduce the fundamentals of proof. Students learn to think at an advanced level as they tackle challenging problems.
Topics addressed in this course will draw from: number theory, set theory, algebra, geometry, combinatorics, graph theory, and probability. The class will also discuss problems from all past AMC 10/12 exams (2000-2015), as well as efficient strategies for taking the test.
Each week, students explore a different math topic or problem-solving strategy in depth, and practice both non-routine and contest problems. In tackling non-routine problems whose solutions are not immediate, students are encouraged to approach problems from different angles. Additionally, they will learn to create inductive and deductive proofs, with a focus on the proper use of notation and terminology and precision in their writing. Our classroom provides interactive and team-building experiences for students.
Each topic covered in the course is independent of the other topics. Students will not necessarily start with “Topic 1” in their first week of enrollment.
Class Outline:
In AMC 10/12 Prep Class, we will focus on efficient tricks, shortcuts, and strategies to solve AMC problems as well as test-taking tactics.
AMC 10/12 Problem Set on geometry, Plus some new problems with a similar difficulty level from the licensed AMC Database
Yes
2
1/17, Sun
Tricks and shortcuts for solving AMC counting and combinatorics problems
AMC 10/12 Problem Set on counting and combinatorics, Plus some new problems with a similar difficulty level from the licensed AMC Database
Yes
3
1/24, Sun
Number bases, modular arithmetic, integer divisions, and linear congruences at the heart of a great many AMC problems
AMC 10/12 Problem Set on number theory, Plus some new problems with a similar difficulty level from the licensed AMC Database
Yes
4
1/31, Sun
The art and craft for solving AMC statistics and probability problems
AMC 10/12 Problem Set on statistics and probability, Plus some new problems with a similar difficulty level from the licensed AMC Database
Yes
5
2/7, Sun
Efficient strategies for testing primality to solve AMC problems
AMC 10/12 Problem Set on arithmetic, Plus some new problems with a similar difficulty level from the licensed AMC Database
Yes
6
2/14, Sun
Problem solving in algebra equation, inequalities, polynomials, rationals, and quadratics
AMC 10/12 Problem Set on algebra and functions, Plus some new problems with a similar difficulty level from the licensed AMC Database
Yes
7
2/21, Sun
Sophisticated and elegant strategies and tactics to solve sequences and series problems in the AMC
AMC 10/12 Problem Set on sequences and series, Plus some new problems with a similar difficulty level from the licensed AMC Database
Yes
8
2/28, Sun
Arts and tricks to solve AMC problems related to circles, polygons, coordinates and graphs, and three-dimensional geometry
AMC 10/12 Problem Set on three-dimensional geometry, Plus some new problems with a similar difficulty level from the licensed AMC Database
Yes
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.
We are only one in the Washington DC metropolitan area to offer elementary, middle, and high-school level competition math courses. Our tutoring model is very unique. We ask that all students complete all the required problems at home, and then email their work to us before come to the class. We will carefully review and check the students’ work. Based on their work, we can detect what are the student’s specific weaknesses and use those problems in class to teach the students all the tricks, shortcuts, strategies, and tactics for taking the contest. The entire two hours are used for instructional teaching only. We firmly believe that learning is extremely important, and that a student should not waste time doing problems with our supervision if they can do those problems at home. So our 2-hour session is equivalent to a regular 4-hour session, and thus our hourly rate is equivalent to $20 per hour.
Our Students
The American Mathematics Contest 12 (AMC 12) is the first exam in the series of exams used to challenge bright students, grades 12 and below, on the path toward choosing the team that represents the United States at the 
在D的经历和思考：死亡行军
我的进一步思考：美国理科基础教育的薄弱
我的更多思考：依赖外国人才输入的科研模式
结语
作者：changshou，来源：转载自西西河中文网
Featured Instructors
Although the rules of AMC state that no calculators are allowed, students are permitted to use scratch paper, 
For example, 2014 AMC 10 Problem #22 is a very difficult problem to solve mathematically. But by simply using a ruler and a protractor, one can easily solve this problem.
. What is AE?
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: 
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.
Ivy League Education Center 