AMC 8/10/12/AIME Problems and Answers

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AMC 8 Problems and Answers

Year Test
Mock Tests 20 Sets of AMC 8 Mock Test with Detailed Solutions
2024 AMC 8
2023 AMC 8
2022 AMC 8
2020 AMC 8
2019 AMC 8
2018 AMC 8
2017 AMC 8
2016 AMC 8
2015 AMC 8
1999-2014 18 Sets of Past Official AMC 8 Tests with Answer Keys (PDF files)
1985-1999 14 Sets of Previous Real AJHSME (AMC 8) Tests with Answer Keys (PDF files)

Also read:

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AMC 10 Problems and Answers

Year Test A Test B
2023 AMC 10A AMC 10B
2022 AMC 10A AMC 10B
2021 Fall AMC 10A AMC 10B
2021 Spring AMC 10A AMC 10B
2020 AMC 10A AMC 10B
2019 AMC 10A AMC 10B
2018 AMC 10A AMC 10B
2017 AMC 10A AMC 10B
2016  AMC 10A AMC 10B
2000-2015 35 Sets of Previous Official AMC 10 Tests with Answer Keys (PDF files)

Also read:

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AMC 12 Problems and Answers

Year Test A Test B
2023 AMC 12A AMC 12B
2022 AMC 12A AMC 12B
2021 Fall AMC 12A AMC 12B
2021 Spring AMC 12A AMC 12B
2020 AMC 12A AMC 12B
2019 AMC 12A AMC 12B
2018  AMC 12A AMC 12B
2017 AMC 12A AMC 12B
2016 AMC 12A AMC 12B
2000-2015 35 Sets of Previous Official AMC 12 Tests with Answer Keys (PDF files)

Also read:

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AIME Problems and Answers

Year Test I Test II
2017  AIME I AIME II
2016 AIME I AIME II

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More details can be found at:

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The AMC 10/12 Contests at Montgomery College on February 7, 2018, and February 15, 2018

2018 AMC10-12

We will offer the AMC 10/12 contests to OUR CURRENT LOCAL students at the Montgomery College.

The 2018 AMC 10/12 Online Registration is now open!

AMC 10/12 A
Date: Wednesday, February 7, 2018
Time: 3:30pm-5:00pm (please arrive 10 minutes early)

AMC 10/12 B
Date: Thursday, February 15, 2018
Time: 3:30pm-5:00pm (please arrive 10 minutes early)

Germantown Campus:
Address: 20200 Observation Drive, Germantown, MD 20876
Location: HT113 (Global Hall)
View Germantown campus map here

Rockville Campus:
Address: 900 Hungerford Drive #110, Rockville, MD 20850
Location: SC362
View Rockville campus map here

Note: Parking permit will be available.

You can find 2017 real AMC 10/12 problems and answers, for your child’s practice, at:

*************************************************************
Henry Wan, Ph.D.
Senior Instructor in Math
Senior Math Coach Certified by the MAA
Tel: 240-406-3402
Email:  amcmarylandcenter@gmail.com *************************************************************
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The main purpose of the AMC 10/12 is to spur interest in mathematics and to develop talent through the excitement of solving challenging problems in a timed multiple-choice format. The problems range from the very easy to the extremely difficult. Students who participate in the AMC 10/12 should find that most of the problems are challenging but within their grasp. The contest is intended for everyone from the average student at a typical school who enjoys mathematics to the very best student at the most special school.

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In 2017, over 510,000 students from over 4,100 U.S. and international schools competed for school, regional, and national awards in this contest and found it fun and rewarding. Top 20, well-known U.S. universities and colleges, including internationally recognized U.S. technical institutions, ask for AMC scores on their application forms. Our students deserve the chance to list these scores on their applications!

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With these contests, there are awards in each school for the student with the highest score, certificates for high-scoring students in each school, state-wide awards, regional awards, and even national awards. These contests lead to other more selective math contests, all the way to the USA team sent to the International Mathematical Olympiad, the premier international high school level problem solving contest.

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But the real rewards come from challenging each student with mathematics that is new, different, and “outside of the box.” The problems on the contest are hard, but designed to be within reach. Just by participating in the contest your student should still feel accomplishment, because these problems are meant to be more challenging than routinely encountered in mathematics courses.

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Mathematics is increasingly important in our technological and scientific age. Taking enough mathematics in school is the gateway to jobs and careers of all kinds, even those that are not explicitly mathematical, scientific or technological. We hope that by offering these contests, we can challenge and inspire students to want to learn more mathematics. We hope that your son or daughter enjoys the contests and will continue to take mathematics courses in middle school, high school and beyond.

More details can be found at:

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Click HERE to find out more about Math Competitions!

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The AMC 8 Contest at the Montgomery College on Tuesday, November 14, 2017

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We will offer the AMC 8 contest to local students at the Montgomery College.

AMC 8 Online Registration is now open!

Please click HERE to register

Date: Tuesday, November 14, 2017
Time: 3:30pm-4:30pm (please arrive 10 minutes early)

Germantown Campus:
Address: 20200 Observation Drive, Germantown, MD 20876
Location: HT113 (Global Hall)
View Germantown campus map here

Rockville Campus:
Address: 900 Hungerford Drive #110, Rockville, MD 20850
Location: HU010 or HU011
View Rockville campus map here

Note: Parking permit will be available.

You can find 2015 and 2016 real AMC 8 problems and answers, for your child’s practice, at:

*************************************************************
Henry Wan, Ph.D.
Senior Instructor in Math
Senior Math Coach Certified by the MAA
Tel: 240-406-3402
Email:  amcmarylandcenter@gmail.com
*************************************************************

For more details, see: Calendar for the American Mathematics Competitions

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The AMC 8 is a fun mathematics competition, aimed primarily at middle school students in grades 6, 7, and 8. Highly motivated 4th and 5th grade students are encouraged to participate as well. Last year the AMC 8 contest involved over 150,000 students worldwide.

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With these contests, there are awards in each school for the student with the highest score, certificates for high-scoring students in each school, and state-wide awards. The AMC 8 contest can lead to other more selective math contests, even all the way to the United States of America team sent to the International Mathematical Olympiad, the premier international high school level mathematical problem solving contest. But the real rewards come from challenging each student with mathematics that is new, different, and “outside of the box.” The problems on the contest are difficult, but designed to be within the reach of students. Even so, if your son or daughter managed to solve only one or two problems, this should be an encouragement to learn more, because these problems are meant to be more challenging than students routinely encounter in their mathematics courses.

you-can-do-it-1r8

Mathematics is increasingly important in our technological and scientific age. Taking enough mathematics in school is the gateway to jobs and careers of all kinds, even those that are not explicitly mathematical, scientific or technological. We hope that by offering these contests, we can challenge and inspire students to want to learn more mathematics. We hope that your son or daughter enjoys the contests and will continue to take mathematics courses in middle school, high school and beyond.

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More details can be found at:

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Purple_fancy_lineRead more at:

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Every Student Should Take Both the AMC 10A/12A and 10 B/12B!

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There are two sets of exams per year, the AMC 10A and AMC 12A, and the AMC 10B and AMC 12B. Both the A and the B versions of the AMC 10 and the AMC 12 have the same number of questions, the same scoring, and the same rules for administration. The only differences are the competition dates and that each version has a distinct set of questions, although the two examinations are designed to be equal in difficulty and distribution of topics. See more at:

All students should take both the A-date and B-date AMC tests. The AMC 10B/12B gives a student a second chance to qualify for the American Invitational Mathematics Exam (AIME). If a student does not qualify for the AIME through the AMC10A/12A, then he/she can qualify for the AIME through the AMC10B/12B which provides a great chance at qualifying. See more at:

logo_americanmath2.jpgIf a student earns a higher score on the AMC 10B/12B than AMC 10A/12A, then he/she can put the higher score on his/her college application form and resume, and/or write about it in a college application essay. Top 10, well-known U.S. universities and colleges, including internationally recognized U.S. technical institutions, ask for AMC scores on their application forms. Achieving a high score in the AMC will greatly increase the chances of an applicant being accepted to these top universities! See more at:

It is especially important to attend both the AMC 10A/12A and AMC 10B/12B for those students who want to qualify for the United States of America Mathematical Olympiad (USAMO) and the United States of America Junior Mathematical Olympiad (USJMO). Selection to the USAMO is based on the USAMO index which is defined as your AMC 12 score plus 10 times your AIME score. Selection to the USJMO is based on the USJMO index which is defined as your AMC 10 score plus 10 times your AIME score. If you take both the A-date and B-date AMC tests, then the USA(J)MO index will use the higher numerical score. One of our students got a score of 120 on the 2015 AMC 10A, and 138 on the 2015 AMC 10B later. He was able to qualify for the USJMO precisely because he was able to get such a high score on the AMC 10B even though his AMC 10A score did not make the cut. See more at:

We always strongly encourage our students in grades 6 and below to attend both the AMC 10A and AMC 10B. Do not worry about the potential score; it is the experience that is truly valuable, and should not be missed. Students who take more tests tend to have more opportunities and be more experienced to work toward honing their skills! Some of our students in grades 6 and below have qualified for the AIME. It is very impressive. Most of them earned a score of 90 or more out of 150 on the AMC 10, and then received National Achievement Honor Roll Certificates. They got big improvements each year and successfully became AIME qualifiers within 1 to 4 years. See more at:

We can help you register for both AMC A and B tests. See more at:

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Click HERE find out more about Math Competitions!sat-logo-3Click HERE to find out more about SAT Prep!

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Students Can Easily Qualify for the AIME Through the AMC 12 During 11th and 12th Grades

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Most of our students who are in the 10th grade and below qualify for AIME, even those who are in the 6th grade. Only a few students did not qualify for AIME who are in the 10th grade, because they happened to join our classes too late. However, all of them successfully did so with our help when they came back as 11th graders. Actually, 10th graders who did not qualify for AIME in 10th grade should not worry or feel disappointed. It is much easier to qualify for AIME through the AMC 12 than AMC 10 because the curve for the AMC 12 is much more generous. Any student who scores in the top 2.5% on the AMC 10, or in the top 5% on the AMC 12 is invited to take the AIME. 10th graders still have a great chance at qualifying in 11th grade!

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The AMC 12 cutoff scores for AIME qualification ranged from 88.5 to 100, while the AMC10 scores from 106.5 to 120, between 2009 to 2016. Qualification parameters for AIME vary with the results of the AMC 10/12 competitions. The exact cutoffs depend on the difficulty of each competition. See more at:

Even for a student in grades 10 and below, who is familiar with trigonometry and precalculus, it easier to score a 100 on the AMC 12 than to score a 120 on the AMC 10. Even if the AMC 12 problems are harder, the difference in 20 points is over three problems. To qualify for AIME through the AMC 10, the minimum correct answers needed is 19. For the AMC 12, however, you only need at least 14 correct answers. Furthermore, the AMC 12 questions have about at least 9 questions out of the first 14 that are the same as the AMC 10’s and they do not get significantly harder until after Problem 16. Thus, it is much easier to qualify for the AIME through the AMC 12 than the AMC 10. See more at:

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AMC 10 versus AMC 12

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The Eligibility of Students to Take the AMC 10 and the AMC 12

Materials Covered on the AMC 10 and 12

  • The AMC 10 tests mathematical problem solving with arithmetic, algebra, counting, geometry, number theory, and probability and other secondary school math topics. Problems are designed to be solved by students without any background in trigonometry, precalculus, or calculus.
  • The AMC 12 tests mathematical problem solving with arithmetic, algebra, counting, geometry, number theory, and probability and other secondary school math topics, including trigonometry and precalculus. Problems are designed to be solvable by students without any background in calculus.

The Difference in the A and B Versions of the AMC10/12 Examinations

  • Both the A and the B versions of the AMC 10 and the AMC 12 have the same number of questions, the same scoring and the same rules for administration.
  • The only differences are the competition dates and that each version has a distinct set of questions, although the two examinations are designed to be equal in difficulty and distribution of topics.

The Similarity between the AMC 10 and AMC 12

  • The AMC 10 and AMC 12 contests are 25 questions long, and take 75 minutes.
  • The AMC10A and AMC12A are offered on the same day, as well as the AMC10B and AMC12B.
  • The A tests and the B tests each have about 10-15 questions in common. In 2016, the AMC 10A and AMC 12A have 14 questions in common, while the AMC 10B and AMC 12B have 12 questions in common. See more at:

Cutoff Scores for AIME Qualification

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2016 AMC 8 Results Announced — Eleven Students Received Perfect Scores

WARMEST CONGRATULATIONS TO THE STUDENTS WHO EARNED TOP SCORES ON THE 2016 AMC 8 CONTEST!

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  • 11 of our students were among the top 264 National Winners (Perfect Scorers).
  • 16 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.
  • 48 out of our 51 students (94%) received National Awards for the AMC 8 from the Mathematical Association of AmericaIn 2016, we had 63 students who earned top scores on the AMC 8 contest!

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The 2016 AMC 8 (American Mathematics Competitions 8) was held on November 15th, 2016. This is one of the most important math competitions in America. The AMC 8 has a total score of 25. Eleven of our students were among 264 National Winners (Perfect Scorers). Click HERE see a full list of students who achieved a perfect score in the USA.

Table 1:  Eleven Perfect Scorers on the 2016 AMC 8 Contest

First Name Last Initial AMC 8 Score Grade Class Year
Joshua F. 25 8 2015-16 AMC 10/12 Prep, 2016-2017 AIME Prep
Andrew H. 25 8 2016-2017 AMC 10/12 Prep
Justin H. 25 8 2016-2017 AMC 10/12 Prep
Stephen J. 25 8 2016-2017 AMC 10/12 Prep
Marvin L. 25 8 2016-2017 AMC 10/12 Prep
Udbhav M. 25 8 2016-2017 AMC 10/12 Prep
Samuel Q. 25 7 2016-2017 AMC 10/12 Prep
Daniel S. 25 8 2016-2017 AMC 10/12 Prep
Joshua Y. 25 7 2016-2017 AMC 10/12 Prep
Andras Z. 25 8 2016-2017 AMC 10/12 Prep
Bryan Z. 25 6 2016-2017 AMC 10/12 Prep

Sixteen of our students received National Distinguished Honor Roll Certificates awarded to top 1% test takers.

Table 2:  Sixteen National Distinguished Honor Roll Awardees

Name AMC 8 Score Grade Class Year
Sri J. 24 8 2016-2017 AMC 10/12 Prep
 Disha K. 24 8 2016-2017 AMC 10/12 Prep
Pravalika P. 24 7 2016-2017 AMC 10/12 Prep
David W. 24 8 2016-2017 AMC 10/12 Prep
Christopher W. 24 7 2016-2017 AMC 10/12 Prep
Arushi A. 23 8 2016-2017 AMC 10/12 Prep
Tristan M. 23 8 2016-2017 AMC 10/12 Prep
Srinath M. 23 8 2016-2017 AMC 10/12 Prep
Samuel T. 23 8 2016-2017 AMC 10/12 Prep
Bill Y. 23 4 2016-2017 AMC 10/12 Prep
Kevin Z. 23 8 2016-2017 AMC 10/12 Prep
Phillip G. 22 7 2016-2017 AMC 10/12 Prep
Aaron M. 22 8 2016-2017 AMC 10/12 Prep
Sanjay S. 22 8 2016-2017 AMC 10/12 Prep
Wyatt T. 22 7 2015-2016 One-on-one Coaching, 2016-2017 AMC 10/12 Prep
James X. 22 7 2016-2017 AMC 10/12 Prep

Twentyone of our students received National Honor Roll Certificates awarded to top 5% test takers.

Table 3:  Twenty-One National Honor Roll Awardees

Name AMC 8 Score Grade Class Year
Matthew C. 21 7 2015-2016 AMC 10/12 Prep
Jeffrey C. 21 6 2014-2015, 2015-2016, 2016-2017 AMC 8/MathCounts Prep
Richard L. 21 7 2016-2017 AMC 8/MathCounts Prep
Sarah Z. 21 8 2015-2016, 2016-2017 AMC 10/12 Prep
Suraj O. 21 7 2016-2017 AMC 8/MathCounts Prep
Ethan O. 20 8 2016-2017 AMC 10/12 Prep
Dhruv P. 20 8 2016-2017 AMC 8/MathCounts Prep
Allen W. 20 7 2016-2017 AMC 8/MathCounts Prep
Caleb Z. 20 7 2016-2017 AMC 8/MathCounts Prep
Akhil C. 19 7 2016-2017 AMC 8/MathCounts Prep
Stella I. 19 7 2016-2017 AMC 8/MathCounts Prep
Eva L. 19 5 2016-2017 AMC 8/MathCounts Prep
Danny S. 19 7 2015-2016 AMC 8/MathCounts Prep
Alison W. 19 8 2016-2017 AMC 8/MathCounts Prep
Daniel C. 18 7 2016-2017 AMC 8/MathCounts Prep
Elliot K. 18 8 2016-2017 AMC 8/MathCounts Prep
David L. 18 5 2016-2017 AMC 8/MathCounts Prep
Ivy L. 18 8 2015-2016 AMC 8/MathCounts Prep
Xuanhe Q. 18 8 2016-2017 AMC 8/MathCounts Prep
Danny S. 18 8 2015-2016 AMC 8/MathCounts Prep
Austin S. 18 6 2016-2017 AMC 8/MathCounts Prep

Furthermore, four students of our in grade 6 or under received National Certificates. Very impressively, Bryan Z., a 6th grader, got a perfect score, and Bill Y., a 4th grader, attained a 23 out of 25.

In 2016, there were 51 students in grades 3-8 who attended our AMC 8 Prep or AMC 10/12 Prep Classes, including One-on-One Private Coaching and Small Group (4-10 students) Classes. All of them attended the AMC 8 contest on November 15, 2016, and their average score is 21.85. Remarkably, 48 students received National Certificates for the Mathematical Associations of America, as shown in Tables 1, 2, 3, and 4.

All our students who achieved the top scores on the AMC 8 actually attend our high level AMC 10/12 classes, not our standard level AMC 8 classes. They know that in order to get a top score, they must aim even higher!

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20,8137 students worldwide participated in the 2016 AMC 8 contest from over 2,000 schools. In the USA, 196,019 students participated, and the overall national average score is 9.35 out of a maximum of 25. All our students achieved a score that is much higher than the overall national average score.

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

Read more at:

Click HERE find out more about Math Competitions!

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The AMC 10 and AMC 12 Have 10-15 Questions in Common

amc-logoBoth the AMC 10 and AMC 12 are 25-question, 75-minute multiple choice examinations, with 10-15 questions in common to both contests.

The AMC 10A and AMC 12A are offered on the same day, as well as AMC 10B/AMC 12B. So you can take two AMC’s officially in a year.

In 2016, the AMC 10A and AMC 12A have 14 questions in common, while the AMC 10B and AMC 12B have 12 questions in common, as shown in the following two tables.

2016 AMC 10A

2016 AMC 12A
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# 9

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# 8
# 13

# 10

# 17

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# 14

# 21

# 15
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# 18

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Click HERE to see all 14 problems appeared on both the 2016 AMC 10A and AMC 12A.

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2016 AMC 10B

2016 AMC 12B

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# 1

# 3

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# 7

# 4

# 9

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# 10

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# 11

# 9
# 13

# 10

# 14

# 11
# 15

# 12

# 16

# 14

# 17

# 15

# 21

# 18

 Click HERE to see all 12 problems appeared on both the 2016 AMC 10B and AMC 12B.

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Some Problems on the 2016 AMC 10/12 are Exactly the Same as Previous AMC/ARML Problems

copyright-small Henry Wan, Ph.D.

We have developed a comprehensive, integrated, non-redundant, well-annotated database “CMP” consisting of competitive math problems, including all previous AMC 10/12 problems, AIME problems, ARML problems, HMMT problems, Math League problems, PUMaC problems, Stanford Math Tournament (SMT) problems. The CPM is an invaluable “big data” system we use for our research, and is a golden resource for our students, who are the ultimate beneficiaries.

We have also devised a data mining and predictive analytics tool for math problem similarity searching. Using this powerful tool, we can align query math problems against those present in the target database “CPM,” and then find those similar problems in the CMP database.

For the 2016 AMC 10/12A and 10/12B problems, based on the database searching, we have found:

  • 2016 AMC 10A Problem 15 is similar to 2002 AMC 10A #5.
  • 2016 AMC 10A Problem 18 is similar to 2007 AMC 10A #11.
  • 2016 AMC 10B Problem 21 is completely the same as 2014 ARML Team Round Problem 8 
  • 2016 AMC 10B Problem 21 is similar to the following problems:
    • 2008 AMC 12A Problem 14
    • 1987 AIME Problem 4
    • 2014 University of Maryland High School Mathematics Competition Problem 16

Click HERE to see my complete detailed article on the similarities between the 2016 AMC 10/12 problems and previous math competition problems.

In my AMC 10/12 Prep Class on Feb. 14, 2016, I used Problem 8 in the 2014 ARML Team Round and the 2008 AMC 12A Problem 14, as two typical examples, to illustrate how to efficiently compute the area of the region defined by inequalities or bounded by a simple closed curve. Thus, when my students attended the 2016 AMC 10B, they already knew how to solve this exact problem and its answer. So they took one second to bubble the correct answer (B) and then got 6 points easily!

Click HERE find out more about Math Competitions!

Click HERE to find out more about SAT Prep!

Copyright copyright-small Dr. Henry Wan. All rights reserved

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2016 AMC 8 Problems and Answers

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The 2016 AMC 8 was held on November 15th-22nd, 2016. According to the AMC policy, students, teachers, and coaches are 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 2016 AMC 8 Problems and Answers. You can click the following to download them:

Detailed Solutions of the Hardest Problems on the 2016 AMC 8 can be found at:

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This year’s AMC 8 has a similar difficulty level as last year’s AMC 8; however, it was more difficult than the AMC 8 of the years before 2015. We predict that this year’s AMC 8 honor roll and Distinguished Honor Roll cut-off scores will be: 18 and 22, respectively. Read more at: AMC 8 Historical Results from 2011 to 2015

Because the AMC 8 problems are getting harder, we must practice not only previous AMC 8 problems but also easy or medium 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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