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AMC and AIME

American Mathematics Competition (AMC) 

What: The AMC 10 and 12 are 25-question 75-minute multiple-choice contests. Questions range from easy to difficult with approximately 12 questions common to both. The AMC 12 covers the typical high school math curriculum, including precalculus. The AMC 10 covers typical 9th and 10th grade material.

Who:
AMC 12 - Students under 17.5 years of age on the day of the contest
AMC 10 - Students under 17.5 years of age on the day of the contest and not enrolled in grades 11 or 12
 
When: November 6, 2024, 8:40 am (Block 1). Register by September 18 using this link.
 
Where: LGI (B229)
 
Why: Because you want to challenge yourself and develop your mathematical skills. Also, students scoring in the top 5% nationally on the AMC 12 qualify for the American Invitational Mathematics Exam (AIME). Students scoring in the top 1% nationally (or score at least 120) on the AMC 10 also qualify for the AIME.
 

Which Test Should I Take?

The AMC 10 and 12 are 25-question 75-minute multiple-choice contests. Questions range from easy to difficult with approximately 12 questions common to both.

The AMC 10 is a 25-question, 75-minute multiple-choice competition designed for students in grades 10 and below. The content covers mathematics typically taught in grades 9 and 10, including elementary algebra, basic geometry (such as the Pythagorean Theorem), area and volume formulas, elementary number theory, and elementary probability. Advanced topics like trigonometry, advanced algebra, and advanced geometry are excluded.

The AMC 12 is a 25-question, 75-minute multiple-choice competition designed for students in grades 12 and below. It covers the full high school mathematics curriculum, including trigonometry, advanced algebra, and advanced geometry. Calculus is excluded.

You should take the AMC if you want to develop your problem-solving abilities. The test also serves as the first step in qualifying for prestigious international mathematics competitions, including the USA International Mathematical Olympiad. 
 

 

Sample questions - AMC 10

1. Which of the following numbers is a perfect square?
A) 98! * 99! B) 98! * 100! C) 99! * 100! D) 99! * 101! E) 100! * 101!
 
2. A square has sides of length 10 and a circle centered at one of its vertices has radius 10. What is the area of the union of the regions enclosed by the square and the circle?
A) 200 + 25(pi) B) 100 + 75(pi) C) 75 + 100(pi) D) 100 + 100(pi) E) 100 + 125(pi)
 
3. Patty has 20 coins consisting of nickels and dimes. If her nickels were dimes and her dimes were nickels she would have 70 cents more. How much are her coins worth?
A) $1.15 B) $1.20 C) $1.25 D) $1.30 E) $1.35
 
4. Let 1, 4.... and 9, 16.... be two arithmetic progressions. The set S is the union of the first 2004 terms of each sequence. How many distinct numbers are in S?
A) 3722 B) 3732 C) 3914 D) 3924 E) 4007
 

Sample questions - AMC 12

5. Minneapolis-St. Paul International Airport is 8 miles southwest of downtown St. Paul and 10 miles southeast of downtown Minneapolis. Which of the following is closest to the number of miles between downtown St. Paul and downtown Minneapolis?

A) 13 B) 14 C) 15 D) 16 E) 17

6. All the students in an algebra class took a 100-point test. Five students scored 100, each student scored at least 60, and the mean score was 76. What is the smallest possible number of students in the class?
A) 10 B) 11 C) 12 D) 13 E) 14
 
7. Points A and B are on the parabola y = 4x2 + 7x - 1 and the origin is the midpoint of AB. What is the length of AB?
A) 2\/5 B) 5 + 2/ \/2 C) 5 + \/2 D) 13 E)  5 \/2
 
8. A truncated cone has horizontal bases with radii 18 and 2. A sphere is tangent to the top, bottom and lateral surface of the truncated cone. What is the radius of the sphere?
A) 6 B) 4\/5 C) 9 D) 10 E) 6\/3
 
Answers at the bottom of the page.
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American Invitational Mathematics Exam (AIME)

What: The AIME is a 15-questions 3-hour examination in which the answers are integers from 0 to 999. The problems are difficult and can be solved using pre-calculus methods. Calculators are not allowed.

Who: Students who are invited to participate as a result of their high score on the AMC 12 or AMC 10.
 
When: TBD
 
Where: LGI (B229)
 
Why: Because you qualified! This is another opportunity to challenge your abilities.
 
 
 

Answers

1-C, 2-B, 3-A, 4-A, 5-A, 6-D, 7-E, 8-A