Pengi Editor's Note
This comprehensive guide from Think Academy maps out the US math competition landscape from grade 1 through high school — covering Math Kangaroo, Noetic, AMC 8, AMC 10, AMC 12, AIME, USAMO, MOP, and IMO. It is an essential reference for parents deciding when and where to enter their child into the competition pipeline, with specific grade recommendations and award structures for each contest. The Pengi editorial team recommends this as a starting point for any family considering math competition prep.
Source: Think Academy Blog
From Grade 1 to 10: Choose the Right Math Competition
From elementary school students starting their mathematical journeys to high schoolers mastering complex equations, math competitions offer exciting challenges for learners of all ages. This guide explores math competitions from Math Kangaroo for beginners to prestigious contests like the Mathematical Olympiad Program (MOP) and International Mathematical Olympiad (IMO).
Recommended Math Competitions for Various Age Groups
Math Kangaroo
Originating in Australia in 1980, Math Kangaroo (MK) has expanded to 93 countries worldwide, with over 6 million participants. Since its introduction to Chicago in 1998, it has conducted 25 sessions, dedicated to nurturing a love for math among students across the country. In 2023, a total of 36,421 contestants took part nationwide.
Key Information
- Number of questions: 24
- Question type: Multiple-choice
- Full score: 96 points
- Duration: 75 minutes
- Competition time: Third Thursday of March
- Recommended grades for participation: G1–G4
MK is an individual competition, with Grades 1 and 2 competing together and Grades 3 and 4 doing the same. However, awards are granted separately by grade.
Types of Awards
National Scale: The top three high-scoring students in each grade receive gold (96 points), silver (93 points), and bronze medals (92 points).
State Level: The top three high-scoring students in each grade receive blue, red, and white ribbons, respectively.
Those who score above 75 can win a National Winners award.
Why Should Students Participate in Math Kangaroo During Grades 1 to 4?
Math Kangaroo serves as a fundamental and popular math competition, universally suitable for all students. MK emphasizes logic and geometry, complementing American in-class math which focuses on number sense and calculation. Introducing children to Math Kangaroo at an early age also serves as an early diagnostic tool for assessing mathematical abilities and long-term competitive potential.
Noetic
Noetic Learning Math Contest (NLMC) is a semiannual problem-solving competition designed for elementary and middle school students (Grades 2 to 8). Its goal is to develop students' problem-solving skills, foster interest in math, and inspire them to excel in mathematics.
Recommended grades for participation: G1–G2
Math League
Math League is the largest network of local and state math competitions at elementary, middle, and high school levels in the United States and abroad. It hosts over 400 contests worldwide and engages more than 30,000 students annually.
Recommended grades for participation: G3–G4
AMC 8
The American Mathematics Contest 8 (AMC 8) commenced in 1985 and is organized by the Committee on the American Mathematics Competitions. It is open to students in eighth grade (14.5 years old) and below.
Key Information
- Number of questions: 25
- Question type: Multiple-choice
- Full score: 25 points
- Duration: 40 minutes
- Competition time: January
- Commonly participating grades: G4–G8
Types of Awards
- Distinguished Honor Roll: Top 1%, typically scoring 21 or above
- Honor Roll: Top 5%, usually scoring 19 or above
- Achievement Roll: For students in grade six and below, scoring above 15 points
Why Should Students Start Participating in AMC 8 During Grades 4 to 6?
Although AMC 8 is designed for students up to eighth grade, many students in sixth grade — and even younger ones in fourth and fifth grades — have achieved excellent results. Those interested in math competition should aim at different score milestones in stages and fully utilize every opportunity to take the exam.
AMC 10
The American Mathematics Contest 10 (AMC 10) started in 2000 and is organized by the Committee on the American Mathematics Competitions. It is open to students in grade 10 and under 17.5 years old.
Key Information
- Number of questions: 25
- Question type: Multiple-choice
- Full score: 150 points
- Duration: 75 minutes
- Competition time: November
- Commonly participating grades: G6–G10
Types of Awards
- Distinguished Honor Roll: Top 1%, usually a score of 120 or above
- Honor Roll: Top 5%, typically scoring 95 or above
- Achievement Roll: For students in grade eight and below, a score of at least 90
- AIME Qualification: Top 2.5%, usually scoring over 100
Difference between AMC 10A and AMC 10B
The two exams are held at different times within the year, allowing registration at distinct testing centers for each. While the questions vary, the difficulty level remains consistent.
Early involvement in AMC 10 during grades 7–8 provides ample time for preparation for the AIME, and for achieving higher scores in more advanced AP courses.
AMC 12
The precursor to AMC 12 was the American High School Mathematics Examination, which began in 1951. AMC 12 is open to students in grade 12 and below.
Key Information
- Number of questions: 25
- Question type: Multiple-choice
- Full score: 150 points
- Duration: 75 minutes
- Competition time: November
- Commonly participating grades: G9–G12
Note: The AMC 10A and 12A exams are scheduled on the same day, as are the 10B and 12B. Students can only sit for one of these exams on each date.
AIME
The American Invitational Mathematics Examination (AIME) was established in 1983 as a bridge between the AMC 10/12 exams and the USAMO.
Eligibility:
- AMC 12 participants with scores exceeding 100 (out of 150) or ranking in the top 5%
- AMC 10 participants with scores above 120 or ranking in the top 2.5%
Key Information
- Number of questions: 15
- Question type: Fill in the blank (answers 0–999)
- Full score: 15 points
- Duration: 3 hours
- Competition time: February
- Commonly participating grades: G9–G12
The AIME is typically held twice each year (AIME I and AIME II). Students can choose to participate in one session.
USA(J)MO
The United States of America (Junior) Mathematical Olympiad (USAMO) selects participants from the AMC 10 and AMC 12 exams. Its primary purpose is to identify candidates for the US Olympic team competing in the International Mathematical Olympiad (IMO).
Key Information
- Number of questions: 6
- Question type: Essay discussion and proof problems
- Full score: 42 points
- Duration: 9 hours over two days (4.5 hours per day)
- Competition time: March
- Commonly participating ages: 16–20 years old
USAMO Index = AMC10/12 score + 10 × AIME score. An index above 210 indicates a strong chance of receiving an invitation.
Note: Only U.S. citizens are eligible to participate.
MOP and IMO
MOP (Mathematical Olympiad Program) is a comprehensive three-week intensive problem-solving training camp held at Carnegie Mellon University. The top 27 USAMO contestants nationwide are selected for extensive training. MOP is provided free of charge.
- Entry requirements: Outstanding performance in the USAMO or USAJMO
- Format: Lectures, tests, and problem-solving sessions
- Competition time: Summer, approximately three weeks
IMO (International Mathematical Olympiad) is the most prestigious international mathematics competition. The top six US contestants from MOP represent the United States.
- Entry requirements: Top performers from national Mathematical Olympiads
- Format: Two-day event, 4.5 hours per day, three problems per day (algebra, combinatorics, geometry, number theory)
- Competition time: Summer
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