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 blog post explores math competitions, from Math Kangaroo for beginners to prestigious contests like the Mathematical Olympiad Program (MOP) and International Mathematical Olympiad (IMO). Whether you’re a parent seeking opportunities for your child, an educator inspiring students, or a student testing your abilities, this guide covers various math competitions, each with its unique challenges and rewards, shaping mathematical skills and future academic opportunities.

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, and it offers twelve levels, with Level 1 to 4 (below Grade 5) accounting for 55% of the total contestants.

Key Information

• Number of questions: 24
• Question type: Multiple-choice
• Full score: 96 points
• Duration: 75 minutes
• Competition time: The 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 – missing one question worth three points), and bronze medals (92 – missing one question worth four points).

State Level: The top three high-scoring students in each grade receive blue, red, and white ribbons, respectively.

In addition to awards for the top three places, those who score above 75 can win 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. It offers an excellent platform for honing math skills through competition. Additionally, MK emphasizes logic and geometry, complementing American in-class math, which focuses on number sense and calculation. Importantly, introducing children to Math Kangaroo at an early age can serve as an early diagnostic tool for assessing their mathematical abilities and long-term competitive potential.

For detailed insights into interpreting 2023 Math Kangaroo scores, please visit this link.

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 their 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. Mathleague.org 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’s 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 the eighth grade, many students in sixth grade, and even younger ones in fourth and fifth grades, have achieved very excellent results. Therefore, we encourage those who are interested in math and want to pursue the path of competition to start actively preparing for AMC 8 from fourth grade. You should aim at different scores and awards in stages and fully utilize every opportunity to take the exam!

To learn about the AMC 8 trends and find preparation guides, please visit this link.

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.

The AMC10 is a selective exam with clearly increasing difficulty.

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.

Why Should Students Participate in AMC 10 During Grades 7 to 8?

This early involvement provides ample time for preparation for the AIME, and afterward, for achieving higher scores in more advanced AP courses.

To find answers to frequently asked questions about AMC 10, please visit this link.

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 and shares the same content and exam settings with AMC 10, differing by only one extra point of examination.

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

Can Students Participate in AMC 8,10,12 at the same time?

Participating in both AMC 8 and AMC 10 within the same year is feasible. The AMC 10A and 12A exams are scheduled on the same day, as are the 10B and 12B. However, students can only sit for one of these exams.

Why Should Students Participate in AMC 10/12 Multiple Times?

Engaging in the AMC 10/12 exams multiple times serves several purposes. The primary goal is to qualify for the AIME. The secondary aim is to strive for higher scores, as achieving a high score opens the door to the USA(J)MO stage. For more insights on this, please continue reading below. 

AIME

The American Invitational Mathematics Examination (AIME) was established in 1983 as a bridge between the AMC 10/12 exams and the USAMO. Eligibility for the AIME is as follows:

• All students who participate in AMC 12 with scores exceeding 100 (out of a full score of 150) or rank in the top 5% of all participants are invited to participate in the AIME.
• Students who have taken the AMC 10 and achieved scores above 120 or ranked in the top 2.5% of all students are also eligible for the AIME.

* Note: The exact cutoffs may vary depending on the competition’s difficulty. 

Key Information

• Number of questions: 15
• Question type: Fill in the blank, with answers ranging from 0 to 999
• Full score: 15 points
• Duration: 3 hours
• Competition time: February
• Commonly participating grades: G9 – G12

The AIME is typically held twice in the spring each year, known as AIME I and AIME II. Students can choose to participate in one of these sessions.

The number of students invited to participate in the AIME largely depends on their scores in the AMC 10/12 exams of that year and established thresholds, which may vary annually. 

* Note: It is advisable for your AIME exam location to align with the center where you achieved your highest AMC score. In the event they are at different centers, it is recommended to submit a form or ensure that both centers are aware of your examination situations.

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, which competes 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, with each day having 4.5 hours for solving three problems
• Competition time: March
• Commonly participating ages: 16 – 20 years old

The selection criterion is called the USAMO index,

USAMO Index = AMC10/12 score + 10*AIME score.

If this index is greater than 210, there is a strong chance of receiving an invitation to the USAMO.

* Note: Only U.S. citizens are eligible to participate in this competition.

MOP and IMO

MOP: The Mathematical Olympiad Program is a comprehensive three-week intensive problem-solving training camp, held at Carnegie Mellon University. Its primary objective is to equip high school students with the skills and knowledge required to excel in the International Mathematical Olympiad (IMO). MOP is provided to participants free of charge, but only the most exceptional performers from the USAMO gain admission. The top 27 USAMO contestants from across the nation are selected to partake in MOP for extensive training.

• Entry requirements: Typically, students invited to participate in MOP are those who have demonstrated outstanding performance in the USAMO or USAJMO.
• Format: In reality, MOP is more akin to a summer camp than a competition. It offers an array of activities, including lectures, tests, and problem-solving sessions.
• Competition time: MOP usually transpires during the summer each year, extending over approximately three weeks.

The number of students invited to participate in MOP predominantly relies on their performance in the USAMO/USAJMO and the set thresholds for that particular year. The count of invitees may vary from year to year, and it typically remains relatively small.

IMO: The International Mathematical Olympiad commonly referred to as the International Mathematical Olympiad competition, is the most prestigious event in the realm of international mathematics competitions. Selection criteria for the U.S. team are contingent on a combination of USAMO scores and performance in the MOP selection examination. The top six contestants, who achieve the highest scores, are chosen to represent the United States in the International Olympiad competition.

• Entry requirements: Competitors in the IMO are typically exceptional students selected through their respective countries’ national Mathematical Olympiads. This selection process generally demands outstanding performance in domestic competitions.
• Format: The IMO unfolds over a two-day period, with each day offering a testing time of 4.5 hours. Participants are tasked with solving three problems per day, encompassing diverse mathematical areas such as algebra, combinatorics, geometry, and number theory.
• Competition time: The IMO traditionally occurs during the summer each year, attracting students from across the globe.
• Admission numbers: Each participating country is permitted to dispatch up to six contestants to partake in the competition.

At every stage, these competitions offer students a platform to nurture their skills and shape their future. Stay informed about educational insights and stay updated with the latest trends by subscribing to Think Academy’s newsletter.