## I. Why Participate in Math Competitions?

### 1. High-Value International Math Competitions are Recognized by World-Renowned Universities

Some top-tier U.S. universities suggest that students submit their AMC 10/12 or AIME scores when applying, explicitly considering math competition results as one of the factors for admission. The increasing number of high school students participating in the AMC in recent years is precisely because of this reason—they hope to enhance the weight of their application materials with high-value competition scores.

### 2. A Strong Proof of Academic Capability

Among the many contenders for admission to prestigious universities, there are plenty who have high SAT scores or language test scores, as well as several with more than five AP scores of 5, three or more A Level grades of A*, or an IB score above 42. Having one or multiple competition scores, especially awards from competitions with high prestige, can further prove an applicant’s exceptional academic potential.

### 3. Enhance Logical Thinking Skills for Lifelong Benefits

Unlike domestic math competitions, although some international math competitions also test pure mathematical problem-solving skills, most of them emphasize the fun of mathematics and the application of mathematical knowledge to solve problems. Essentially, they test logical thinking abilities.

After studying for math competitions for a certain period, many students express that the experience has benefited them for life. These students often show stronger problem-solving abilities in new situations. Since the logic of problem-solving is universal, a higher level of logical thinking means that one can better organize and utilize the knowledge and methods they have mastered to solve new problems.

## II. How to Choose?

## III. How to Plan?

### 1. Suggested Start: Grade 4, Latest: Grade 10

The competition planning for most students suggests starting as early as grade 4, discouraging an earlier start to learning mathematical competition content. Studying for math competitions by grade 10 (first year of high school) isn’t too late either—if you make good use of your time, significant improvement is still possible.

Starting to engage in math competitions in grade 11 makes it difficult to achieve good results because, by grade 11, students need to prepare for various exams required for college applications and the submission of application materials. Beginning math competitions then would be overwhelming.

### 2. Elementary Students Should Focus on Fun

The difficulty of math competitions for elementary students should not be too high; it’s advisable to choose math competitions that are fun and friendly for younger students, such as the Kangaroo Math Competition, North American Reindeer Math Competition, UK Junior Mathematical Challenge, and the Australian Mathematics Competition (Primary Division).

For the latest dates of the above competitions, registration website links, etc., please refer to the “International Competition Calendar.”

### 3. Middle Schoolers Should Focus on Building a Mathematical Knowledge System

After entering grade 7, middle school students already have a certain system of mathematical knowledge. With systematic study and preparation, they can cope with the American Mathematics Competitions AMC 8 or other competitions of similar level, such as the UK Intermediate Mathematical Challenge, the University of Waterloo’s Gauss Math Contest in Canada, and so forth.

After reaching grade 9, the goal can be set to AMC 10/12 or other competitions of equivalent level such as the UK Senior Mathematical Challenge, the University of Waterloo’s Euclid Mathematics Contest, etc.

### 4. High School Students Should Focus on Long-term Planning and Increasing Difficulty

Students in grade 10 should set their competition and award-winning goals a bit further out, preparing for taking the AMC 12 in grade 11 to advance to AIME or participating in SMC to progress to BMO 1 as well as the Euclid Mathematics Contest. These competitions are highly prestigious and valued by world-renowned universities. Naturally, to win awards in these competitions requires a longer preparation period and tests the comprehensive abilities of students more rigorously.

For grade 11 students, winning one or two high-value math competition awards is of great significance for applying to prestigious universities, but this is also the year to achieve results in language proficiency and other major exams. Therefore, the vast majority of students are unlikely to spend much time and effort preparing for competitions and tackling difficult problems. This is why Mr. Xie Tao strongly recommends allocating more time and effort to study for math competitions and improve math levels in grade 10.

## IV. How to Prepare?

Math competitions in different countries may cover different ranges of knowledge and focus on different aspects, but the core abilities and qualities assessed are consistent. It is recommended to primarily focus on the math competitions of a specific country and to study the knowledge and problem-solving skills related to math competitions as comprehensively and systematically as possible. This approach aims to train and enhance logical thinking abilities in order to comfortably handle various types of math competitions.