# Composition and Scope of the Test

## 6th Grade

1. Composition of the test:

- Problems 1~20: 20 multiple choice questions (5 choices)

- Problems 21~25: The answer consists only of integers from 0 to 9999 (0 and 9999 inclusive)2. Eligibility requirements:

- Any students in the 6th grade or lower can apply.3. Test time is 60 minutes. Calculators are prohibited.

4. Scoring Method

150 points in total

6 points for each question from 1 to 25

### Scope of the Test (same as common core)

1. Ratios and Proportional Relationships

- Understand ratio concepts and use ratio reasoning to solve problems.2. The Number System

- Apply and extend previous understandings of multiplication and division to divide fractions by fractions.- Compute fluently with multi-digit numbers and find common factors and multiples.

3. Expressions and Equations

- Apply and extend previous understandings of arithmetic to algebraic expressions.- Reason about and solve one-variable equations and inequalities.

- Represent and analyze quantitative relationships between dependent and independent variables.

4. Geometry

- Solve real-world and mathematical problems involving area, surface area, and volume.5. Statistics and Probability

- Develop understanding of statistical variability.- Summarize and describe distributions.

## 8th Grade

1. Composition of the test:

- Problems 1~20: 20 multiple choice questions (5 choices)

- Problems 21~25: The answer consists only of integers from 0 to 9999 (0 and 9999 inclusive)2. Test time is 90 minutes. Calculators are prohibited.

3. Eligibility requirements:

- Any students in the 8th grade or lower can apply.4. Scoring Method

150 points in total

6 points for each question from 1 to 25

### Scope of the Test (same as common core)

1. The Number System

- Know that there are numbers that are not rational, and approximate them with rational numbers.2. Expressions and Equations

- Work with radicals and integer exponents.- Understand the connections between proportional relationships, lines, and linear equations.

3. Functions

- Define, evaluate, and compare functions.- Use functions to model relationships between quantities.

4. Geometry

- Understand congruence and similarity using physical models, transparencies, or geometry software.- Understand and apply the Pythagorean Theorem.

- Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

5. Statistics and Probability

- Investigate patterns of association in bivariate data.## 10th Grade

1. Composition of the test:

- Problems 1~20: 20 multiple choice questions (5 choices)

- Problems 21~25: The answer consists only of integers from 0 to 9999 (0 and 9999 inclusive)2. Test time is 90 minutes. Calculators are prohibited.

3. Eligibility requirements:

- Any students in the 10th grade or lower can apply.4. Scoring Method

150 points in total

6 points for each question from 1 to 25

### Scope of the Test

-Number Theory (Integers)

-Graph Theory, Equations, Inequality

-Trigonometry (Definition of Trigonometric Functions, Law of Sines, Law of Cosines)

-Counting (Combinations, Permutations, Combinations with repetition) & Probability

-Plane Geometry (Pythagorean Theorem, similarity, application of Pythagorean Theorem and similarity)

-Space Geometry

-Sequences, Series

## 12th Grade

1. Composition of the test:

- Problems 1~20: 20 multiple choice questions (5 choices)

- Problems 21~25: The answer consists only of integers from 0 to 9999 (0 and 9999 inclusive)2. Test time is 90 minutes. Calculators are prohibited.

3. Eligibility requirements:

- Any students in the 12th grade or lower can apply.4. Scoring Method

150 points in total

6 points for each question from 1 to 25

### Scope of the Test

-Number Theory (Integers)

-Graph Theory, Equations, Inequality

-Trigonometry (Definition of Trigonometric Functions, Law of Sines, Law of Cosines, Various Formulas (Sum & Difference Formulas, Double Angle Formula...etc.))

-Counting (Combinations, Permutations, Combinations with repetition) & Probability

-Plane Geometry (Pythagorean Theorem, similarity, application of Pythagorean Theorem and similarity)

-Space Geometry & Vectors

-Sequences, Series

-Complex Numbers

## College/University Grade

1. Eligibility requirements:

- Problems 1~20: 20 multiple choice questions (5 choices)

- Problems 21~25: The answer consists only of integers from 0 to 9999 (0 and 9999 inclusive)2. Composition of the test:

- Problems 1~10: 10 multiple choice questions (5 choices)

- Problems 11~20: 5 short-answer questions (Short answer type, where the correct answer is an integer from 0 to 9999)

- Problems 21~25: The answer consists only of integers from 0 to 9999 (0 and 9999 inclusive)3. Test time is 90 minutes. Calculators are allowed.

4. Scoring Method

150 points in total

6 points for each question from 1 to 25

### Scope of the Test

#### All of Calculus

-Limits

-Differentiation

-Integration

-Differential Equations

-Polar Curves

-Series

# Team Round Test

1. It consists of two tests for middle school students and high school students.

2. The total duration of the test is 120 minutes, and the use of a calculator is prohibited.

3. Each question is worth 10 points, for a total of 150 points.

4. The answers should be written directly on the test with a black ballpoint pen.

5. Minimum of 1 to 4 players per team.

### Scope of the Test

#### Middle School Students

1. The Number System

- Know that there are numbers that are not rational, and approximate them with rational numbers.

2. Expressions and Equations

- Work with radicals and integer exponents.

- Understand the connections between proportional relationships, lines, and linear equations.

3. Functions

- Define, evaluate, and compare functions.

- Use functions to model relationships between quantities.

4. Geometry

- Understand congruence and similarity using physical models, transparencies, or geometry software.

- Understand and apply the Pythagorean Theorem.

- Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

5. Statistics and Probability

- Investigate patterns of association in bivariate data.

#### High School Students

-Number Theory (Integers)

-Graph Theory, Equations, Inequality

-Trigonometry (Definition of Trigonometric Functions, Law of Sines, Law of Cosines, Various Formulas (Sum & Difference Formulas, Double Angle Formula...etc.))

-Counting (Combinations, Permutations, Combinations with repetition) & Probability

-Plane Geometry (Pythagorean Theorem, similarity, application of Pythagorean Theorem and similarity)

-Space Geometry & Vectors

-Sequences, Series

-Complex Numbers

# IMC Math Modeling Contest (IMMC)

1. A test to read the given research paper, make a problem that is happening around us in relation to the paper, solve the problem with mathematics, and write a solution.

2. It is a total of 4 hours; the solution is written as a word file and submitted.

3. The length should be between 500 and 1500 words.

4. You can use books, Internet, calculator, and coding but if you use ChatGPT to copy it, the test will be canceled and several universities in collaboration with us will be notified. Using ChatGPT is judged as cheating.

5. IMC Math Modeling Contest (IMMC) This is designed to test students' creative math skills.

6. Minimum of 1 to a maximum of 4 students per team.

7. Each team member does not have to be from the same school or country.