Number System Case Study Questions Class 10

Number System Case Study Questions Class 10

Number System Case Study Questions Class 10 | Free Online Test

Number System Case Study Questions Class 10

Students preparing for exams often search for Case Study math questions for class 10. These exercises help strengthen concepts in the number system. Our online tests include interactive math case study questions class 10 that focus on real-life applications of numbers. Practicing these questions regularly improves accuracy and speed. Additionally, students develop problem-solving skills while applying formulas in practical situations.

Importance of Number System Case Study Questions Class 10

Math case study questions class 10 encourage analytical thinking and logical reasoning. For instance, questions on rational and irrational numbers allow deeper understanding. Furthermore, solving these problems enhances critical thinking. Short exercises help reinforce key formulas. Therefore, students gain confidence and clarity in the number system through consistent practice.

Benefits of Online Test Practice

Our math case study questions online tests provide instant feedback and performance tracking. Students can identify errors quickly and improve their approach. The number system case study questions class 10 cover various difficulty levels. Consequently, learners strengthen concepts efficiently and are better prepared for exams. Regular practice ensures mastery of fundamental number system topics.

Prime Factorization Case Study

Case Study 1: Prime Factorization and the Fundamental Theorem of Arithmetic

Rohan is preparing a math model for his school exhibition based on the concept of prime factorization. While demonstrating the Fundamental Theorem of Arithmetic, he selects numbers such as 36, 48, and 60 and expresses them as products of prime numbers. He then tries to explore the HCF and LCM of these numbers using their prime factorizations. Rohan realizes that understanding this theorem helps in solving many real-life problems related to divisibility and factorization.

Key Concepts:

  • Prime Factorization: Expressing a number as a product of prime numbers
  • Fundamental Theorem of Arithmetic: Every integer greater than 1 can be represented uniquely as a product of prime numbers
  • HCF (Highest Common Factor): The largest number that divides two or numbers
  • LCM (Least Common Multiple): The smallest number that is a multiple of two or more numbers

1. What is the prime factorization of 60?

Answer: A) \(2 \times 2 \times 3 \times 5\)
Solution: \(60 = 2^2 \times 3 \times 5\)

2. Find the HCF of 36 and 60 using prime factorization.

Answer: B) 12
Solution: \(36 = 2^2 \times 3^2\), \(60 = 2^2 \times 3 \times 5\), HCF = \(2^2 \times 3 = 12\)

3. Find the LCM of 36 and 60 using prime factorization.

Answer: B) 360
Solution: LCM = \(2^2 \times 3^2 \times 5 = 360\)

4. Which of the following numbers is a composite number?

Answer: C) 21
Solution: 21 has more than two factors: 1, 3, 7, 21

5. If HCF(48, x) = 12 and x is a multiple of 12, what can be a possible value of x?

Answer: B) 12
Solution: \(48 = 2^4 \times 3\), \(12 = 2^2 \times 3\), HCF = \(2^2 \times 3 = 12\)

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