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Mathematics Quiz

Instructions

Please answer the following questions. Each question requires an open-ended response where you must provide a brief explanation or calculation to demonstrate your understanding.


  1. What is the Pythagorean Theorem? Provide an example of how it can be applied to find the length of the hypotenuse in a right triangle.

  2. Define a quadratic equation and explain how to find its roots using the quadratic formula. Provide an example with specific values.

  3. What is the difference between a permutation and a combination? Give an example to illustrate each concept.

  4. Describe the concept of limits in calculus. What is the significance of limits when evaluating the behavior of functions as they approach specific values?

  5. Explain the fundamental theorem of arithmetic. How does it relate to prime factorization, and why is prime factorization unique for every integer?


Please respond to each question thoughtfully and comprehensively. Good luck!