Harder Math Problems

1. What is the area of an equilateral triangle, with base length x?

2. The Equations r=2sin(θ) Creates an circle. What is the center of the circle created?

3. What is sin(75°) equal to? (75 is in degrees).

4. Camila writes down five positive integers. The unique mode of these integers is 2 greater than their median, and the median is 2 greater than their arithmetic mean. What is the least possible value for the mode? (2022 AMC 10B Question 10)

5. Hex 16 number A9B3EE14A1932 Divided by F (Or 15 in base 10) has an remainder of:

6. You have coins valued 5 dollars and 8 dollars. Using POSITIVE INTEGER amounts of both, what's the largest value you cannot pay without needing change? (For example, you cannot pay 6 dollars without needing change).

7. You have coins valued 101 dollars and 97 dollars. What's the largest value you cannot pay without needing change? You can pay only in NON NEGATIVE Integer amounts. Using zero of a coin is ok.

8. What is the formula for sinh(x)?

9. Find the median of all the three-digit palindromes.

10. [sin(12°)i + cos(12°)] * [sin(78°)i + cos(78°)] = (i stands for imaginary)