1. Airline A and Airline B operate in a local airport. 22% of all the flights that arrive at this airport are late. Airline A shares a certain amount of flights and Airline B runs the rest. If Airline A is late on 40% or its flights and Airline B is late on 10% of its flights. What percentage of the flights are run by Airline A?

2. Supposes $$$f(x)= \frac{3x^2-2x-16}{x+2}$$$. How many of the following statements is (are) true?
1) does not exist
2) does not exist
3) f(x) has a horizontal asymptote at x⁡=-2
4) f(x) has a removable singularity at x⁡=-2

3. A rectangle is formed by using part of the coordinate axes and point (m, n) on the function f(x)= $$$\sqrt{x+4}$$$ (- 4 < m < 0).

Which of the following is the maximum area of the rectangle?

4. If function f(x) is a differentiable function. The local minimum is occurred at c, then which of the following is true?

5. Find $$$f_x$$$ and $$$f_y$$$ where $$$f(x,y)=\cos(x^2y)+y^3$$$

6. If $$$a=\int_0^{2\pi} x^2dx$$$, $$$b=\int_0^{2\pi} x^3dx$$$, $$$c=\int_0^{2\pi} \sin(x)dx$$$, then which of the following is ture?

7. Find the volume generated when $$$y=3x^2$$$ is rotated about the x-axis between x=1 and x=3

8. IF y satisfied the differential equation $$$2xy+6x+(x^2-4)\frac{dy}{dx}$$$, solve for y. When x=0, y=-4.

9. What is solution of $$$(1+i)^{15}$$$

10. If matrix A = $$$\left[\begin{array}{ccc}2&5&7\\1&1&1\\2&1&-1\end{array}\right]$$$, what is determinant of A?