...wins a special present, but I'm going to keep that present under wraps for now.

Don't forget to show your work so I can see that you understand the concepts that underlie all of these problems. These problems get harder as you proceed.

9 questions, gogogo:

1. Solve for x: 2x^2 - 4x - 3 = 0
2. In circle O, the radius is 8, and the measure of minor arc AB is 110 degrees. Find the length of minor arc AB to the nearest integer.
3. Expand: (x^2 + 3)^6
4. In triangle ABC, b = 12, c = 20, and A = 45 degrees. Find side a to the nearest integer. (Note: the lower-case letters indicate sides of the triangle, and the capital letters indicate the angles.)
5. y = sec(1 - 5x). Find the derivative, y'
6. Evaluate the following integral: integral[sqrt(25x^2 - 4)/x]dx
7. Evaluate the following line integral: integral(xy^4)ds about C, where C is the right half of the circle given by the equation x^2 + y^2 = 16
8. Find all of the eigenvalues of the following matrix:
[6 5]
[-8 -6]
9. Solve for y(t): y''(t) - 6y'(t) + 15y(t) = 2sin(3t); initial conditions are y(0) = 1 and y'(0) = -4