1. In the figure shown below, ÎABC is a right triangle, is 8 inches long, and is 10 inches long. What is the area, in square inches, of square ACDE?
2. In the standard coordinate plane, what is the distance between the points (5, 7) and (13, 11)?
3. What value must be added to 9x2 - 30x in order to complete the square (that is, make it a perfect square trinomial)?
4. A circle in the standard (x, y) coordinate plane is tangent to the x-axis at -a, and tangent to the y-axis at a, with a > 0. The radius of the circle is 4 units. What is the equation of the circle?
5. Compared to the graph of y = sin x, the graph of y = 2 sin(4x) has:
6. Which of the following is the solution set for x such that 3x - 9 ⥠- 3(9 - x)?
7. In the figure below, square ABCD has a side length of 6 inches, and squares AEFG and CHIJ each have a side length of 1 inch. What is the area, in square inches, of the shaded pentagon DGFIJ?
8. Let the operation # be defined for the set of real numbers by:
Which of the following statements are true for all real numbers x, y, and z?
I. x # y = y # x
II. (x # y) # z = x # (y # z)
III. 0 # x = 0
9. If x2 - 36a2 = 5ax, what are the two solutions for x in terms of a?
10. For all values of θ over which sin θ and cos θ are nonzero,
11. For values of x where csc x, sec x, and tan x are all defined, (csc x) o (sec x) o (tan x) = ?
12. What is the solution set for the equation |-x| = x?
13. For which of the following values of a will there be exactly one real solution to the equation 2x2 - ax + 8 = 0?
14. If x = 3T + 4 and y = 5 - T, then which of the following equations expresses y in terms of x?
15. In the circle below, radius has a length of 10 meters, and central angle â AOB measures 30°. What is the area, in square meters, of shaded sector AOB?