1. In the diagram b, d, and c are collinear. b = 30° and c = 45°. is perpendicular to and = 6. What is the perimeter of ÎABC to the nearest tenth?
2. Quadrilateral ABCD is a trapezoid with parallel to . and are perpendicular to . AB = 6, CD = 12, and AE = 4. What is the sum of the areas of ÎAED and ÎBFC?
3. (2 - 3i)2 = ? [Note: i = ]
4. How many prime numbers are there between 50 and 70?
5. If (x + 2) is a factor of 3x2 - 13x + k, what is the value of k?
6. If the radius of a sphere is tripled, the volume of the resulting sphere is how many times the volume of the original sphere?
[The volume of a sphere = ]
7. If f(x) = x2 - 2x + 4, then f (T + 2) = ?
8. In the circle illustrated, the radius is 8 feet. The measure of central angle AOB is 60°. What is the length, in feet, of arc AB?
9. If x = 4y + 2, what is y + 6 in terms of x?
10. If sin then cos θ = ?
11. If logbx = g and logby = p, then logb = ?
12. The measures of a and b are 35° and 44°, respectively. The length of is 12 miles. Which of the following expressions, if any, gives the approximate distance, in miles, of side ?
[Note: The law of sines states that the ratio between the length of the side opposite an angle and the sine of that angle is the same for all interior angles in the same triangle.]
13. When -2 ⤠x ⤠5 and -3 ⤠y ⤠3, what is the maximum possible value for x - y?
14. For how many different integers b (consider positive integers, negative integers, and zero) does x2 + bx + 20 factor into linear factors with integer coefficients?
15. m and n are prime numbers. If is a rational number, then (m)(n) = ?