PSAT Math Multiple-Choice Practice Test 9: Advanced Math

1.

The circle shown above has its center at O. If x = 60 and the length of minor arc AB is 2π, what is the area of circle O?

2. A circle with center O has diameter AB. Segment AC is tangent to the circle at point A and has a length of 5. If the area of the circle is 36π, what is the perimeter of triangle ABC?

3. What is the center of a circle with equation x² + y² - 2x + 8y + 8 = 0?

4.

In the figure above, what is the value of b, in terms of a?

5.

Cone A and Cone B are both right circular cones with the same height. If the radius of Cone A is of the radius of Cone B, which of the following is the ratio of the volume of Cone A to the volume of Cone B?

6.

If sin a^o = x, then cos b^o =

C.

7.

In the figure above, O is the center of the circle, the radius of the circle is x, and the length of minor arc PQ is . What is the area of sector POQ?

A.

B.

C.

D.

8. Three spherical balls with radius r are contained in a rectangular box. Two of the balls are each touching 5 sides of the rectangular box and the middle ball. The middle ball also touches four sides of the rectangular box. What is the volume of the space between the balls and the rectangular box?

(Note: The volume of a rectangular solid is given by the equation V = lwh. The volume of a sphere is given by the equation V = πr³).