1. Find the rate of change of the volume of a sphere with respect to the radiusr. What is the rate whenr=3?

a) dVdr=4r2;rate=18

b) dVdr=4r;rate=12

c) dVdr=2r;rate=6

d) dVdr=4r2;rate=36

e) dVdr=2r2;rate=18

2. Find the rate of change of the surface area of a sphere with respect to the radiusr. What is the rate whenr=6?

a) dSdr=8r;rate=48

b) dSdr=2r;rate=12

c) dSdr=4r;rate=24

d) dSdr=4r2;rate=144

e) dSdr=8r2;rate=288

3. An object moves along a coordinate line, its position at each timet0is given byx(t)=t2+t+2. Find the velocity at timet0=5.

a) 1

b) 18

c) 9

d) 19

e) 11

4. An object moves along thex-axis, its position at each timet0is given byx(t)=14t483t3+6t2. Determine the time interval(s), if any, during which the object moves right.

a) (0,43)(4,)

b) (2,6)

c) (0,2)(6,)

d) (0,1)(3,)

e) (0,2)(9,)

5. An object is dropped and hits the ground 0.5 second(s) later. From what height, in feet, was it dropped?

a) 0

b) 4

c) 20

d) 10

e) 14

6. A stone is thrown upward from ground level. The initial speed is 96 feet per second. In how many seconds will the stone hit the ground?

a) 5

b) 6

c) 10

d) 12

e) 8

7. A particle is moving along the parabolax2=4(y+3). As the particle passes through the point(8,13), the rate of change of itsy-coordinate is 2 units per second. How fast, in units per second, is thex-coordinate changing at this instant?

a) 34

b) 13

c) 12

d) 12

e) 8

8. A heap of rubbish in the shape of a cube is being compacted into a smaller cube. Given that the volume decreases at a rate of 3 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 64 cubic meters.

a) 116

b) 16

c) 48

d) 3

e) 316

9. A rectangle is inscribed in a circle of radius 3 inches. If the length of the rectangle is decreasing at the rate of 2 inches per second, how fast is the area changing at the instant when the length is 4 inches?

a) 165-in2/sec

b) 45-5in2/sec

c) 85-3in2/sec

d) 45-5in2/sec

e) 85-in2/sec

10. A spherical snowball is melting in such a manner that its radius is changing at a constant rate, decreasing from 36 cm to 14 cm in 30 minutes. At what rate, in cm³per minute, is the volume of the snowball changing at the instant the radius is 3 cm?

a) 2645

b) 825

c) 1325

d) 198

e) 665

11. A 13-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 4 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 5 feet from the wall?

a) 1193

b) 11912

c) 1193

d) 1196

e) 1196

12. A man standing 10 feet from the base of a lamppost casts a shadow 6 feet long. If the man is 6 feet tall and walks away from the lamppost at a speed of 50 feet per minute, at what rate, in feet per minute, will the length of his shadow be changing?

a) 60

b) 30

c) 15

d) 60

e) 30