5 Steps to a 5 AP Calculus BC 2019

162 STEP 4. Review the Knowledge You Need to Score High

8. Find a number in the interval (0, 2) such
   that the sum of the number and its
   reciprocal is the absolute minimum.


9. An open box is to be made using a piece of
   cardboard 8 cm by 15 cm by cutting a
   square from each corner and folding the
   sides up. Find the length of a side of the
   square being cut so that the box will have a
   maximum volume.


10. What is the shortest distance between the

point

(

2,−

1

2

)

and the parabolay=−x^2?

11. If the cost function isC(x)= 3 x^2 +
    5 x+12, find the value ofxsuch that the
    average cost is a minimum.


12. A man with 200 meters of fence plans to
    enclose a rectangular piece of land using a
    river on one side and a fence on the other
    three sides. Find the maximum area that the
    man can obtain.

Part B Calculators are allowed.

13. A trough is 10 meters long and 4 meters
    wide. (See Figure 8.4-2.) The two sides of
    the trough are equilateral triangles. Water is
    pumped into the trough at 1 m^3 /min. How
    fast is the water level rising when the water
    is 2 meters high?

4 m

10 m

Figure 8.4-2

14. A rocket is sent vertically up in the air with
    the position functions= 100 t^2 wheresis
    measured in meters andtin seconds. A
    camera 3000 m away is recording the
    rocket. Find the rate of change of the angle
    of elevation of the camera 5 sec after the
    rocket went up.


15. A plane lifts off from a runway at an angle
    of 20◦. If the speed of the plane is 300 mph,
    how fast is the plane gaining altitude?


16. Two water containers are being used. (See
    Figure 8.4-3.)

10 ft

4 ft

6 ft

8 ft

Figure 8.4-3

One container is in the form of an inverted

right circular cone with a height of 10 feet

and a radius at the base of 4 feet. The other

container is a right circular cylinder with a

radius of 6 feet and a height of 8 feet. If

water is being drained from the conical