AP Multiple Choice Practice Set (G)





4

1. If y  x 5  7 , then a. b. c. d. e. 2.



4 x5  7



dy  dx

3

  4 x x  7  5 x x  7  20 x x  7  20 x x 5  7

3

4

5

3

4

5

3

4

5

3

x2  x 2 x  2 a.  2 lim

b. 0 c. 1 d.

2

e. Limit does not exist 3. If f ( x)  sin x , then f ' ( x) 

x a. x cos x 2 sin x x b. cos x  2x sin x x cos x  sin x c. 2 x sin x  cos x d. x2 2 e. x sin x 2 x cos x x

4ax 3  7 x

4. Given the piecewise function f defined as f ( x)  

x 1

(a  2) x  4 x  1 4

.

For what value of a is f (x) continuous at x  1? a. – 3 b. – 2 c. 1 d. 2 e. 3 5. The graph of y  f ' ( x) is shown to the right. If f (0)  5 , then f (5)  a. b. c. d. e.

5 10 15 20 25

          

y

y = f '(x) x 







6. For the graph of g shown to the right, which of the following statements is NOT true for g (x) ? a. g (6) is undefined. b. c.

lim g ( x)  3 x

lim g ( x) does not exist

x6

d.

g (5)  1

e.

lim g ( x)  1 x5

7. If y   a. b. c.

1 x2  1

x x 1 x x2 1 x 3 x 2  12 2

, then

dy  dx d. e.

x 3 x 1 2



2



x x 1 2

8. The graph of a function f with point C as an inflection point is shown. Which of the following statements is true for the graph of g if g ( x)  2  f ( x) ? a. g (x) is concave down on the interval 2,6 b. g (x) is concave up on the interval 0,8 c. g (x) has an inflection point at x  5 d. g (x) is concave down on the interval 0,3 e. g (x) is concave down on the interval 0,8 9. The volume of a cube is increasing at a rate of 300 cubic inches per minute. At the instant when the edge is 20 inches, at what rate is the length of the edge changing? a. 1/4 inch per minute b. 1/3 inch per minute c. 1/2 inch per minute d. 3/4 inch per minute e. 1 inch per minute 10. If x and y are two positive numbers with a sum of 20, and their product is at a maximum, then which one of the following is true? a. x = 15 and y = 5 b. x = 12 and y = 8 c. x = 14 and y = 6 d. x = 11 and y = 9 e. x = 10 and y = 10

6n 2  1 , then k  n  200  4n  kn2 2

11. If lim a. b. c. d. e.

2 3 6 8 12

12. Given the curve 4 x 2  2 xy  xy 3  3 , find the values of a. b. c. d. e. 13. Let a. b. c. d. e.

dy at the point 1, 1 . dx

5 6 7 9 11

f ( x)  1 only 2 only 1 and 2 1 and 4 4 only

x  1 . Find all the values of x in the interval 1,5 guaranteed by the Mean Value Theorem.

14. If y  A sin x  B cos x , then y 

d2y  dx 2

a. 0 b.

( A  B) sin x  ( A  B) cos x

c.

( A  B) sin x  ( A  B) cos x

AB sin x  AB cos x e. 2 AB sin x cos x d.

2 ? sec x csc x III.  cos 2 x  C 2

15. Which of the following are antiderivatives of f ( x)  I. sin x  C

II.  cos x  C

2

a. b. c. d. e.

2

I only II only I and II only II and III only I, II, and III

16. The graph shown to the right represents y  f ' ( x) . Which of the following could be the graph of y  f (x) ?

y=f'(x) b

a

c

d

x

y

a

b

c

d

a.

b

c

d

b

c

d

c.

a

x

e.

a

x

b.

a d.

a

x

b

c

d

x

b

c

d

x

cd b

17. What is the rate of change of the area A of an equilateral triangle with respect to its side s when s  2 ? a. 0.43 b. 0.50 c. 0.87 d. 1.73 e. 7.00





18. f ( x)  x  3 a.

2

2 3

is increasing for which of the following interval(s)?

 3, 3   , 3  or 

3, 



b. c.

 3,3

d. e.

3,0 or 3,  f (x) is never increasing



 



19. What is the slope of the line normal to the graph of y  a. b. c. d. e.

0.945 1.058 – 1.058 – 2.11 – 3.17

20. If 3x cos y  sin x  y  , then a. b. c. d. e.

3

x2 at x  1? 3x 2  1

cosx  y   3x sin y 3 cos y  cos x  y  3 cos y  cosx  y  cosx  y   3x sin y 3 cos y  cosx  y  cosx  y   3x sin y 3 cos y  cosx  y  cosx  y   3x sin y 3 cos y  cosx  y  cosx  y   3x sin y

dy  dx

3 21. lim 8 x  27 x 3 2

a. b. c. d. e.

2x  3

1 8 27 28 36

22. Point A moves right along the positive x-axis at 7 units per second while B moves upward along the negative y-axis at 2 units per second. At what rate is the distance between A and B changing when A is at 8,0 and B is at 0,6 ? a. –32/5 b. –22/5 c. 22/5 d. 5 e. 32/5

23. A particle moves along the line y  2 x  7 . What is its minimum distance from the origin? a. 0.32 b. 1.40 c. 2.80 d. 3.13 e. 3.50 24. In BCD , let BD  c and CD  b where b and c are both constants and c  b . Let angle BDC   . Find the

instantaneous rate of change of the area of BCD when    if angle α changes at a constant rate of 2 radians

3

per second. (Note: side BC changes length as the measure of α changes.) a. bc 2 b. bc 3

bc 3 2 bc 2 d. 2 e. bc 2 c.

25. Suppose a particle moves on a straight line with a position function s such that its position at any time t is given by s(t )  3t 3  11t 2  8t . In what interval of time is the particle moving to the left? a.  ,0 b. 0,1

1, 8   3 d.  4 ,2  9  e. 2,   c.

26. For which of the following graphs does lim f ( x) exist? x3

I. a. b. c. d. e.

II.

III.

I only II only III only I and III only II and III only 1 E 2 E 3 A 4 A 5 E 6 D 7 D 8 D 9 A 10 E 11 E 12 C 13 B 14 A 15 E 16 A 17 D 18 D 19 C 20 D 21 C 22 C 23 D 24 E 25 D 26 E