AP CALCULUS SEMESTER EXAM
1. If
, then
A)
C)
B)
D)
2. If
E)
then, at the point
A)
B)
A)
B)
C)
D)
E)
C)
D)
E)
3.
DNE
4. We want to contruct a box with a square base and we only have 30 sq meters of material.
Assuming that all the material will be used in the construction process and that the box
will have a top, determine the maximum volume that the box can have.
A) 2.236 cu in
C) 4.123 cu in
B) 11.180 cu in
D) 12.432 cu in
E) 24.864 cu in
5.
A)
C)
B)
D)
E)
6. Let f be a function that is continuous on the closed interval [-2 , 3] such that
exist,
for all x except x = 0. Which of the following could be the
graph of f ?
A)

D)
y


y



x






x




B)







E)
y


y



x







C)

y

x







x



does not








7.
A)
B)
C)
D)
E)
8.
A)
C)
B)
D)
A)
C)
B)
D)
E)
9.
E)
10. An equation of the line normal to the graph of
at the point where
is
A)
C)
B)
D)
E)
11. The volume of a cone of radius r and height h is given by
the height both increase at a constant rate of
If the radius and
centimeter per second, at what rate, in
cubic centimeters per second, is the volume increasing when the height is 9 centimeters
and the radius is 6 centimeters?
A)
12. If
B)
C)
D)
E)
then
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
13.
14.
The graph of
on the closed interval
inflection does this graph have on this interval?
is shown above. How many points of
A)
2
B)
4
C)
3
15. At what values of x does
5
E)
1
have a relative maximum?
A) -1, 0 and 1
C) 0 only
B) -1 only
D) 1 only
16. If
D)
E) -1 and 1
, then the set of values for which f increases is
A)
C)
B)
D)
E)
17. If f is the continuous, strictly increasing function on the interval
as shown below,
y=
f(
x
)
which of the following must be true?
I
O a
II
III
b
for some
number c such that a<c<b
A) I, II and III
C) I and III only
B) I only
D) II only
E) III only
18. If f is a function such that
, which of the following must be true?
A) The derivative of f(x) at x = 2 is 0
B) f is continuous at x = 0.
C) The limit of f(x) as x approaches 2 does not exist
D) f is not defined at x = 2.
E) f(2) = 0
19. Which of the following functions shows that the statement “ If a function is continuous at
x = 0 , then it is differentiable at x = 0” is false?
A)
B)
D)
E)
where c is a constant, then
20. If
A)
C)
c-5
B)
5-c
C)
5+c
D)
21. Calculate the approximate area under the curve
5
E)
-5
on the interval [1,2] by the
trapezoidal method with divisions at
A)
B)
C)
D)
E)
22. Let g be a continuous function on the closed interval [0,1]. Let g(0) =1 and g(1)=0. Which
of the following is NOT necessarily true?
A) There exists a number h in [0,1] such that
B) There exists a number h in [0,1] such that
C) For all h in the open interval (0,1) ,
D) For all a and b in [0,1], if a = b, then g(a) = g(b)
for all x in [0,1]
E) There exists a number h in [0,1] such that
23. Let f and g be differentiable functions such that
If h(x) = f(g(x)) , then
A)
-9
B)
24.
12
C)
0
D)
-4
E)
15
is
A)
B)
25. The derivative of
A)
-1
B)
26. Given the function defined by
is concave up.
A)
B)
C)
D)
E)
C)
D)
E)
attains its maximum value at x =
C)
0
D)
1
E)
, find all values of x for which the graph of f
27.
A)
B)
C)
D)
E)
C)
D)
E)
, then k =
28. If
A)
B)
29. Let f be the function given by
What are all values of c that satisfy the
conclusion of the Mean Value Theorem of differential calculus on the closed interval [0,
3]?
A)
0 and 3
B)
0 only
C)
3 only
D)
2 and 3
E)
2 only
and the domain is the set of all such x such that
30. If
then the absolute maximum value of the function f occurs when x is
A)
31. If
4
B)
9
C)
2
D)
0
, then
A)
C)
B)
D)
E)
E)
6
,
32. The average value of
A)
over the interval
B)
is
C)
33. Find the tangent line to the curve
A)
C)
B)
D)
D)
E)
at x = 1
E)
34. Corners in the form of sqaures from an 10 inch x 12 inch piece of paper are cut out and
the paper is folded up to create a box without a top. What size cut out will maximize the
volume of the box?
A) .256 in
B)
2.023 in
C)
5.321 in
D)
1.682 in
E)
1.811 in
AP CALCULUS SEMESTER EXAM
Answer Section
1. ANS: E
PTS: 1
2. ANS: A
PTS: 1
3. ANS: A
PTS: 1
4. ANS: B
PTS: 1
5. ANS: C
PTS: 1
6. ANS: A
PTS: 1
7. ANS: E
PTS: 1
8. ANS: E
PTS: 1
9. ANS: B
PTS: 1
10. ANS: A
PTS: 1
11. ANS: C
PTS: 1
12. ANS: E
PTS: 1
13. ANS: C
PTS: 1
14. ANS: C
PTS: 1
15. ANS: B
PTS: 1
16. ANS: D
PTS: 1
d
17. ANS: A
PTS: 1
18. ANS: A
PTS: 1
19. ANS: B
PTS: 1
20. ANS: D
PTS: 1
21. ANS: A
PTS: 1
22. ANS: E
PTS: 1
23. ANS: B
PTS: 1
24. ANS: A
PTS: 1
25. ANS: D
PTS: 1
26. ANS: C
PTS: 1
27. ANS: D
PTS: 1
28. ANS: B
PTS: 1
29. ANS: E
PTS: 1
30. ANS: B
PTS: 1
31. ANS: B
PTS: 1
32. ANS: D
PTS: 1
33. ANS: C
PTS: 1
34. ANS: E
PTS: 1