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AP Calc Exam Review

Total questions: 45

Worksheet time: 1hrs 11mins

Name
Class
Date
1.
a)
A
b)
B
c)
D
d)
E
2.
a)
A
b)
B
c)
D
d)
E
3.
a)
A
b)
C
c)
D
d)
E
4.
a)
A
b)
B
c)
D
d)
E
5.
a)
A
b)
B
c)
C
d)
D
6.

Which of these are applications of the derivative? Select all that apply.

a)

Distance

b)

Displacement

c)

Increasing/Decreasing

d)

Max/min

e)

Instantaneous Velocity

7.

Which of these is NOT an application of the definite integral?

a)

Distance

b)

Displacement

c)

Average Value

d)

Average Rate of Change

8.

What is the derivative of y = sinx?

a)

y' = -cosx

b)

y' = cosx

c)

y' = sin2x

d)

y' = sinxcosx

9.

What is the derivative of tanx?

a)

sec2x

b)

secxtanx

c)

-csc2x

d)

tan2x

10.

What is the derivative of secx?

a)

secx

b)

tan2x

c)

sec2x

d)

secxtanx

11.

What is the derivative?

a)
b)
c)
d)

Undefined

12.
a)
b)
c)
d)
13.
a)
b)
c)
d)
14.

The position of a particle is given by s(t) = 5t2 - 10t. What is the acceleration of the particle?

a)

a(t) = 0

b)

a(t) = 10t

c)

a(t) = 10

d)

a(t) = 10t - 10

15.
The function f is twice differentiable with f(2) = 1, f'(2)=4, and f''(2)=3.  What is the value of the approximation of f(1.9) using the line tangent to the graph of f at x = 2?
a)
0.4
b)
0.6
c)
0.7
d)
1.4
16.
a)
6
b)
2
c)
1
d)
0
17.
f' is given, which could be f?
a)
A
b)
B
c)
C
18.
An absolute maximum must occur at a critical point or at an endpoint.
a)
True
b)
False
19.

A critical number, c, on a function f is a number such that:

a)

f'(c) = 0

b)

f'(c) is undefined

c)

f'(c) = o or f'(c) is undefined

d)

None of the above

20.
What is the integral of sin x?
a)
cos x
b)
-cos x
c)
cos x + C
d)
-cos x + C
21.
Find g(2)
a)
-1/2
b)
-1
c)
1
d)
1/2
22.
Find g'(2)
a)
-1/2
b)
-1
c)
1
d)
DNE
23.
Find g(-3)
a)
-2π
b)
-π
c)
π
d)
2π
24.
Where is g an absolute maximum? (Dont forget how to justify...)
a)
1
b)
-3
c)
2
d)
4
25.
Integrate
a)
A
b)
B
c)
C
d)
D
26.
Use LRAM and 4 subintervals to estimate Area under the curve
a)
A
b)
B
c)
C
d)
D
27.
Find F'
a)
A
b)
B
c)
C
d)
D
28.
What are the value of k for which...
a)
-2
b)
0
c)
2
d)
-2,2, and 0
29.
Find h'(3)
a)
-2
b)
0
c)
1
d)
3
30.
a)
1/2
b)
0
c)
Positive Infinity
d)
Negative Infinity
31.
A bug begins to crawl up a vertical wire at time t = 0.  The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction? 
a)
2
b)
4
c)
6.5
d)
7
32.
Given a graph of f'', which could be a Point of Inflection?
a)
A
b)
B
c)
C
d)
D
33.
Where is the graph not differentiable?
a)
x = -2, -1, 0, 1
b)
x = -2, -1, 1
c)
x = -2, -1
d)
x = -1, 
34.

Which of the following are synonyms for find the derivative?

a)

f'(x)

b)

dy/dx

c)

y'

d)

slope of the tangent line

e)

instantaneous rate of change

35.
The function f has positive 1st derivatives and a negative 2nd derivative. Which of the following could be a table of values for f ? 
a)
A
b)
B
c)
C
36.
Which is true at a?
a)
f'(a) < f''(a) < f(a)
b)
f'(a) < f(a) < f''(a)
c)
f''(a) < f'(a) < f(a)
d)
f'(a) = f''(a) < f(a)
37.
Where does f(x) have a point of inflection?
a)
x = -3
b)
x = 3,-3
c)
x= -1
d)
x = -1,3
38.
A particle's speed is decreasing if
a)
it's acceleration is positive
b)
it's velocity is positive
c)
it's velocity and acceleration have the same sign
d)
it's velocity and acceleration have different signs
39.

An objects distance from its starting point at time t is given by the equation

s(t) = t3 - 6t2 - 4.

What is the speed of the object when its acceleration is 0?

a)

2

b)

-24

c)

12

d)

44

40.

Use the sign chart for f'(x) and the table of f(x). There is ...

a)

a maximum at (-10,5).

b)

an absolute minimum at (-2,0).

c)

a minimum at (20,7).

d)

all of the above

41.

If H(x) = f -1(x), then H'(3) equals

a)

4

b)

1/4

c)

- 1/4

d)

-4

42.
Find dy/dx at a given point.
a)
5/4
b)
4/5
c)
1
d)
-5
43.

Evaluate the derivative at

x = π

a)

-1 - 3/(π3)

b)

9/(π4)

c)

3/(π4)

d)

9

44.

Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec. How fast is the area of the outer circle changing when the diameter is 8 in?

a)

80π in/sec

b)

20π in/sec

c)

60π in/sec

d)

40π in/sec

45.

A hypothetical cube shrinks so that the length of its sides are decreasing at a rate of 4 m/min. At what rate is the volume of the cube changing when the sides are 5 m each?

a)

-296 m3/min

b)

-297 m3/min

c)

-300 m3/min

d)

-307 m3/min

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