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AP Exam Review Part 1

Total questions: 64

Worksheet time: 3hrs 6mins

Name
Class
Date
1.
A function is continuous if the limits to left exist and is equal to the function value.
a)
True
b)
False
2.
If f(x) is continuous at interval [a,b], and f(a) is positive and f(b) is negative, then f(c)=0, where c is include in [a,b].
a)
True
b)
False
3.

Find the limit as x approaches 4

a)

1

b)

5

c)

0

d)

DNE

4.

Find the limit as x approaches 7+

a)

1

b)

5

c)

0

d)

DNE

5.

Find f(4)

a)

1

b)

5

c)

0

d)

DNE

6.

Find the limit as x approaches 7

a)

1

b)

5

c)

0

d)

DNE

7.

Select all the values where f(x) is NOT continuous

a)

1

b)

4

c)

5

d)

9

8.
What is the limit?
a)
5/2
b)
-2/3
c)
Infinity
d)
17/3
9.
What is the limit?
a)
DNE
b)
Infinity
c)
6
d)
12
10.
a)
1/2
b)
0
c)
Positive Infinity
d)
Negative Infinity
11.
a)
I only
b)
I and II Only
c)
I, II, and III
d)
II Only
12.

Find the limit as x approaches -3

a)

0

b)

1

c)

-6

d)

DNE

13.

Find the limit as x approaches -1

a)

-1

b)

1

c)

0

d)

DNE

14.

Is this function continuous?

a)

Yes

b)

No, The limit does not exist

c)

No, the value does not exist

d)

No, the value does not equal the limit.

15.

List the horizontal and vertical asymptotes of the function.

a)

x = 3

b)

x = -3

c)

y = -2

d)

y = 2

16.
a)
A
b)
B
c)
C
d)
D
17.
a)

5

b)

infinity

c)

-1

d)

1

18.
Find the derivative:
y = 3ln(x2-3)
a)
6x/(x2-3)
b)
3/(x2-3)
c)
3x/(x2-3)
d)
9x/(x2-3)
19.
Find the derivative f(x) = xex 
a)
f'(x) = ex
b)
f'(x) = xex + xex
c)
f'(x) = ex - xex
d)
f'(x) = ex + xex
20.

f (x) =e3x

a)

f '(x) =6ex

b)

f '(x) =3e3x

c)

f '(x) =3e2x

d)

f '(x) =e3x

21.

d/dx(esinx) =

a)

esinx

b)

-esinx(cosx)

c)

esinx(cosx)

d)

ecosx

22.
Find the derivative:
y=4ex²
a)
y'=8xex
b)
y'=8xex²
c)
y'=8xe2x
d)
y'=8xe4x²
23.

d/dx ln(x3)

a)

3/x

b)

1/x3

c)

ln(3x2)

d)

1 / 3x2

24.

Find the derivative

a)

A

b)

B

c)

C

d)

D

e)

E

25.

Find the Derivative

a)

A

b)

B

c)

C

d)

D

26.
Which rule would you need to use?
a)
Power Rule
b)
Product Rule
c)
Quotient Rule
d)
Chain Rule
27.
a)
b)
c)
d)
28.
Find h'(3)
a)
-2
b)
0
c)
1
d)
3
29.
Find the second derivative of f(x) = x2 + ex  - cosx
a)
f"(x) = 2 + ex + cosx
b)
f"(x) = 2x + ex + cosx
c)
f"(x) = 2x + xex - cosx
d)
f"(x) = 2x + ex + sinx
30.
a)
Average Rate of Change
b)
Average Value of f
c)
Intermediate Value Theorem
d)
Rolle's Theorem
31.

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

32.

Given u(x) = f(x)g(x), f(2) = 3, g(2) = -3, f '(2) = 5, and g'(2) = 1,

then u'(2) = ?

a)

-12

b)

4

c)

5

d)

12

33.
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
34.

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

35.
During which interval is the object speeding up?
a)
A to B
b)
B to C
c)
D to E
d)
E to F
36.

Find a value for d'(8)

a)

3.3 feet per second

b)

-10 feet per second

c)

-3.3 feet per second

d)

10 feet per second

37.

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

a)

4

b)

1/4

c)

- 1/4

d)

-4

38.
Find dy/dx
a)
A
b)
B
c)
C
d)
D
39.
Find the derivative of the inverse
a)
12
b)
1/12
c)
146
d)
1/146
40.
find y'
a)
A
b)
B
c)
C
d)
D
41.

Find the Derivative

a)

A

b)

B

c)

C

d)

D

42.
Find h'(3)
a)
-2
b)
0
c)
1
d)
3
43.
Use implicit differentiation to find y' for the following equation:   4x cos(y) = 1
a)
y' = cos(y) / x sin(y)
b)
y' = 4x sin(y)
c)
y' = cot(y)
d)
y' = 4 / sec(y)tan(y)
44.

A 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

45.

Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 3 cm/min. How fast is the area of the pool increasing when the radius is 12 cm?

a)

76π cm2min⁡76\pi\ \frac{cm^2}{\min}

b)

72πcm2min⁡72\pi\frac{cm^2}{\min}

c)

77πcm2min⁡77\pi\frac{cm^2}{\min}

d)

62πcm2min⁡62\pi\frac{cm^2}{\min}

46.
a)

A

b)

B

c)

C

d)

D

47.

The function C(x) gives the costs (in dollars) of producing x liters of a certain sauce. What is the best interpretation for the following statement?

The slope of the line tangent to the graph of C at x=12 is equal to 4.

a)

At the time when 12 liters of sauce are produced, the costs increase by 4 dollars.

b)

When the amount of sauce produced is 12 liters, the costs increase at a rate of 4 dollars per liter.

c)

The costs of producing the sauce increase at a rate of 4

dollars per 12 liters.

d)

It costs 4 dollars to produce 12 liters of the sauce.

48.

A tank is being filled with a liquid. The function V gives the volume of liquid in the tank, in liters, after t minutes.

What is the best interpretation for the following statement?

The value of the derivative of V at t=1 is equal to 2.

a)

After 1 minute, the tank was being filled at a rate of 2 liters.

b)

After 1 minute, the tank had 2 liters of liquid.

c)

After 1 minute, the tank was being filled at a rate of 2 liters per minute.

d)

During the first minute, the tank was being filled at a rate of 2 liters per minute.

49.
f' is given, which could be f?
a)
A
b)
B
c)
C
50.
Which could be f?
a)
A
b)
B
c)
C
51.
Given a graph of f'', which could be a Point of Inflection?
a)
A
b)
B
c)
C
d)
D
52.
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)
53.
Where does f(x) have a point of inflection?
a)
x = -3
b)
x = 3,-3
c)
x= -1
d)
x = -1,3
54.
a)
[-2,1]
b)
[-2,3]
c)
[3,5]
d)
[0,1.5] and [3,5]
55.

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

a)

a local maximum at x = -10.

b)

an absolute minimum at x = -2

c)

a local minimum at x = 20

d)

all of the above

56.

What is x-value at which the function below has the same instantaneous rate of change as the average rate of change over the indicated interval?

f(x) = x2 - 3x - 28, [-4,7]

a)

1.5

b)

-1.5

c)

0.5

d)

-0.5

57.

In order for the Extreme Value theorem to apply, which of these must be true. Select all that apply.

a)

It must be discontinuous

b)

It must be closed

c)

It must be open

d)

It must be continuous

58.

The Mean Value Theorem applies to  f(x)=3x−x2f\left(x\right)=3x-x^2 on the interval [2, 5]. Find the value of x where the slope of the tangent line (derivative) is equal to the slope of the secant line (average rate of change)

a)

2

b)

-4

c)

3.5

d)

-2

59.

Find

a)

0

b)

1/ln(5)

c)

1

d)

ln(5)

60.
a)
0
b)
5/3
c)
e5x
d)
DNE
61.

Suppose f(x) = x3 – x.

Use a linear approximation at x = 2 to estimate f(2.5).

a)

10.5

b)

11

c)

11.5

d)

12

62.

The following is a description of what theorem?


If a function is continuous, then it is guaranteed to get every y value in between the endpoints on an interval.

a)

Intermediate Value Theorem

b)

Mean Value Theorem

c)

Exteme Value Theorem

d)

Differentiable Value Theorem

63.

The following is a description of what theorem?


If a function is differentiable, then the derivative must be equal to the Average Rate of Change somewhere on that interval.

a)

Intermediate Value Theorem

b)

Mean Value Theorem

c)

Exteme Value Theorem

d)

Differentiable Value Theorem

64.

The following is a description of what theorem?


If you have a closed, continuous interval, there MUST be an absolute max and min.

a)

Intermediate Value Theorem

b)

Mean Value Theorem

c)

Exteme Value Theorem

d)

Differentiable Value Theorem

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