# AB_Practice_Test_2

Education

48

All Questions

29

Multiple Choice

0

True False

19

Essay

0

Short Answer

0

Not Answered

Q 1

In what interval is increasing?
A)
B)
C)
D)

Free

Multiple Choice

C

Q 2

Find the limit increasing?
A)0
B)1
C)-1
D)The limit does not exist.

Free

Multiple Choice

D

Q 3

Find for .
A)
B)
C)
D)

Free

Multiple Choice

D

Q 4

The position of a particle moving along the x-axis is given by .What is the speed of the particle at ?
A)66
B)-106
C)90
D)100

Multiple Choice

Q 5

A region R is bounded by the curve and the y-axis.What is the volume generated when region R is rotated about the y-axis?
A)
B)
C)
D)

Multiple Choice

Q 6

Which of the following statements is true for ? I. is always increasing, .
II)The tangent to the curve at is horizontal.
III)The Mean Value Theorem can be applied to in the closed interval .
A)I only
B)II only
C)III only
D) I,II,and III

Multiple Choice

Q 7

The acceleration of a model car along an incline is given by cm/sec,for .If cm/sec,what is ?
A) cm/sec
B) cm/sec
C) cm/sec
D) cm/sec

Multiple Choice

Q 8

If ,then has how many points of inflection?
A)2
B)0
C)1
D)3

Multiple Choice

Q 9

A particle moves along the x-axis so that its velocity for is given by .At what time is the acceleration of the particle a minimum?
A)
B)
C)
D)0

Multiple Choice

Q 10

What is the value of ?
A)-3
B)4
C)π
D)The limit does not exist.

Multiple Choice

Q 11

Which of the following is the equation of the tangent to the curve of at ?
A)
B)
C)
D)

Multiple Choice

Q 12

If ,what is in terms of x?
A)
B)
C)
D)

Multiple Choice

Q 13

What is the slope of the line normal to the curve at the point where ?
A)
B)5
C)
D)-5

Multiple Choice

Q 14

Let in the interval .What is the average rate of change of y with respect to x in this interval?
A)
B)
C)
D)

Multiple Choice

Q 15

Find k so that the relative minimum of occurs at .
A)9
B)3
C)-6
D)

Multiple Choice

Q 16

The concentration of an anti-inflammatory drug in the bloodstream t mins after taking a single dose is , .At what time is the concentration the greatest?
A)70 minutes
B)4900 minutes
C)8 minutes
D)35 minutes

Multiple Choice

Q 17

If ,what is a?
A)No such value of a exists.
B)40
C)-5
D)-8

Multiple Choice

Q 18

The volume of an open-topped rectangular box is 24 cm

^{3},and the length of the rectangular base is twice as long as its width.What is the width of the base so that the surface area of the open box is minimized? A) B) C) D) Multiple Choice

Q 19

The base of a solid is bounded by the curve ,the x-axis,and the line .The cross sections,taken perpendicular to the x-axis,are squares.Find the volume of the solid.
A)4
B)
C)32π
D)32

Multiple Choice

Q 20

Two cars are converging on a point P as they drive at right angles to each other.Car A is traveling at 70 miles per hour and car B is traveling at 33 miles per hour.At the instant when car A is 11 miles from the point P and car B is 10 miles from the point P,at what rate is the distance between the cars decreasing? Round the answer to three decimal places.
A)8.341 miles per hour
B)22.198 miles per hour
C)51.796 miles per hour
D)73.994 miles per hour

Multiple Choice

Q 21

A line tangent to the curve at the point has a slope of -1.What is the x-intercept of this tangent? Round the answer to three decimal places.
A)14.3
B)0.938
C)1.118
D)0.254

Multiple Choice

Q 22

Consider the function in the open interval .How many times are the tangents to parallel to the line ?
A)8
B)9
C)never
D)7

Multiple Choice

Q 23

What is the sum of all k values that satisfy ?
A)19
B)
C)1
D)

Multiple Choice

Q 24

A bug travels along the y-axis such that its velocity,in centimeters per second,is given by ,and t is in seconds.Find the total distance traveled by the bug in the first 1.8 sec.Round the answer to three decimal places.
A)284.129 cm
B)243.49 cm
C)106.079 cm
D)288.644 cm

Multiple Choice

Q 25

Consider a differentiable function that has an x-intercept of 2 and a y-intercept of 4.In the interval , is decreasing and concave down.Which of the following must be true?
I)The Mean Value Theorem is satisfied when .
II) .
III)A tangent approximation of the function for any value in the interval will underestimate the function value.
A)I only
B)II only
C)III only
D)I and II only

Multiple Choice

Q 26

What is the area of the regions between and on the interval ?
A)0.628
B)2.037
C)2.405
D)2.926

Multiple Choice

Q 27

The volume of the solid generated by revolving the region enclosed between the graph of ,the y axis,and the lines and about the x axis is given by which of the following integral expression?
A)
B)
C)
D)

Multiple Choice

Q 28

The rate of decay of a radioactive isotope is directly proportional to the amount remaining.If the half-life of the radioactive isotope,Einsteinium,is 276 days and a sample initially weighs 25 grams,what is its rate of decay on the 150th day? Round your answer to three decimal places.
A)-0.043 grams per day
B)-0.021 grams per day
C)-17.182 grams per day
D)-107.389 grams per day

Multiple Choice

Q 29

A region is bounded by the function ,the line ,and the x-axis.A solid is formed when the region is rotated about the line .What is the radius of the volume of rotation?
A)
B)
C)
D)

Multiple Choice

Q 30

Region R is bounded by the functions , ,and the x-axis as shown in the figure above.
-What is the area of region R? Round the answer to three decimal places.

Essay

Q 31

Find the volume of the solid generated when region R is rotated about the x-axis.Round the answer to three decimal places.

Essay

Q 32

Find all values c for and in the closed interval for which each function equals the average value in the indicated interval.Round the answers to three decimal places if necessary.

Essay

Q 33

A particle is moving along the x-axis with velocity ,for .The initial position of the particle is -1.6.
-At what time(s)in the open interval does the particle change direction? Round the answers to three decimal places.

Essay

Q 34

Where is the particle when it is farthest to the left? Round the answer to three decimal places.

Essay

Q 35

How far does the particle travel in the interval 3 ≤ t ≤ 6 ? Round the answer to three decimal places.

Essay

Q 36

At what times in the closed interval is the speed of the particle decreasing? Round the answers to three decimal places.

Essay

Q 37

1
1
10
2 2
2
4
0 3
3
3
1 4
4
2
0 10
2
1
The functions and are differentiable for all real numbers,and is strictly decreasing.The table above gives values of the functions and their first derivatives at selected values of x.The function is given by .
-Use linear approximation to estimate the value of at .

Essay

Q 38

Explain why there must be a value c on the interval such that .

Essay

Q 39

Let .Find the value of .

Essay

Q 40

Find .

Essay

Q 41

Consider the differential equation for .
-On the axes provided,sketch a slope field for the given differential equation at the 11 points indicated.

Essay

Q 42

If ,then find the particular solution to the given differential equation.

Essay

Q 43

Draw a function through the point on your slope field which represents an approximate solution of the given differential equation with initial condition .

Essay

Q 44

Consider the function .
-Evaluate and interpret its meaning.

Essay

Q 45

What is the equation of the tangent to at ?
Use the tangent to approximate at .
Is the approximation greater or less than the actual value of at ?

Essay

Q 46

Consider the functions and ,as shown above,in the closed interval .
-Let be the vertical distance between the functions.Find the value of x in the open interval ,where is a maximum value.Explain your reasoning.

Essay

Q 47

At what value of x in the open interval is the rate of change of increasing the most rapidly? Explain your reasoning.

Essay

Q 48

For ,find the x-coordinate of all points at which has horizontal tangents on the open interval .

Essay