# BC_Practice_Test_2

Education

52

All Questions

33

Multiple Choice

0

True False

19

Essay

0

Short Answer

0

Not Answered

Q 1

If ,then
A)
B)
C)
D)

Free

Multiple Choice

D

Q 2

Let .Which of the following integral expressions represents the area between and the horizontal axis on the interval ?
A)
B)
C)
D)

Free

Multiple Choice

A

Q 3

If is a function which is increasing and concave down on the interval ,then which of the following could be the graph of ?
A)
B)
C)
D)

Free

Multiple Choice

B

Q 4

Let .The first three terms of the Maclaurin series for are
A)
B)
C)
D)

Multiple Choice

Q 5

If ,then the slope of the tangent line to at is
A)-21
B)0
C)21
D)undefined

Multiple Choice

Q 6

Let be the solution to the differential equation .Using Euler's method,starting at the point − with step size ,what is the approximate value of ?
A)8.75
B)-0.75
C)-2.25
D)-1.5

Multiple Choice

Q 7

A particle moves in the xy-plane such that its velocity vector for time is , .If the particle is at the point when ,then what is the position vector of the particle when ?
A)
B)
C)
D)

Multiple Choice

Q 8

Let .Which of the following values are x-intercepts of the graph of ?
A)
B)
C)
D)

Multiple Choice

Q 9

Let on the interval The absolute maximum of on this interval is
A)
B)
C)
D)e

Multiple Choice

Q 10

The Maclaurin series represents the function
A)
B)
C)
D)

Multiple Choice

Q 11

Which one of the following statements is false?
A) diverges.
B) diverges.
C) converges.
D) converges absolutely.

Multiple Choice

Q 12

The tangent line to the curve at intersects the x-axis at
A)
B)
C)-2
D)

Multiple Choice

Q 13

Consider the curve defined by the parametric equations and .For any time t,
A)
B)
C)
D)

Multiple Choice

Q 14

The first four terms of the Taylor expansion for about are .What is the value of ?
A)
B)
C)
D)

Multiple Choice

Q 15

What are all values of x for which the series converges?
A)The series converges for only.
B)
C)
D)

Multiple Choice

Q 16

If on the interval ,then what is the value of c on the interval that satisfies the Mean Value Theorem?
A)
B)
C)
D)

Multiple Choice

Q 17

If and ,then find the value of a such that .
A)
B)
C)
D)

Multiple Choice

Q 18

A particle moves in the xy-plane for time according to the parametric equations and .Which of the following statements about the particle are true?
I)
The particle is moving to the right when .
II)
The particle is moving upward when .
III)
The particle is at rest when
A)I only
B)I and II only
C)II and III only
D)I,II,and III

Multiple Choice

Q 19

If y is a function of x such that and ,then
A)
B)
C)
D)

Multiple Choice

Q 20

Let .The first two nonzero terms of the Taylor expansion for about are
A)
B)
C)
D)

Multiple Choice

Q 21

If and ,then
A)
B)
C)
D)

Multiple Choice

Q 22

What is the area enclosed by the lemniscate ?
A)50
B)
C)
D)25

Multiple Choice

Q 23

What is the value of .
A)
B)
C)
D)Does not exist

Multiple Choice

Q 24

Which of the following gives the length of the curve over the closed interval
A)
B)
C)
D)

Multiple Choice

Q 25

Let .If represents the nth derivative of ,then what is ?
A)
B)
C)
D)

Multiple Choice

Q 26

A particle moves along the x-axis so that its acceleration is for .If the initial velocity of the particle is 12,then what is the average velocity of the particle during the time interval ?
A)36.955
B)35.045
C)61.045
D)37.045

Multiple Choice

Q 27

Oil is pumped continuously from a certain oil well at a rate modeled by the function .Let t be the number of days for a 25-day period and let be measured in barrels per day.To the nearest barrel,according to the model,how much oil will be pumped from the well from the 11th day to the 22nd day?
A)-33,275
B)45,829
C)21,629
D)52,907

Multiple Choice

Q 28

A particle moves in the xy-plane according to the parametric equations and for .What is the average speed of the particle during the time interval ?
A)7.187
B)6.468
C)7.906
D)6.047

Multiple Choice

Q 29

For the function , .If is the inverse of ,what is the slope of the tangent to at the point ?
A)0.276
B)0.226
C)0.251
D)0.211

Multiple Choice

Q 30

If is a function defined on such that ,then which of the following could be the graph of ?
A)
B)
C)
D)

Multiple Choice

Q 31

A particle moves along the x-axis such that its velocity is given by for time .If the particle has position 15 when ,then what is its position when it comes to rest for the first time?
A)14.889
B)14.188
C)16.094
D)14.594

Multiple Choice

Q 32

You may use a calculator for any problem in this section.
The rate that water flows into two identical tanks during a 24-hour period is given by the models below.Both and are measured in gallons per hour for hours,and both tanks are empty at time t = 0.
Tank 1: The graph of consists of the line segments indicated in the figure.
Tank 2:
-What is the value of ? What is the value of ? Give units for both answers.Round your answer to 3 decimal places.
___________
___________

Essay

Q 33

How much water is in Tank 1 after 21 hours? Justify your answer.Round your answer to 3 decimal places.

Essay

Q 34

What is the average rate at which water flows into Tank 2 for the entire 19-hour period? Justify your answer.Round your answer to 3 decimal places.

Essay

Q 35

During the 24-hour period,is there ever a time other than when the amount of water in the two tanks is the same? If yes,find all such values of .If no,explain why not.If needed,round your answer to 3 decimal places.

Essay

Q 36

You may use a calculator for any problem in this section.
Let R be the region enclosed by the graph of and the horizontal line ,as shown in the figure above.
-Find the volume of the solid generated when R is rotated about the line .Round your answer to 3 decimal places.

Essay

Q 37

Region R is the base of a solid.For this solid,each cross section perpendicular to the x-axis is a rectangle whose height is twice as long as the length in R.Find the volume of the solid.Round your answer to 3 decimal.

Essay

Q 38

The vertical line divides region R into two regions with equal areas.Write,but do not solve,an equation involving integral expressions whose solution gives the value .

Essay

Q 39

Consider the function defined on the closed interval whose endpoints are and .
-Find the absolute maximum of on this interval.Justify your answer.Round your answer to 3 decimals.

Essay

Q 40

Find all values of x in the open interval such that .

Essay

Q 41

Determine the point(s)of inflection for .

Essay

Q 42

A particle moves in the xy-plane with position for all real values of given by the parametric equations and .
-Give the coordinates of the velocity vector for any time .

Essay

Q 43

Is the particle moving to the left or right when ? Is the particle moving up or down when ?
A)left and up
B)left and down
C)right and up
D)right and down

Multiple Choice

Q 44

What is the slope of the path of the particle when ?

Essay

Q 45

How fast is the particle moving when its horizontal position is

Essay

Q 46

Give the coordinates of the acceleration vector at a time when the particle is at rest.

Essay

Q 47

Use the values to sketch a slope field for on the axes provided.
A)
B)
C)
D)

Multiple Choice

Q 48

Using Euler's method starting at with step size ,estimate the value of .

Essay

Q 49

Find the particular solution .

Essay

Q 50

Let .
-Find all values of for which converges.

Essay

Q 51

Use the first three terms of to estimate the value of .Round your answer to 3 decimal places.

Essay

Q 52

Show that is a solution to the differential equation .

Essay