# BC_Practice_Test_1

Education

64

All Questions

43

Multiple Choice

0

True False

21

Essay

0

Short Answer

0

Not Answered

Q 1

If ,then
A)
B)
C)
D)

Free

Multiple Choice

D

Q 2

If is a function such that is increasing for and is decreasing for ,then which of the following could be the graph of ?
A)
B)
C)
D)

Free

Multiple Choice

B

Q 3

Find the limit .
A)0
B)
C)
D)∞

Free

Multiple Choice

C

Q 4

Consider the differential equation ,where is the solution to the equation and .Using Euler's method starting at with step size ,what is the approximation for ?
A)-3.5
B)-3
C)-2.5
D)-2

Multiple Choice

Q 5

The equation of the tangent line to the function at is
A)
B)
C)
D)

Multiple Choice

Q 6

The position vector for a particle moving in the -plane for is 1st The slope of the tangent line to the path of the particle at is
A)
B)
C)
D)162.5

Multiple Choice

Q 7

Evaluate .
A)0
B)1
C)2e
D)∞

Multiple Choice

Q 8

The graph of is pictured below.Which of the following statements about are true?
I)A left endpoint approximation is greater than .II.A right endpoint approximation is less than .III.A trapezoidal approximation is less than
A)None are true
B)III only
C)I and III only
D)I,II,and III

Multiple Choice

Q 9

The general solution to the differential equation is
A)
B)
C)
D)

Multiple Choice

Q 10

What is the slope of the curve at the point ?
A)
B)
C)
D)

Multiple Choice

Q 11

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

Multiple Choice

Q 12

The first four terms of the Taylor expansion for about are .What is the value of ?
A)- 6
B)- 3
C)-
D)-

Multiple Choice

Q 13

The graph of has inflection points at
A)- and
only.
B)0 and only.
C)0 and only.
D)- ,0 and
.

Multiple Choice

Q 14

Which of the following series converge?
I) II. III.
A)I only
B)I and II
C)I and III
D)I,II,and III

Multiple Choice

Q 15

If ,then
A)
B)
C)
D)

Multiple Choice

Q 16

Let ,where is pictured above.
-What is the domain of ?
A)All real numbers except -1 and 5
B)
C)
D)

Multiple Choice

Q 17

What is the value of ?
A)0
B)1
C)2
D)4

Multiple Choice

Q 18

The slope of the normal line to at is
A)
B)0
C)
D)10

Multiple Choice

Q 19

A particle moves in the -plane according to the parametric equations and .An expression for the length of the path of the particle from to is
A)
B)
C)
D)

Multiple Choice

Q 20

Which expression below represents the first four terms of the Maclaurin approximation to the area under the curve from to ?
A)
B)
C)
D)

Multiple Choice

Q 21

The slope field at the bottom represents an approximation to the general solution to which differential equation?
A)
B)
C)
D)

Multiple Choice

Q 22

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

Multiple Choice

Q 23

The area enclosed by the polar curve in the interval is
A)
B)
C)
D)

Multiple Choice

Q 24

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

Multiple Choice

Q 25

The acceleration vector of a particle moving in the -plane is ,for .If the velocity vector at is ,then how fast is the particle moving when ?
A)5
B)6
C)
D)

Multiple Choice

Q 26

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

Multiple Choice

Q 27

Evaluate the limit,if it exists: .
A)0
B)1
C)-1
D)The limit does not exist

Multiple Choice

Q 28

The graph of below,consisting of a pair of line segments,is pictured below.
If ,then
A)3
B)4
C)4.5
D)5.5

Multiple Choice

Q 29

If ,what is the average of on the closed interval ? Round your answer to 3 decimal places.
A)-2.101
B)1.810
C)3.233
D)2.942

Multiple Choice

Q 30

A particle moves in the -plane along the path of the curve for time .When the particle is at the point , .What is the value of at the same point?
A)47.400
B)65.581
C)-64.932
D)30.518

Multiple Choice

Q 31

Let be a function defined for such that .How many inflection points does the graph of have on this interval?
A)2
B)3
C)4
D)5

Multiple Choice

Q 32

Which of the following functions has the smallest average value on the given interval?
A) on
B) on
C) on
D) on

Multiple Choice

Q 33

A particle moves along a line for time such that its velocity is .What is the velocity of the particle when its acceleration is zero for the first time?
A)-0.349
B)-0.670
C)-0.047
D)-0.268

Multiple Choice

Q 34

Which of the following series are conditionally convergent?
I) II. III.
A)I only
B)II only
C)I and II
D)I and III

Multiple Choice

Q 35

The base of the right triangle pictured below is 8 centimeters and the angle is increasing at the constant rate of 0.03 radians per second.How fast,in centimeters per second,is the altitude of the triangle increasing when ? Round your answer to 3 decimal places. cm
A)0.900 cm/sec
B)0.751 cm/sec
C)0.874 cm/sec
D)0.970 cm/sec

Multiple Choice

Q 36

Let and let be the equation of the tangent line to at .If is used to produce an estimate for ,then which of the following statements is true?
A) for all values of
.
B) for all values of
.
C) for some values of
and
for other values of
.
D) for at least one value of
.

Multiple Choice

Q 37

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

Multiple Choice

Q 38

What is the total area enclosed between the graphs of the functions and ?
A)213.721
B)211.398
C)220.690
D)232.306

Multiple Choice

Q 39

A large auto dealer is running a special sales promotion.They expect to sell cars at the rate of cars per day for the first days of the sale.According to the model,about how many cars will the dealer sell in the first 20 days of the sale?
A)40
B)156
C)300
D)400

Multiple Choice

Q 40

The base of a certain solid is the region in the first quadrant bounded by the - and -axes and the curve .If each plane cross section of the solid perpendicular to the -axis is a semicircle with diameter across the base,then the volume of the solid is
A)51.108
B)43.442
C)46.508
D)41.909

Multiple Choice

Q 41

Let be a continuous function with the properties that and .What is the value of ?
A)0
B)1
C)7
D)∞

Multiple Choice

Q 42

Consider the differentiable function on the closed interval .What is the value of in the interval that satisfies the Mean Value Theorem? Round your answer to 3 decimal places.
A)1.356
B)1.874
C)1.517
D)1.785

Multiple Choice

Q 43

In the figure below, ,is the shaded region in the first quadrant bounded by the graph of ,the horizontal line ,and the vertical line .
-Find the area of .Round your answer to 3 decimal places.

Essay

Q 44

Find the volume of the solid when is revolved about the horizontal line .Round your answer to 3 decimal places.

Essay

Q 45

The region in the base of a solid.For this solid,each cross section perpendicular to the -axis is a semicircle.Find the volume of the solid.Round your answer to 3 decimal places.

Essay

Q 46

The Taylor expansion for a function about is given by .
-What are all values of for which converges? Enter your answer as an interval.

Essay

Q 47

Find the first three nonzero terms and the general term of .Use the first three terms to estimate the value of .Round your answer to 3 decimal places.

Essay

Q 48

Let be the second degree Taylor polynomial for ,and let be the function such that .If ,find .

Essay

Q 49

A particle moves in the -plane with position vector ,such that and in the time interval .
-At what time is the particle at rest?

Essay

Q 50

Give the velocity vector at .

Essay

Q 51

How fast is the particle moving when ? Round your answer to the nearest whole number.

Essay

Q 52

Is the speed of the particle increasing or decreasing when ?
A)The speed is decreasing at .
B)The speed is increasing at .

Multiple Choice

Q 53

What is the average speed of the particle for the time interval ? Round your answer to 3 decimal places.

Essay

Q 54

Let be a continuous function defined on whose graph,consisting of three line segments and a semicircle centered on the -axis at .Let be the function given by .
-Find the values of and .

Essay

Q 55

For each value and ,find the value or state that it does not exist.

Essay

Q 56

Find the -coordinate of each point at which the graph of has a horizontal tangent line.For each of these points,determine whether has a relative minimum,maximum,or neither a minimum or maximum at the point.Round your answers to 2 decimal places,if necessary.
has a relative maximum at _____________.
has neither a relative maximum nor a relative minimum at _____________.

Essay

Q 57

For ,find all the values of for which the graph of has a point of inflection.

Essay

Q 58

A concrete reservoir in the shape of a triangular prism is being filled with water at the constant rate of 1 cubic feet per minute.The reservoir is 4 feet deep,measures 6 feet across the top,and is 30 feet long,as shown in the figure below.For any time ,let represent the depth of the water in the reservoir,and let represent the width of the rectangular region of water at the top.
a = 30 ft
b = 6 ft
c = 4 ft
-If the reservoir is initially empty,how long will it take to fill completely? Round your answer to the nearest whole number.

Essay

Q 59

How fast is the depth of the water in the reservoir changing when the reservoir is half full? Indicate units of measure.

Essay

Q 60

How fast is the rectangular area of the surface of the water changing when the reservoir is half full? Indicate units of measure.

Essay

Q 61

Consider the function ,for .The graph of is pictured below along with a table of values of .
1
0
2
1.733
3
1.221
4
0.866
5
0.644
6
0.498
7
0.397
-Evaluate .

Essay

Q 62

Find the -coordinate of the relative maximum of .

Essay

Q 63

Use a midpoint Riemann sum with to estimate the value of .Round your answer to 3 decimal places.

Essay

Q 64

Evaluate .

Essay