# AB_Practice_Test_1

Education

61

All Questions

39

Multiple Choice

0

True False

22

Essay

0

Short Answer

0

Not Answered

Q 1

What is
A)
B)
C)
D)

Free

Multiple Choice

B

Q 2

What is the value of
A)2
B)0
C)-2
D)limit does not exist

Free

Multiple Choice

A

Q 3

What is the equation of the normal to
A)
B)
C)
D)

Free

Multiple Choice

D

Q 4

A particle moves along the y-axis so that its position at any time t,for ,is given by .In which interval(s)is the particle speeding up?
A)
B)
C)
D)

Multiple Choice

Q 5

Which of the following statements is (are)false for ?
A)I only
B)II only
C)III only
D)None of the statements is false.

Multiple Choice

Q 6

The region R,bounded by f(x),g(x),and the x-axis,is shown in the diagram above.Which one of the following integrals represents the volume of the solid generated when R is rotated about the line ?
A)
B)
C)
D)

Multiple Choice

Q 7

Let be defined for the closed interval .If M is the y-coordinate of the absolute maximum and m is the y-coordinate of the absolute minimum,what is ?
A)-386
B)8
C)4096
D)386

Multiple Choice

Q 8

Find the equation of the curve that passes through the point (1,4)and has a slope of at any point (x,y)on the curve.
A)
B)
C)
D)

Multiple Choice

Q 9

Find the coordinates of the point on that is closest to the origin.
A)
B)
C)
D)

Multiple Choice

Q 10

Evaluate .
A)
B)0
C)
D)The limit does not exist.

Multiple Choice

Q 11

If ,what is the value of at the point (3,0)?
A)-27
B)29
C)27
D)24.5

Multiple Choice

Q 12

A particle moves in a line with velocity .What is the average velocity of the particle in the closed interval ?
A)
B)
C)
D)

Multiple Choice

Q 13

What is the value of if
is everywhere differentiable?
A)38
B)6
C)35
D)41

Multiple Choice

Q 14

A particle moves along the x-axis with a velocity given by for .If the particle is 5 units to the left of the origin at ,where is the particle at ?
A)25 units to the right of the origin
B)20 units to the right of the origin
C)15 units to the right of the origin
D)4 units to the left of the origin

Multiple Choice

Q 15

The tangent line to the graph of g(x)at the point (2,5)has a slope of -4.Use the equation of the tangent to estimate g(1.96).
A)5.04
B)5.12
C)5.08
D)5.16

Multiple Choice

Q 16

Which of the following is the slope field for ?
A)
B)
C)
D)

Multiple Choice

Q 17

Consider the piecewise function,
Find the value of C so that exists.
A)The limit does not exist
B)
C)
D)

Multiple Choice

Q 18

If ,what is ?
A)
B)
C)
D)

Multiple Choice

Q 19

What is the value of g(2)if
A)88
B)67
C)85
D)79

Multiple Choice

Q 20

Which of the following statements is true for ?
A) has a relative maximum at
.
B) has a y-intercept at
.
C) is decreasing for all
.
D) has a vertical asymptote at
.

Multiple Choice

Q 21

A particle moves along the x-axis.At which time on the velocity versus time graph given above is the particle farthest left of its starting point?
A)C
B)E
C)A
D)D

Multiple Choice

Q 22

If ,what is ?
A)
B)
C)
D)

Multiple Choice

Q 23

A calculator may not be used on this part of the examination.
The graph of consists of four line segments as shown below.Let g be the function given by .Use this information for Problems 26-28.
-What is ?
A)4
B)2
C)6
D)-2

Multiple Choice

Q 24

What is the equation of the tangent to g(x)at the point ?
A)
B)
C)
D)

Multiple Choice

Q 25

Which of the following is false for g(x)?
A)g(x)has a relative maximum at .
B)g(x)has a relative minimum at
C)g(x)has a relative maximum at
D)g(x)is decreasing in the interval

Multiple Choice

Q 26

What is the area of the first closed region to the left of the y-axis,bounded by the curves and ?
A)0.978
B)0.720
C)1.070
D)0.939

Multiple Choice

Q 27

What is the average rate of change of in the interval ?
A)0.011
B)-0.005
C)0.016
D)0.002

Multiple Choice

Q 28

Consider the integral expression .If then which integral below is equivalent to the given integral?
A)
B)
C)
D)

Multiple Choice

Q 29

Let and .If the area between the x-axis and the graph of in the closed interval is 0.115 where ,then what is the value of ? Round your answer to 3 decimal places.
A)8.125
B)8.315
C)8.120
D)8.205

Multiple Choice

Q 30

A solid has its base in the xy-plane,bounded by the x-axis,the y-axis,and the function .If cross sections taken perpendicular to the x-axis are semicircles whose diameters are in the xy-plane,what is the volume of this solid? Round your answer to 3 decimal places.
A)15.347
B)15.781
C)15.379
D)16.009

Multiple Choice

Q 31

Shampoo drips from a crack in the side of a plastic bottle at a rate modeled by ,where is in ounces per minute.If there are 37 ounces in the bottle at ,how many ounces are left in the bottle after 5 minutes? Round your answer to 3 decimal places.
A)31.937
B)23.351
C)39.713
D)41.834

Multiple Choice

Q 32

Consider the function in the closed interval .If the value guaranteed by the Mean Value Theorem in the closed interval is ,then what is the value of ? Round your answer to 3 decimal places.
A)1.158
B)1.338
C)1.438
D)0.978

Multiple Choice

Q 33

The sketch of is shown below,with regions bounded by and the x-axis indicated by P,Q,and R.If
A)-8
B)4
C)-15
D)-2

Multiple Choice

Q 34

The height of a conical sand pile is always twice the radius.If sand is being added to the pile at a rate of ,how fast is the height of the pile increasing when the circumference of the base of the sand pile is ?
A)
B)
C)
D)

Multiple Choice

Q 35

The graphs of and are shown below.If ,use the graphs to find .
A)
B)
C)
D)

Multiple Choice

Q 36

The number of home fires each day in a certain city increases as the temperature drops.The rate of home fires is modeled by ,for days,where midnight on January 1st corresponds to .Which of the following is closest to the approximate number of fires in the first quarter of the year? Round your answer to the nearest whole number.
A)393
B)378
C)356
D)383

Multiple Choice

Q 37

The graphs of the derivatives of three functions,f,g,and h,are given below.Which of the functions has at least one point of inflection in the open interval ?
A)only
B)only
C)only
D)only and

Multiple Choice

Q 38

The price of a newly issued stock varies during the first 10 days after its initial offering and is modeled by ,where t is in days.To the nearest cent,what is the price of the stock when the price of the stock is decreasing most rapidly in the interval ?
A)$7.98
B)$9.49
C)$19.91
D)$20.12

Multiple Choice

Q 39

The graph of is shown on the graph above.For which of the stated interval(s)is the function both increasing and concave up?
A)
B)
C)
D)

Multiple Choice

Q 40

The velocity of a particle moving on the y-axis is given by on the interval .At time ,the particle is 2 units above the origin.Round tour answer to 3 decimal places.
-During what time interval is the particle moving down?

Essay

Q 41

What is the position of the particle when it is farthest south of the origin?

Essay

Q 42

At what time is the particle's average velocity twice the instantaneous velocity on ?

Essay

Q 43

Find the total distance traveled by the particle during the time where ?

Essay

Q 44

A solution is draining through a conical filter into an identical conical container as shown in the diagram to the right.The solution drips from the upper filter into the lower container at a rate of .
Where, .
-How fast is the level in the upper filter dropping when the solution level in the upper filter is at 8 cm?

Essay

Q 45

If the conical filter is initially full,what is the level of the solution in the lower level when the solution level in the upper filter is at 5 cm and how fast is the level in the lower filter rising? Round your answer to 3 decimal places.

Essay

Q 46

How fast is the surface area of the solution in the lower filter increasing when the volume in the upper filter equals the volume in the lower container? Round your answer to 3 decimal places.

Essay

Q 47

A 1,000 gallon tank is initially empty.A valve is opened and water begins to flow into the tank at a variable rate,R(t),in gallons per minute,where t is the number of minutes since the valve was opened.The rate is recorded in the chart and graph below.
t,min
R(t),gal/min
0
0
5
7
15
19
20
33
25
13
35
0
-Approximate the volume of water that flows into the tank for the time interval using a right Riemann sum for the five unequal sub-intervals indicated by the data in the chart.Indicate units of measure.

Essay

Q 48

Approximate the value of using the trapezoidal rule.Indicate units of measure with your answer.Interpret the meaning of your answer in the context of the problem.

Essay

Q 49

At time minutes,a drain is opened at the bottom of the tank and water leaves the tank at a rate of gallons per minute.Set up,but do not evaluate,an integral expression in terms of a single independent variable that represents the volume of the water in the tank at time minutes.

Essay

Q 50

Consider the curve defined by .
-Find in terms of and .

Essay

Q 51

Find the equations of all horizontal tangent lines.

Essay

Q 52

Find the equation of the tangent line at the point .

Essay

Q 53

If at the point ,find .

Essay

Q 54

Use the tangent in question 58 to estimate the value of for the point on the curve.

Essay

Q 55

Let L be the tangent to at any point on the curve as shown in the diagram to the right.
-Show that the -intercept of the tangent to the curve at the point is .

Essay

Q 56

Find the area of the region bounded by the tangent to the curve at ,the curve,and the x-axis.

Essay

Q 57

What is the volume when the region found in question 62 is rotated about the line .

Essay

Q 58

Let be a function defined in the closed interval .The graph of consists of three line segments and a semicircle.Let
-Find

Essay

Q 59

What is the average rate of change of in the interval ?

Essay

Q 60

Identify the x-coordinate of any extrema of on .Explain your reasoning.

Essay

Q 61

Identify the x-coordinate of any points of inflection of in ?

Essay