تكلم مع الذكاء الاصطناعي
Deck 4: Polynomial and Rational Functions
ملء الشاشة (f)
سؤال
For the following function, find a number 
such that the graph of 
contains the point 
A)
B)
C)
D)
E)
such that the graph of contains the point A)
B)
C)
D)
E)
سؤال
Find all solutions of the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Sketch the graph of 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
Find all values of 
such that 
A)
B)
C)
D)
E)
such that A)
B)
C)
D)
E)
سؤال
A meteorologist determines that the temperature T 
for a certain 24-hour period in winter was given by the following formula. 
is time in hours and 
corresponds to 6 A.M.
A)-16 < t < -24
B)0 < t < 8
C)0 < t < 24
D)16 < t < 24
E)0 < t < 16
for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.A)-16 < t < -24
B)0 < t < 8
C)0 < t < 24
D)16 < t < 24
E)0 < t < 16
سؤال
Show that the number is a zero of 
of the given multiplicity, and express 
as a product of linear factors. 
A)
B)
C)
D)
E)
of the given multiplicity, and express as a product of linear factors. A)
B)
C)
D)
E)
سؤال
Use the remainder theorem to find 
, 
A)f ( 8 ) = 4,576
B)f ( 8 ) = 4,620
C)f ( 8 ) = 4,572
D)f ( 8 ) = 4,580
E)f ( 8 ) = 4,548
, A)f ( 8 ) = 4,576
B)f ( 8 ) = 4,620
C)f ( 8 ) = 4,572
D)f ( 8 ) = 4,580
E)f ( 8 ) = 4,548
سؤال
Use the factor theorem to decide whether 
is a factor of the polynomial. 
; 
A)x - c is not a factor
B)x - c is a factor
is a factor of the polynomial. ; A)x - c is not a factor
B)x - c is a factor
سؤال
Find the polynomial function of degree 
whose graph is shown in the figure. 
A)
B)
C)
D)
E)
whose graph is shown in the figure. A)
B)
C)
D)
E)
سؤال
Find the quotient and remainder if 
is divided by 
. 
, 
A)quotient:
, remainder:
B)quotient:
, remainder:
C)quotient:
, remainder:
D)quotient :
, remainder :
E)quotient:
, remainder:
is divided by . , A)quotient:
, remainder:B)quotient:
, remainder:C)quotient:
, remainder:D)quotient :
, remainder :E)quotient:
, remainder: سؤال
A herd of 575 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose that the number of deer after 
years is given by the following formula. 
where 
How many years does it take for the population to become extinct?
A)t = 8
B)t = 10
C)t = 4
D)t = 5
E)t = 6
years is given by the following formula. where How many years does it take for the population to become extinct?A)t = 8
B)t = 10
C)t = 4
D)t = 5
E)t = 6
سؤال
An aspirin tablet is in the shape of a right circular cylinder. The manufacturer also wishes to market the aspirin in capsule form. The capsule is to be 
centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If 
denotes the radius of a hemisphere, find a formula for the volume of the capsule. 
A)
B)
C)
D)
E)
centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule. A)
B)
C)
D)
E)
سؤال
Find a polynomial with leading coefficient of 
, degree 
, and zeros: - 
.
A)f ( x ) = x 4 - 3x 3 - 26x 2 + 26x + 160
B)f ( x ) = x 4 - 6x 2 - 22x + 40
C)f ( x ) = x 4 - 26x 2 + 48x + 160
D)f ( x ) = x 4 - 3x 3 - 26x 2 + 160
E)f ( x ) = x 4 - 3x 3 - 26x 2 + 48x + 160
, degree , and zeros: - .A)f ( x ) = x 4 - 3x 3 - 26x 2 + 26x + 160
B)f ( x ) = x 4 - 6x 2 - 22x + 40
C)f ( x ) = x 4 - 26x 2 + 48x + 160
D)f ( x ) = x 4 - 3x 3 - 26x 2 + 160
E)f ( x ) = x 4 - 3x 3 - 26x 2 + 48x + 160
سؤال
An arch has the shape of the parabola 
A rectangle is fit under the arch by selecting a point 
on the parabola (see the figure). If 
the rectangle has base 
and height 
. Find the base of a second rectangle that has the same area. 
A)10.85
B)9.85
C)8.85
D)8.62
E)10.8
A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area. A)10.85
B)9.85
C)8.85
D)8.62
E)10.8
سؤال
Use synthetic division to decide whether 
is a zero of 
; 
A)c is a zero of f ( x )
B)c is not a zero of f ( x )
is a zero of ; A)c is a zero of f ( x )
B)c is not a zero of f ( x )
سؤال
سؤال
Sketch the graph of 
for the indicated value of 
. 
A)
B)
C)
D)
E)
for the indicated value of . A)
B)
C)
D)
E)
سؤال
Find all solutions of the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find all solutions of the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find all solutions of the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
A flat metal plate is positioned in an xy-plane such that the temperature T (in 
C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 20 
C, find the temperature at the point Q (6, 5).
A)
B)
C)
D)
E)
C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 20 C, find the temperature at the point Q (6, 5).A)
B)
C)
D)
E)
سؤال
Use synthetic division to decide whether 
is a zero of 
; 
A)c is a zero of f ( x )
B)c is not a zero of f ( x )
is a zero of ; A)c is a zero of f ( x )
B)c is not a zero of f ( x )
سؤال
Find an equation of a rational function 
that satisfies the conditions. vertical asymptote: x = - 8, x = 0
Horizontal asymptote: y = 0
X-intercept: 7; f (8) = 1
A)
B)
C)
D)
E)
that satisfies the conditions. vertical asymptote: x = - 8, x = 0Horizontal asymptote: y = 0
X-intercept: 7; f (8) = 1
A)
B)
C)
D)
E)
سؤال
An arch has the shape of the parabola 
A rectangle is fit under the arch by selecting a point 
on the parabola (see the figure). If 
the rectangle has base 
and height 
. Find the base of a second rectangle that has the same area. 
A)2.61
B)3.61
C)4.61
D)4.46
E)5
A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area. A)2.61
B)3.61
C)4.61
D)4.46
E)5
سؤال
Find a polynomial with leading coefficient of 
, degree 
, and zeros: - 
.
A)f ( x ) = x 4 - 6x 2 - 13x + 15
B)f ( x ) = x 4 - 2x 3 - 28x 2 + 50x + 75
C)f ( x ) = x 4 - 2x 3 - 28x 2 + 75
D)f ( x ) = x 4 - 2x 3 - 28x 2 + 28x + 75
E)f ( x ) = x 4 - 28x 2 + 50x + 75
, degree , and zeros: - .A)f ( x ) = x 4 - 6x 2 - 13x + 15
B)f ( x ) = x 4 - 2x 3 - 28x 2 + 50x + 75
C)f ( x ) = x 4 - 2x 3 - 28x 2 + 75
D)f ( x ) = x 4 - 2x 3 - 28x 2 + 28x + 75
E)f ( x ) = x 4 - 28x 2 + 50x + 75
سؤال
A herd of 575 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose that the number of deer after 
years is given by the following formula. 
where 
How many years does it take for the population to become extinct?
A)t = 10
B)t = 8
C)t = 5
D)t = 6
E)t = 4
years is given by the following formula. where How many years does it take for the population to become extinct?A)t = 10
B)t = 8
C)t = 5
D)t = 6
E)t = 4
سؤال
A thin flat plate is situated in an xy-plane such that the density d ( in lb/ft 2 ) at the point is inversely proportional to the square of the distance from the origin. What is the effect on the density at P if the x- and y-coordinates are each multiplied by 
A)d is multiplied 2
B)d is multiplied 2.83
C)d is multiplied 0.25
D)d is multiplied 0.50
E)d is multiplied 4
A)d is multiplied 2
B)d is multiplied 2.83
C)d is multiplied 0.25
D)d is multiplied 0.50
E)d is multiplied 4
سؤال
Show that the number is a zero of 
of the given multiplicity, and express 
as a product of linear factors. 
A)
B)
C)
D)
E)
of the given multiplicity, and express as a product of linear factors. A)
B)
C)
D)
E)
سؤال
An aspirin tablet is in the shape of a right circular cylinder. The manufacturer also wishes to market the aspirin in capsule form. The capsule is to be 
centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If 
denotes the radius of a hemisphere, find a formula for the volume of the capsule. 
A)
B)
C)
D)
E)
centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule. A)
B)
C)
D)
E)
سؤال
Find all values of 
such that 
A)
B)
C)
D)
E)
such that A)
B)
C)
D)
E)
سؤال
Sketch the graph of 
for the indicated value of 
. 
A)
B)
C)
D)
E)
for the indicated value of . A)
B)
C)
D)
E)
سؤال
A meteorologist determines that the temperature T 
for a certain 24-hour period in winter was given by the following formula. 
is time in hours and 
corresponds to 6 A.M.
A)-8 < t < -24
B)0 < t < 24
C)0 < t < 16
D)8 < t < 24
E)0 < t < 8
for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.A)-8 < t < -24
B)0 < t < 24
C)0 < t < 16
D)8 < t < 24
E)0 < t < 8
سؤال
The period P of a simple pendulum - that is, the time required for one complete oscillation - is directly proportional to the square root of its length l. Express P in terms of l and a constant of proportionality k. If a pendulum 3.8 feet long has a period of 2.3 seconds, find the value of k.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the quotient and remainder if 
is divided by 
. 
, 
A)quotient :
, remainder :
B)quotient:
, remainder:
C)quotient:
, remainder:
D)quotient:
, remainder:
E)quotient:
, remainder:
is divided by . , A)quotient :
, remainder :B)quotient:
, remainder:C)quotient:
, remainder:D)quotient:
, remainder:E)quotient:
, remainder: سؤال
For the following function, find a number 
such that the graph of 
contains the point 
A)
B)
C)
D)
E)
such that the graph of contains the point A)
B)
C)
D)
E)
سؤال
Find the polynomial function of degree 
whose graph is shown in the figure. 
A)
B)
C)
D)
E)
whose graph is shown in the figure. A)
B)
C)
D)
E)
سؤال
Express the statement as a formula that involves the variables u, v and a constant of proportionality k, and determine the value of k from the condition : u is directly proportional to v and if v = 40, then u = 3
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the remainder theorem to find 
, 
A)f ( 7 ) = 3,064
B)f ( 7 ) = 3,094
C)f ( 7 ) = 3,054
D)f ( 7 ) = 3,040
E)f ( 7 ) = 3,059
, A)f ( 7 ) = 3,064
B)f ( 7 ) = 3,094
C)f ( 7 ) = 3,054
D)f ( 7 ) = 3,040
E)f ( 7 ) = 3,059
سؤال
Use the factor theorem to decide whether 
is a factor of the polynomial. 
; 
A)x - c is not a factor
B)x - c is a factor
is a factor of the polynomial. ; A)x - c is not a factor
B)x - c is a factor
سؤال
Find all solutions of the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find all values of 
such that 
A)
B)
C)
D)
E)
such that A)
B)
C)
D)
E)
سؤال
A herd of 575 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose that the number of deer after 
years is given by the following formula. 
where 
How many years does it take for the population to become extinct?
A)t = 4
B)t = 6
C)t = 10
D)t = 8
E)t = 5
years is given by the following formula. where How many years does it take for the population to become extinct?A)t = 4
B)t = 6
C)t = 10
D)t = 8
E)t = 5
سؤال
Find a polynomial with leading coefficient of 
, degree 
, and zeros: - 
.
A)f ( x ) = x 4 - 33x 2 + 50x + 200
B)f ( x ) = x 4 - 2x 3 - 33x 2 + 200
C)f ( x ) = x 4 - 2x 3 - 33x 2 + 33x + 200
D)f ( x ) = x 4 - 2x 3 - 33x 2 + 50x + 200
E)f ( x ) = x 4 - 7x 2 - 18x + 40
, degree , and zeros: - .A)f ( x ) = x 4 - 33x 2 + 50x + 200
B)f ( x ) = x 4 - 2x 3 - 33x 2 + 200
C)f ( x ) = x 4 - 2x 3 - 33x 2 + 33x + 200
D)f ( x ) = x 4 - 2x 3 - 33x 2 + 50x + 200
E)f ( x ) = x 4 - 7x 2 - 18x + 40
سؤال
The period P of a simple pendulum - that is, the time required for one complete oscillation - is directly proportional to the square root of its length l. Express P in terms of l and a constant of proportionality k. If a pendulum 3.5 feet long has a period of 1.3 seconds, find the value of k.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Sketch the graph of 
for the indicated value of 
. 
A)
B)
C)
D)
E)
for the indicated value of . A)
B)
C)
D)
E)
سؤال
Find all solutions of the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Express the statement as a formula that involves the variables u, v and a constant of proportionality k, and determine the value of k from the condition : u is directly proportional to v and if v = 30, then u = 3
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
سؤال
A meteorologist determines that the temperature T 
for a certain 24-hour period in winter was given by the following formula. 
is time in hours and 
corresponds to 6 A.M.
A)13 < t < 24
B)0 < t < 11
C)0 < t < 24
D)-13 < t < -24
E)0 < t < 13
for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.A)13 < t < 24
B)0 < t < 11
C)0 < t < 24
D)-13 < t < -24
E)0 < t < 13
سؤال
Sketch the graph of 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
Use the remainder theorem to find 
, 
A)f ( 3 ) = 228
B)f ( 3 ) = 181
C)f ( 3 ) = 221
D)f ( 3 ) = 235
E)f ( 3 ) = 203
, A)f ( 3 ) = 228
B)f ( 3 ) = 181
C)f ( 3 ) = 221
D)f ( 3 ) = 235
E)f ( 3 ) = 203
سؤال
Use synthetic division to decide whether 
is a zero of 
; 
A)c is not a zero of f ( x )
B)c is a zero of f ( x )
is a zero of ; A)c is not a zero of f ( x )
B)c is a zero of f ( x )
سؤال
For the following function, find a number 
such that the graph of 
contains the point 
A)
B)
C)
D)
E)
such that the graph of contains the point A)
B)
C)
D)
E)
سؤال
Find an equation of a rational function 
that satisfies the conditions. vertical asymptote: x = - 2, x = 0
Horizontal asymptote: y = 0
X-intercept: 3; f (4) = 1
A)
B)
C)
D)
E)
that satisfies the conditions. vertical asymptote: x = - 2, x = 0Horizontal asymptote: y = 0
X-intercept: 3; f (4) = 1
A)
B)
C)
D)
E)
سؤال
Find all solutions of the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the factor theorem to decide whether 
is a factor of the polynomial. 
; 
A)x - c is a factor
B)x - c is not a factor
is a factor of the polynomial. ; A)x - c is a factor
B)x - c is not a factor
سؤال
An arch has the shape of the parabola 
A rectangle is fit under the arch by selecting a point 
on the parabola (see the figure). If 
the rectangle has base 
and height 
. Find the base of a second rectangle that has the same area. 
A)6.66
B)6.74
C)5.74
D)4.74
E)6.1
A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area. A)6.66
B)6.74
C)5.74
D)4.74
E)6.1
سؤال
A thin flat plate is situated in an xy-plane such that the density d ( in lb/ft 2 ) at the point is inversely proportional to the square of the distance from the origin. What is the effect on the density at P if the x- and y-coordinates are each multiplied by 
A)d is multiplied 0.14
B)d is multiplied 7
C)d is multiplied 49
D)d is multiplied 0.02
E)d is multiplied 9.90
A)d is multiplied 0.14
B)d is multiplied 7
C)d is multiplied 49
D)d is multiplied 0.02
E)d is multiplied 9.90
سؤال
Find all solutions of the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
A flat metal plate is positioned in an xy-plane such that the temperature T (in 
C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 30 
C, find the temperature at the point Q (6, 8).
A)
B)
C)
D)
E)
C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 30 C, find the temperature at the point Q (6, 8).A)
B)
C)
D)
E)
سؤال
Find the polynomial function of degree 
whose graph is shown in the figure. 
A)
B)
C)
D)
E)
whose graph is shown in the figure. A)
B)
C)
D)
E)
سؤال
An aspirin tablet is in the shape of a right circular cylinder. The manufacturer also wishes to market the aspirin in capsule form. The capsule is to be 
centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If 
denotes the radius of a hemisphere, find a formula for the volume of the capsule. 
A)
B)
C)
D)
E)
centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule. A)
B)
C)
D)
E)
سؤال
Find all solutions of the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find all solutions of the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find all values of 
such that 
A)
B)
C)
D)
E)
such that A)
B)
C)
D)
E)
سؤال
A flat metal plate is positioned in an xy-plane such that the temperature T (in 
C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 15 
C, find the temperature at the point Q (9, 8).
A)
B)
C)
D)
E)
C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 15 C, find the temperature at the point Q (9, 8).A)
B)
C)
D)
E)
سؤال
Find the quotient and remainder if 
is divided by 
A)
B)
C)
D)
E)
is divided by A)
B)
C)
D)
E)
سؤال
Find all solutions of the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Show that the number is a zero of 
of the given multiplicity, and express 
as a product of linear factors. 
A)
B)
C)
D)
E)
of the given multiplicity, and express as a product of linear factors. A)
B)
C)
D)
E)
سؤال
From a rectangular piece of cardboard having dimensions W = 16 and L = 30 an open box is to be made by cutting out identical squares of area x 2 from each corner and turning up the sides (see Illustration). Find all positive values of x such that the volume of the box V ( x ) > 0. Include only allowable values of x in your answer. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Express the statement as a formula that involves the variables u, v and a constant of proportionality k, and determine the value of k from the condition : u is directly proportional to v and if v = 40, then u = 3
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find an equation of a rational function 
that satisfies the conditions. vertical asymptote: x = - 1, x = 0
Horizontal asymptote: y = 0
X-intercept: 8; f (9) = 1
A)
B)
C)
D)
E)
that satisfies the conditions. vertical asymptote: x = - 1, x = 0Horizontal asymptote: y = 0
X-intercept: 8; f (9) = 1
A)
B)
C)
D)
E)
سؤال
Find all values of 
such that 
A)
B)
C)
D)
E)
such that A)
B)
C)
D)
E)
سؤال
Find the quotient and remainder if 
is divided by 
. 
, 
A)quotient:
, remainder:
B)quotient:
, remainder:
C)quotient :
, remainder :
D)quotient:
, remainder:
E)quotient:
, remainder:
is divided by . , A)quotient:
, remainder:B)quotient:
, remainder:C)quotient :
, remainder :D)quotient:
, remainder:E)quotient:
, remainder: سؤال
Sketch the graph of 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
A thin flat plate is situated in an xy-plane such that the density d ( in lb/ft 2 ) at the point is inversely proportional to the square of the distance from the origin. What is the effect on the density at P if the x- and y-coordinates are each multiplied by 
A)d is multiplied 0.11
B)d is multiplied 0.33
C)d is multiplied 3
D)d is multiplied 9
E)d is multiplied 4.24
A)d is multiplied 0.11
B)d is multiplied 0.33
C)d is multiplied 3
D)d is multiplied 9
E)d is multiplied 4.24
سؤال
The period P of a simple pendulum - that is, the time required for one complete oscillation - is directly proportional to the square root of its length l. Express P in terms of l and a constant of proportionality k. If a pendulum 2.7 feet long has a period of 2.3 seconds, find the value of k.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find all values of 
such that 
.
A)
B)
C)
D)
E)
such that .A)
B)
C)
D)
E)
سؤال
Find all solutions of the equation. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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العب
ملء الشاشة (f)
Deck 4: Polynomial and Rational Functions
1
For the following function, find a number such that the graph of contains the point
A)
B)
C)
D)
E)
such that the graph of contains the point A)
B)
C)
D)
E)
2
Find all solutions of the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
3
Sketch the graph of .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
4
Find all values of such that
A)
B)
C)
D)
E)
such that A)
B)
C)
D)
E)
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5
A meteorologist determines that the temperature T for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.
A)-16 < t < -24
B)0 < t < 8
C)0 < t < 24
D)16 < t < 24
E)0 < t < 16
for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.A)-16 < t < -24
B)0 < t < 8
C)0 < t < 24
D)16 < t < 24
E)0 < t < 16
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6
Show that the number is a zero of of the given multiplicity, and express as a product of linear factors.
A)
B)
C)
D)
E)
of the given multiplicity, and express as a product of linear factors. A)
B)
C)
D)
E)
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7
Use the remainder theorem to find ,
A)f ( 8 ) = 4,576
B)f ( 8 ) = 4,620
C)f ( 8 ) = 4,572
D)f ( 8 ) = 4,580
E)f ( 8 ) = 4,548
, A)f ( 8 ) = 4,576
B)f ( 8 ) = 4,620
C)f ( 8 ) = 4,572
D)f ( 8 ) = 4,580
E)f ( 8 ) = 4,548
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8
Use the factor theorem to decide whether is a factor of the polynomial. ;
A)x - c is not a factor
B)x - c is a factor
is a factor of the polynomial. ; A)x - c is not a factor
B)x - c is a factor
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9
Find the polynomial function of degree whose graph is shown in the figure.
A)
B)
C)
D)
E)
whose graph is shown in the figure. A)
B)
C)
D)
E)
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10
Find the quotient and remainder if is divided by . ,
A)quotient: , remainder:
B)quotient: , remainder:
C)quotient: , remainder:
D)quotient : , remainder :
E)quotient: , remainder:
is divided by . , A)quotient:
, remainder:B)quotient:
, remainder:C)quotient:
, remainder:D)quotient :
, remainder :E)quotient:
, remainder: فتح الحزمة
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11
A herd of 575 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose that the number of deer after years is given by the following formula. where How many years does it take for the population to become extinct?
A)t = 8
B)t = 10
C)t = 4
D)t = 5
E)t = 6
years is given by the following formula. where How many years does it take for the population to become extinct?A)t = 8
B)t = 10
C)t = 4
D)t = 5
E)t = 6
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12
An aspirin tablet is in the shape of a right circular cylinder. The manufacturer also wishes to market the aspirin in capsule form. The capsule is to be centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule.
A)
B)
C)
D)
E)
centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule. A)
B)
C)
D)
E)
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13
Find a polynomial with leading coefficient of , degree , and zeros: - .
A)f ( x ) = x 4 - 3x 3 - 26x 2 + 26x + 160
B)f ( x ) = x 4 - 6x 2 - 22x + 40
C)f ( x ) = x 4 - 26x 2 + 48x + 160
D)f ( x ) = x 4 - 3x 3 - 26x 2 + 160
E)f ( x ) = x 4 - 3x 3 - 26x 2 + 48x + 160
, degree , and zeros: - .A)f ( x ) = x 4 - 3x 3 - 26x 2 + 26x + 160
B)f ( x ) = x 4 - 6x 2 - 22x + 40
C)f ( x ) = x 4 - 26x 2 + 48x + 160
D)f ( x ) = x 4 - 3x 3 - 26x 2 + 160
E)f ( x ) = x 4 - 3x 3 - 26x 2 + 48x + 160
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14
An arch has the shape of the parabola A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area.
A)10.85
B)9.85
C)8.85
D)8.62
E)10.8
A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area. A)10.85
B)9.85
C)8.85
D)8.62
E)10.8
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15
Use synthetic division to decide whether is a zero of ;
A)c is a zero of f ( x )
B)c is not a zero of f ( x )
is a zero of ; A)c is a zero of f ( x )
B)c is not a zero of f ( x )
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16
Does there exist a polynomial of degree 3 with real coefficients that has zeros 9 , - 9, and i ?
A)no
B)yes
A)no
B)yes
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17
Sketch the graph of for the indicated value of .
A)
B)
C)
D)
E)
for the indicated value of . A)
B)
C)
D)
E)
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18
Find all solutions of the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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19
Find all solutions of the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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20
Find all solutions of the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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21
A flat metal plate is positioned in an xy-plane such that the temperature T (in C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 20 C, find the temperature at the point Q (6, 5).
A)
B)
C)
D)
E)
C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 20 C, find the temperature at the point Q (6, 5).A)
B)
C)
D)
E)
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22
Use synthetic division to decide whether is a zero of ;
A)c is a zero of f ( x )
B)c is not a zero of f ( x )
is a zero of ; A)c is a zero of f ( x )
B)c is not a zero of f ( x )
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23
Find an equation of a rational function that satisfies the conditions. vertical asymptote: x = - 8, x = 0
Horizontal asymptote: y = 0
X-intercept: 7; f (8) = 1
A)
B)
C)
D)
E)
that satisfies the conditions. vertical asymptote: x = - 8, x = 0Horizontal asymptote: y = 0
X-intercept: 7; f (8) = 1
A)
B)
C)
D)
E)
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24
An arch has the shape of the parabola A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area.
A)2.61
B)3.61
C)4.61
D)4.46
E)5
A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area. A)2.61
B)3.61
C)4.61
D)4.46
E)5
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25
Find a polynomial with leading coefficient of , degree , and zeros: - .
A)f ( x ) = x 4 - 6x 2 - 13x + 15
B)f ( x ) = x 4 - 2x 3 - 28x 2 + 50x + 75
C)f ( x ) = x 4 - 2x 3 - 28x 2 + 75
D)f ( x ) = x 4 - 2x 3 - 28x 2 + 28x + 75
E)f ( x ) = x 4 - 28x 2 + 50x + 75
, degree , and zeros: - .A)f ( x ) = x 4 - 6x 2 - 13x + 15
B)f ( x ) = x 4 - 2x 3 - 28x 2 + 50x + 75
C)f ( x ) = x 4 - 2x 3 - 28x 2 + 75
D)f ( x ) = x 4 - 2x 3 - 28x 2 + 28x + 75
E)f ( x ) = x 4 - 28x 2 + 50x + 75
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26
A herd of 575 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose that the number of deer after years is given by the following formula. where How many years does it take for the population to become extinct?
A)t = 10
B)t = 8
C)t = 5
D)t = 6
E)t = 4
years is given by the following formula. where How many years does it take for the population to become extinct?A)t = 10
B)t = 8
C)t = 5
D)t = 6
E)t = 4
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27
A thin flat plate is situated in an xy-plane such that the density d ( in lb/ft 2 ) at the point is inversely proportional to the square of the distance from the origin. What is the effect on the density at P if the x- and y-coordinates are each multiplied by
A)d is multiplied 2
B)d is multiplied 2.83
C)d is multiplied 0.25
D)d is multiplied 0.50
E)d is multiplied 4
A)d is multiplied 2
B)d is multiplied 2.83
C)d is multiplied 0.25
D)d is multiplied 0.50
E)d is multiplied 4
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28
Show that the number is a zero of of the given multiplicity, and express as a product of linear factors.
A)
B)
C)
D)
E)
of the given multiplicity, and express as a product of linear factors. A)
B)
C)
D)
E)
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29
An aspirin tablet is in the shape of a right circular cylinder. The manufacturer also wishes to market the aspirin in capsule form. The capsule is to be centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule.
A)
B)
C)
D)
E)
centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule. A)
B)
C)
D)
E)
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30
Find all values of such that
A)
B)
C)
D)
E)
such that A)
B)
C)
D)
E)
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31
Sketch the graph of for the indicated value of .
A)
B)
C)
D)
E)
for the indicated value of . A)
B)
C)
D)
E)
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32
A meteorologist determines that the temperature T for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.
A)-8 < t < -24
B)0 < t < 24
C)0 < t < 16
D)8 < t < 24
E)0 < t < 8
for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.A)-8 < t < -24
B)0 < t < 24
C)0 < t < 16
D)8 < t < 24
E)0 < t < 8
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33
The period P of a simple pendulum - that is, the time required for one complete oscillation - is directly proportional to the square root of its length l. Express P in terms of l and a constant of proportionality k. If a pendulum 3.8 feet long has a period of 2.3 seconds, find the value of k.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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34
Find the quotient and remainder if is divided by . ,
A)quotient : , remainder :
B)quotient: , remainder:
C)quotient: , remainder:
D)quotient: , remainder:
E)quotient: , remainder:
is divided by . , A)quotient :
, remainder :B)quotient:
, remainder:C)quotient:
, remainder:D)quotient:
, remainder:E)quotient:
, remainder: فتح الحزمة
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35
For the following function, find a number such that the graph of contains the point
A)
B)
C)
D)
E)
such that the graph of contains the point A)
B)
C)
D)
E)
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36
Find the polynomial function of degree whose graph is shown in the figure.
A)
B)
C)
D)
E)
whose graph is shown in the figure. A)
B)
C)
D)
E)
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37
Express the statement as a formula that involves the variables u, v and a constant of proportionality k, and determine the value of k from the condition : u is directly proportional to v and if v = 40, then u = 3
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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38
Use the remainder theorem to find ,
A)f ( 7 ) = 3,064
B)f ( 7 ) = 3,094
C)f ( 7 ) = 3,054
D)f ( 7 ) = 3,040
E)f ( 7 ) = 3,059
, A)f ( 7 ) = 3,064
B)f ( 7 ) = 3,094
C)f ( 7 ) = 3,054
D)f ( 7 ) = 3,040
E)f ( 7 ) = 3,059
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39
Use the factor theorem to decide whether is a factor of the polynomial. ;
A)x - c is not a factor
B)x - c is a factor
is a factor of the polynomial. ; A)x - c is not a factor
B)x - c is a factor
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40
Find all solutions of the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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41
Find all values of such that
A)
B)
C)
D)
E)
such that A)
B)
C)
D)
E)
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42
A herd of 575 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose that the number of deer after years is given by the following formula. where How many years does it take for the population to become extinct?
A)t = 4
B)t = 6
C)t = 10
D)t = 8
E)t = 5
years is given by the following formula. where How many years does it take for the population to become extinct?A)t = 4
B)t = 6
C)t = 10
D)t = 8
E)t = 5
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43
Find a polynomial with leading coefficient of , degree , and zeros: - .
A)f ( x ) = x 4 - 33x 2 + 50x + 200
B)f ( x ) = x 4 - 2x 3 - 33x 2 + 200
C)f ( x ) = x 4 - 2x 3 - 33x 2 + 33x + 200
D)f ( x ) = x 4 - 2x 3 - 33x 2 + 50x + 200
E)f ( x ) = x 4 - 7x 2 - 18x + 40
, degree , and zeros: - .A)f ( x ) = x 4 - 33x 2 + 50x + 200
B)f ( x ) = x 4 - 2x 3 - 33x 2 + 200
C)f ( x ) = x 4 - 2x 3 - 33x 2 + 33x + 200
D)f ( x ) = x 4 - 2x 3 - 33x 2 + 50x + 200
E)f ( x ) = x 4 - 7x 2 - 18x + 40
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44
The period P of a simple pendulum - that is, the time required for one complete oscillation - is directly proportional to the square root of its length l. Express P in terms of l and a constant of proportionality k. If a pendulum 3.5 feet long has a period of 1.3 seconds, find the value of k.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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45
Sketch the graph of for the indicated value of .
A)
B)
C)
D)
E)
for the indicated value of . A)
B)
C)
D)
E)
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46
Find all solutions of the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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47
Express the statement as a formula that involves the variables u, v and a constant of proportionality k, and determine the value of k from the condition : u is directly proportional to v and if v = 30, then u = 3
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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48
Does there exist a polynomial of degree 3 with real coefficients that has zeros 7 , - 7, and i ?
A)no
B)yes
A)no
B)yes
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49
A meteorologist determines that the temperature T for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.
A)13 < t < 24
B)0 < t < 11
C)0 < t < 24
D)-13 < t < -24
E)0 < t < 13
for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.A)13 < t < 24
B)0 < t < 11
C)0 < t < 24
D)-13 < t < -24
E)0 < t < 13
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50
Sketch the graph of .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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51
Use the remainder theorem to find ,
A)f ( 3 ) = 228
B)f ( 3 ) = 181
C)f ( 3 ) = 221
D)f ( 3 ) = 235
E)f ( 3 ) = 203
, A)f ( 3 ) = 228
B)f ( 3 ) = 181
C)f ( 3 ) = 221
D)f ( 3 ) = 235
E)f ( 3 ) = 203
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52
Use synthetic division to decide whether is a zero of ;
A)c is not a zero of f ( x )
B)c is a zero of f ( x )
is a zero of ; A)c is not a zero of f ( x )
B)c is a zero of f ( x )
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53
For the following function, find a number such that the graph of contains the point
A)
B)
C)
D)
E)
such that the graph of contains the point A)
B)
C)
D)
E)
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54
Find an equation of a rational function that satisfies the conditions. vertical asymptote: x = - 2, x = 0
Horizontal asymptote: y = 0
X-intercept: 3; f (4) = 1
A)
B)
C)
D)
E)
that satisfies the conditions. vertical asymptote: x = - 2, x = 0Horizontal asymptote: y = 0
X-intercept: 3; f (4) = 1
A)
B)
C)
D)
E)
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55
Find all solutions of the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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56
Use the factor theorem to decide whether is a factor of the polynomial. ;
A)x - c is a factor
B)x - c is not a factor
is a factor of the polynomial. ; A)x - c is a factor
B)x - c is not a factor
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57
An arch has the shape of the parabola A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area.
A)6.66
B)6.74
C)5.74
D)4.74
E)6.1
A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area. A)6.66
B)6.74
C)5.74
D)4.74
E)6.1
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58
A thin flat plate is situated in an xy-plane such that the density d ( in lb/ft 2 ) at the point is inversely proportional to the square of the distance from the origin. What is the effect on the density at P if the x- and y-coordinates are each multiplied by
A)d is multiplied 0.14
B)d is multiplied 7
C)d is multiplied 49
D)d is multiplied 0.02
E)d is multiplied 9.90
A)d is multiplied 0.14
B)d is multiplied 7
C)d is multiplied 49
D)d is multiplied 0.02
E)d is multiplied 9.90
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59
Find all solutions of the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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60
A flat metal plate is positioned in an xy-plane such that the temperature T (in C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 30 C, find the temperature at the point Q (6, 8).
A)
B)
C)
D)
E)
C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 30 C, find the temperature at the point Q (6, 8).A)
B)
C)
D)
E)
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61
Find the polynomial function of degree whose graph is shown in the figure.
A)
B)
C)
D)
E)
whose graph is shown in the figure. A)
B)
C)
D)
E)
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62
An aspirin tablet is in the shape of a right circular cylinder. The manufacturer also wishes to market the aspirin in capsule form. The capsule is to be centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule.
A)
B)
C)
D)
E)
centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule. A)
B)
C)
D)
E)
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63
Find all solutions of the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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64
Find all solutions of the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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65
Find all values of such that
A)
B)
C)
D)
E)
such that A)
B)
C)
D)
E)
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66
A flat metal plate is positioned in an xy-plane such that the temperature T (in C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 15 C, find the temperature at the point Q (9, 8).
A)
B)
C)
D)
E)
C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 15 C, find the temperature at the point Q (9, 8).A)
B)
C)
D)
E)
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67
Find the quotient and remainder if is divided by
A)
B)
C)
D)
E)
is divided by A)
B)
C)
D)
E)
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68
Find all solutions of the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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69
Show that the number is a zero of of the given multiplicity, and express as a product of linear factors.
A)
B)
C)
D)
E)
of the given multiplicity, and express as a product of linear factors. A)
B)
C)
D)
E)
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70
From a rectangular piece of cardboard having dimensions W = 16 and L = 30 an open box is to be made by cutting out identical squares of area x 2 from each corner and turning up the sides (see Illustration). Find all positive values of x such that the volume of the box V ( x ) > 0. Include only allowable values of x in your answer.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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71
Express the statement as a formula that involves the variables u, v and a constant of proportionality k, and determine the value of k from the condition : u is directly proportional to v and if v = 40, then u = 3
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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72
Find an equation of a rational function that satisfies the conditions. vertical asymptote: x = - 1, x = 0
Horizontal asymptote: y = 0
X-intercept: 8; f (9) = 1
A)
B)
C)
D)
E)
that satisfies the conditions. vertical asymptote: x = - 1, x = 0Horizontal asymptote: y = 0
X-intercept: 8; f (9) = 1
A)
B)
C)
D)
E)
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73
Find all values of such that
A)
B)
C)
D)
E)
such that A)
B)
C)
D)
E)
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74
Find the quotient and remainder if is divided by . ,
A)quotient: , remainder:
B)quotient: , remainder:
C)quotient : , remainder :
D)quotient: , remainder:
E)quotient: , remainder:
is divided by . , A)quotient:
, remainder:B)quotient:
, remainder:C)quotient :
, remainder :D)quotient:
, remainder:E)quotient:
, remainder: فتح الحزمة
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75
Sketch the graph of .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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76
A thin flat plate is situated in an xy-plane such that the density d ( in lb/ft 2 ) at the point is inversely proportional to the square of the distance from the origin. What is the effect on the density at P if the x- and y-coordinates are each multiplied by
A)d is multiplied 0.11
B)d is multiplied 0.33
C)d is multiplied 3
D)d is multiplied 9
E)d is multiplied 4.24
A)d is multiplied 0.11
B)d is multiplied 0.33
C)d is multiplied 3
D)d is multiplied 9
E)d is multiplied 4.24
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77
The period P of a simple pendulum - that is, the time required for one complete oscillation - is directly proportional to the square root of its length l. Express P in terms of l and a constant of proportionality k. If a pendulum 2.7 feet long has a period of 2.3 seconds, find the value of k.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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78
Find all values of such that .
A)
B)
C)
D)
E)
such that .A)
B)
C)
D)
E)
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79
Find all solutions of the equation.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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80
Does there exist a polynomial of degree 3 with real coefficients that has zeros 5 , - 5, and i ?
A)yes
B)no
A)yes
B)no
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