Question 1

Use synthetic division to find     ;

Accepted Answer

A) f ( 5 ) = 515 
B) f ( 5 ) = 525 
C) f ( 5 ) = 6 
D) f ( 5 ) = 221 
E) f ( 5 ) = 521 
A) f ( 5 ) = 515 
B) f ( 5 ) = 525 
C) f ( 5 ) = 6 
D) f ( 5 ) = 221 
E) f ( 5 ) = 521

Question 2

Find the domain   of   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Find the quotient and remainder if   is divided by

Accepted Answer

A)   
  
B)   
  
C)   
  
D)   
  
E)   
  
A)   
  
B)   
  
C)   
  
D)   
  
E)

Question 4

The pressure P acting at a point in a liquid is directly proportional to the distance d from the surface of the liquid to the point. Express P as a function of d by means of a formula that involves a constant of proportionality k. In a certain oil tank, the pressure at a depth of 6 feet is 354. Find the value of k.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

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.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

Express the statement as a formula that involves the variables w, z, u and a constant of proportionality k, and then determine the value of k from the condition : w varies directly as z and inversely as the square root of u, if z = 3 and u = 4, then w = 18

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Find a polynomial   of degree   that has the indicated zeros and satisfies the given condition.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

When uranium disintegrates into lead, one step in the process is the radioactive decay of radium into radon gas. Radon enters through the soil into home basements, where it presents a health hazard if inhaled. In the simplest case of radon detection, a sample of air with volume V is taken. After equilibrium has been established, the radioactive decay D of the radon gas is counted with efficiency E over time t. The radon concentration C present in the sample of air varies directly as the product of D and E and inversely as the product of V and t. For a fixed radon concentration C and time t, find the change in the radioactive decay count D if V is multiplied by 2 and E is reduced by 14%.

Accepted Answer

A) increases 255.81% 
B) increases 281.40% 
C) increases 175.44% 
D) increases 232.56% 
E) increases 1,428.57% 
A) increases 255.81% 
B) increases 281.40% 
C) increases 175.44% 
D) increases 232.56% 
E) increases 1,428.57%

Question 9

Find the polynomial function of degree   whose graph is shown in the figure.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

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.

Accepted Answer

A) 10.85 
B) 9.85 
C) 8.85 
D) 8.62 
E) 10.8 
A) 10.85 
B) 9.85 
C) 8.85 
D) 8.62 
E) 10.8

Question 11

A canvas camping tent is to be constructed in the shape of a pyramid with a square base. An 8-foot pole will form the center support, as illustrated in the figure. Find the length x of a side of the base so that the total amount of canvas needed for the sides and bottom is 384 ft 2 .

Accepted Answer

A) 14 ft 
B) 13 ft 
C) 12 ft 
D) 11 ft 
E) 10 ft 
A) 14 ft 
B) 13 ft 
C) 12 ft 
D) 11 ft 
E) 10 ft

Question 12

Use synthetic division to decide whether   is a zero of the equation.   ;

Accepted Answer

A) c is not a zero 
B) c is a zero 
A) c is not a zero 
B) c is a zero

Question 13

Show that the number is a zero of   of the given multiplicity, and express   as a product of linear factors.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Does there exist a polynomial of degree 3 with real coefficients that has zeros 5 , - 5, and i ?

Accepted Answer

A) yes 
B) no 
A) yes 
B) no

Question 15

Sketch the graph of   for the indicated value of   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Find the polynomial function of degree   whose graph is shown in the figure.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Find the quotient and remainder if   is divided by   .   ,

Accepted Answer

A) quotient:   , remainder:
  
B) quotient:   , remainder:
  
C) quotient:   , remainder:
  
D) quotient :   , remainder :
  
E) quotient:   , remainder:
  
A) quotient:   , remainder:
  
B) quotient:   , remainder:
  
C) quotient:   , remainder:
  
D) quotient :   , remainder :
  
E) quotient:   , remainder:

Question 19

Use synthetic division to decide whether   is a zero of     ;

Accepted Answer

A) c is a zero of f ( x ) 
B) c is not a zero of f ( x ) 
A) c is a zero of f ( x ) 
B) c is not a zero of f ( x )

Question 20

Express the statement as a formula that involves the variables q, x, y and a constant of proportionality k, and then determine the value of k from the condition : q is inversely proportional to the sum of x and y, if x = 2.5 and y = 3.6, then q = 3.8

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Use synthetic division to find ;

Find the domain of .

Find the quotient and remainder if is divided by

Express the statement as a formula that involves the variables w, z, u and a constant of proportionality k, and then determine the value of k from the condition : w varies directly as z and inversely as the square root of u, if z = 3 and u = 4, then w = 18

Find a polynomial of degree that has the indicated zeros and satisfies the given condition.

Find the polynomial function of degree whose graph is shown in the figure.

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 canvas camping tent is to be constructed in the shape of a pyramid with a square base. An 8-foot pole will form the center support, as illustrated in the figure. Find the length x of a side of the base so that the total amount of canvas needed for the sides and bottom is 384 ft².

Use synthetic division to decide whether is a zero of the equation. ;

Show that the number is a zero of of the given multiplicity, and express as a product of linear factors.

Does there exist a polynomial of degree 3 with real coefficients that has zeros 5 , - 5, and i ?

Sketch the graph of for the indicated value of .

Find the polynomial function of degree whose graph is shown in the figure.

A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.

Find the quotient and remainder if is divided by . ,

Use synthetic division to decide whether is a zero of ;

Express the statement as a formula that involves the variables q, x, y and a constant of proportionality k, and then determine the value of k from the condition : q is inversely proportional to the sum of x and y, if x = 2.5 and y = 3.6, then q = 3.8

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

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Exam 4: Polynomial and Rational Functions

Use synthetic division to find ;

Find the domain of .

Find the quotient and remainder if is divided by

Express the statement as a formula that involves the variables w, z, u and a constant of proportionality k, and then determine the value of k from the condition : w varies directly as z and inversely as the square root of u, if z = 3 and u = 4, then w = 18

Find a polynomial of degree that has the indicated zeros and satisfies the given condition.

Find the polynomial function of degree whose graph is shown in the figure.

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 canvas camping tent is to be constructed in the shape of a pyramid with a square base. An 8-foot pole will form the center support, as illustrated in the figure. Find the length x of a side of the base so that the total amount of canvas needed for the sides and bottom is 384 ft 2 .

Use synthetic division to decide whether is a zero of the equation. ;

Show that the number is a zero of of the given multiplicity, and express as a product of linear factors.

Does there exist a polynomial of degree 3 with real coefficients that has zeros 5 , - 5, and i ?

Sketch the graph of for the indicated value of .

Find the polynomial function of degree whose graph is shown in the figure.

A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.

Find the quotient and remainder if is divided by . ,

Use synthetic division to decide whether is a zero of ;

Express the statement as a formula that involves the variables q, x, y and a constant of proportionality k, and then determine the value of k from the condition : q is inversely proportional to the sum of x and y, if x = 2.5 and y = 3.6, then q = 3.8

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

A canvas camping tent is to be constructed in the shape of a pyramid with a square base. An 8-foot pole will form the center support, as illustrated in the figure. Find the length x of a side of the base so that the total amount of canvas needed for the sides and bottom is 384 ft².