Question 1

Find a polynomial with leading coefficient of   , degree   , and zeros: -   .

Accepted Answer

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 
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

Question 2

Use synthetic division to decide whether   is a zero of     ;

Accepted Answer

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

Question 3

From a rectangular piece of cardboard having dimensions W = 18 and L = 40 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.

Accepted Answer

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

Question 4

Use the remainder theorem to find     ,

Accepted Answer

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

Question 5

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.

Accepted Answer

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

Question 6

Find a factored form with integer coefficients of the polynomial f shown in the figure.

Accepted Answer

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

Question 7

Find all values of   such that

Accepted Answer

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

Question 8

For the following function, find a number   such that the graph of   contains the point

Accepted Answer

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

Question 9

Use the remainder theorem to find     ,

Accepted Answer

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

Question 10

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 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Find all values of   such that

Accepted Answer

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

Question 14

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

Question 15

Poiseuille's law states that the blood flow rate F ( in L/min ) through a major artery is directly proportional to the product of the fourth power of the radius r and the blood pressure P. During heavy exercise, normal blood flow rates sometimes triple. If the radius of a major artery increases by 10%, approximately how much harder must the heart pump?

Accepted Answer

A) about 3.19 times as hard 
B) about 1.80 times as hard 
C) about 2.05 times as hard 
D) about 1.46 times as hard 
E) about 1.68 times as hard 
A) about 3.19 times as hard 
B) about 1.80 times as hard 
C) about 2.05 times as hard 
D) about 1.46 times as hard 
E) about 1.68 times as hard

Question 16

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 17

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?

Accepted Answer

A) t = 10 
B) t = 8 
C) t = 5 
D) t = 6 
E) t = 4 
A) t = 10 
B) t = 8 
C) t = 5 
D) t = 6 
E) t = 4

Question 18

Salt water of concentration 0.1 pound of salt per gallon flows into a large tank that initially contains 72 gallons of pure water. If the flow rate of salt water into the tank is 6 gal/min, find a formula for the salt concentration   (in lb/gal) after t minutes.

Accepted Answer

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

Question 19

A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zero 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 20

Find all solutions of the equation.

Accepted Answer

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

Find a polynomial with leading coefficient of , degree , and zeros: - .

Use synthetic division to decide whether is a zero of ;

Use the remainder theorem to find ,

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.

Find a factored form with integer coefficients of the polynomial f shown in the figure.

Find all values of such that

For the following function, find a number such that the graph of contains the point

Use the remainder theorem to find ,

Find the quotient and remainder if is divided by . ,

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 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

Find all values of such that

Find the quotient and remainder if is divided by . ,

Salt water of concentration 0.1 pound of salt per gallon flows into a large tank that initially contains 72 gallons of pure water. If the flow rate of salt water into the tank is 6 gal/min, find a formula for the salt concentration (in lb/gal) after t minutes.

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

Find all solutions of the equation.

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

Exam 4: Polynomial and Rational Functions

Find a polynomial with leading coefficient of , degree , and zeros: - .

Use synthetic division to decide whether is a zero of ;

Use the remainder theorem to find ,

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.

Find a factored form with integer coefficients of the polynomial f shown in the figure.

Find all values of such that

For the following function, find a number such that the graph of contains the point

Use the remainder theorem to find ,

Find the quotient and remainder if is divided by . ,

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 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

Find all values of such that

Find the quotient and remainder if is divided by . ,

Salt water of concentration 0.1 pound of salt per gallon flows into a large tank that initially contains 72 gallons of pure water. If the flow rate of salt water into the tank is 6 gal/min, find a formula for the salt concentration (in lb/gal) after t minutes.

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

Find all solutions of the equation.

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 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