Question 1

Find, if possible,   .

Accepted Answer

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

Question 2

Use matrices to solve the system.

Accepted Answer

A)    
B)    
C)    
D) The system is dependent 
E) No solution 
A)    
B)    
C)    
D) The system is dependent 
E) No solution

Question 3

Find the determinant of the matrix.

Accepted Answer

A) 1,616.95 
B) 4,850.85 
C) 3,233.9 
D) 6,467.8 
E) 461.99 
A) 1,616.95 
B) 4,850.85 
C) 3,233.9 
D) 6,467.8 
E) 461.99

Question 4

Find, if possible,   .

Accepted Answer

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

Question 5

Three average monthly low temperatures for Detroit are listed in the table.  
Let   correspond to January,   to February, . . . , and   to December. Determine a quadratic function   that interpolates the data - that is, determine the constants a, b, and c such that   , and   .

Accepted Answer

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

Question 6

Find the partial fraction decomposition.

Accepted Answer

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

Question 7

Use the method of substitution to solve the system.

Accepted Answer

A)    
B)    
C)    
D)    
E) no solution 
A)    
B)    
C)    
D)    
E) no solution

Question 8

Use the method of substitution to solve the system.

Accepted Answer

A) ( - 3, -16 ) 
B) ( - 3, -16 ), ( 6, 11 ) 
C) ( 6, 11 ) 
D) ( - 3, -16 ), ( 5, 11 ) 
E) no solution 
A) ( - 3, -16 ) 
B) ( - 3, -16 ), ( 6, 11 ) 
C) ( 6, 11 ) 
D) ( - 3, -16 ), ( 5, 11 ) 
E) no solution

Question 9

Let   be the identity matrix of order 2, and let   . Find the polynomial   for the given matrix A in order to find the zeros of   .
(In the study of matrices,   is the characteristic polynomial of A, and the zeros of   are the characteristic values (eigenvalues) of A.)

Accepted Answer

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

Question 10

Find the partial fraction decomposition.

Accepted Answer

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

Question 11

A small firm manufactures bookshelves and desks for microcomputers. For each product it is necessary to use a table saw and a power router. To manufacture each bookshelf, the saw must be used for   hour and the router for 1 hour. A desk requires the use of each machine for 2 hours. The profits are $20 per bookshelf and $50 per desk. If the saw can be used for 8 hours per day and the router for 12 hours per day, how many bookshelves and desks should be manufactured each day to maximize the profit?

Accepted Answer

A) 4 bookshelves and 2 desks 
B) 4 bookshelves and 4 desks 
C) 2 bookshelves and 4 desks 
D) 0 bookshelves and 2 desks 
E) 4 bookshelves and 0 desks 
A) 4 bookshelves and 2 desks 
B) 4 bookshelves and 4 desks 
C) 2 bookshelves and 4 desks 
D) 0 bookshelves and 2 desks 
E) 4 bookshelves and 0 desks

Question 12

Find the partial fraction decomposition.

Accepted Answer

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

Question 13

A hospital dietician wishes to prepare a corn-squash vegetable dish that will provide at least   grams of protein and cost no more than   cents per serving. An ounce of creamed corn provides   gram of protein and costs   cents. An ounce of squash supplies   gram of protein and costs   cents. For taste, there must be at least   ounces of corn and at least as much squash as corn. It is important to keep the total number of ounces in a serving as small as possible. Find the combination of corn and squash that will minimize the amount of ingredients used per serving.

Accepted Answer

A)    ounces of corn and   ounces of squash 
B)    ounces of corn and   ounces of squash 
C)    ounces of corn and   ounces of squash 
D)    ounces of corn and   ounces of squash 
E)    ounces of corn and   ounces of squash 
A)    ounces of corn and   ounces of squash 
B)    ounces of corn and   ounces of squash 
C)    ounces of corn and   ounces of squash 
D)    ounces of corn and   ounces of squash 
E)    ounces of corn and   ounces of squash

Question 14

Find the determinant of the matrix after introducing zeros.

Accepted Answer

A) - 9 
B) - 8 
C) - 10 
D) 7 
E) 0 
A) - 9 
B) - 8 
C) - 10 
D) 7 
E) 0

Question 15

Find, if possible,   .

Accepted Answer

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

Question 16

A shop specializes in preparing blends of gourmet coffees. From Colombian, Costa Rican, and Kenyan coffees, the owner wishes to prepare 3-pounds bags that will sell for $8.50. The cost per pound of these coffees is $10, $6, and $8, respectively. The amount of Colombian is to be three times the amount of Costa Rican. Find the amount of each type of coffee in the blend.

Accepted Answer

A) 1.275 lb Colombian , 0.425 lb Costa Rican , 1.3 lb Kenyan 
B) 1.575 lb Colombian , 0.525 lb Costa Rican , 0.9 lb Kenyan 
C) 1.125 lb Colombian , 0.375 lb Costa Rican , 1.5 lb Kenyan 
D) 1.125 lb Colombian , 0.375 lb Costa Rican , 3 lb Kenyan 
E) 1.425 lb Colombian , 0.475 lb Costa Rican , 1.1 lb Kenyan 
A) 1.275 lb Colombian , 0.425 lb Costa Rican , 1.3 lb Kenyan 
B) 1.575 lb Colombian , 0.525 lb Costa Rican , 0.9 lb Kenyan 
C) 1.125 lb Colombian , 0.375 lb Costa Rican , 1.5 lb Kenyan 
D) 1.125 lb Colombian , 0.375 lb Costa Rican , 3 lb Kenyan 
E) 1.425 lb Colombian , 0.475 lb Costa Rican , 1.1 lb Kenyan

Question 17

Solve the system   using the inverse method.

Accepted Answer

A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent 
A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent

Question 18

Find the partial fraction decomposition.

Accepted Answer

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

Question 19

Solve the system   using the inverse method.

Accepted Answer

A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent 
A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent

Question 20

A stationary company makes two types of notebooks: a deluxe notebook with subject dividers, which sells for $1.2, and a regular notebook, which sells for $0.85. The production cost is $1.00 for each deluxe notebook and $0.75 for each regular notebook. The company has the facilities to manufacture between 2,000 and 3,000 deluxe and between 3,000 and 6,000 regular notebooks, but not more than 8,000 altogether. How many notebooks of each type should be manufactured to maximize the difference between the selling prices and the production cost?

Accepted Answer

A) 2,300 deluxe and 5,000 regular 
B) 3,000 deluxe and 6,000 regular 
C) 2,000 deluxe and 6,000 regular 
D) 3,000 deluxe and 5,000 regular 
E) 2,500 deluxe and 5,000 regular 
A) 2,300 deluxe and 5,000 regular 
B) 3,000 deluxe and 6,000 regular 
C) 2,000 deluxe and 6,000 regular 
D) 3,000 deluxe and 5,000 regular 
E) 2,500 deluxe and 5,000 regular

Find, if possible, .

Use matrices to solve the system.

Find the determinant of the matrix.

Find, if possible, .

Three average monthly low temperatures for Detroit are listed in the table. Let correspond to January, to February, . . . , and to December. Determine a quadratic function that interpolates the data - that is, determine the constants a, b, and c such that , and .

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Use the method of substitution to solve the system.

Use the method of substitution to solve the system.

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A in order to find the zeros of . (In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the determinant of the matrix after introducing zeros.

Find, if possible, .

Solve the system using the inverse method.

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Solve the system using the inverse method.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

Exam 9: Systems of Equations and Inequalities

Find, if possible, .

Use matrices to solve the system.

Find the determinant of the matrix.

Find, if possible, .

Three average monthly low temperatures for Detroit are listed in the table. Let correspond to January, to February, . . . , and to December. Determine a quadratic function that interpolates the data - that is, determine the constants a, b, and c such that , and .

Find the partial fraction decomposition.

Use the method of substitution to solve the system.

Use the method of substitution to solve the system.

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A in order to find the zeros of . (In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)

Find the partial fraction decomposition.

Find the partial fraction decomposition.

Find the determinant of the matrix after introducing zeros.

Find, if possible, .

Solve the system using the inverse method.

Find the partial fraction decomposition.

Solve the system using the inverse method.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$