Question 1

Find a system of inequalities for the graph shown.

Accepted Answer

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

Question 2

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) 8 bookshelves and 8 desks 
B) 0 bookshelves and 1 desks 
C) 8 bookshelves and 0 desks 
D) 8 bookshelves and 1 desks 
E) 1 bookshelves and 8 desks 
A) 8 bookshelves and 8 desks 
B) 0 bookshelves and 1 desks 
C) 8 bookshelves and 0 desks 
D) 8 bookshelves and 1 desks 
E) 1 bookshelves and 8 desks D

Question 3

Solve the system.

Accepted Answer

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

Question 4

Find, if possible,   .

Accepted Answer

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

Question 5

Let   be the identity matrix of order 2, and let   . Find the polynomial   for the given matrix A. (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 6

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.

Accepted Answer

A) maximum of 12 at   
B) maximum of 14 at   
C) maximum of 16 at   
D) maximum of 0 at   
E) maximum of 18 at   
A) maximum of 12 at   
B) maximum of 14 at   
C) maximum of 16 at   
D) maximum of 0 at   
E) maximum of 18 at

Question 7

Find the partial fraction decomposition.

Accepted Answer

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

Question 8

Use matrices to solve the system.

Accepted Answer

A)    
B)    
C)    
D) The equations are dependent 
E) No solution 
A)    
B)    
C)    
D) The equations are dependent 
E) No solution

Question 9

The data in the table are generated by the function   . Approximate the unknown constants a and b to four decimal places. x
1 2 3 4
F ( x )
0)88834 0.44394 0.22186 0.11087

Accepted Answer

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

Question 10

A manufacturer of tennis rackets makes a profit of $16 on each oversized racket and $10 on each standard racket. To meet dealer demand, daily production of standard rackets should be between 25 and 80, and production of oversized rackets should be between 8 and 33. To maintain high quality, the total number of rackets produced should not exceed 80 per day. How many of each type should be manufactured daily to maximize the profit?

Accepted Answer

A) 47 standard and 8 oversized 
B) 33 standard and 47 oversized 
C) 47 standard and 33 oversized 
D) 25 standard and 8 oversized 
E) 25 standard and 33 oversized 
A) 47 standard and 8 oversized 
B) 33 standard and 47 oversized 
C) 47 standard and 33 oversized 
D) 25 standard and 8 oversized 
E) 25 standard and 33 oversized

Question 11

Three solutions contain a certain acid. The first contains 10% acid, the second 30%, and the third 50%. A chemist wishes to use all three solutions to obtain a 90-liter mixture containing 26% acid. If the chemist wants to use twice as much of the 50% solution as of the 30% solution, how many liters of each solution should be used?

Accepted Answer

A) 43.8 of 10% , 15.4 of 30% , 30.8 of 50% 
B) 46.8 of 10% , 14.4 of 30% , 28.8 of 50% 
C) 49.8 of 10% , 13.4 of 30% , 26.8 of 50% 
D) 45.8 of 10% , 15.4 of 30% , 28.8 of 50% 
E) 46.8 of 10% , 28.8 of 30% , 14.4 of 50% 
A) 43.8 of 10% , 15.4 of 30% , 30.8 of 50% 
B) 46.8 of 10% , 14.4 of 30% , 28.8 of 50% 
C) 49.8 of 10% , 13.4 of 30% , 26.8 of 50% 
D) 45.8 of 10% , 15.4 of 30% , 28.8 of 50% 
E) 46.8 of 10% , 28.8 of 30% , 14.4 of 50%

Question 12

Find the inverse of the matrix if it exists.

Accepted Answer

A)    
B)    
C)    
D)    
E) Does not exist 
A)    
B)    
C)    
D)    
E) Does not exist

Question 13

Use the method of substitution to solve the system.

Accepted Answer

A) ( - 1, -14 ) 
B) ( - 1, -14 ), ( 9, 66 ) 
C) ( - 1, -14 ), ( 8, 66 ) 
D) ( 9, 66 ) 
E) no solution 
A) ( - 1, -14 ) 
B) ( - 1, -14 ), ( 9, 66 ) 
C) ( - 1, -14 ), ( 8, 66 ) 
D) ( 9, 66 ) 
E) no solution

Question 14

Find the determinant of the matrix.

Accepted Answer

A) - 311,324 
B) - 933,969 
C) - 311,323 
D) 311,323 
E) - 103,774 
A) - 311,324 
B) - 933,969 
C) - 311,323 
D) 311,323 
E) - 103,774

Question 15

Find the determinant.

Accepted Answer

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

Question 16

Find the inverse of the matrix if it exists.

Accepted Answer

A)    
B)    
C)    
D)    
E) Does not exist 
A)    
B)    
C)    
D)    
E) Does not exist

Question 17

Find the partial fraction decomposition.

Accepted Answer

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

Question 18

Use matrices to solve the system.

Accepted Answer

A) ( 0, 0, 0) 
B) ( 0, - z, z ) 
C) ( 2, 2, 2 ) 
D) ( 0, z, z ) 
E) The system is inconsistent 
A) ( 0, 0, 0) 
B) ( 0, - z, z ) 
C) ( 2, 2, 2 ) 
D) ( 0, z, z ) 
E) The system is inconsistent

Question 19

Find the partial fraction decomposition.

Accepted Answer

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

Question 20

Use Cramer's rule, whenever possible, to solve the system.

Accepted Answer

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

Find a system of inequalities for the graph shown.

Solve the system.

Find, if possible, .

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

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.

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

Use matrices to solve the system.

The data in the table are generated by the function . Approximate the unknown constants a and b to four decimal places. x 1 2 3 4 F ( x ) 0)88834 0.44394 0.22186 0.11087

Find the inverse of the matrix if it exists.

Use the method of substitution to solve the system.

Find the determinant of the matrix.

Find the determinant.

Find the inverse of the matrix if it exists.

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

Use matrices to solve the system.

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

Use Cramer's rule, whenever possible, to solve the system.

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 a system of inequalities for the graph shown.

Solve the system.

Find, if possible, .

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

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.

Find the partial fraction decomposition.

Use matrices to solve the system.

The data in the table are generated by the function . Approximate the unknown constants a and b to four decimal places. x 1 2 3 4 F ( x ) 0)88834 0.44394 0.22186 0.11087

Find the inverse of the matrix if it exists.

Use the method of substitution to solve the system.

Find the determinant of the matrix.

Find the determinant.

Find the inverse of the matrix if it exists.

Find the partial fraction decomposition.

Use matrices to solve the system.

Find the partial fraction decomposition.

Use Cramer's rule, whenever possible, to solve the system.

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. $Find the partial fraction decomposition.$