Math exam help
1.
Which of the following is the correct matrix representation of the October Inventory of small and large tshirts and pants?
Inventory for August  Inventory for September  Inventory for October  
Small  Large  Small  Large  Small  Large  
TShirts  2  3  4  6  7  8 
Pants  1  4  3  5  5  6 
Answer
1.
If find 2A.
Answer
1.
If and find A – B.
Answer
1.
If find 2A.
Answer
1.
Matrix A has dimensions 2 x 3. Matrix B has dimensions 3 x 6. These two matrices can be multiplied to find the product AB.
Answer True False
1.
Evaluate
Answer
Does not exist. 
1.
Evaluate
Answer
Does not exist 
1.
Evaluate
Answer
Does not exist. 
1.
Find the determinant of
Answer
14  
14  
1  
1 
1.
Find the determinant of
Answer
48  
56  
56  
48 
1.
What is the determinant of the following matrix?
Answer
10  
14  
20  
25 
1.
What is the determinant of the following matrix? Does the matrix have an inverse?
Answer
5; no  
5; yes  
1; no  
1; yes 
1.
Is the following system consistent or inconsistent?
8x + y + 4 = 0
y = 8x – 4
Answer
consistent  
inconsistent 
1.
Is the following system consistent or inconsistent?
7x + 6 = 2y
14x 4y + 2 = 0
Answer
consistent  
inconsistent 
1.
Is the following system consistent or inconsistent?
2x – 2y = 6
10x + 10y = 30
Answer
consistent  
inconsistent 
1.
Is the following system consistent or inconsistent?
2y = x – 7
2x – 6y = 14
Answer
consistent  
inconsistent 
1.
Is the following system consistent or inconsistent?
y = 2x + 5
2x + y = 2
Answer
consistent  
inconsistent 
If a system has exactly one solution it is called _______________.
Answer
consistent  
inconsistent  
independent  
dependent 
1.
Does the following system of equations have a solution?
Answer
Yes  
No 
1.
What is the approximate solution of the following system of equations?
Answer
(2, 7)  
(7, 2)  
(7, 2)  
(7, 2) 
1.
Solve the following system of equations by using the substitution method. 3y – 2x = 11 y + 2x = 9
Answer
(2, 5)  
(2, 5)  
(4, 5)  
Inconsistent 
1.
Solve the following system of equations by using the substitution method. y = 3x + 5 5x – 4y = 3
Answer
(1, 2)  
(2, 1)  
(3, 4)  
(1, 2) 
1.
Solve the following system of equations by using the elimination method. x – y = 11 2x + y = 19
Answer
(1, 10)  
(1, 1)  
(12, 2)  
(10, 1) 
1.
Solve the following system of equations by using the elimination method. 4x – 2y = 12 4x + 8y = 24
Answer
(5, 3)  
(6, 6)  
(3, 1)  
(6, 6) 
1.
Solve the following system of equations using matrices. 3x – 2y = 31 3x + 2y = 1
Answer
(5, 8)  
(3, 5)  
(3, 9)  
(2, 8) 
1.
Solve the following system of equations using matrices. 4x + 5y = 7 3x – 6y = 24
Answer
(1, 4)  
(2, 3)  
(5, 6)  
(3, 4) 
1.
The sum of two numbers is 7. Four times the first number is one more than 5 times the second. Find the two numbers.
Answer
2 and 1  
4 and 3  
5 and 7  
2 and 3 
1.
Which of the following is a solution to the following system of inequalities?
Answer
(2, 2)  
(0, 1)  
(1, 0)  
(4, 4) 
1.
Which of the following is a solution to the following system of inequalities?
Answer
(1, 1)  
(4, 0)  
(3, 2)  
(5, 0) 
1.
One possible solution of this system of inequalities is (1, 4).
Answer
TRUE  
FALSE 
1.
What is the system of equations that describes the following graph?
Answer
x + 3y > 4; 3x – y > 2  
x + 3y < 4; 3x – y > 2  
x + 3y < 4; 3x – y < 2  
x + 3y = 4; 3x – y ≥ 2 
1.
What is the system of equations that describes the following graph?
Answer
x + y < 3; x – y > 2; y ≥ 0  
x + y > 3; x – y < 2; x ≥ 0  
x + y < 3; x – y > 2; y ≤ 0  
x + y < 3; x – y > 2; x ≥ 0 
1.
What is the system of equations that describes the following graph?
Answer
x + y < 3; x – y ≥ 2  
2x + 3y ≥ 1; x – y ≥ 2  
2x – y ≥ 13; x + y = 2  
x + y ≥ 32; x – y = 2 
1.
What is the system of equations that describes the following graph?
Answer
y ≥ 0; x ≤ 3  
x > 0; y < 3  
x ≥ 0; y ≤ 3  
x ≤ 0; y ≥ 3 
1.
What is the system of equations that describes the following graph?
Answer
x + 2y ≥ 4; x ≥ 2  
x + 2y ≥ 4; y ≥ 2  
x + 2y > 4; y > 2  
x + 2y > 4; x > 2 
1.
What is the system of equations that describes the following graph?
Answer
x + y ≤ 1; x – y ≥ 4  
x + y > 1; x – y ≥ 4  
x + y ≤ 1; x – y < 4  
x + y ≤ 1; x – y > 4 
1.
What is the system of equations that describes the following graph?
Answer
x > 2; x ≥ 5; y ≤ 6; y > 1  
x ≤ 2; x < 5; y > 6; y ≥ 1  
x ≤ 2; x ≥ 5; y ≤ 6; y ≥ 1  
x ≤ 2; x ≥ 5; y ≤ 6; y ≤ 1 
1.
Solve 3x – y + 2z = 6 x + y = 2 x – 2z = 5
Answer
(1, 3, 3)  
(1, 3, 3)  
(1, 3, 3)  
(1, 3, 3) 
1.
Solve x + y = 9 y + z = 7 x – z = 2
Answer
Infinite number of solutions  
no solutions  
(9, 7, 2)  
(3, 6, 1) 
1.
Solve x + 3y + z = 1 2x – y – z = 6 5x + y + z = 1
Answer
(1, 6, 1)  
(1, 2, 6)  
(2, 1, 4)  
(1, 2, 6) 
1.
Solve 4x + y – 2z = 0 2x – 3y + 3z = 9 6x – 2y + z = 0
Answer
(0, 9, 0)  
(0, 9, 0)  
1.
Solve x – 2y – 3z = 3 3x + y + z = 12 3x – 2y – 4z = 15
Answer
(0, 0, 1)  
(3, 12, 15)  
(3, 9, 6)  
(3, 9, 6) 
1.
Solve 4x + y + z = 1 8x – 4y – 7z = 2 5y – 9z = 3
Answer
1.
Solve x + 3y + 4z = 0 x – 2z = 8 y + z = 3
Answer
1.
In her wallet, Ms. Thompson has onedollar, fivedollar, and tendollar bills, totally $171. She has the same number of fivedollar bills as onedollar and tendollar bills put together. If she has 30 bills in all, how many bills of each denomination does she have?
Answer
11 onedollar bills, 10 fivedollar bills, 9 tendollar bills  
6 onedollar bills, 17 fivedollar bills, 8 tendollar bills  
11 onedollar bills, 16 fivedollar bills, 8 tendollar bills  
6 onedollar bills, 15 fivedollar bills, 9 tendollar bills 
1.
Twice the first number is eleven more than the sum of the other two numbers. The sum of twice the first number and three times the third number is one more than the second number. The second number is equal to the sum of the first number and the third number. Find the three numbers.
Answer
1st number = 6, 2nd number = 3.5, 3rd number = 2.5  
1st number = 8, 2nd number = 4, 3rd number = 1  
1st number = 8, 2nd number = 4, 3rd number = 1  
1st number = 6, 2nd number = 3.5, 3rd number = 2.5 
1.
What is the correct matrix for the inventory of boots in sizes 10 and 12.
Boots  Flats  Sneakers  
Blue  Gray  Blue  Gray  Blue  Gray  
Shoes Size 10  3  5  9  10  1  4 
Shoes Size 12  2  0  2  7  4  0 
Answer
1.
Evaluate
Answer
1.
Evaluate
Answer
1.
Matrix A has dimensions 3 x 2. Matrix B has dimensions 3 x 2. A x B will have dimensions 3 x 2.
Answer
TRUE  
FALSE 
1.
Evaluate
Answer
1.
Evaluate
Answer
1.
Find the determinant of
Answer
0  
6  
10  
5 
1.
Find the determinant of
Answer
0  
20  
10  
20 
1.
The following system of equations is consistent.
Answer
TRUE  
FALSE 
The following system of equations has a solution.
Answer True False
1.
What is the solution to this system of equations?
Answer
(4, 4)  
(4, 4)  
(2, 4)  
(4, 2) 
1.
Solve y = 2x – 4 by the substitution method. 7x – 5y = 14
Answer

1.
Solve 4x + 3y = 13 by the substitution method. x + y = 4
Answer
1.
Solve 9x + 2y = 2 by the elimination methods. 21x + 6y = 4
Answer

1.
Solve –x + 2y = 12 using the elimination method. x + 6y = 20
Answer
1.
Solve 2x + y = 3 using matrices. 3x – 2y = 8
Answer
(2, 1)  
(1, 1)  
(4, 5)  
(2, 1) 
1.
Solve 3x – 7y = 25 using matrices. 5x – 8y = 27
Answer
(25, 27)  
(27, 25)  
(1, 4)  
(4, 1) 
1.
The degree measure of one of two complementary angles is 30 less than twice that of the other. What are the degree measures of the angles? (Remember that complimentary angles add to be 90 degrees)
Answer
45 degrees and 45 degrees  
30 degrees and 60 degrees  
27 degrees and 63 degrees  
40 degrees and 50 degrees 
1.
Which of the following is NOT a solution to the system of inequalities?
Answer
(2, 2)  
(2, 0)  
(1, 0)  
(4, 1) 
1.
What is the system of inequalities associated with the following graph?
Answer
y > 2 x + y ≥ 1  
y < 2 x + y > 1  
y < 2 x + y ≥ 1  
y < 2 x + y < 1 
1.
Solve 3x – y + 2z = 9 using matrices. x – 2y – 3z = 1 2x – 3y + z = 10
Answer
(9, 1, 10)  
(1, 2, 2)  
(1, 2, 2)  
(1, 2, 2) 
Solve 3x – 2y + z = 5 using matrices. 2x + 3y – 3z = 12 3x – 2y – 2z = 4
Answer
(1, 0, 3)  
(1, 3, 0)  
(0, 1, 3)  
(0, 3, 1) 
1.
Joe has a total of 14 pennies, dimes and quarters in his pocket, which total $1.52. The number of dimes and quarters combined is equal to the number of pennies. How many of each coin does Joe have?
Answer
7 pennies, 5 dimes, 2 quarters  
7 pennies, 2 dimes, 5 quarters  
5 pennies, 7 dimes, 2 quarters  
2 pennies, 7 dimes, 5 quarters 
1.
Evaluate
Answer
1.
Evaluate
Answer
1.
If matrix A has dimensions 3 x 2 and matrix B has dimensions 3 x 2, can matrix A and matrix B be multiplied?
Answer
yes  
no 
1.
If matrix A has dimensions 2 x 5 and matrix B has dimensions 5 x 5, can matrix A and matrix B be multiplied?
Answer
yes  
no 
Evaluate
Answer
1.
Evaluate
Answer
1.
Find the determinant of
Answer
1.
Find the determinant of
Answer
1.
Solve y – 3x = 5 by the substitution method. y + x = 3
Answer
1.
Solve 3x – 5y = 15 by the substitution method. y = 2x + 4
Answer
1.
Solve 3x – 2y = 1 using the elimination method. 4y = 6x – 2
Answer
1.
Solve x – 3y = 17 using the elimination method. x + 8y = 52
Answer
1.
Solve 4x + 5y = 40 using matrices. x – y = 1
Answer
1.
Solve 5x – 6y = 50 using matrices. x + 5y = 48
Answer
1.
Find the value of two numbers if their sum is 12 and their difference is 4.
Answer
1.
What is the system of inequalities associated with the following graph?
Answer
x – y ≥ 3 5x – y ≤ 3  
x – y ≥ 3 5x + y ≤ 3  
x – y ≥ 3 5x – y ≤ 3  
x + y ≥ 3 5x – y ≤ 3 
1.
What is the system of inequalities associated with the following graph?
Answer
3x + y ≥ 3 x + 2y ≤ 4  
3x – y ≥ 3 x + 2y ≤ 4  
3x + y ≥ 3 x – 2y ≥ 4  
3x – y ≤ 3 x – 2y ≥ 4 
Solve x – 3y + z = 10 using matrices. x + y – 3z = 10 3x – y + z = 2
Answer
1.
Which matrix represents the image of the triangle with vertices at (2, 0), (1, 5), and (4, 8) when reflected over the line, y = x?
Answer
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