1. Graph the inequality x +y < –5.
2. Compute
A. -19
B. -18
C. -17
D. -16
3. Compute the optimal traffic flow along each of the four roads marked x, y, z, and w in the diagram of the city block below.
A. There's no solution, because the system is dependent.
B. There's one correct answer, which is x = 400, y = 600, z = 200, w = 900.
C. There are infinitely many correct answers, one of which is x = 400, y = 600, z = 200, w = 900.
D. There's one correct answer, which is x = 500, y = 500, z = 100, w = 1900.
4. Solve the system of equations below.
x + y = 6
3 x - 4y - 4z = -9
x- z = 3
A. {(–2, 1, 5)}
B. {(1, –2, 5)}
C. {(–2, 5, 1)}
D. {(1, 5, –2)}
5. Which one of the following ordered pairs is a solution of the system below?
x + y = 1
x- y = 9
A. (5, 4)
B. (–5, –4)
C. (5, –4)
D. (–5, 4)
6. A steel company produces two types of machine dies, part A and part B, and is bound by the following constraints:
• Part A requires 1 hour of casting time and 10 hours of firing time.
• Part B requires 4 hours of casting time and 3 hours of firing time.
• The maximum numbers of hours per week available for casting and firing are 100 and 70, respectively.
• The cost to the company is $0.75 per part A and $3.00 per part B. Total weekly costs can't exceed $45.00.
Let x = the number of part A produced in a week and y = the number of part B produced in a week.
Write a system of three inequalities that describes these constraints.
7. Graph the inequality –2x – 3y = 6.
8. Write the partial fraction decomposition of the rational expression below.
9. Solve the system below by the addition method.
A. {(0, 3), (0, –3)}
B. {(3, 0), (–3, 0)}
C. {(0, 3)}
D. {(3, 0)}
10. Graph the inequality x
11. Which of the following augmented matrices represents a dependent system?
12. Write the partial fraction decomposition of the rational
expression below.
13. Which of the following is true about the identity matrix In?
A. Any matrix A has the same order as every I
B. Any matrix A can be multiplied by some I
C. Any matrix A can be multiplied by some I
D. Every I
14. Use the substitution method to solve the system of equations below.
-4x - 3y = -117
x = - 4y
A. {(36, 9)}
B. {(36, -9)}
C. {(-9, 36)}
D. {(37, -9)}
15. Solve the system below by the method of your choice.
A. {(0, 0), (8, –512)}
B. {(–1, 1), (–8, 512)}
C. {(0, 0), (–8, 64)}
D. {(0, 0), (–8, 512)}
16. Write the partial fraction decomposition of the rational expression below.
17. Use the substitution method to solve the system below.
A. {(2, 1), (3, 0)}
B. {(3, 0)}
C. {(–2, 5), (–3, 6)}
D. {(2, 5), (3, 0)}
18. Use the addition method to solve the system below.
x + 3y = 8
-2x + 2y = 16
A. {(4, 5)}
B. {(–4, 4)}
C. 0
D. {(–5, 5)}
19. Which of the following equations comes from the system used to create the augmented matrix ?
A. -4x + 4y = 14
B. 2x - 6y = 0
C. 4x - 4y = 0
D. -8x - 24y = 0
20. A steel company produces two types of machine dies, part A and part B. The company makes a $3.00 profit on each part A that it produces and a $6.00 profit on each part B that it produces. Let x = the number of part A produced in a week and y = the number of part B produced in a week. Write the objective function that describes the total weekly profit.
A. z = 3(x – 6) + 6(y – 3)
B. z = 3x + 6y
C. z = 9(x + y)
D. z = 6x + 3y
