Name:    Chapter 6 Pre Test

1.

Solve the system by the method of substitution. Check your solution(s) graphically.

 a. (0, 0), (1, –1) b. (0, 0), (1, 1) c. (0, 0), (–1, –1) d. (0, 1), (0, –1) e. (1, 0), (0, –1)

2.

Use a graphing utility to solve the system of equations. Find the solution accurate to two decimal places.

 a. b. c. d. no real solution e.

3.

Use any method to solve the system.

 a. b. c. d. e.

4.

Solve the system by the method of elimination.

 a. d. b. e. c.

5.

Solve the system by the method of elimination.

 a. d. b. e. c.

6.

Solve using any method.

 a. b. c. inconsistent d. e.

7.

Determine whether the ordered triple is a solution of the system of equations.

 a. Yes b. No

8.

In Super Bowl I, on January 15, 1967, the Green Bay Packers defeated the Kansas City Chiefs by a score of 15  to 30 . The total points scored came from 13 different scoring plays, which were a combination of touchdowns, extra-point kicks, and field goals, worth 6, 1, and 3 points, respectively. The same number of touchdowns and extra-point kicks were scored. There were six times as many touchdowns as field goals. How many touchdowns, extra-point kicks, and field goals were scored during the game?

 a. 6  touchdowns, 6 extra-point kicks,1 field goal b. 6  touchdowns, 1 extra-point kick, 1 field goal c. 6  touchdowns, 6 extra-point kicks, 6 field goal d. 1  touchdown, 6 extra-point kicks, 1 field goal e. 1  touchdown, 6 extra-point kicks, 6 field goal

9.

Determine which one of the ordered triples below is a solution of the given system of equations.

 a. b. c. d. e.

10.

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

 a. b. c. d. e.

11.

The predicted cost C (in thousands of dollars) for a company to remove of a chemical from its waste water is given by the model

.

Write the partial fraction decomposition for the rational function. Verify your result by using the table feature of a graphing utility to create a table comparing the original function with the partial fractions.
 a. b. c. d. e.

12.

Select an inequality for the shaded region shown in the figure.

 a. b. c. d. e.

13.

Find the consumer surplus and producer surplus.

Demand

Supply
 a. Consumer surplus: Producer surplus: b. Consumer surplus: Producer surplus: c. Consumer surplus: Producer surplus: d. Consumer surplus: Producer surplus: e. Consumer surplus: Producer surplus:

14.

Use a graphing utility to graph the inequality.

 a. d. b. e. c.

15.

Sketch the graph and label the vertices of the solution set of the system of inequalities. Shade the solution set.

 a. d. b. e. c.

16.

Find the minimum value of the objective function and where they occur, subject to the indicated constraints.

Objective function:

Constraints:

 a. Minimum at b. Minimum at c. Minimum at d. Minimum at e. Minimum at

17.

Find the minimum value of the objective function and where they occur, subject to the constraints:

Objective function:

Constraints:

 a. Minimum at b. Minimum at c. Minimum at d. Minimum at e. Minimum at

18.

Find the minimum value of the objective function and where they occur, subject to the constraints:

Objective function:

Constraints:

 a. Minimum at b. Minimum at c. Minimum at d. Minimum at e. No minimum

19.

The linear programming problem has an unusual characteristic. Select a graph of the solution region for the problem and describe the unusual characteristic. Find the maximum  value of the objective function (if possible) and where they occur.

Constraints:

 a. The constraint is extraneous. Maximum at d. The constraint is extraneous. Maximum at b. The constraint is extraneous. Maximum at e. The constraint is extraneous. No maximum. c. The constraint is extraneous. Maximum at

20.

Find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints.
 Objective function: Constraints:

 a. b. c. d. e.