MATH 210
Final Exam
December 10, 1996
1.
Which of the following represents the same line as 3x + 2y = 5?(a)
y = -3/2 x + 5
(b)
y = -3/2 x + 5/2
(c)
y = 3 x + 5
(d)
y = -3 x + 5
(e)
None of the above.
2.
Find an equation for the line passing through ( 1, 5 ) that is parallel to the line 3x + 2y = 5.(a)
6x + 4y = 26
(b)
2x - 3y = -13
(c)
3x + 2y = 17
(d)
x + 5y =2
(e)
None of the above.
3.
Find the slope of the line with equation 3x - 6y = 15.(a)
2
(b)
-2
(c)
-1/2
(d)
1/2
(e)
None of the above.
4.
Find all solutions of the following system of linear equations.x - y - z =1
2x - 3y + z = 10
x + y - 2z = 0
(a)
The system has no solutions.
(b)
The system has infinitely many solutions.
(c)
The system has a unique solution. In this solution x = 5.
(d)
The system has a unique solution. In this solution x = 3.
(e)
None of the above.
5.
Consider the following systems of linear equations.I.
x + y + z = 6
3x - y + 2z = 1
2x - 2y + z = -4
II.
x + y + z = 6
3x - y + 2z = 1
2x - 2y + z = -5
Which of the following statements is true?
(a)
I has infinitely many solutions and II has no solutions.
(b)
II has infinitely many solutions and I has no solutions.
(c)
Each system has infinitely many solutions.
(d)
Each system has a unique solution.
(e)
None of the above.
6.
Let
If possible, find the entry in the second row and first column
of the matrix product AB.
(a)
4
(b)
8
(c)
-3
(d)
13
(e)
The product is undefined.
7.
Is the following matrix invertible? If it is, find its inverse.
(a)
The matrix is not invertible.
(b)
The entry in the first row and the first column of the inverse is 1.
(c)
The entry in the second row and the first column of the inverse is 1/2.
(d)
The entry in the first row and the first column of the inverse is -1.
(e)
None of the above.
For the next two problems, solve the following linear programming problem.
Maximize the objective function P = -2x + y subject to the constraints
8.
The maximum value is:(a)
2
(b)
3
(c)
5
(d)
0
(e)
None of the above.
9.
The maximum occurs at a point with x equal to:(a)
0
(b)
1
(c)
2
(d)
3
(e)
None of the above.
10.
Let A={1,2,3,4,5}, let B={2,4,6,8,10}, and let U be the set of all integers between 0 and 11. Find
(a)
{2,4}
(b)
{1,2,3,4,5,6,8,10}
(c)
{1,3,5}
(d)
{6,8,10}
(e)
None of the above.
For the next two problems, consider the following information.
300 people were surveyed about their pets.
130 have cats.
135 have dogs.
80 have birds.
57 have dogs and cats.
45 have dogs and birds.
27 have cats and birds.
15 have cats and birds and dogs.
11.
How many have dogs, but no cats and no birds?(a)
36
(b)
48
(c)
135
(d)
120
(e)
None of the above.
12.
How many do not have any of these three types of pets?(a)
69
(b)
0
(c)
55
(d)
123
(e)
None of the above.
13.
A team of 6 is to be selected from a group of 15 athletes. How many different teams can be selected?(a)
720
(b)
5005
(c)
3,603,600
(d)
362,880
(e)
None of the above.
14.
A restaurant offers 5 different entrees and 3 different desserts. How many different meals consisting of an entree and a dessert can be ordered?(a)
8
(b)
15
(c)
125
(d)
C(5,3)
(e)
None of the above.
15.
A club has 12 members, 7 men and 5 women. The club wants to choose a president, a vice president and a treasurer. The club bylaws state that at least one of these offices must be held by a woman. In how many different ways can the club fill these offices?(a)
1320
(b)
220
(c)
185
(d)
1110
(e)
None of the above.
16.
A red and a green die are cast. What is the probability that the sum of the numbers on the top faces is 9?(a)
1/6
(b)
1/9
(c)
1/18
(d)
1/36
(e)
None of the above.
17.
A red and a green die are cast. What is the probability that the sum of the numbers on the top faces is 9, given that the red die is a 3?(a)
1/6
(b)
1/9
(c)
1/18
(d)
1/36
(e)
None of the above.
18.
A coin is tossed 10 times. Find the probability that at least one of the tosses is a head.(a)
9/10
(b)
1/1024
(c)
1023/1024
(d)
1
(e)
None of the above.
19.
A coin is tossed 10 times. Find the probability that exactly one of the tosses is a head.(a)
1/1024
(b)
1/10
(c)
1/20
(d)
5/512
(e)
None of the above.
20.
A certain political party will accept as members only people who own guns or make more than $60,000 a year.They will accept anyone who satisfies at least one of these criteria.
In Kalbville, 20% of the residents own guns, and 10% of the residents make more than $60,000 a year.
Assume that the events "making more than $60,000" and "owning guns" are independent.
If a person from Kalbville is chosen at random, what is the probability that the person is acceptable as a member of this party?
(a)
0.25
(b)
0.3
(c)
0.28
(d)
0.02
(e)
None of the above.
21.
A box contains 15 oranges. Two of the oranges are rotten, and 13 of the oranges are good. A sample of 5 oranges is selected from the box. What is the probability that at least one of the oranges in the sample is rotten?(a)
2/15
(b)
5/13
(c)
3/7
(d)
4/7
(e)
None of the above.
For the next two questions, consider the following information.
In Sycamore County, a proposition setting term limits for municipal council members will be on the ballot in the next election. Of the registered voters in this county, 35% are Republicans, 25% are Democrats, and 40% are Independents. 60% of Republicans favor the proposition. 40% of Democrats favor the proposition. 50% of Independents favor the proposition.
22.
A registered voter in Sycamore County is chosen at random. What is the probability that this person favors the proposition?(a)
0.48
(b)
0.5
(c)
0.51
(d)
0.55
(e)
None of the above.
23.
A registered voter in Sycamore county is chosen at random. The voter favors the proposition. What is the probability that this voter is a Republican?(a)
7/17
(b)
7/20
(c)
2/5
(d)
5/8
(e)
None of the above.
For the next two problems, consider the following information.
The town of Kalbville has two food stores. This week, 60% of the population bought their goceries at Store I and 40% bought their groceries at Store II. Every week, 20% of Store I's customers switch to Store II, and 10% of Store II's customers switch to Store I.
24.
What percent of the population will buy their groceries at Store II two weeks from now?(a)
40
(b)
53
(c)
46.4
(d)
53.6
(e)
None of the above.
25.
After many weeks, what fraction of the population will buy their groceries at Store II?(a)
1/3
(b)
2/3
(c)
2/5
(d)
3/5
(e)
None of the above.
26.
Which of the following are absorbing stochastic matrices?
(a)
All of them.
(b)
B and C only.
(c)
C only.
(d)
A only.
(e)
Some other selection.
For the next three problems, consider the following information.
A class of five people took a ten-point quiz. The scores were 9, 8, 8, 5, 5.
27.
The mean score is:(a)
7
(b)
8
(c)
22/3
(d)
22/5
(e)
None of the above.
28.
The variance is:(a)
259/5
(b)
14/5
(c)
14/25
(d)
3
(e)
None of the above.
29.
The standard deviation is:(a)
(b)
(c)
(d)
(e)
None of the above.
30.
In a carnival game, the player rolls a die. If the number showing on top is 6, the player wins $5. If the number is 1 or 2, the player loses $2. If the number is 3, 4, or 5, the player loses $1.If you play this game 1000 times, how much money should you expect to win or lose?
(Round off your answer to the nearest cent.)
(a)
Lose $166.67.
(b)
Win $166.67.
(c)
Lose $333.33.
(d)
Win $333.33.
(e)
None of the above.
© Department of Mathematical Sciences, Northern Illinois University, DeKalb IL 60115
Prepared 11/27/97 by Dr. Anders Linnér (
alinner@math.niu.edu)