Finite Math
A Track
Name: _
Test #2
Nov. 13, 2000
R. Hammack
Score: _
(1) Suppose that A and B are subsets of a universal set U, and that n( U ) = 50, n(A) = 10, n(A
B) = 20, and n(A B) = 3. Supply the following information.
(a) n( A' ) = 40
(b) n( B ) =
Finite Math
Test #1
A Track
Name: _
Oct. 9, 2000
R. Hammack
Score: _
(1) Multiply the matrices.
[
3
7
1
][
1
0
1
2
-5
2
5
]
=
(2) Sketch the solutions of the following system of inequalities.
2x1 +
x1 +
x2
x2
x1
x2
6
4
0
0
(3)
Maximize
subject to .
P = x1
Finite Math
Final Exam
A Track
Name: _
Dec. 13, 2000
R. Hammack
Score: _
(1) Solve the following systems of equations.
(a)
3x1 + 6x2 + 9x3 + 6x4 = 9
2x1 + 4x2 + 6x3 + 2x4 = 4
(b)
x + y - z = 0
x + y + z = 2
x - y + z = 2
(2) Find the maximum of the object
Section 4-3
(26) Solve the system:
3x1 + 5x2 - x3 = -7
x1 + x2 + x3 = -1
2x1
+ 11x3 = 7
First, we transform the system to an augmented matrix, and then reduce the matrix. In our first
step, we switch two rows to get a 1 at the top left corner.
3
1
2
[
1
0
Section 4-1
(5) Solve by graphing:
cfw_
3x - y = 2
x + 2y = 10
By looking at the graph, we see that the solution is (x,y) = (2,4).
(8) Solve by graphing:
cfw_
3u + 5v = 15
6u +10v = -30
Since the lines are parallel, they never intersect. Therefore the sys
Section 1-3
(6) Graph y = x/2 +1.
This is of the form y = mx + b (with m = 1/2) so
the graph will be a straight line.
To find the x-intercept, set y = 0:
0 = x/2 +1
-x/2 = 1
-2(-x/2) = -2(1)
x = -2
To find the y-intercept, set x = 0:
y = 0/2 + 1
y=1
Thus
Finite Math
Final Exam
F Track
Name: _
Dec. 14, 2000
R. Hammack
Score: _
(1) Solve the following systems of equations:
(a)
x - 2y = -8
3x - 6y = -24
x - y = -5
(b)
x + y + z = 2
x + y - z = 0
x + y + 2z = 3
(2) Maximize of the objective function P = x + 5
Finite Math
F Track
Name: _
Test #2
Nov. 14, 2000
R. Hammack
Score: _
(1) Suppose a college has 1200 students, 600 of whom are men. Suppose also that 500 students
are democrats, and that 200 students are women who are not democrats.
(a) How many students
Finite Math
F Track
Name: _
Test #2
Nov. 14, 2000
R. Hammack
Score: _
(1) Suppose a college has 1200 students, 600 of whom are men. Suppose also that 500 students
are democrats, and that 200 students are women who are not democrats.
(a) How many students
Finite Math
A Track
Name: _
Test #2
Nov. 13, 2000
R. Hammack
Score: _
(1) Suppose that A and B are subsets of a universal set U, and that n( U ) = 50, n(A) = 10, n(A
B) = 20, and n(A B) = 3. Supply the following information.
(a) n( A' ) =
(b) n( B ) =
(c