Download Practice Exam M 176 Spring 2003

Practice Exam M 176
1) Given the following system of equations
x  2y  z 1
2 x  5 y  3z  7
 x  y  5z  2
Write the augmented matrix.




DO NOT ATTEMPT TO SOLVE
2)
Find
Given the following matrix




1 2 3 9 
0 1 2 2 


0 0 1 3
x
y
z
3)
Form the augmented matrix for the following system of linear
equations:
3 x  10 y  15
5 x  4 y  22
4)
Solve the system:
3x  2y  6
x  2y  10
5)
Solve the system:
x2  y  6
x y 0
6)
Find the value of the following determinants:
6 4
a)

1 3
7)
b)
3 1

4 2
c)
3 4 2
1 1 5 
1 2 2
Use Cramer’s rule for determinants to solve the following system of
equations:
3x  3 y  5 z  1
3x  5 y  9 z  2
5 x  9 y  17 z  4
8)
Find the standard form for the equation of each parabola given the following
conditions.
a. Vertex (0,0)
Focus (-2,0)
9)
b. Vertex (4,2)
Focus (4,0)
Find the standard form of the equation of each ellipse.
a. Vertices: (-3,0), (3,0)
Foci: (-1,0), (1,0)
b. Vertices (2,0), (2,4)
Foci (2,1), (2,3)
10)
Classify each conic without completing the square or graphing.
a. 3x2  2 y 2  3x  2 y  11  0
b. 5x 2  4 y  3x  11  0
c. 4 x 2  y 2  32 x  16  0
11)
Complete the square to determine whether the equation represents an ellipse, a
parabola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices,
and lengths of the major and minor axes. If it is a parabola, find the vertex, focus, and
equation of the directrix. If the equation has no graph, explain why.
a)
y2  4  x  2 y 
b)
2 x2  y 2  2 y  1
12) Find the partial fraction decomposition of the following rational functions.
a)
4x  1
 x  1  x  2 
2
b)
3x  1
x  2 x  15
2