Download Sample Test 1 Solutions

Math 140
Spring, 2007
Test 1
Name___________________
Version A
The test is worth a total of 106 points.
Part 1: Show all necessary work. Follow directions! No credit will be received
for answers I cannot find, cannot read, or that magically appear without the
proper supporting work.
1. (4 points each) Graph each of the following lines on the graph below. Clearly
label each line with its equation.
a) x = 3
9
b) y = -2
7
8
6
c) y = -3x + 2
d) 8x – 3y = 24
5
4
3
2
1
−9 −8 −7 −6 −5 −4 −3 −2 −1
−1
1
2
3
4
5
6
−2
−3
−4
−5
−6
−7
−8
−9
10
2. (8 points) Find an equation of the line through the points (-3, -2) and (-4, 1).
7
8
9 10
⎡ 6 −2⎤
3. (4 points each) Let A = ⎢
⎥ and let B =
⎣ −5 3 ⎦
⎡ 2 7⎤
⎢ −2 4 ⎥ . Find:
⎣
⎦
a) 2A – 3B
b) 3A + B
c) AB
d) BA
4. (10 points) Solve using the method of substitution:
2x + y = 9
x2 + x – 2y = 18
5. (10 points) Solve using the addition method (method of elimination). Do not
use matrices to solve the system.
2x + 5y = 31
8x – 9y = 37
6. (12 points) Solve using the method of elimination (the addition method). Do
not use matrices to solve the system.
5x + 3y – 2z = 20
2x + y + 3z = -11
x + 5y + 2z = -8
7. (4 points each) Use the system below to answer the following questions.
2x + 2y – 3z = -12
4x + y + z = 8
3x + 5y + 2z = -17
a) Write down the augmented matrix for this system.
b) Use your calculator to put the augmented matrix in reduced row echelon
form. Write down the reduced row echelon form of the matrix.
c) Write down the solution of the system.
8. (4 points each) Use the system below to answer the following questions.
x + 2y – 3z = -6
3x + y + 2z = 9
10x + 14z = 48
a) Write down the augmented matrix for this system.
b) Use your calculator to put the augmented matrix in reduced row echelon
form. Write down the reduced row echelon form of the matrix. Use
fractions instead of decimals.
c) Write down the solution of the system.
Part II. Multiple Choice. Circle the best answer. (5 points each)
9. Find an equation of the line parallel to y = 8x + 1 that contains the point
(0, -3).
a) y = −
1
x+3
8
b) y = 8x + 3
1
c) y = − x – 3
8
d) y = 8x – 3
10. Solve the system:
4x + y + 2z = -2
3x + 2y – 3z = -17
-6x + y – 12z = 28
a) (-3, 2, 4)
c) (-7, 18, 5)
b) (-1.4t, 3.6t, t)
d) no solution