Online Practice Test 1a for MATH 141.

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Test Questions:

1. An equation of the line through the points (2, 5) and (-8, 6) is:

    y = 0.1x + 5.2
    y = 4.3x + 5.2
    y = 5.2x - 0.1
    y = -0.1x + 4.3
    y = -0.1x + 5.2

2. What is the y-intercept of the line passing through the point (2, -1) with a slope of 3?

    (0, -5)
    (7/3, 1)
    (0, 7/3)
    (0, -7)
    (5/3, 0)

3. What is the x-intercept of the line passing through the point (-5, 2) with a slope of -2?

    (6, 0)
    (4, 0)
    (1/2, 0)
    (0, 1/2)
    (0, 4)

4. For which value of k will the following system have infinite solutions?
            6x - 4y = 8
            -3x + ky = -4

    -3
    -2
    -1
    2
    3

5. Find the value of k which makes the system below have no solution:
            3x - y = 4
            -6x + ky = 10

    -2
    0
    1
    2
    3

Questions 6 and 7 use the following information: A company makes feather pens. The fixed costs are $600 and the pens cost 50 cents each to make but will be sold for $2.00 each.

6. What is the cost function for the production of the feather pens?

    C(x) = 600 + 50x
    C(x) = 600 + .5x
    C(x) = 600 + 2.00x
    C(x) = 2 + 600x
    C(x) = 50 + 600x

7. What is the BREAK-EVEN quantity for the pen company?

    200
    300
    400
    600
    1200

8. At a price of $30, 50 purses can be sold. At a price of $45, 20 purses can be sold. Find the DEMAND equations for the sale of purses.

    D(x) = -0.5x + 35
    D(x) = -0.5x + 55
    D(x) = 0.5x + 70
    D(x) = -2x + 110
    D(x) = 2x + 35

9. What is the solution to the following system of equations? Answers are expressed in (x, y) form.
        3x - 2y = -2
        y = x + 2

    (2, -4)
    (3, 5)
    (2, 4)
    (5, 3)
    (3, -5)

10. Given:
            A = | 1   2 |
                  | 0   a |
and
            B = | b   b |
                  | 2 -1 |

Find c21 if C = AB

    b + 2
    2a
    -a
    b + 4
    b + 2b

11. A company's demand equations is given by 2p + 3x = 7 and it's supply equation is given by 4p - 2x = 6. Find the equilibrium point.

    (1, 2)
    (3, 5)
    (2, 1)
    (-1, 2)
    (2, 5)

Questions 12 and 13 use the following table of data. Use your calculator to find the least squares line from the data in the table to ESTIMATE the values asked for in each question.

Math SAT score (x) 510 580 600 550 470
First test score (y) 55 98 89 70 62

12. Estimate the first test score of a person who received a 540 on the SAT.

    73
    74
    75
    76
    77

13. If a person received a 48 on the first test, based on the table's data (and least squares result) what would you predict the person scored on the SAT?

    420
    430
    440
    450
    460

14. What is the linear system corresponding to AX = B if
A = | 1   3 |     X = | x |     B = | 4 |
  | 2   -1|       | y |       | 0 |

    x = 4, y = 0
    x = 3, 2y = -1
    3x + y = 4, 2x - y = 0
    2x + y = 4, x - 3y = 0
    x + 3y = 4, 2x - y = 0

15. Farmer Bob is planting lettuce and onions. He plans on using 100 acres for planting them and he wants the number of acres of lettuce to be 10 acres more than twice the acres of onions. Assuming he will use all 100 acres of land, which of the below equations will be needed to decide how much of each vegetable he should plant?
Assume x = acres of lettuce and y = acres of onions.

    x + 10 = 2y
    2x = y + 10
    x = 2y + 10
    2x + 10 = y
    10 = x + y

16. Find x and y given:
3 |   x | - | 1 | = | 11 |
  | -1 |   | 2 |   |   y |

    x = 6, y = -4
    x = 5, y = 4
    x = 10, y = -4
    x = 4, y = -3
    x = 4, y = -5

17. Sarah has $10,100 to invest in two different stocks. Stock M costs $32 per share and pays dividends of $1.20 per share. Stock Q costs $23 per share and pays dividends of $1.40 per share. If she wants to earn a total of $540 in dividends, how much should she invest in each stock?

    $1000 in M and $9000 in Q
    $1500 in M and $8600 in Q
    $3200 in M and $6900 in Q
    $5050 in M and $5050 in Q
    $9600 in M and $2500 in Q

18. Solve the following system of equations, the answer should be expressed in (x, y, z) form.
        2x + 3y +   z = 1
          x +   y +   z = 3
        3x + 4y + 2z = 4

    (8 - 2z, z - 5, z)
    (8, -5, 0)
    (8, -5, z)
    (8 - 2z, z, 0)
    no solution