Online Practice Test 3a for MATH 151.

This online test was created by Brent M. Dingle.
To receive your current score you should find a button to press at the bottom of this page which says something like: Click Here For Curent Score.
When you are done with the test click the button that says: I am done.
Assuming everything is working (i.e. your browser supports JavaScript and has it enabled) you should have been notified of a time limit to complete this test and you should see the words: "JavaScript Enabled" immediately below. The timer should be counting down in the lower left part of your browser window (assuming Internet Explorer). You may get your current score at any point, until time runs out.

Test Questions:

1. The derivative of ln(x1/2) is?

    (1/2) * x-1/2
    (1/2) * x-1
    1/(x1/2)
    1/2
    (1/2) * x

2. A bactericide is introduced into a colony of 50,000 bacteria. The number of bacteria is known to decrease exponentially. It is observed after 9 hours there remain 20,000 bacteria. How many hours (to the nearest tenth of an hour) had elapsed when the bacteria population was reduced to half.

    8 hours
    8.4 hours
    7.2 hours
    6.8 hours
    4.5 hours

3. What is the derivative of arcsin(2x - 1)?

    1/(x - x2)1/2
    1/(1 - x2)1/2
    1/(x2 - 1)1/2
    1/(x2 - x)1/2
    1/(2x)

4. Evaluate limx --> 0 (1 - cos x) / x2

    -1
    -0.5
    1
    0.5
    positive infinity

5. Find the absolute minimum of 3x5 - 5x3 - 1 on the interval [-1, 2].

    -3
    -2
    0
    1
    there is no absolute minimum

6. On what interval(s) is x4 - 2x2 - 100 concave DOWN ?

    it is never concave down
    (-1, 0)
    (0, 1)
    (-1, 1)
    (-infinity, -1) and (0, infinity)

7. A farmer wants to fence a rectangular plot with an area of 1250 square feet. One side will be adjacent to a river. The cost of fencing for the side near the river is $15 per foot. The cost of fencing everywhere else is only $5 per foot. Find the dimensions of the plot if the cost of fencing is to be as low as possible. What is the minimal cost?

    $1113.13
    $1060.66
    $1000.00
    $978.23
    $550.00

8. A ball is thrown at an angle of 45 degrees to the ground. If the ball lands 90 meters away, what was its initial speed? (Gravity is 9.8 m/s2)

Hint: Because there is nothing slowing the ball in the horizontal direction you can assume the ball reaches its maximum height when it has traveled half the total horizontal distance (45 meters).

    18.3 m/s
    21.4 m/s
    23.1 m/s
    25.0 m/s
    29.7 m/s

9. Evaluate ò01 (2 - x)2 dx

    -5/3
    -7/3
    0
    7/3
    5/3

10. Evaluate
    ó 2       1 - 2t + t2
    ô     ¾¾¾¾¾
    õ1         3 - 3t

    -1/6
    -1/3
    1/3
    1/6
    this integral does not exist