Time and Date Stamps (logged): 01:42:01 08-29-2008
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Precalculus I
Precalculus I Major Quiz
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Instructions:
- Test is to be taken without reference to text or
outside notes.
- Graphing Calculator is allowed, as is blank paper or
testing center paper.
- No time limit but test is to be taken in one
sitting.
- Please place completed test in Dave Smith's folder,
OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va.,
24212-0828 OR email copy of document to dsmith@vhcc.edu,
OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken. Student may, if proctor deems it feasible, make and retain a copy of the test..
Directions for Student:
- Completely document your work.
- Numerical answers should be correct to 3 significant
figures. You may round off given numerical information to a precision consistent
with this standard.
- Undocumented and unjustified answers may be counted
wrong, and in the case of two-choice or limited-choice answers (e.g., true-false or
yes-no) will be counted wrong. Undocumented and unjustified answers, if wrong, never get
partial credit. So show your work and explain your reasoning.
- Due to a scanner malfunction and other errors some
test items may be hard to read, incomplete or even illegible. If this is judged by
the instructor to be the case you will not be penalized for these items, but if you
complete them and if they help your grade they will be counted. Therefore it is to
your advantage to attempt to complete them, if necessary sensibly filling in any
questionable parts.
- Please write on one side of paper only, and staple
test pages together.
Test Problems:
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Problem Number 1
Problem: Obtain a quadratic depth vs. clock time model if depths of 24.44286 cm, 11.90066
cm and 4.373413 cm are observed clock times t = 11.80271, 23.60543 and 35.40814 seconds.
Problem: The quadratic depth vs. clock time model corresponding to depths of 24.44286 cm,
11.90066 cm and 4.373413 cm at clock times t = 11.80271, 23.60543 and 35.40814 seconds is depth(t) = .018 t2
+ -1.7 t + 42. Use the model to determine whether the depth will ever reach zero.
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Problem Number 2
Problem: Sketch a graph representing the linear function family y = m x + b for b
= 2.05, with m varying over all negative real numbers.
Problem: What are the values of the following: f( 32.76081) and f(
q - p ) for the function y = f(t) = .01 t^2 + -1.1 t + 88? What is the value of
the function for clock time t = 16.38041? What equation would you solve to determine the value
of t for which f(t) = 63.75813? (You need not actually evaluate the equation).
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Problem Number 3
Sketch a graph of the fundamental function y = x^2.
Using arrows to indicate the stretching or shifting of the function, show how the graph
is transformed by each of the following:
- A vertical stretch by factor .25.
- A horizontal shift of 1.25 units.
- A vertical shift of 1.75 units.
Using the knowledge that a function y = f(x) is transformed to the function y = A f(x)
by a vertical stretch by factor A, to y = f(x-h) by a horizontal shift of h units, or to y
= f(x) + k by a horizontal shift of k units, what give the form of each transformed
function.
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Problem Number 4
At clock times 12, 18, 24 and 30 sec, we observe water depths of 44.6, 41.2, 39.2 and
38.8 cm.
- At what average rate does the depth change during each time interval?
Sketch a graph of depth vs. clock time.
- Use a sketch to explain why the slope of this graph between 12 and 18 sec represents
the average rate at which depth changes during this time interval.
If f(x) = x2, what are the vertex and the three basic points of the graphs
of f(x- 1.25), f(x) - 1.85, .2 f(x) and .2 f(x- 1.25) + 1.85. Quickly sketch each graph.
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Problem Number 5
At clock time t = 12 sec the depth of water in a container is 64 cm, while at clock
time t = 28 sec the depth is 36 cm. Plot the corresponding points on a graph of depth
vs. clock time and determine the slope of the straight line segment connecting these
points. Explain why this slope represents the average rate at which the water depth
changes over this time interval.
For the quadratic function y = f(t) = .02 t2 + -2.58 t + 93, determine the
average rate of change of y with respect to t, between clock times t = 28 and t = 31.