Time and Date Stamps (logged): 01:52:01 08-29-2008
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Precalculus II
Precalculus I Test 1
Completely document your work and your reasoning.
You will be graded on your documentation, your reasoning, and the
correctness of your conclusions.
Test should be printed using Internet Explorer. If
printed from different browser check to be sure test items have not been cut off. If
items are cut off then print in Landscape Mode (choose File, Print, click on Properties
and check the box next to Landscape, etc.).
- Write on ONE SIDE of paper only
- If a distance student be sure to email
instructor after taking the test in order to request results.
Name and Signature of Student
_____________________________
Signed by Attendant, with Current Date and Time:
______________________
If picture ID has been matched with student and name as
given above, Attendant please sign here: _________
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
At clock time t = 11 sec the illumination of a source is 47 watts/m^2, while at clock
time t = 29 sec the illumination is 23 watts/m^2. Plot the corresponding points on a
graph of illumination vs. clock time and determine the slope of the straight line segment
connecting these points. Explain why this slope represents the rate at which the
illumination changes over this time interval.
For the power function y = f(t) = 69 t-2, determine the average rate of
change of y with respect to t, between clock times t = 29 and t = 34.
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Problem Number 2
Use the slope = slope formulation to find the linear function streamRange(t) for
the range of the water stream flowing from the side of a uniform cylinder, if the stream
range is 50 centimeters at clock time t = 71 seconds, and if the stream range changes by
-9 centimeters over a period of 9 seconds. Use your function to find the clock time at
which the stream range first falls to 15 centimeters.
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Problem Number 3
A sandpile 9 cm in diameter has a mass of 656.1 grams.
- What is the appropriate proportionality to use for this situation?
Solve the proportionality equation for the proportionality constant k and use the
resulting function to find the mass of a geometrically similar sandpile of diameter 14 cm.
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Problem Number 4
If a(n) = a(n-1) + b, with a(1) = 4, then if a( 240) = 0, what is the value of
b?
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Problem Number 5
What equation would you have to solve to find the doubling time, starting at t =
3, of a population that starts at 3200 organisms and grows at annual rate 3.1%?
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Problem Number 6
Find the first 4 terms of the sequence defined by a(n) = a(n-1) + -1 n^2, a(0) =
-3.
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Problem Number 7
Problem: Sketch a graph representing the linear function family y = m x + b for b
= 2.33, with m varying over all positive real numbers.
Problem: Find f( 20.04717) and f( t - 1 ) for the function y = f(t) = .029 t^2 + -2
t + 67. What equation would you solve to determine the value of t for which f(t) =
48.91846? (You need not actually evaluate the equation). What is the value of the function for
clock time t = 10.02358?
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Problem Number 8
Find the clock time when water depth is 49.66111, given the depth vs. clock time function y
= f(t) = .018 t2 + -2.42 t + 96. Using the same function determine the depth at
clock time t = 13. Find t such that f(t) = 91.66111. Find f(t) when t = 32.