Time and Date Stamps (logged): 17:12:20 06-10-2020
°¶Ÿ°±Ÿ±¯¯µŸ°¯Ÿ±¯±¯
Precalculus I
Precalculus I Major Quiz
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:
. . . . .
. . . .
. . . .
. . .
.
.
.
.
.
.
.
.
.
.
Problem Number 1
Problem: Obtain a quadratic depth vs. clock time model if depths of 50.08925 cm, 38.1759
cm and 31.25993 cm are observed clock times t = 13.86389, 27.72778 and 41.59167 seconds.
Problem: The quadratic depth vs. clock time model corresponding to depths of 50.08925 cm,
38.1759 cm and 31.25993 cm at clock times t = 13.86389, 27.72778 and 41.59167 seconds is depth(t) = .013 t2
+ -1.4 t + 67. Use the model to determine whether the depth will ever reach zero.
.
.
.
.
.
.
.
.
.
.
Problem Number 2
Problem: Sketch a graph of the basic exponential function y = 2 x. If
this function is stretched vertically by factor -2.54 then shifted -2.44 units vertically, what
is the algebraic form of the function obtained? Sketch a graph of this new function,
and show that the graph is different than that obtained if the vertical shift is performed
before the vertical stretch.
Problem: Water depths of 51.641, 38.364, 30.169 and 27.056 cm are observed at clock times t =
11, 22, 33 and 44 seconds. What is the average rate of depth change during each
of the three time intervals? Predict what the next average rate would be, and use this
result to predict the depth at t = 55 seconds.
.
.
.
.
.
.
.
.
.
.
Problem Number 3
At clock times 9.072462, 18.14492 and 27.21739 we have depths 64.50987, 51.95831 and 44.34533. What system of
simultaneous equations do we get when we substitute the coordinates of the corresponding
points into the form y = a t 2 + b t + c of a quadratic function?
.
.
.
.
.
.
.
.
.
.
Problem Number 4
Sketch a graph of y = x^2, from x = -3 to x = 3. Then sketch a graph of y = 3 x^2 over
the same domain.
- By what factor do we vertically
stretch the first graph to obtain the second?
- What are the three basic points of
the first graph (i.e., the vertex and the points 1 unit to the right and left of the
vertex)?
- What are the three basic points of
the second graph?
Sketch the second graph shifted
-1.75 units in the x direction and .25 units in the y direction.
What are the three basic points
of this graph?
If f(x) = x^2, then what are
- f(x--1.75), f(x) +
.25, 3 f(x) and 3 f(x--1.75) + .25?
.
.
.
.
.
.
.
.
.
.
Problem Number 5
At clock time t = 10 sec the illumination of a source is 47 watts/m^2, while at clock
time t = 31 sec the illumination is 19 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) = 66 t-2, determine the average rate of
change of y with respect to t, between clock times t = 31 and t = 33.