Time and Date Stamps (logged): 12:34:21 05-21-2012
°±Ÿ²³Ÿ±°¯´Ÿ±°Ÿ±¯°±
Calculus I
Calculus I Major Quiz
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:
. . . . .
. . . .
. . . .
. . .
.
.
.
.
.
.
.
.
.
.
Problem Number 1
Problem: Derive the expression for the derivative of the function y(t) =
a t3 at clock time t.
Problem: If the rate of depth change is rate(t) = .042 t + -1.3, then what
is the depth function if the depth at clock time t = 0 is 99? How long does it take for
the depth to decrease from 82.87249 to 79.44964? What is the average rate which depth changes over
this period?
.
.
.
.
.
.
.
.
.
.
Problem Number 2
Problem: At what average rate does the exponential population function P(t) = 15 *
1.19 ^ t change between clock times 4.1 and 4.10001?
- Write the same expression for the symbolic population function P(t) = P0 * 2 ^ (kt).
- Using the laws of exponents simplify your expression as much as possible.
Problem: If the weight of a sandpile whose diameter is 4 meters is 140.8 tons,
then what function gives the weight in tons of geometrically similar sandpiles as a
function of diameter in meters?
- How many tons of sand would take to increase the diameter of this
sandpile to 4.0001 meters?
- At what average rate is the weight of the sandpile changing with respect
to diameter between these two diameters?
.
.
.
.
.
.
.
.
.
.
Problem Number 3
The depth vs. clock time function y = .027 t2 + -1.1 t + 87 indicates the depth
y of water in a certain uniform cylinder at clock time t.
- At what average rate does depth changes between clock times t = 6 and t = 12?
- What clock time lies midway between t = 6 and t = 12, at what rate is depth changing
at this instant?
What is the function that represents the rate r of depth change at clock time t?
- Evaluate this function at the clock time halfway between t = 6 and t = 12.
If the rate of depth change is given by dy/dt = .068 t + -2.4 represents the rate at which
depth is changing at clock time t, then how much depth change will there be between clock
times t = 6 and t = 12?
- Give the function that represents
the depth. What would this specific function be if at clock time t = 0 the depth is 170?
.
.
.
.
.
.
.
.
.
.
Problem Number 4
The depth of water in a certain nonuniform container is y = .02 t4 + -2.6 t2
+ 89, where depth y is in cm when clock time t is in seconds.
- At what average rate is the depth of water changing between clock times t = 17.2 and t =
17.3 seconds?
- At what average rate is the depth of water changing between clock times t = 17.2 and t =
17.21 seconds?
- At what average rate is the depth of water changing between clock times t = 17.2 and t =
17.201 seconds?
- What do you estimate is the rate at which water depth is changing at clock time t = 17.2
seconds?
The rate at which water flows from a certain nonuniform cylinder is given by rate = .02
t3 + -2.6 t cm3 per minute, where t is in minutes. How much do
water do you think will flow between clock times t = 17.3 minutes and t = 34.4 minutes?
.
.
.
.
.
.
.
.
.
.
Problem Number 5
Solve using proportionalities by stating the appropriate proportionality law and
finding the proportionality constant:
- If a sand pile 2 meters high has a mass of 3840 kg,
then what would we expect to be the mass of a geometrically similar sand pile 5.8 meters
high?
- If there are .92 billion grains of sand exposed on
the surface of the first sand pile, how many grains of sand we expect to be exposed on the
surface of the second?