Time and Date Stamps (logged): 17:12:20 06-10-2020
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Precalculus II
Precalculus II Test 4
Completely document your work and your reasoning.
You will be graded on your documentation, your reasoning, and the
correctness of your conclusions.
Except where the need for more precision dictates otherwise (e.g., in
nuclear physics) all quantities may be rounded to three significant figures. The
generating program works in binary and often generates extraneous digits (e.g., 1.5001 for
1.5, 3.6999 for 3.7).
** Write clearly in dark pencil or ink, on one side of the paper
only. **
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
Give the nth term of the sequence 5, 13, 21, 29, . . . . Give the
expression for the sum of the first n terms, and use this expression to find the sum of
the first 256 terms of the sequence.
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Problem Number 2
What is the nth term of the sequence suggested by the pattern
3, - 9, 27, - 81?
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Problem Number 3
Set up the system below as an augmented matrix and solve using row operations.
-5 x + -5 y + -5 z = 120 .
8 x + -5 y + 6 z = -34 .
4 x + -4 y + -5 z = -79 .
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Problem Number 4
A ball is dropped from 256 centimeters and with every bounce its height decreases
by 36%. How far does it travel before its bounces become completely undetectable
(after which time we assume the ball travels no measurable distance)?
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Problem Number 5
Set up the system below as a matrix multiplication of the form A B = C.
Find the inverse A^-1 of A and use it to solve the system.
6 x + -5 y = -6 .
-4 x + 5 y = 14 .
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Problem Number 6
Find the x^ 8 term in the expansion of ( x + 2 y^2 ) ^ 13.
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Problem Number 7
Solve the following system; if the system is inconsistent say so. Use
elimination.
-10 x + -5 y + -8 z = 480 .
6 x + -8 y + -9 z = 73 .
-5 x + 8 y + 7 z = -51 .
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Problem Number 8
How many 4-letter codes can be formed from the first 16 letters of the alphabet
if repeated letters are not allowed?
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Problem Number 9
Solve the following system; if the system is inconsistent say so. Use
Cramer's Rule to obtain the solution.
3 x + -4 y = 12 .
-7 x + 6 y = -8 .