Time and Date Stamps (logged): 05:07:08 12-05-2008 ¯´Ÿ¯¶Ÿ¯·°±Ÿ¯´Ÿ±¯¯· Precalculus II

Precalculus II Test 3

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.). 

Name and Signature of Student _____________________________

Signed by Attendant, with Current Date and Time: ______________________

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Instructions:

Directions for Student:

Test Problems:

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Problem Number 1

Find the vertex, focus and directrix of the parabola whose equation is given by x^2 - -5.001 x = -7.001 y + -3.001.

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Problem Number 2

Give the rectangular form of the equation 1 / (1 + 8 r cos(`theta) ) = r^2.

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Problem Number 3

Transform the equation r tan (`theta) = 3 r cos (`theta) to rectangular coordinates and graph.

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Problem Number 4

Find the equation of a parabola with vertex at ( 7.5, .1) and directrix x = -8.101.

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Problem Number 5

Vector v has initial point P = (-4.301, .5) and terminal point Q = (-8.301, -8.501), while vector w has initial point (0, 0) and terminal point halfway between P and Q. Find the vector -4.301 v + .5 w , and use a sketch to show how this vector can be constructed from v and w .

 

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The remaining problems appear on Test 4 for distance students and these problems will not be counted on the test for distance students. These problems are required as part of Test 3 for in-class students, who will not have Test 4.

However in-class students should note that problems related to the binomial theorem, to permutations and combinations are optional on this test and will be counted only if they help your grade.

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Problem Number 6

Express the following sequence using summation notation:

7 / 14 + 14 / 21 + 21 / 28 + ...

 

 

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Problem Number 7

A staircase contains 4 stairs.  The last stair is paved with 32 tiles.   As you ascend the stairs you see that each stair is narrower than the one before it, and that each therefore uses 4 less tiles than the one below it.  How many tiles pave the staircase?

 

 

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Problem Number 8

Using the Binomial Theorem expand the expression ( x + 4) ^ 6.

 

 

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Problem Number 9

Explain why the number of permutations of 4 objects chosen from a set of 12 objects is C( 12, 4).

 

 

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Problem Number 10

Solve the following system; if the system is inconsistent say so.  Use Cramer's Rule to obtain the solution.

-7 x + -7 y = 91 .

-13 x + -13 y = -79 .

 

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Problem Number 11

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 + 8 y = 2 .

20 x + 26 y = -23 .

 

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Problem Number 12

Solve the following system; if the system is inconsistent say so.  Use substitution.

-10 x + -4 y = -14 .

9 x + 7 y = -18 .

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Problem Number 13

Set up the system below as an augmented matrix and solve using row operations.

-8 x + 3 y = -75 .

-8 x + 4 y = -84 .

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Problem Number 14

If a business starts out earning $ 81 per week, and if every week the amount increases by 8 %, how much will the business earn in its first 32 years of operation?