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Department of Mathematics
The City College of New York
Math 19000
Final Examination
Fall 2005
Instructions:
Show all work. You may use a scientific calculator.
There are 4 parts. In each part choose 5 questions.
Each question is worth 5 points.
Part I. Choose any 5 questions from this part.
1)
Find the midpoint of the line segment joining (3, 8) and (9,6).
2)
Find an equation of the line through point (7, 6) that is perpendicular to the line
.
13
5
2
=
+
y
x
3)
Find the distance between the points
and
Q
.
)
3
,
8
(
P
)
4
,
4
(
4)
Find the equation of the straight line through points
and
.
)
3
,
8
(
−
−
P
)
4
,
4
(
−
−
Q
5)
Use long division to simplify the fraction
1
1
3
+
+
x
x
.
6)
Rewrite
4
4
2
1
2
1
2
−
+
+
−
x
x
x
as a simplified fraction.
Part II. Choose any 5 questions from this part.
7)
Simplify
2
1
3
3
−
−
−
a
b
b
a
so that only positive powers appear in your answer.
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 Spring '11
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 Math

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