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Department of Mathematics
The City College of New York
Math 19000
Final Examination
Spring 2005
Instructions:
This Exam consists of two parts.
In Part I you must do all 5 questions.
In Part II choose any 5 complete questions.
A scientific calculator is required for some questions. Graphing calculators are not
permitted.
Show all work.
Part I. Do all 5 questions.
1.
Simplify completely each of the following. Your answers should be fractions that are
completely reduced.
a)
2
2
4
1
44
1
x
xx
−
+−
b)
22
2
232
2
12
12
yyx
x
yy
xy
x
y
−−
÷
2
2.
32
43
x
+
−
−+
−
1
1
3. a)
52
25
x
x
−
+
b)
Solve:
11
23
−=
−
1
4. a)
4
59
/
8
3
3
2
27
x
−
−
b)
58
2
7
2
1
2
1
37
2
7 1
8
x y
−
4
5
5.
Solve the equation
17
4
7
x
=
x
and check your answers.
End of Part I. You should have answered all questions from this Part.
Please turn the page for Part II.
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View Full DocumentPart II. Choose any 5 complete questions (omit 2).
6.
Find the center and radius of the circle whose equation is
.
22
4
4
52
40
24
xy
x
++=−
y
Solution: center (5,3)
radius
21
7.
Solve for x only.
40
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 Spring '11
 Ocken
 Math

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