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 1 
Math 111
Review Exercises for the Final Exam
The following are review exercises for the Math 111 final exam. These exercises
are provided for you to practice or test yourself for readiness for the final exam. There are
many more problems appearing here than would be on the final. These exercises
represent many of the types of problems you would be expected to solve on the final, but
are not meant to represent all possible types of problems that could appear on the final
exam.
Your final exam will be in two parts: the first part does not allow the use of a
calculator, and the second part does allow the use of a graphing calculator.
Since the
exercises in this review sheet are mixed together, we have put a
symbol next to
exercises or parts of exercises where you WILL be allowed to use the graphing
calculator: otherwise you should be able to solve the problem WITHOUT a calculator.
Such a symbol will not be on the final exam. Please note that for the final, you may use
any graphing calculator except
the TI89, TIInspire, and any calculator with a QWERTY
keypad.
Show all your work: unsupported results may not receive credit.
1.
Perform the operations and express your answer in simplest form with positive
exponents only:
a)
2
5
3
2
5
3
4
−
−
−
−
x
y
x
x
b)
3
/
1
4
5
2
3
3
3
12
2
−
−
y
x
y
x
y
c)
x
x
x
x
+
+
−
+
−
1
)
1
(
)
1
(
3
2
/
1
2
/
1
2.
Perform the operations and express your answer in simplest form.
a)
2
1
8
2
5
2
+
+
−
−
−
−
x
x
x
x
x
b)
3
1
2
27
3
4
3
−
+
−
−
−
x
x
x
x
x
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3.
Express the following as a simple fraction reduced to lowest terms:
3
2
2
2
1
4
4
1
z
z
z
z
−
+
−
.
4.
Solve for y in the equation:
z
x
y
1
1
1
=
+
5.
Simplify the radical: (LEAVE IN RADICAL FORM)
a)
3
4
9
5
54
z
y
x
b)
2
5
2
3
12
24
xyz
z
y
x
c)
x
x
3
2
6.
Rationalize the denominator and simplify:
a)
3
2
2
8
xy
x
b)
7
10
6
−
c)
3
3
−
−
x
x
d)
x
h
x
h
−
−
3
7.
Solve for
x
:
8
2
3
=
−
+
x
8
. Solve the inequality: and graph the solution on the number line:
a)
7
2
3
<
−
x
b)
3
4
3
≥
−
x
 3 
9
.
An entertainment system was purchased for $3,000 in 1997. A linear relationship
was used to determine that the value of the system in 1999 was $1,500.
a) Express the value,
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This note was uploaded on 01/22/2012 for the course MATH 115 taught by Professor Plotkin during the Spring '08 term at Rutgers.
 Spring '08
 PLOTKIN
 Math, Calculus

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