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[
PRACTICE EXAM FOR FINAL
]
Solution
1.
Simplify:
2.
Factor:
3.
Simplify:
4.
Subtract and simplify:
5.
:
Divide and simplify
6.
,
Let W be the amount of total work
and suppose that 2
nd
person takes
.
hours to do the job alone
Then the amount of work done by
the 1
st
person alone in 1 hour is
,
and by 2
nd
person alone in 1 hour is
.
Hence The amount of work done
together in 4 hours is
,
and
note that this is equal to total work
. .
.
i e
7.
:
Write without negative exponents
.
8
Simplify by rationalizing the
:
denominator
9.
,
,
and
.
Hence
10.
,
then
11.
Let
be the time taken the car to
.
overtake the truck Then the
distance traveled by the truck is
.
This should be equal to the
,
distance traveled by the car which
is
.
.
Hence the the distance is
12.
Observe that the diagonal of the
.
square is the diameter of the circle
Since the length of a side of the
square is
,
the length of the

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PRACTICE EXAM FOR FINAL
]
Solution
diagonal is
.
Hence the radius of
the circle is
.
,
Thus the area of
the circle is
13.
Since

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