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FINAL EXAM SAMPLE PROBLEMS
MATH 148 AUTUMN 2008
1.
a)
Find the midpoint of the line segment connecting the two points, (–52, 17) and (–10, 10).
b)
Find the distance from the midpoint found in part a) to the point (–52, 17). (Round to 4
significant figures.)
2.
Solve the following systems of equations:
a)
⎪
⎩
⎪
⎨
⎧
−
+
=
+
−
=
+
24
13
41
8
2
2
x
x
y
x
y
x
b)
⎩
⎨
⎧
−
=
=
−
1
2
9
2
x
y
y
x
c
)
⎪
⎩
⎪
⎨
⎧
+
+
−
=
−
=
15
3
4
1
9
2
2
2
x
x
y
x
y
3.
Gary leaves New York at 3 p.m. in his old car and averages 45 mph. Jeff Gordon, the famous
NASCAR driver, leaves New York at 10 p.m. in his race car along the same route and averages
180 mph. Let
t
represent the number of hours after 3 p.m.
Write the distances traveled by Gary
and Jeff. How many hours will Gary travel before he is passed by Jeff? Round your answer to 2
decimal places.
4.
An alchemist is trying to turn lead into gold. In order to do this, he must combine lead and
copper in such a way that the resulting mixture is
2
9
lead.
He currently has 30 kilograms of a
mixture which is
1
7
lead and
6
7
copper.
How many kilograms of lead must he add to the mixture
to get the required “magical” mixture?
(Round to the nearest hundredth.) Did the mixture really
turn to gold?
5.
A decorator has 92 onefootsquare tiles that will be laid around the edges of a 12by15foot
room.
A rectangular rug that is 3 feet longer than it is wide is to be placed in the center area
where there are no tiles.
To the nearest quarter foot, find the dimensions of the smallest rug that
will cover the untiled part of the floor.
[Assume that all the tiles are used and that none of them
are split.]
6.
Draw a complete graph of the equation
895
444
147
8
2
3
+
−
−
=
x
x
x
y
. Be sure to find and label
the roots. Round your answer to 2 decimal places.
7.
Give a window for a complete graph of
3
0.05
15
16
yx
x
=
−+
+
.
Find the zeros and round to 2
decimal places.
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 Spring '08
 Mcginnis
 Math

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