Mathematics 11
2nd Long Exam
1st Sem, AY 20152016
October 19, 2015
Directions:
Show all necessary solutions. No solution, no credit. Use nonerasable blue or black ink pen
only. Box your final answers.
I. Write TRUE if the statement is always true. Otherwise, write FALSE.
(1 point each)
1. The set
f
=
{
(1
,
5)
,
(2
,
0)
,
(3
,
6)
,
(4
,
0)
}
is a function.
2. The graph of
y
+ 3
x

6 = 0 has
y
intercept

6.
3. The equation 2
x
2

5
x

1 = 0 has solutions
x
=
5
±
√
17
4
.
II. Simplify the following expressions. Express rational powers as radicals in simplest form.
(Assume all denominators are nonzero.)
1.
√
3
4

2
√
3
(3 points)
2.
(
16
x

2
)
3
/
4
x
5
/
2
y

6
16
y

2
(3 points)
3. 3
√
12 +
√
18

2
√
75
(3 points)
III. Find the solution set of the following equations and inequality.
1. 5 +
√
13

2
x
=
x
(4 points)
2.
2
x
+ 7
x
+ 1
= 3
(4 points)
3. (
x
2
+ 3)
2

4(
x
2
+ 3)

5 = 0
(4 points)
4.
2
x

1
x
+ 3
≤
1
(4 points)
IV. Do as indicated.
1. Given the points
M
(4
,

1) and
N
(7
,
3).
(a) Find the
length
and
midpoint
of the line segment
MN
.
(2 points)
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 Fall '16
 Math, Algebra, Equations, Academic dishonesty, Line segment