Sample Questions for Mathematics Placement Diagnostic Test.
Elementary functions
1. If
3
x
+4
x
2
+
x

6
=
A
x
+3
+
B
x

2
, then
A
=
.
(
a
)1
(
b
)2
(
c
)
2
5
(
d
)
13
5
(
e
)None of these
2. Let
f
(
x
) =
ax
+ 2 and
g
(
x
) = 3
x

b
. Find values for
a
and
b
so that
f
and
g
are inverse functions.
(
a
)
a
=
1
3
, b
= 6
(
b
)
a
=
1
3
, b
=

6
(
c
)
a
=

1
3
, b
= 6
(
d
)
a
=

1
3
, b
=

6
3. The coefficient of
x
2
y
6
in the binomial expansion of (
x
+
y
)
8
is
(
a
)0
(
b
)28
(
c
)56
(
d
)360
(
e
)None of these
4. If
f
(
x
) = 2
(
x
3
)
, then the inverse function of
f
(
x
) is
(
a
)(log
2
x
)
1
3
(
b
) log
2
(
x
3
)
(
c
) log
2
(
√
x
)
(
d
)(
1
2
)

x
3
(
e
)
1
2
(
x
3
)
5. The slope of the line 3
x

5
y

7 = 0 is
(
a
)
5
3
(
b
)
3
5
(
c
)

5
3
(
d
)

7
5
(
e
)

3
5
6. A right triangle has a hypotenuse of length 13 and one side of length 12. The other side must be of length
(
a
)
√
313
(
b
)25
(
c
)1
(
d
)5
(
e
)None of these
7. If
f
(
x
) =
1
3
x
+
x
, then
f
(

1) equals
(
a
)4
(
b
)

4
3
(
c
)

2
3
(
d
)
2
3
(
e
)2
8. An equation of the line passing through (

2
,
4) with slope
5
4
is
(
a
)5
x

4
y
=

26
(
b
)5
x
+ 4
y
=

26
(
c
)5
x
+ 4
y
= 6
(
d
)4
x
+ 5
y
= 12
(
e
)5
x

4
y
=

6
9. The graph of the parabola
y
=
x
2

100
x
is symmetric with respect to the line
(
a
)
y
= 10
(
b
)
y
=

10
(
c
)
x
=

10
(
d
)
x
= 10
(
e
)
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 Spring '09
 crespo
 Math, Calculus, Trigonometry, Sin, Cos, Inverse function

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