AP CALCULUS
PRECALCULUS SUPPLEMENTARY VI
Problems
:
1)
From a rectangular piece of cardboard having dimensions
a
cm
=
3
and
b
cm
=
7
, an open box is to be made by
cutting out an identical square with side length
x
from each corner and turning up the sides (see diagram below).
Which of the following choices gives the correct equation of the volume
V
of the box as a function of
x
?
A)
(
)
(
)(
)
V x
x
x
x
=
−
−
3
7
B)
(
)
(
)(
)
V x
x
x
x
=
−
−
3
2
7
2
C)
(
)
(
)(
)
V x
x
x
=
−
−
3
2
7
2
D)
(
)
(
)(
)
V x
x
x
x
=
−
−
2
3
7
E)
(
)
(
)(
)
V x
x
x
x
=
−
−
4
3
7
2)
Let
(
)
f
x
x
x
k
=
+
+
2
3
.
If
(
)
f
x
is divisible by
(
)
x
−
1
, then what is the remainder when
(
)
f x
is divided by
(
)
x
+
1
?
3)
Let
(
)
f
x
x
x
kx
=
+
+
+
3
2
8
3
and
(
)
g x
x
=
+
4
1
2
.
When each of these respective functions is divided by
(
)
x
+
2
,
their remainders are equal.
What is the value of
k
?

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