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Pre-‐Calculus
Midterm
Exam
!
Score:
______
/
______
Name:
____________________________
Student
Number:
___________________
Short
Answer:
Type
your
answer
below
each
question.
Show
your
work.
1
Verify
the
identity.
cot
θ
·∙
sec
θ
=
csc
θ
2
A
gas
company
has
the
following
rate
schedule
for
natural
gas
usage
in
single-‐family
residences:
Monthly
service
charge
$8.80
Per
therm
service
charge
1st
25
therms
$0.6686/therm
Over
25
therms
$0.85870/therm
What
is
the
charge
for
using
25
therms
in
one
month?
What
is
the
charge
for
using
45
therms
in
one
month?
Construct
a
function
that
gives
the
monthly
charge
C
for
x
therms
of
gas.
Pre-‐Calculus
Midterm
Exam
!
3
The
wind
chill
factor
represents
the
equivalent
air
temperature
at
a
standard
wind
speed
that
would
produce
the
same
heat
loss
as
the
given
temperature
and
wind
speed.
One
formula
for
computing
the
equivalent
temperature
is
W(t)
=
𝑡
33 −
!”.!”!!” !!! !!!
!
!!”#
33 − 1.5958 33 − 𝑡
if 0 ≤ v < 1.79 if 1.79 ≤ v < 20
if v ≥ 20
where
v
represents
the
wind
speed
(in
meters
per
second)
and
t
represents
the
air
temperature
.
Compute
the
wind
chill
for
an
air
temperature
of
15°C
and
a
wind
speed
of
12
meters
per
second.
(Round
the
answer
to
one
decimal
place.)
4
Complete
the
following:
(a)
Use
the
Leading
Coefficient
Test
to
determine
the
graph’s
end
behavior.
(b)
Find
the
x-‐intercepts.
State
whether
the
graph
crosses
the
x-‐axis
or
touches
the
x-‐axis
and
turns
around
at
each
intercept.
(c)
Find
the
y-‐intercept.
f(x)
=
x2(x
+
2)
(a).
(b).
(c).
Pre-‐Calculus
Midterm
Exam
!
5
For
the
data
set
shown
by
the
table,
a.
Create
a
scatter
plot
for
the
data.
(You
do
not
need
to
submit
the
scatter
plot)
b.
Use
the
scatter
plot
to
determine
whether
an
exponential
function
or
a
logarithmic
function
is
the
best
choice
for
modeling
the
data.
Number
of
Homes
Built
in
a
Town
by
Year
6
Verify
the
identity.
(1
+
tan2u)(1
-‐
sin2u)
=
1
7
Verify
the
identity.
cot2x
+
csc2x
=
2csc2x
-‐
1
8
Verify
the
identity.
1
+
sec2xsin2x
=
sec2x
Pre-‐Calculus
Midterm
Exam
!
9
Verify
the
identity.
cos(α
-‐
β)
-‐
cos(α
+
β)
=
2
sin
α
sin
β
10
The
following
data
represents
the
normal
monthly
precipitation
for
a
certain
city.
Draw
a
scatter
diagram
of
the
data
for
one
period.
(You
do
not
need
to
submit
the
scatter
diagram).
Find
the
sinusoidal
function
of
the
form
that
fits
the
data.
Pre-‐Calculus
Midterm
Exam
!
Multiple
Choice:
Type
your
answer
choice
in
the
blank
next
to
each
question.
_____11.
The
graph
below
shows
the
percentage
of
students
enrolled
in
the
College
of
Engineering
at
State
University.
Use
the
graph
to
answer
the
question.
Does
the
graph
represent
a
function?
A.
Yes
B.
No
_____12.
Find
the
vertical
asymptotes,
if
any,
of
the
graph
of
the
rational
function.
f(x)
=
!!!
!(!!!)
A.
x
=
0
and
x
=
4
B.
x
=
0
C.
x
=
4
D.
no
vertical
asymptote
Pre-‐Calculus
Midterm
Exam
!
_____13.
The
formula
A
=
118e0.024t
models
the
population
of
a
particular
city,
in
thousands,
t
years
after
1998.
When
will
the
population
of
the
city
reach
140
thousand?
A.
2008
B.
2005
C.
2006
D.
2007
_____14.
Find
the
specified
vector
or
scalar.
u
=
-‐4i
+
1j
and
v
=
4i
+
1j;
Find
𝑢 + 𝑣 .
A.
34
B.
8
C.
2
D.
5
_____15.
Find
the
exact
value
of
the
trigonometric
function.
Do
not
use
a
calculator.
cot −
5𝜋
4
A.
-‐1
B.
− 2
C.
1
D.
− !
!
Pre-‐Calculus
Midterm
Exam
!
_____16.
Find
the
x-‐intercepts
(if
any)
for
the
graph
of
the
quadratic
function.
6×2
+
12x
+
5
=
0
Give
your
answers
in
exact
form.
A.
B.
C.
D.
_____17.
Use
the
compound
interest
formulas
A
=
Pert
and
A
=
P 1 + !
!
!”
to
solve.
Suppose
that
you
have
$11,000
to
invest.
Which
investment
yields
the
greater
return
over
10
years:
6.25%
compounded
continuously
or
6.3%
compounded
semiannually?
A.
$11,000
invested
at
6.25%
compounded
continuously
over
10
years
yields
the
greater
return.
B.
Both
investment
plans
yield
the
same
return.
C.
$11,000
invested
at
6.3%
compounded
semiannually
over
10
years
yields
the
greater
return.
_____18.
Find
functions
f
and
g
so
that
h(x)
=
(f
∘
g)(x).
h(x)
=
(6x
-‐
14)8
A.
f(x)
=
6x
-‐
14,
g(x)
=
x8
B.
f(x)
=
6×8
-‐
14,
g(x)
=
-‐14
C.
f(x)
=
x8,
g(x)
=
6x
-‐
14
D.
f(x)
=
(6x)8,
g(x)
=
-‐14
Pre-‐Calculus
Midterm
Exam
!
_____19.
Begin
by
graphing
the
standard
absolute
value
function
f(x)
=
|
x
|.
Then
use
transformations
of
this
graph
to
graph
the
given
function.
h(x)
=
2
|
x
|
+
2
A.
B.
C.
D.
Pre-‐Calculus
Midterm
Exam
!
_____20.
Find
the
reference
angle
for
the
given
angle.
-‐404°
A.
44°
B.
46°
C.
134°
D.
136°
