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f (x) = 2x
,
g(x) =
, and
h(x) = x - 1
. What is
f
o(g
o
h)
?

(A)

(B)
x -

(C)
2

(D)
- 1

What is the end behavior of the function
3x^{7} +2x^{6} -3x^{4} - x^{2} + x - 46
?

(A)
As
x→ - ∞
,
f→ - ∞
, and as
x→∞
,
f→ - ∞
.

(B)
As
x→ - ∞
,
f→∞
, and as
x→∞
,
f→ - ∞
.

(C)
As
x→ - ∞
,
f→∞
, and as
x→∞
,
f→∞
.

(D)
As
x→ - ∞
,
f→ - ∞
, and as
x→∞
,
f→infty
.

What is
?

(A)
x^{3} - x^{2} + 5x - 13

(B)
x^{2} + 13x - 7

(C)
x^{2} + 7x - 13

(D)
x^{2} - 3x + 13

Which of the following polynomials have exactly three real roots,
x = 1
,
-1
,
and
3
?

(A)
x^{4} -3x^{2} + 2x - 8

(B)
x^{4} - x^{3} -7x^{2} + x + 6

(C)
x^{5} -3x^{4} - x + 3

(D)
x^{4} +3x^{2} - 4

What is the remainder of
?

(A)
18

(B)
38

(C)
0

(D)
28

How many possible positive and negative real roots does the function
x^{3} -4x^{2} + 3x - 2
have?

(A)
1
or
3
positive,
0
negative

(B)
0or2
positive, and
1
negative

(C)
0
positive and
1
negative

(D)
1
positive and
0
or
2
negative

The function
has what asymptotes, if any?

(A)
A vertical asymptote at
x = 2

(B)
A horizontal asymptote at
x = 3

(C)
A vertical asymptote at
x = 0
and an oblique asymptote at
y = x

(D)
A vertical asymptote at
x = 2
and an oblique asymptote at
y = x - 2

Which of the following expressions is not equal to the others?

(A)
log_{a}x

(B)

(C)

(D)

The exponential rate of decay of a substance is
.08
per year. What is the
half-life of this substance in years?

(A)
12.5
years

(B)
56.5
years

(C)
8.66
years

(D)
10.035
years

Which of the following bank accounts will be worth the most in 10 years?

(A)
$11,000 at 10% simple interest

(B)
$9,450 at 9.0% compounded daily

(C)
$9,800 at 8.5% compounded continuously

(D)
$9,500 at 9.0% compounded quarterly

In which quadrants do sine and cosine have the same sign?

(A)
I and II

(B)
I and IV

(C)
II and III

(D)
I and III

Which of the following is a formula for all of the quadrantal angles?

(A)
0≤θ < 2Π

(B)
θ =
, where
n
is an integer

(C)
θ = 2nΠ
, where
n
is an integer

(D)
θ = ( +1)
, where
n
is an integer

Which of the following is not equal to the others?

(A)
sin(Π/2)

(B)
cos(2Π)

(C)
tan(

(D)
csc

Which expression is unequal to the others?

(A)
sin^{2}(x)csc^{2}(x)

(B)
cos^{2}(x) - sin^{2}(x)

(C)
sec^{2}(x) - tan^{2}(x)

(D)
csc^{2}(x) - cot^{2}(x)

Which of the following does not solve the equation
sin(x)cos(x) = 0
?

(A)
x =

(B)
x =

(C)
x =

(D)
x =

What is the amplitude and period of the function
f (x) = 2 cos(2x)
?

(A)
Amplitude:
1
; Period:
2Π

(B)
Amplitude:
; Period:
Π

(C)
Amplitude:
4
; Period:

(D)
Amplitude:
2
; Period:
Π

Which value is defined?

(A)
arcsin(2)

(B)
arctan(0)

(C)
tan()

(D)
sec()

Which polar coordinates correspond to the rectangular coordinates
(2, 2)
?

(A)
(,)

(B)
- ,

(C)
(2, Π)

(D)
(,)

Convert the polar equation
4 = r sin(θ)
to rectangular form.

(A)
x = 4

(B)
y = 4x

(C)
y = 4

(D)
y = - 4

What are the
x
-intercepts, if there are any, for the function defined by
x = 3t - 2
,
y = t^{2} - 4
,
-3≤t≤3
.

(A)
(,)

(B)
(- 8, 0)
and
(4, 0)

(C)
(- 8, 0)
and
(0, 0)

(D)
(- 2, 0)
and
(2, 0)

The graph of
r = 1 + 2 sin(θ)
is symmetric with respect to what?

(A)
The pole

(B)
The polar axis

(C)
The line
θ =

(D)
It is not symmetrical at all

The graph of
r = 2 cos(4θ)
is an example of what?

(A)
A limacon

(B)
A spiral

(C)
A circle

(D)
A rose curve

What is
ı^{7}7
?

(A)
1

(B)
-1

(C)
ı

(D)
- ı

What is the polar form of
z = 1 + ı
?

(A)
(4,)

(B)
,)

(C)
(1,)

(D)
(2,)

Which of the following complex numbers has a different modulus than the rest?

(A)
3 - 4ı

(B)
5 - ı

(C)
+ ı

(D)
-2ı

What are the imaginary roots of the polynomial
x^{4} +3x^{3} +5x^{2} + 27x - 36
,
if there are any?

(A)
ı
,
- imath

(B)
ı
,
- ı

(C)
2ı
,
-2ı

(D)
None of these options is correct

What is
( + ı)^{4}
?

(A)
-16

(B)
4ı

(C)
ı - ı

(D)
2

Which of the following options is not a
4
th root of
1
?

(A)
1

(B)
- ı

(C)
1 - ı

(D)
ı

3x^{2} + 6x - 5y - 7 = 0
is what kind of conic?

(A)
An ellipse

(B)
A parabola

(C)
A hyperbola

(D)
A circle

x^{2} +2xy - 5y^{2} + 4x - 4y + 7
is what kind of conic?

(A)
An ellipse

(B)
A parabola

(C)
A Hyperbola

(D)
A circle

Given
25x^{2} +4y^{2} - 100 = 0
, solve for
a
,
b
, and
c
.

(A)
a = 25
,
b = 4
, and
c = 21

(B)
a = 5
,
b =
,
c = 2

(C)
a = 2
,
b = 5
,
c =

(D)
a = 5
,
b = 2
,
c =

Given
-4x^{2} +2xy - 5y^{2} + 6x - 2y - 1 = 0
, about how many degrees must the
axes be rotated in order to eliminate the
xy
-term?

(A)
31.7^{
o
}

(B)
41.3^{
o
}

(C)
43.7^{
o
}

(D)
27.1^{
o
}

Given the polar equation for a conic is
, what
kind of conic is it?

(A)
An ellipse

(B)
A parabola

(C)
A hyperbola

(D)
A circle

Given
is the polar form of a conic,
where is the directrix in relation to the pole?

(A)
The directrix is to the left of the pole.

(B)
The directrix is above the pole.

(C)
The directrix is to the right of the pole.

(D)
The directrix is below the pole.

What is the next apparent term in the sequence
1, 2, 4, 5, 7, 8, 10,…

(A)
11

(B)
12

(C)
13

(D)
Impossible to tell

Define the sequence
a_{n} = 3n + 6
recursively.

(A)
a_{1} = 9
;
a_{n+1} = 3a_{n} + 6

(B)
a_{1} = 6
;
a_{n+1} = 2a_{n} + 6

(C)
a_{1} = 9
;
a_{n+1} = a_{n} + 3

(D)
a_{1} = 9
;
a_{n+1} = a_{n} - 9

Define the sequence
a_{n} =
recursively.

(A)
a_{1} =
;
a_{n+1} =

(B)
a_{1} =
;
a_{n+1} =

(C)
a_{1} = 3
;
a_{n+1} =

(D)
This sequence cannot be defined recursively.

Find an explicit formula for the following sequence:
1,, 2,, 3,, 4,…
.

(A)
a_{n} =

(B)
a_{n} = 2n - 1

(C)
a_{n} = n +

(D)
a_{n} =

What is
7(4n - 2)
?

(A)
476

(B)
500

(C)
578

(D)
1238

What is
(3^{i})
?

(A)
32400

(B)
3240

(C)
456

(D)
128

Calculate the sum of the first
200
terms of
a_{n} = n + 1
.

(A)
20300

(B)
23000

(C)
203000

(D)
203203

What is the sum of the first five terms in the sequence
a_{n} = 2×3^{n}
?

(A)
240

(B)
726

(C)
126

(D)
1452

What is the limit of the infinite geometric series
a_{n} = 3×
^{n}

(A)

(B)

(C)
3

(D)
∞

Evaluate
5x
.

(A)
10

(B)

(C)

(D)
The limit does not exist.

Evaluate
.

(A)
The limit doesn't exist.

(B)
Impossible to Calculate

(C)
1

(D)
-1

Calculate
x^{2} - 4x - 2

(A)
5

(B)
3

(C)
0

(D)
- ∞

Let
f (x) = 1
for all
x≠ 0
,
f (x) = 4
for
x = 0
. Calculate
f (x)
.

(A)
2

(B)
4

(C)
1

(D)
The limit doesn't exist

Over which of the following intervals is
f (x) =
discontinuous?

(A)
[1, 3]

(B)
[0, 1]

(C)
(2,∞]

(D)
The function is continuous on all of these intervals.

Over which of the following intervals is the function
f (x) =
discontinuous?

(A)
(0, 1]

(B)
All
x > 0

(C)
Any interval including
0

(D)
The function is continuous everywhere

Which type of discontinuity happens to the function
f (x) =
at the vale
x = 5
?