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

2
 1
2. What is the end behavior of the function
3
x
^{7}
+2
x
^{6}
3
x
^{4}

x
^{2}
+
x
 46
?
As
x
→  ∞
,
f
→  ∞
, and as
x
→∞
,
f
→  ∞
.
As
x
→  ∞
,
f
→∞
, and as
x
→∞
,
f
→  ∞
.
As
x
→  ∞
,
f
→∞
, and as
x
→∞
,
f
→∞
.
As
x
→  ∞
,
f
→  ∞
, and as
x
→∞
,
f
→
infty
.
3. What is
?
x
^{3}

x
^{2}
+ 5
x
 13
x
^{2}
+ 13
x
 7
x
^{2}
+ 7
x
 13
x
^{2}
 3
x
+ 13
4. Which of the following polynomials have exactly three real roots,
x
= 1
,
1
, and
3
?
x
^{4}
3
x
^{2}
+ 2
x
 8
x
^{4}

x
^{3}
7
x
^{2}
+
x
+ 6
x
^{5}
3
x
^{4}

x
+ 3
x
^{4}
+3
x
^{2}
 4
5. What is the remainder of
?
18
38
0
28
6. How many possible positive and negative real roots does the function
x
^{3}
4
x
^{2}
+ 3
x
 2
have?
1
or
3
positive,
0
negative
0
or
2
positive, and
1
negative
0
positive and
1
negative
1
positive and
0
or
2
negative
7. The function
has what asymptotes, if any?
A vertical asymptote at
x
= 2
A horizontal asymptote at
x
= 3
A vertical asymptote at
x
= 0
and an oblique asymptote at
y
=
x
A vertical asymptote at
x
= 2
and an oblique asymptote at
y
=
x
 2
8. Which of the following expressions is not equal to the others?
log
_{a}
x
9. The exponential rate of decay of a substance is
.08
per year. What is the halflife of this substance in years?
12.5
years
56.5
years
8.66
years
10.035
years
10. Which of the following bank accounts will be worth the most in 10 years?
$11,000 at 10% simple interest
$9,450 at 9.0% compounded daily
$9,800 at 8.5% compounded continuously
$9,500 at 9.0% compounded quarterly
11. In which quadrants do sine and cosine have the same sign?
I and II
I and IV
II and III
I and III
12. Which of the following is a formula for all of the quadrantal angles?
0≤
θ
< 2
Π
θ
=
, where
n
is an integer
θ
= 2
nΠ
, where
n
is an integer
θ
= (
+1)
, where
n
is an integer
13. Which of the following is not equal to the others?
sin(
Π
/2)
cos(2
Π
)
tan(
csc
14. Which expression is unequal to the others?
sin
^{2}
(
x
)csc
^{2}
(
x
)
cos
^{2}
(
x
)  sin
^{2}
(
x
)
sec
^{2}
(
x
)  tan
^{2}
(
x
)
csc
^{2}
(
x
)  cot
^{2}
(
x
)
15. Which of the following does not solve the equation
sin(
x
)cos(
x
) = 0
?
x
=
x
=
x
=
x
=
16. What is the amplitude and period of the function
f
(
x
) = 2 cos(2
x
)
?
Amplitude:
1
; Period:
2
Π
Amplitude:
; Period:
Π
Amplitude:
4
; Period:
Amplitude:
2
; Period:
Π
17. Which value is defined?
arcsin(2)
arctan(0)
tan(
)
sec(
)
18. Which polar coordinates correspond to the rectangular coordinates
(2, 2)
?
(
,
)

,
(2,
Π
)
(
,
)
19. Convert the polar equation
4 =
r
sin(
θ
)
to rectangular form.
x
= 4
y
= 4
x
y
= 4
y
=  4
20. What are the
x
intercepts, if there are any, for the function defined by
x
= 3
t
 2
,
y
=
t
^{2}
 4
,
3≤
t
≤3
.
(
,
)
( 8, 0)
and
(4, 0)
( 8, 0)
and
(0, 0)
( 2, 0)
and
(2, 0)
21. The graph of
r
= 1 + 2 sin(
θ
)
is symmetric with respect to what?
The pole
The polar axis
The line
θ
=
It is not symmetrical at all
22. The graph of
r
= 2 cos(4
θ
)
is an example of what?
A limacon
A spiral
A circle
A rose curve
23. What is
ı
^{7}
7
?
1
1
ı
 ı
24. What is the polar form of
z
= 1 +
ı
?
(4,
)
,
)
(1,
)
(2,
)
25. Which of the following complex numbers has a different modulus than the rest?
3  4ı
5  ı
+
ı
2ı
26. What are the imaginary roots of the polynomial
x
^{4}
+3
x
^{3}
+5
x
^{2}
+ 27
x
 36
, if there are any?
ı
,

imath
ı
,

ı
2ı
,
2ı
None of these options is correct
27. What is
(
+
ı)
^{4}
?
16
4ı
ı  ı
2
28. Which of the following options is not a
4
th root of
1
?
1
 ı
1  ı
ı
29.
3
x
^{2}
+ 6
x
 5
y
 7 = 0
is what kind of conic?
An ellipse
A parabola
A hyperbola
A circle
30.
x
^{2}
+2
xy
 5
y
^{2}
+ 4
x
 4
y
+ 7
is what kind of conic?
An ellipse
A parabola
A Hyperbola
A circle
31. Given
25
x
^{2}
+4
y
^{2}
 100 = 0
, solve for
a
,
b
, and
c
.
a
= 25
,
b
= 4
, and
c
= 21
a
= 5
,
b
=
,
c
= 2
a
= 2
,
b
= 5
,
c
=
a
= 5
,
b
= 2
,
c
=
32. Given
4
x
^{2}
+2
xy
 5
y
^{2}
+ 6
x
 2
y
 1 = 0
, about how many degrees must the axes be rotated in order to eliminate the
xy
term?
31.7
^{o}
41.3
^{o}
43.7
^{o}
27.1
^{o}
33. Given the polar equation for a conic is
, what kind of conic is it?
An ellipse
A parabola
A hyperbola
A circle
34. Given
is the polar form of a conic, where is the directrix in relation to the pole?
The directrix is to the left of the pole.
The directrix is above the pole.
The directrix is to the right of the pole.
The directrix is below the pole.
35. What is the next apparent term in the sequence
1, 2, 4, 5, 7, 8, 10,…
11
12
13
Impossible to tell
36. Define the sequence
a
_{n}
= 3
n
+ 6
recursively.
a
_{1}
= 9
;
a
_{n+1}
= 3
a
_{n}
+ 6
a
_{1}
= 6
;
a
_{n+1}
= 2
a
_{n}
+ 6
a
_{1}
= 9
;
a
_{n+1}
=
a
_{n}
+ 3
a
_{1}
= 9
;
a
_{n+1}
=
a
_{n}
 9
37. Define the sequence
a
_{n}
=
recursively.
a
_{1}
=
;
a
_{n+1}
=
a
_{1}
=
;
a
_{n+1}
=
a
_{1}
= 3
;
a
_{n+1}
=
This sequence cannot be defined recursively.
38. Find an explicit formula for the following sequence:
1,
, 2,
, 3,
, 4,…
.
a
_{n}
=
a
_{n}
= 2
n
 1
a
_{n}
=
n
+
a
_{n}
=
39. What is
7(4
n
 2)
?
476
500
578
1238
40. What is
(3
^{i}
)
?
32400
3240
456
128
41. Calculate the sum of the first
200
terms of
a
_{n}
=
n
+ 1
.
20300
23000
203000
203203
42. What is the sum of the first five terms in the sequence
a
_{n}
= 2×3
^{n}
?
240
726
126
1452
43. What is the limit of the infinite geometric series
a
_{n}
= 3×
^{n}
3
∞
44. Evaluate
5
x
.
10
The limit does not exist.
45. Evaluate
.
The limit doesn't exist.
Impossible to Calculate
1
1
46. Calculate
x
^{2}
 4
x
 2
5
3
0
 ∞
47. Let
f
(
x
) = 1
for all
x
≠ 0
,
f
(
x
) = 4
for
x
= 0
. Calculate
f
(
x
)
.
2
4
1
The limit doesn't exist
48. Over which of the following intervals is
f
(
x
) =
discontinuous?
[1, 3]
[0, 1]
(2,∞]
The function is continuous on all of these intervals.
49. Over which of the following intervals is the function
f
(
x
) =
discontinuous?
(0, 1]
All
x
> 0
Any interval including
0
The function is continuous everywhere
50. Which type of discontinuity happens to the function
f
(
x
) =
at the vale
x
= 5
?
Infinite discontinuity
Jump Discontinuity
Point Discontinuity
It is continuous at this point.
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