___
Math 1050—4 Final Exam (practice)
#3
April 17, 2015
• No notes, books, etc. are allowed
.
• Answer the questions in the spa
ces provided.
• You have 2 hours to complete this
exam.
•_Good_luck!
Name:
uNID:
Page
Points
2
6
3
6
4
7
5
9
6
5
7
7
8
8
9
3
10
12
11
12
12
6
13
4
14
4
Total:
89
Score
Points earned:
out of a possible 0 points
___
1)
1. (1 point) Find 1
2
(22
(2)
+ (i
4-
U
(2
-))
—)
(q
(112_i)
f
-I)
(.
i)
i)
1.
-
t
2. (1 point) Find
Z
I
I’
&l..
CL)
r-::
CL
—
I—
2
‘/3
—
‘/3
5
Si”,
5
2.
-
.?
of the sequence 7, 11, 15 19,
3. (1 point) What is the 61-st term
..
I
4
(rL)
.i-
-
[I C
U:Lk
a 1i
v
(l
r—
r9#AO
z4r7
3.
of—3, 6, —12, 24,...?
4. (1 point) What is the 57-th term
t vi
c ç
,
a
(r)
(-B)C-)
s..1 -l
4.
()(_;)
7. 9....?
the first 60 terms of the sequence 3, 5,
5. (2 points) What is the sum of
j\n1 yij h c
e
‘t1ii.
ti
-
s•
5
5c())
Page2
30
Points earned:
out of a possible 6 points
C
6. (1 point) Suppose a set A contains 243 obje
cts. How many 92 object subsets of A are
there?
aoQ
/1
Vc*
r
i3
0V
qa
(bo, Q
1)
.
9
/
(i
6.
7. (1 point) How many ways are there to
choose and order 49 objects from a collection
of 304
objects?
_._
)
7.
8. (1 point) How many different ways are
there to order 93 different objects?
8.
9. (1 point) You’re decorating a room by
choosing a color of paint for the walls,
and a color of
carpet. You have 6 different colors of pain
t to choose from, and 11 different colors
of carpet
to choose from. How many different wall
and floor color combinations could you creat
e?
h
c) S
‘
e
9.
10. (2 points) Write
C’
(:)
as an integer standard form
t:
Ci)
Page 3
Points earned:
out of a possible 6 points
cr
-J
C
tf
-4
-4
C
—
r’
‘J
d
c;D1c’
—
c’c
C
C
-‘--I
C
-4
-4
c’i
•1
0
-4
C
u
-j
.
!
.
N[\
cD—)’
A—‘
‘
-
c
‘
E
I
C
;
.EC
-4
-4
cd
c:)
-
-
-
Ii
ci
,—“
s__i
?-
_
“_1
s—’
¶-L.
—r
;—._
L
C
(j
C
-
!
,-
±
t
cr’
‘
.-
%—J
m
;%___,
-4
/
-%
T
L
4’
C
C
z
_____
___
___
___
___
_
_
16. (1 point) Find g o f(x) if f(x)
x + 2 and g(x)
=
(c÷a)
( t)
+
17. (2 points) Find x where x
3
3)
=
8
C)
:t
cv
—
a1J
.X(Xt
)
.4- ?X
—
±“I 9j4
17.
18. (2 points) Find x where 2
a(e
7
/ e
X \
2
1I ex+3)1
+
5
7
—CLt)
‘2
-3\
--
(.)
1.
7
e.
18.__
19. (2 points) Find x where 4log(,(x)
3
Iog,(
)
x
±
+
qQ
8=11
s(j
L
1q.
J.
(. J
*
-
Q
)
,
1T
._
3
20. (2 points) Find the inverse of g(x)
19.LXE
=
7 1og, (x
+
3)
(%)
1N
(i3)
20.
Page 5
Points earned:
out of a possible 9 points
ain of g(x)
21. (1 point) What is the implied dom
=
—
7x
4?
21.
ain of f(x)
22. (2 points) What is the implied dom
=
2
x
—
2x + log(3
i)
—
2
3x
2
x
—
-
7x)?
.
.
23. (2 points) Find
—
IR
22.(1/)
5x + 14
4
—3
-
-
3l
5x
zL_
H
—
23.
Page 6
)c—3-
-i-a
Points earned:
out of a possible 5 points
____
24. (1 point) Find a root of x
3
+
2
2x
—x
+
____
____
6
I) -2 -3 I -b
2()
%2,
—Ci)
7
f
1_/t
t
o)
t
3,
+/
.
(
f; +
—
252 points) How many roots does 2x
2
I
— 3x . ±4have?
.
j
c\
—7
(- ()v)
‘-
26. (2 points) Completely factor —2x
-i-
2x
+
-a
b- ‘icc
.-zi
—‘i
fL3
25.
12. (Hint: 2 is a root.)
C,
—
<C)
=
(-e)-
4Q)()
(ç
-a
--—
(
2
:26.
27. (2 points) Complete the square: Wr
2
—2x
— 4x —5 in the form a(x
—5
_(2
•—
—
÷13)2 + y
where a, /3, y
E
R.
:1 (--a)
a
-...-.
27.
Page 7
Points earned:
out of a possible 7 points
28. (1 point) x
—
een which two numbers?
y is the distance betw
I(IHt-(--’)I
—‘
-Vc-Q
6QfJOfr1
29. (2 points) Solve for x if 13x
2
<
(
-.
28.X
a
4
4
3
3x-1
.‘9/3
-?x2
2(Z<
—2
(44)/
the matrix below?
30. (1 point) What is the determinant of
2
1
—3
5
ZEOt3
30.
31. (2 points) Find the product
(1
o(i
—
2
(N
C’
2
(
matrix below?
32. (2 points) What is the inverse of the
=
)
=
)
32.
/
e8
Points earned:
out of a possible 8 points
33. (1 point) Write [he following system of three linear equations in three variables as a matrix
equation
2x
—
y
—x
+
+ z
=
2
+ 2z
=
1
z
=
0
y
y
—
v H(’
I
0
I
34. (2 points) Solve for x, y, and z if
—1
2 —1
—22—1
3
—1
1
x
y
z
=
—2
2
1
and
Ii
—1
2 —1
—22—1
3 —1
1
=
—1 0
1
—121
—4 5 2
0*
-(
2
/
(-)
(
a
•i-1
“I
.
C)
1
/
/
),L(
Ii
cj
/
I*
Page 9
Points earned:
out of a possible 3 points
For #35—#40, mark and label x- and y-intercepts (if there are any).
38. (2
35. (2 points) 3
1
points) x
(o,o)
39. (2 points) i;:
36. (2 points) x
/
(o,k)
(oo)
2
37. (2 points) x
40. (2 points)
‘V 7
Page 10
Points earned:
out of a possible 12 points
For #41—#46, mark and label x- and tj-intercepts (if there are any).
44. (2 points) log((x)
41. (2 points)
42. (2 points)
1
45. (2 points)
—2e
—
46. (2 points) —3’Yx + 2
43. (2 points) eX
(c
i)
Page 11
Points earned:
out of a possible 12 points
f
: (—2, 01
47. (2 points)
where f(x) 2
x
—
R
49.
points) 4(x
+
-4
j
4
3
-3
-2
—1
I
—4
I
I
I
—3
—2
—1
—
I
-
1
—1
2
3
—4
—3
—2
—1
4
1
—1
234
—2
-
-
—2
—3
—3
—4
-
E
—4
48. (2 points) g : {—4, —2,2)
where g(x)
—
—
1
-
-4
-2--f
-3
-2
‘I
31_2)
(—z)
.-
3
-
I
(—2,—2)
—
-
-
(-ii
( 4)
-
1
—1
234
(‘z
—2
—3
—4
Page 12
Points earned:
out of a possible 6 points
LcCL(t
k?cn
50. (2 points) Graph p(x) and label all x-intercepts:
p(x) _2(x+1)(x+1)(x_2)(x2+1)
/
—5
—?
—4
—3
0
—2
1
2
C2 o)
5
io
51. (2 points) Graph r(x), and label all x-intercepts and all vertical asymptotes:
ir(x)
r( 0)
—
-3(x- 1)(x- 1)
4(x + 2)(x
2 + 1)
rv_
1_C1C..
ç2
-
sy’.
1
—zz i(c) <0
—-3
If
(‘i,o)
—5
—4
—3
—2
Page 13
Points earned:
out of a possible 4 points
ex
ifx1
52. (2 points) Ii(x)
if
1
=
I)
CL)
-1
—4
—3
—2
—1
-
-
1
—1
2
3
4
—2
• (L3)
-
53. (2 points) m(x)
=
—4
(1
ifx
3
x2
if x
(—c, 1)
=
1
ifx e (1,2]
)(214)
--2
—4
I
I
—3
—2
—1
I
I
1
—1
2
3
4
—2
—3
—4
Page 14
Points earned:
out of a possible 4 points