Practice Fiiial Exam
The aiiswer sheets
Naiiw:
sCell 011
previous practice exaiiis are omitted
iii
an effort to save paper.
Discrete Math
1. \rit.e (2i2 +
3i)
as an mteger
in
standard form.
)j
(io)
2. What (lOes tile followmg qinil: 1 +
r
+
--
+
?
+
2
3. \\liat is the 129th tvrin in the sqiunce
.
1.5. 22. 29.. .7
.
-
4. What is the l3rd t cmi in the sequence 2,
.
ft,
.
.
.7
—
5. \Vha.t is the suiii of t lie first 70
in standard form?
teriiis
of the
Se(lllt’ll(t’
39. 3.1. 29, 2 1
...
as
au
it
(‘1?,er
Cc
G
-
(I
.
(
)
90
(i. 1\ti
(all
i(e—(reaiii Kilol) has 2 11aV( )rs. You
Ilese flavors?
Volt sV1(’cI
(i
(‘e(l
Io
tlvct 12 flavors. In 1io’v nìaiiy ways
C2()
7. A office supply store has 15 employees. A (lepaitmelital te in ne ds to be selected
with a head illaliager, assist allt iiiaiiager, stock persOli, aiid greeter. In how iiiany
ways aii you select these positions?
H5!
z
-
8. The world cllaflipioilshij) of boxing has 61
competitors.
How many possible ways are
there to rank the (onipetitors froni first to last?
9. You iiee to stop at three places during a road trip. At the first si oJ) there are I gas
xtatious, at the second stop there are 15 gas stations, and at the tlmd stop therv are
4 gas stations. How many cli[er nt gas stations an on stop at if V (0 401) at ouie
station at each place?
Th
10. What is ()‘? Your aHsW< ‘r should h
a natural imiiiher in st
im lard fort n.
A.lgc 1) ra
ii
Writ (
ratioiial
a
‘\25)
iiiiiiil cr in
st andai’d fonii.
q3
-
)
1
12. \\ iii V h_g (S)
)
Hi
(h’
what
)
.
HX H 1HtlOIlfll lll111J)C1 111
rational nuinbi’i
13. Ii
(1
14. If
a > 0. thwii what is log,, (1) as
0,
tlwii
is a
0 as a
a
St.HH(lU1d form.
In
stan(larcl fonn?
rational wmibr
iii
si a 1I(laI(1
CD
15. \Vrit log
1
()
(
aS a
rat ioiial
itiiiiilwr iii st aiI(Ia1(I foriii.
13
loiiii?
__
_
__
Iü. Salve
mi
i
wlieij
—
3
17. Solve br :r when 4(
sc
—
18. Solve for
:1:
Sr
t -51oc
-
X
when 2 + loge
(:i
)
=
7
—
log,
1
(_)
e
19. If (c)
3
= .L
(x)
+ 2 and
—:i’
+ 8, then what is
(-
,f o
a
+
20. Find tl1(
o
1llV(15(’
of
f(.z)
4 (x
—
1) + 12. You
(H11
(11(’ek your
allsw(’r
by s’iii if
-\
(
H-
+
4-
-4.
Dz
ç)
4.
+
+
-
H’
_s
U-,
Lfl
u-J
cD
x
I’
4
•2<
4-
(
‘TN
x
‘<I
\1
c)
-C
L51
+
cc
t’z
+
t’D
+
Tj
x
cD
II
x
JJ
+
25. how iiiaii root s lops
_:z2
+ 14;,
—
49 llav(’?
-
-L
Z
26. Find thu roots of 2.r2 + 3.r
.
.5. (Writu 1)0th root s.)
.
+ 19r2 + 2x
27. Coiiiplutuly fctor
V.
7
—
il
—
3 (Hint: —3 is a root.)
2
r
Th
3
LQ
‘.
(D
28. (c
—
Ce
-‘L-r\T’
i
whun
—
—
1
---k
t
‘
is thu 1istiiicu butwuuii v1iic1r1\vonunibTs.
29. Solvu for
‘
5 < 11.
-
)
Linear Algebra
3. W1iil
i
I 11(
(lVtUlIllilllhIlt
ol t lie iiOiI iix 1 )U1OV?
(
:3
—1
4
S
(- (()
31
Fiiid the
11O(lllCt
1
(2
8
I
12
3
—5N(
a÷(-i
.±
32. \\‘1iit
1
tl1(
illVels(’
of the intrix below?
3
0
(11
)
( O-’
1)
(
(o)
‘3
\\T
V
11 I(’ xyt (1 ii of t lIl(’V
li1iVI (‘(1lla1iO11 ill
t llrvV
1
Val1H
)1VH 1 )V1OW
1S 1 lllHt UiX
i( )1 I.
:1+
y + 3z
=
10
y
=
6
=
13
—3:r + 3y + 2z
o
(
1
)
/
3
34. Usc that
(4 2
(02
0 1
to find r. y. z
—u \
i)
1)
-
/
=1
1/1
0
0
—2
1
—1
7/2
—1
2
R if
kc + 2J 6z = --4
2-j-- z= 4
—
6
\(Y
\
)f J/
2
X
(
\ /
)/
0
-Z
<6
L/
J
(‘(
35. (rnpli I lie IoIIowin I vu voiiniioii functions: 8 ,:i,:r
2 :r
,
3
36. 4
(
n
11)li
f:
37. Graph q:
38. Graph
[—5.3) —> R where f(:r)
{ 1,2,3, 4}
(‘
39. Graph —2(:i
40. Graph
—
—
V:r + 4
4)2
—:r + 2.
=
R where gr)
and label its
— 1 and
E—
/J, 1 /.r, I /:,2,
= ,.2
aiid y— mt.ercept.s (if there are any).
label its vertex.
and label its
:i—
and
7)—
iitercepts.
41. Graph p(r). Label all x—mtercepts.
p(x)
=
(:r + 1)(x — 2)(x
—
2 + 1)
6)(x
42. Graph ‘i(:z). Label all x—itercepts and all vertical asymptotes.
—3(x + 1)(x + 1)
(x + 4)(x — 1)(x —4)
43. Graph
j’x
_
2
3
1
.1(x)—
ifx1
44. Graph
jj’
1
)
2
if x
—
—x+4
(—co, 1);
ifx[1,5]
(‘U’,
1o(
(i).
:.
)
‘c)
o
1
(c
(c’, t,
(oo)
1/r
c’)
1
(,
tt’, a)
1og, (x)
37. g
36. f
°
10
9
8
7
6
5
4
3
2
1
_5
3 —2 —1
—1
i
\ 3
4
5
—1
—2
—3
—4
—5
e
t3,3)
1
2
3
4
0
(‘2---’)
(c..yol
c_-i
+
I
I
I
—
—
I
c_-I
III,’
Ic_
D
(,Q\)
:11. p(:i)
(2,0)
1-
42. r(:i)
—7
43.
—6
-5
44.
f
f
5
5
4
4
3
3
2
1
(sL)
—3
—4
—4
—5
—5