Final Review
Discrete Math
For #1-5 find the specific term:
1) Find the 18° term for: 67,61,55,
...
25
2) Find the 21’° term for:
3) Find the 83
term for:
-
11,
10,
6,
1(L8.4..,,
t
4) Find the 57° term for:
5) Find the 32’’ term for:
3.6,
(
12.24.... (? C
3,4.
Q
For #6—12 find
time given sum:
4
6)
2
Z(i
1)
1
‘Z
Nl
C.
N
CD
CD
N
CD
H
ND
o1(
1’
4
c)
J
—cc)
et
‘.
L
+
4-
C
(
i1
L
c
)
ND
r4c’
DID
N
CD
-t
C
DiD
CD
j
3
J
N
1-
U4I
—
3
I
II
4
I -J
cd
V
I
N
t.
a
N
For #13-21 find the following:
13) You’re at. Café Rio and want to order a burrito. There are three kinds of beans, two types of rice, and
four kinds of meat fillings for the burrito. How many different kinds of burritos can you make if you select
one of each? (You dont need to simplify)
14) Write
()
as an integer
r.
Ofec
Th& €
(
c(er
c14)€Sfl
yo’LX*4 ec
Or
ae(
,i
c
_IL
15) Suppose a set A contains 243 objects. How niany 92 object subsets of A arc there? (You don’t need to
simplify)
—
92
16) How many ways are there to choose and order 49 objects from a collection of 304 objects? (You clout
need to simplify)
17) How many different 4 letter words can you make with the letters MATH if you use each letter once? (You
don’t need to simplify)
18) How many different ways can you order 21 different objects? (You don’t need to simplify)
(
19) There are 20 people competing for 3 scholarships each worth $5000 per year. How many different ways
can you select three different people? (You don’t riced to simplify)
Th
cc e(
‘ce S
20) There are 20 people competing for a $1000, $3000, and $5000 scholarship. How many different ways can
you select the three different people? (You don’t need to simplify)
ao
o
2
21) How luau
3 people comnuttees can you make from 12 people? (You (lout need to sinphfv)
/L
ccTesY
(2
-
Graphing
Graph and state the xuuitercept (s), v—intercept, [omnain (D), range (R), lead mug
(EB) or vertical asymptote (VA) when specified:
22) Graph
f(r)
2
23) Graph
•
D=
2-1) Graph
-it;=
I,-.
f(r)
x-int(s)=
terni
(LI), end behavior
=
(
—
11=
‘
(r)
—
1.2
x-int(s)=IP b
2i) Graph
y-int=
f(.r)
=
x-int(s)=N
DB
4
-
y-int=
_‘)
___
26) Graph (a)
or any even root function
27) Graph
f(.r)
—
or any odd root function
—z
yintr
x-int(s)
Lc
D=-ff R
28) Graph
x-iiit (s)
D
30) Graph
f()
-
29) Graph
—
Lt
y-intNOi
f(a)
xint(s) Jxe
it
L
4
Graph f(r) = Iog(x) where a
D
f(e)
a where a
xint(s)=
D
y-iut—
__B
2
>
1
y-int—
31)
± ±X
x-int(s)
D±B
-
y-int=
>
1
32) Graph
f : (—2,0]
—>
3:3) Graph g {4. 2, 2}
1
1
=
R where
=
—
R where
—
—3
‘2/
0
0
e
e
........::......:....
.i.
D=J2 B
34) Graph g(x)
=
—
1og
(i
—
1)
:35) Graph f(x)
=
—\
0
:og
ci
?
rj.
‘
(G
‘
(D:
x-int(s)=J v-iiit=JI€
D=4I R=L
x-int(s)= N0€
B =JOI__
7”
t\_
F
1
-
($-3
.
—
LV-*
\
1Ct
6
\Je(cc
b. Z
+
T
) 0 C)
4
-
C
Cl
IC
‘e
r’1
•
J1-
L
ç
C
L
-
I
J
U-
1
4
r’J
÷
?
1
—
-
-
‘‘
-4
—4
±
-
+
C”
c1
t\
+
4
4
J
C
2H
C
‘0
J
4
C)
o
-
43
0
:
-4-
41) Graph
—
1)(a: —1)
2 + 1)
4(a: + 2)(a
10) Graph r(i)
=
f(x)=
1
3
2
r
if .e E (—, 1)
ifx=1
if :r E (1. 2J
-3&1Lzi
(\
\S
Lk
A3€
I;
2
Lk=
J LT/EB=ZL±ffa
a
42) State the x and
f(x)
intercept for:
if x <2
if a> 2
=
J
1
D=fE)
—
\L>
i-’—
(c:
DN
Algebra
/16
a
as a rational
r>LQ
0
if
rU2 t,cz
43) Write
R=
-
number.
a:
8
fOj
14) Write
7
(7)
integer.
9/
L
/
45) Write log
3
I
I
)
1
(q
S
an,
/
S
46) Write
\cc(3
70
47) Write 7
Iog
(
1)
S)
irteger.
us
au integer.
J
L
1
)
3
48)Find.rwhe
4
.
re
/
/
C,
\fj
2/
49) Find .r where 2
(c2
+5
7
%__
9
0
50) Find r where (2 5) (3)
f
2”
J
)aN
S\/
/ 3
4 hñ(
—j
51) Find r where 1og)()
—
1
Iog
(
2
—
r)
3
i--j1
‘1
52) Find
i
where dlog (r) + 1og
(3)
+
=
/
e(i) e(
1Ø
ii
I
-
J
r-(
/
/‘
-
53) Find
i
where 2
=
(r
6
3 log
1)
/
(2)
i-\
54) Find q
f(r)
if
.r + 3
f(r)
and g(r)
=
/
55) Find the inverse of g(.r)
=
2)/—r
r
(
10
OrvC&
I
•
56) FInd the Inverse of m(x) = 31og(5
‘t
-
2x)
Z
t°!)e(S-2.6’
S-ant
5?) FInd the Implied vlnnrnin hr p(x) =
(ft
a
58) FIndthehnplied&uii*inbra(z)=
rt4t*I
-3z+log
2
Flndthelmplieddomsdnoff(z)=z
(
4-5x)
59) 5
5fgb’H
+
60) FInd the Implied domain of g(z)= j _?WZZ
61) Completethesquare: 2
-4x-8lnthebnnofa(z+fl)
write2x
+
’ywherea,fl,yER.
cD
Z(ij_a,—3
—3
5
3
11
62) How ninny roots does 212
of i2
64) Find a rcot of ;z:i +
—
Sr ± 2
2
2;r
cLTDof
3a: ± 4 have
() -y
j:i vr\CC\1
63) Find the roots
—
—
.r + 6
.
27
C3* 2-’3
65) Completely factor: f(r)
I
66) Solve fir
i
i Zr
=
2 + 2x
x
2
;u ± 6 (Hint: —3 is a root)
-\
—
3 + 2 <10
rDc
-c’ccPi-N
-2
L
—
orrN
-3
Zr/\\
12
L
/ +L
I
kJ
67) Solve for
.
if 3:r
5 > 1
21
ck+
(
e:>i
Linear Algebra
() Find the
determinant
of the matrix:
—3
0
(—9
O
69) Find the determinant of the matrix:
i-\
—
2.
‘S
—1
—1
0
—1
I’
(
o
a\
1
2
3
(o\)
70) Find the product of
71) Find the inverse of
c*
11
4
3
2
-
—\\
ID
k
l
13
S
Li.
n
fT
jT
?
i
I—
I
=
I-
\(
g
\xJ \
1*
z ‘II ‘x ioj ajos (
\gJ
/z /T
/I
I—
TJ
I
T—
-
1
—
I
Ii +
=
x
—
+ Ii
z + 11
/
aiqJ ITT sIloi4ITnbJ .111)1111 JLJtI4 JO UT)45\5 tILXOJJOJ HJ1 3!’X\.
=
—
/
:I1OUIuIb- XIJWU1
su
(\Q)cç
(rL
<7
(1
/IJ
0
i
J p IMTJd
0
(L
—
P11Td
(