Last Name:
First Name:
2.)
3.)
EaIse
False
4.)
5.)
0
13.)
1.)
14.)
2x2-3x÷l
15.)
~x2÷8x+II4
6.)
17.)
a_i
•t
28
-~
2
16.)
True
-3x3
2
(11)Z3
C
18.)
s-47?
~~47jT
7.)
Tnt.e
19.)
8.)
Poise
20.)
9.)
S
21.)
—zGz
22.)
2. x~7 x-I x-~≤
23.)
x÷2. x—
10.)
11.)
12.)
n~ ~
r-~~)
2.
and
—2
3’)(XZ÷1)
24.) -2~i
26.) 2x
—
3
If
$
S
‘I
-If-S-a-)
a
I
tat
4
1fa34-)
—I
—I
-2
—s
25.) V’~ —1
27.) —3(x + 2)2
If
If’
S
5,
1
—
a
I
-4 -ì 4 -iS
Ays’.secs tLt
—I
-z
—s
-z
—s
-4.’
-4.
wo~!A 6e wv*cktS
g
19.)2x2-Sx+l
-Sx÷3
tx+3
Z%1
1c”)L+xz+~xtI1 R 26
i’i.) ~
LI.
19.’)
~±z-1i’
9.
liij
—I
on
tJCaiti
ii.) f~’(y)=
x3-It
II.’) f’fr)s
b1o’~.,e.itç
is a
incLude:
2.
3..Lf.
2.
writn3
co(T€’-t
Iifx)=
OflSvtt(
x3~L
*11
~
Second Practice Exam
True/False
For #1-8 write the entire word “True” or the entire word “False”.
1.) a(b+c)=ab+ac
2.)
(x+y)ht=a92+yn
r~L~:
3.) ~/x+y=Ø+~J~~ False
(J~OZ*J2,j2
:~Ji’~ifi’÷VT’
4.) (xy)~ =
&) ç4~i=ç’?E~j
~
“•)
(X\n
—
yfl
—
7) nIi-~~
8.) —x4+x~+17x2—3x+4has7roots.
Fa~
~
≥frs
roots)
Algebra
9.) Findxwhere(7—x)3+4= 12.
(7-x?= 2~~r3
7—x z!J3 ‘:2
-Zr
2-7=--5
LX5
10.) If g(x) is an invertible function, and g(2) = 7, then what is g1(7)?
2=
~‘(7)
11.) Find the inverse of
seeing if ~ 1 o f(x) x.)
f(x)
~12x + 4. (You can check your answer by
(~-)
~~2x÷Lf
6JoIve for;)
~
12.) What is the implied domain of
should be an interval.)
~eIe
can’t
flun4~.e(.
J4ence,
IMrIiec~~
t0k€
g(x)
2~5x + 1
an eJen root
5x ~I ?O.
5x~—1 wkic.t~
23? (Your answer
a
So
~‘r1’~~
oo’)
Joynapn.
13.) Suppose that a 0 0 and that b2 —4ac ≥ 0. Write the following number
as an integer in standard form:
—b+ ~.,/b2
—
4ac
)2
+ b( —b + ~/b2
2a
root- a~ axtt6x+c. 7]iat n’eans
abo’te
iS
—
4ac) +
2a
t
t
the
nuniLer
14.)
Find
4x4 6x3 +2
2x2 1
—
zza_sx +1
2xZ~I ~~i~_~xs
—
(cii
-2z2
—
6x3tZz
tZ
)
~3x
—
Zza~31
_(2z2
+
2.
-I)
-3x÷3
15.)
Find
4x3—5x+6
x—2
2-
o-5≤
S i~ 22
‘+8 II 28
16.) What is the slope of the straight line in R2 that passes through
the points (2,4) and (5, 10) 7
10
lO_Lf
6-z 3
1+
2.
5
17.) Complete the square: Write 2x2
where ct,8,7 eR.
_Lf
2
2(’x—I)
18.) How many roots does 2x2
E-O2~
no
So
4x + 5 in the form cr(x +
(~)Z
+5
Discriw~nant
—
—
~3)2
+7
+3
6x + 10 have?
Lflz)(,o’)
3~
—so
<a,
roots
19.) Find the roots of —2x2 + 6x + 2
≤2_1+(_2~)(a)
D~scnni~inontt
2.
So
3~-’-1≤=52
coats
q~’~ fl.z.is’ ~2Ti?
g~-5: -≤±-1-ir -~±24i?
a&z)
z( a)
20.) Find a root of —3x3
F
tots
t\’ese
—
7x2
are
—
a
4a~~
~
W;U
nu,M~24CS
to
3±41?
ste
~
One
root.
4~ctt
-3&Z?7(2~-t&23&7&~)-%2)~
2’t-lBtB-’+
0
so -2
15
a
root.
21.) (2 points) Completely factor —2w3 + 6w2 2w + 6. (Hint: 3 is a root.)
(Your answer should be a product of a constant and maybe some linear and
quadratic polynomials that have leading coefficients equal to 1, and such that
any of the quadratics in the product have no roots.)
—
3
-a
~
-2
—6
a
DSCfmnSflt S —2x2-2
~ ‘+&2)(-2) = 0- IC
~
-2x2-2. kos ~
so
-z a -z!o
IS
<0
roots.
lltu, _ZxZ_2 covnpietc~y 12actocs
°.S
So
~2x3+~x2-2zt~
-Li1. ~x~-Zy.:i-~
/
(_2.z2 -2)
(irS)
(_212_2’)
(-2)
(zati)
22.) (2 points) Completely factor 2w3 + liz2 20w + 7. (Hint: -7 is a root.)
(Your answer should have the same form as described in #2 )
—
—7
111-207
2. 1
2~
~-7
D;scr~-~nont olD ~Z3x+(
(31)2 ‘+(z
)(i)z 1_Sz I
So
Zxtr3ztI kcas 2.
They are:
-3
3.e(
so
coatS.
is
zxt÷I1xa~2ox,7
z(i)
/\
(x÷7’)
(zx1~3x+I)
t.j.
‘-I
/
2
Lf.
~4. fl~s1
Zxt-3xtI
cac-~cs as 2 fr-OCx- 14~)
2x3tIItt-ZOxt7
CoYfl?I€tt~/
(ztl)
(at- 3x+I)
I
(a) fr-I) C
Graphs
23.) List all of the monic linear factors of p(x) that you know of from the
graph below.
p&c)
I literceff~, —4Vo.ctors
24.) Graph —2.~’x 1 and label its x- and -intercepts. G~r~~k ~Ji’.
Fi;p over x-a*Ts. StatcSi vect~c4~y. 5k t n lit f. z_int€rcert is soIt4tioi,i
—
i-f
to
25.) Graph ~
r;nttcCer
5
:2
1 and label its x- and y-intercepts.
e
;j~ ao.in 1..
x-hvteccept ;~ I ti ~ to
~€
naa~4.i-l. a_~nttrctpt ~
26.) Graph 2x 3 and label its x- and y-intercepts.
3: 2.(x _3/)
So ‘root anA x-iwtttcc1t ~s ~
3tfl~t4~9)t is 2(o)
k a stca;31’et )ine
x- an8
-inteccۍts
27.) Graph —3(x + 2)2 1 and label its ertex.
—
ch9
—
~
—
s\.~;11e 1St 2. si,;ct
LtO%4frl
I..