Download Exam I - kfupm

~IATH
1.
Page 1 of 6
001 Exam I (062)
(5 points) Given the sets
A = {xix is an even positive integer < 10}
B = {xix is a composite number < 12}
C = {yly = x 2 - 1, where x is an integer with 0 ~ x < 4}
(a)
List all elements in each of the above sets to get:
~
A=
B=
c=
(b)
1­ , Lf , 6
,
b ,8 Jq)fO}
i
l -I ) , 3 , 8 , 15J­
0
(A n B) U c.
Find the set
B
=( l-f,
(Pi () B) V C
b) g }­
= [ _I)
0)
3/1)
(2 points) Write the polynomial (7 - 5x) (.5 + 8x ­ 3x 2 )
35 i- ( - 25 t 5 G)
=
3.
J-­
£1
A ()
2.
,8
JS:f­
3.
(;/ X
-
2
x. + (_ 40
-r
in standard form.
_ 21) X z
+
31X t3S
(2 points) Find the polynomial, in standard form, of the third degree for
which: the leading coefficient = -5, coefficient of x 2 = 0,
coefficient of x = 3, and constant term = -4.
-5)(.. 3 t oX 2.
-
5
'V'
.~
3
-/"
')"'-r
.,..A-
j
+ 3X
--
L .I
-1
_
L.
\
I
I
Page 2 of 6
MATH 001 Exam I (062)
4.
(4000) (8.1 x 10- 2 )
0.0018
(3 points) Write the number
[Show your steps] .
3)
.( '-I X 10
(
'6 I X 10­
in scientific notation.
3)
/g- X lo-Lt
18' X
/OL.f
5
/.g X 10
where
5.
x > 0, Y > 0, then
'.5"
6.
Factor each of the following as completely as possible over the set of inte­
gers:
(a)
+ 36 y 2 -
z2.
( x: 2_ 12 Y'J + 56j 2)
_
(3 points) x 2
-
12xy
,
(x--
b'j}~
_
'?
~'-
I I». - 6~) - ?] [
(X-bj
t 2­
CX. - 6 'j)'+ l -]
--2) (.X-6) 4.:t.)
.5
Page 3 of 6
MATH 001 Exam I (062)
(b)
I" CS
I
(c)
(3 points) _3x 3n
= _3X
tV'
-_3X
(d)
(2 points) x 4
+ 6x 2n
( X
'Y\
-
3x n
-
21'v\
(
.
IY\
+I
_ 1,):
M
X--\
)
, .5
)2­
r. 5
3~~2 - 4.
_ (X 4 _ 4) ( X 2. +\)
,
'2
CX-2) tx + 2; (x +1)
7.
.
(4 pomts) If
A =
2+J5
2­
J5
5
then write
and
A
+B
in
simplest form.
= '++5 t _,Lf,"-_._-VS
{5) (2 t f5)
(2 - J5) (2. - F5)
A = (2..+
-
,-~
"Ir::- " 2-"
+.~ -=. [: q_LI
-
{S,)
,
.
1,5
Lf - 5
0. 5
-9 _LffS
::: 'iJF.l
I)
------,. ..... .......
2
'!fl.
I..
5
4r~
V2.
+2 ::
-7-'-IJ5
0-5
1(£'(
MATH 001 Exam I (062)
8.
Page 4 of 6
(4 points) The graph of a subset A of real numbers is given by
.....
)3
I
-4
J
I
-2
I
I
0
2
3I
~
I
4
and the graph of a subset B of real numbers is given by
OIl
I
-g
-6
-1
0
(b)
Write C using interval notation.
=
*
I
I
I
I
I
2
3
4
5
6
An B.
Sketch the graph of
(c)
C
-2
(a)
[ - l)) 3) V [- I
C
,
I)
Write C using inequality notation.
C
9.
-3
-4
=f
X
I - 5" ~ X
<~
C1(
-I
~ X <I
1
(2 points) Find the product (2x - 3y) 3
(J.X)
$X
3
s
3 (2X)
36
z
l
:;L
.,
(5:J) +
j
-r
3 ( 2;() (3.'))
5'-1
1
){j
_(3j)',~
~7 j
3
~
MATH 001 Exam I (062)
10.
Page 5 of 6
Simplify each of the following expressions:
.
5
2y - 5
2y 2 + Y - 15
(3 pomts) (y+3 )2 + Y2 - 4 y- 21 --:7
y­
(a)
--
5
(~+S)'1.
+
D
( 'j -7) ( ':1 + s)
x- 1 y3
(4 points)
~3
-zc
--
'j
.x.
-
-1 .
:;'5_ .x2j
X
­ -
~ 2_
X
j
- -
(4 points)
)( 'j
;(1 )
•
-3
2(x - l)(x
-~(X-'S)
.2.
-
-
(X. - \)
t
2.
sc 1
Xj
+
+ 2)
5(X~t)
-
(X +'2)
--
,}j 2 _ .J' t.
X
(c)
(~+-~)~
2-
xy
Y - xy
_ x: :1
~(i-
--
X
-1
,.....,-,
(X
-
5
2(x + 2)(x - ;j)
C)
2X
-~-
_._-~
?;J
1­
j
•
+ L-(
- - - - - - -----,--_.-,-.
-
2. (X_I) (10f t ) (-r- s)
,
2 /(X -t 2 )
/
2
(X~·\) (1'-T
2
C,
t (:J 1- 3)
(:::JtS)2
(b)
:1-7
(2j-S) (~+ 3)
I
5
b
2j -5
1) (:1- s)
(X-I) (::(_?)
2
I<r'(
Page 6 of 6
MATH 001 Exam I (062)
11.
Write each of the following complex numbers in standard form (where
i = yCI).
(a)
(2 - 2i)2
(4 points)
3 + 4i
.
• "l.
1./ - f6. t. of
.
_
4.t-
4-t;1(.-
u
- 3+ '"Ii..
_2c.f~
(~-~It)
(3+4-<')
3'2
2
2Y'
<­
(4 points) The complex conjugate z of the complex number
z
=
yC2 /=8 + ~-27 + i 2007 .
=u: ;. ) ({f; ~
I
-
. L
)
+ (.7
- 3
.3
4-<-
-5 -t"{
-4 -
5 -
I
.
tl
-
.
- 7 + -{
12.
,7.
+32A.
9 -I-/b
-2. 5 - -25
(b)
1
7 -,(
I
(4 points) Write the following expression in simplest form and without the
absolute value symbols:
J9 - 12x
+ 4x 2
where x
Ix - ~I
J~~~~:);:
3
i:- - .
2
%l
\
I .3 - 2X J
I »: -% I
~ I X- fl
2
l:x~
I
x - \
I
-
?