King Fahd University of Petroleum and Minerals
Prep-Year Math Program
'
~ Code: 001
II
Prep-Year Math II
EXAM II
Term 082
Saturday, May 30, 2009
Net Time Allowed: 110 minutes
~ Code: 001
.s.~.~ M.-.t. t~~.\'1
Student's Name:
ID #:
..
II
.
Section #:
.
Important Instructions:
1.
All types of CALCULATORS, PAGERS, OR MOBILES ARE NOT
ALLOWED to be with you during the examination.
2.
Use an HB 2.lpencil.
3.
Use a good eraser. Do not use the eraser attached to the pencil.
4.
Write your name, ID number and Mathematics Section number on the
examination paper and in the upper left corner of the answer sheet.
5.
When bubbling your ID Number and Math Section Number, be sure that
bubbles match with the number that you write.
6.
The Test Code Number is already typed and bubbled in your answer sheet.
Make sure that it is the same as that printed on your question paper.
7.
When bubbling, make sure that the bubbled space is fully covered.
8.
When erasing a bubble, make sure that you do not leave any trace of
penciling.
9.
Check that the exam paper has 22 questions.
2
Second Major
Saturday, May 30,2009
Math002
Tenn:082
Code: 1
Page: 1
Ql.
If Ax + By 2 + Cy + D
directrix x
=4
=0
is the equation of a parabola with focus (-2,4) and
=
,then A + B +C
"L.
A)
-3
('.:)-k-)
B)
-7
f0
CoU S
= l.tF(X- k )
=- (- 2.. ) ~)
(h -t y> ) \<: )
-:::
C) 17
~D)
Dty.ec..t v , " ot"
5
E) 11
)l:::"
h.- It'
-1.\) ::: -
1..
12...
~
12...t-'-~
he -1" ~
c:: -
k-r
=-
<::)( -\)
==
-g'J +L+
f2.X;- 'j -
',{.
h.:=:.l
1..-
(Ij
-:::::=.)
-;:::..)
=:,
"2­
~
J
0
Q2.
If the vectors u = 5r i
7
value of r IS
+!j
3
and v =!-;
5
-~j
are orthogonal, then a possible
7
VA)J6
-
3
B)
Jj
3
----7 ---- --­
y-
'l..­
'-
3(1-)
C)
12
2
Y
V
Jj
E)
2
2­
"'\.­
J
.......
-+
--­
ri
]
-
o
(j
=~
p=-J
Math002
Tenn:082
Second Major
Saturday, May 30, 2009
Code: 1
Pa e: 2
Q3.
The equation of the directrix of the parabola that has vertex (1, -4) , has its axis of
symmetry parallel to the x-axis, and passes through the point
A) x =-1
B) ): == 2
(2, -2)
is given by
2.­
( ~ -+~.
C-
-=
f L JC.-t)
It
t-t; )""L __ ~ y::' (2..-- \)
'2-
C) x =-2
Lotto
Lf~
D) Y == 2
)(::
~E) x=o
p-
=-)
~-r
Q4.
The number of solutions of the equation 3 + cos 2() == 5cos (), 0 ~ () ~ 41r is equal to
A) 8
B) 10
~C) 4
D) 6
E) 2
1..­
:$ -t
2..
L ~~ (3, - t
""l..
~)
(2
~1
I'~
C7
G -I) (
"
.6 :::=. --
=
)
'"2.....
IT
5
':i C-er1G
5~G-t2.=o
G ­
t.v.>
-=
~
rr3
C;s (7 /' --<
(....Q)
2..)
=-
e­
/'~ =: ..,
-+ 2..0
Y' -eJ~ c:
~
\7
""
----J ---­
, If -t 2...Tf
51r
')
e:..:\­
")
J
Math002
Term: 082
Second Major
Saturda ,Ma 30, 2009
Q5.
. ( sm
. -I "4
7l"J
tan -I ( tan 37l"J +sm
4
=
~ A) 0
B)
2
o
7l"
C) 2
D)
7l"
.fi
4
2
--+­
E) 7l"
Q6.
Given the vectors u
= (9,24)
direction angle of the vector
and v
HI
= 10; + 12j
IS
77l"
) ­
A
4
B)
C)
57l"
4
1I7l"
6
D) 57l"
3
~E)
37l"
4
-1fT
y
. If w
I
2
3
4
= -u --v , then the
Second Major
Saturday, May 30, 2009
Math002
Term: 082
Code: 1
Page: 4
Q7.
If a point
P(x ,y)
is on the ellipse
9(x + 2)2 + 4(y - 3)2 = 36
A) 0 s x S 4, 0 S Y S 6
B)
-4 S x ~ 0, - 6 s y s-2
C) - 5 ~ x
~
1, 1 S Y
~
5
D) -1 ~ x ~ 5, - 5 S Y s -1
v' E)
-4 ~ x
Q8.
If (x
,y)
~
0, 0 s y
~
6
is the solution of the system
1
1
7
x y
3 .5
10
1
-----
-+-=­
x
tIlerl xy ==
A)
y
i
-----~
9
2
-- - -S8
2
B) ­
C)
5
13
5
3
D) 10
~) -10
--- ::: _It:?
,then
Math002
Term: 082
Second Major
Saturday, May 30,2009
Code: 1
Page: 5
Q9.
The value of k for which the system
3x -2y ==-1
x +ky == 0
has no solution.
A)
if 1.-z.. ----'
~
l
2
B)
"'L.
\< -::: - --­
-2
3
2
3
3
D) - ­
2
2
E) ­
3
QI0.
-2­
J
LLf ?»'Y1 6" )?­
[l.f - If
[4-(X -3)2J/2
If x
t,/
= 3 + 2 sin B
A) '!'cot
2
2
, 0 < B < 1r, then
6
=
(2x-6)2
J
BcosB
G C-tn'L-~ J
2
(2.~
~
~G
~
2
C) '!'cot Bcos
4
D) 4cotBcos
2
2
--- ---\
-z-
B
-
J-.
~
B.
E) 2 tan BsinB
"l.­
(.,n~
'\
C:;,
~G-
"'-
l1.
~-t
"
"L
6
e
"
"L.
'7
~
$L·Y/
' I {,
B) '!'tan 2 BsinB
2
St'rJ"l-G
~6
t#)e)
I'" S; J ")11~ 6
Math002
Term: 082
Code: 1
Page: 6
Second Major
Saturday, May 30, 2009
Qll.
The equation ofa hyperbola with foci at (-5,2), (7,2) and eccentricity e
A)
B)
5
(x + 1)2 (Y - 2 )2
== 1
36
. 16
C­
(y - 2)2 (x -1 )2 = 1 '
20
--
36
--­
16
,
C
'Z­
20
D)
16
-"
(Y_2)2
-
(x-l)2
E)
c-~
--
b
'1.....­
L.,
~Vi
~c::.
-~
1..­
~
. ~ (x-l)2
-­
a....
5
t,.../'
= 315 is
16
=1
(Y_2)2
-
20
=1
Q12.
If
· a
SIn
3
4
- - IT < a < -IT
5'
2
'
== -
cos(a+ P) =
A)
(-)/~)
and
COS
(;5
P == -VJ
5
3IT
,
IT
< P < - , th en
2
1
3J5
25
B) _
3J5
J
25
:
J
I
'i
•
•
~) IIJ5
(-&,-J;If5)
25
D) _
J5
25
E)
~.s (~-t
fJ) =
-::::
14J5
4'1 ~ C<T) (3 -3
-{f
--.--
- - If
3lf +
<;
$"
-
25
__
$1.:1\
l(
2.5
r?
2.S­
,
5
-l S ,'n
..
f
-2«
~
rs:­
z,
Math002
Second Major
Term: 082
Saturday, May 30, 2009
Code: 1
Page: 7
Q13.
The graph of the function
A)
f
- -1r s x
(x) == -sinx -cosx ,
rc -1r] and [51r
- -71r]
[-4'4
4'4 .
f
4
~
(D()
Z
E)
-
-
(
Q
71r..
.
, IS IncreasIng on
S-
4
S I'y\
~ ~ c,~)
(S ,'n ( )( -t :
)
J
TC -3TC] an d [5TC
- - -71fl
­
[-4'4
4'4J
-
---
-tr
~
~
-ft
Q14.
If S is the distancebetweell the foci of the ellipse 4x 2 + 9y
then S2 =
A)
-4/5
B)
4/5
C) 16
D) 15
~
E) 20
9- Y --'7
cL.:::;
J5
c.. -
5 = A
S
1..­
=:
ri
zo
2-
8x + 36y + 4 = 0 ,
Math002
Term: 082
Code: 1
Page: 8
Second Major
Saturday, May 30, 2009
Q15.
(csc
2
X
)(1 + COSX )2 =
secxcscx + 1
secxcscx -1
CJ -r
A)---­
V
B)
secx + cscx
secx - cscx
C)
secx '+ 1
secx'-1
1
D)
secx -1
E)
·secx + 1
secx
....
--l4s
U.SoY. (I -;­
~~
-t ,
0(
-:= ------­
-l- - \
&)11<.
S e <:
~ -,
Q16.
The sum of solutions of the equation cosx cos2x - sinx sin 2x = 0 ,Os x < 1i
A) 7f!
6
B) 5f!
2
T\
]><-:::­
'-­
x==
) 5"
D
­
6
E) 3Jr
-­Lrr
JrJ
'1
5)(.=­
t­
)
1T
J(. ::: - ­
2.-.
")
3~
Xc
3rr
,ff
-- ----­
'-­
,rr,
----­
,IS
Math002
Second Major
Term: 082
Code: 1
Saturday, May 30, 2009
Page:
9
Q17.
f
The domain D and the range R .of the function
v/ A)
D = [0 , 2] and R =
(x ) = Jr + cos -1 (x -1) are
[Jr , 2Jr]
-\ ~
B) D
= [0 ,
2] and R = [0 , 2Jr]
C) D = [ ~ 1 , 1] and R =
D) D
E) D
= [-1
zt
, 2Jr]
= [0 , 2] and R = [-1l" , 1l"]
~
~
e::.- L.
c:::::
o
\
'-J
D-= [a l
[Jr , 2Jr]
, 1] and R = [0
~-\
--\
~ U?) (oZ-\)
o-\-{\
L.. U- ~
{f
/
'::::
\\
tcs' (0(-\)
:=
~
\.j ~ L\f ,
R. -= (rr) A.\\~
Q18.
If tan a
v/ A) -7
~2
,and tan p = 3 ,then tan
(~ - ,a + p) = ~[~ ­ (~- P) ]
--­
B) 1
C)
~e(o/-p)
l 1-
-9
t:
(Ah\.
-btwt.-
D) 5
~
P{ ­
l .,.. 2-(')
.--"'>
E) - ­
tew" fl
t f
5
-2.-
6
-7-­
-:r
W1'1
IT-t-{T
Second Major
Saturday, May 30, 2009
Math002
Tenn:082
Code: 1
Page:
Q19.
. 19Jr
3Jr
Sln-cos-=
8
8
A)
1.
4
E)
13
2
Q20.
2sin427.5° =
A)
2J2-Ji
B)
JI+Ji
V- C)
J2+Ji
D)
-J2-Ji
E)
JJi-1
•
l?
:l S I J1 ( l.t 2..1 . S -
'3'
,e:>
l$
)
~ 2- S l ~ (1. 5"
e:"
~
z...
,
l35
S, \-'\. -----­
4-­
0
10
Math002
Ternl: 082
Second Major
Saturday, May 30, 2009
Code: 1
Page: 11
Q21.
· 2X
SIll -
2
A)
B)
C)
D)
~
E)
( --- ~k
==
tan x + sinx
tan x
1- tanxsinx
2tanx
2 tanx - sinx
2tanx
2tanx
tan x + sinx
tanx - sinx
2tanx
Q22.
If y == Ax + B
is the equation of the asynlptote with a positive slope of the
hyperbola 4x 2 - Y
V""
A) -10
2-
6y - 8x + 31 = 0 ,then the product AB
'2-
If (X -
?- X
B) 8
+
I) - ( 'j
1.­
~
L
't(X-I) -('j-t])
C)
-12
D)
-4
(~+J)
16
E) 16
+'
'-
2­
ex.-I)
C1
'J + ~ ) ::: - J \ + t.t-'1
= -3'
=- \
is equal to