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MATH002
Term: 121
Major Exam I1
Saturday, 8th December 2012
Code: 000
Page: 1
1) If n is an integer, then an equation of the vertical asymptotes of the graph of
Y=3cot[b-%]
V/ A) x=[2n+3)[
4
B) w=[n+2)$
far
is
bt, vrrhcctl
a
2%
D) x = [ 2 n + 1 ) 3
For
- -1 < x < 1
2
2'
-
-
nG i
--
2nE $ 3 R
C
Isa
2%- 3s = 6
C) x=[2n+l)f
2)
sgrnp+oks
a
the graph of the function y = - 2 sec (rrx - 3rr) is below the
x-axis in the interval(s)
[Hint: Sketch the graph]
3) If tan 0
4)
Code: 000
Page: 2
Major Exam I1
Saturday, 8th December 2012
MATH002
Term: 121
=
If cot x =
rn, for 90°< 0 < 180°, then csc 0
-4 ,
5
n c x < n , then
where 2
=
csc x - sec x tan x
Sin 'K =
a
-
MATH002
Term: 121
Major Exam I1
Saturday, 8th December 2012
B) sin 8 - C O S
c)
6)
cos 8 - s i n 8
sec2x
D
E)
e
-
Zsecxtanx + tan 2 x =
1 - cosx
1 + cosx
1 + cosx
1 - cosx
- kn.rl2
Code: 000
Page: 3
MATH002
Term: 121
7)
Major Exam I1
Saturday, 8th December 2012
Code: 000
Page: 4
tan 285" =
and sec /? = - 5 , where a is in quadrant I and
13
3
quadrant 11, then cos [a +/?) is equal to
8) If cos[:-a]
=
-
is in
MATH002 . .
Term: 121
9)
If sin6 =
6 + sin 26
-- with 180"< 6 < 270°, then cos 5'
2
hid;n3
24-56
25
A)
D)
E)
-
B)
sec2x
C)
csc 2x
D)
- csc 2x
E)
cot 2x
=+ 0wakqn4 H
L
?Y
b$=
7
.
-
as@ +\
- - d-31pl
7
2
--
6
$ A) - sec 2x
90* <
1
7
-7p -3
-4
24+56
25
24+5$
25
-8
5
by%
=
1
54-24
25
B)
C)
Code: 000
Page: 5
Major Exam I1
Saturday, 8th December 2012
Sin
28-
-
2sinB60~8.
-
-
6
5
Major Exam I1
Saturday, 8th December 2012
MATH002
Term: 121
11) sin [ cos-'
(- 112) + tan-' [-a)]=
I
12) For u > 0, cos 2 tan-'
I.
3
=
Code: 000
Page: 6
MATH002
Term: 121
Major Exam I1
Saturday, 8th December 2012
13) The sum of the sokrtions of the equation cs?x
- 2cotr
Code: 000
Page: 7
= 0 over the interval
[0, 27-c) is
14) The number of solutions of the equation sin2x = cos2x + 1 over the interval
MATH002
Term: 121
Major Exam I1
Saturday, 8th December 2012
15) The solution set of the equation cos-'x + tan-'x
S/ A) one rational number
CosD'r
Code: 000
Page: 8
-
=
= 8
2
contains
2
, -I
b,,,rr
B) two rational numbers
C) one irrational number
D) two irrational numbers
E) no real number
LLt 8
=@
16)
kh"r
:
.
&,,a,
bK
-..
Let u = (- 6, 1) and v = (- 4, 3). If w = 4u - 3v, then a unit vector
having the same direction as w is
t
MATH002
Term: 121
17)
Major Exam I1
Saturday, 8th December 2012
If f3 is the smallest positive angle between the two vectors u = ( 3, 4 ) and
v
18)
Code: 000
Page: 9
= 2i + j ,
u*V = < 3 , 4 ) < % 1 \ ) = 6 +4
then sec f3 =
If (a, b) is the solution of the following system of linear equations
then a + b =
5
1-0
=10
MATH002
Term: 121
Major Exam I1 '
Saturday, 8th December 2012
19) If
x
and x
are the x - coordinates of the points of intersection of the graphs
0
-0
0
e
x 2 + 2 x y = 1 5 + 2 x 0 a n d x y - 3 x + 3 = 0 , then
20) If f(x)
=
Code: 000
Page: 10
[q
q.=- 3
1
+
x
2
-
[y), then the phase shift of the graph of f (x)
-2sin - + 2 4 ~ 0 s
is equal to
x
,a
b= 2 6