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King Fahd University of Petroleum and Minerals
Prep-Year Math Program
Prep-Year Math I1
MIDTERM EXAM
Semester I, Term 061
Tuesday, November 14, 2006
Net Time Allowed: 120 minutes
MASTER VERSION
MATH 002-TO61 (MIDTERM EXAM)
1.
+
If for the function f (x) = -3 sin(?rx - 2) 5, A is its
amplitude, P is its period, M is its maximum value
and m is its minimum vlaue, then
2.
[MASTERI
Page 1 of 13
A+P
M+m
-
If f
is the inverse of the function f (x) = 2- x+l - 3,
then f -'(x) =
+ 3)
- 10g2(x
+ log,(x - 1)
-1+ 10g2(x+ 3)
3 + log, (x + 3)
(b) 3
(c)
(d)
(e) -1 +log2(3-
ezpme4tiJ
-4
?fifiM*r'
-fumrCim~, M ; m y e m
m o
X)
*
,q & r a t ~ p p l ' c * h ~
H.l
r e / ~ t i mkt-
my
4
MATH 002-TO61 (MIDTERM EXAM)
3.
Page 2 of 13
Which one of the following statements is TRUE about the
function f(x) = -21lnxl and itsgraph?
N
increases on ( 0 , l )
See P r a b J ~61)
(b) increases on (I, w)
(c) decreases on
( 2 7
2,
(d) f has no maximum value
(e) x = 2 is a vertical asymptote
4.
The domain of
f (x) = log,-, x is
m'f
62
M A 67
392
MATH 002-TO61 (MIDTERM EXAM)
5.
Which one of the following statements is TRUE for all
x > O , y > O , b > O and b # 1 ?
% p r d b l ~ 21 &
Yoi P44@4
In x
(plf log, 6= 2lnb
-
(b)
+ Y) =logbx+
(c) logbx ' logby = logbx
(d) log,
6.
I MASTER I
Page 3 of 13
logby
+ logby
-=-
The value of
(In 10000)(log 6)
(log3 fi)
(log59)
is
MATH 002-TO61 (MIDTERM EXAM)
7.
tan 155" - cot 35" 1 tan 155" cot 35"
+
/-
tan 80"
(b) tan 20"
(d) -tan 25"
( e ) tan 15"
8.
If
10" - lo-" - 1
- - then x =
10" lo-"
2'
+
Page 4 of 13
MATH 002-TO61 (MIDTERM EXAM)
9.
pixs%iq
Page 5 of 13
The number of intersection points of the graphs of y
3
and y = cos 2ax, over the interval 0 x 5 -, is
4
= sin 27rx
<
3
If x = - sin 9, where 0
2
12x2
simplifies to
(9 - 4x2)3/2
)'pf t an26 sec 6
(b) t an28 sin 8
(c) t an28 cos 8
(d) cot 9 sec 9
(e) cot29 sin 9
7r
< 8 < -, then the expression
2
MATH 002-TO61 (MIDTERM EXAM)
11.
The expression
i.f
Page 6 of 13
sin3x - cos3x
sin z - cos x
+
1 sinx cosx
simplifies to
SQQ pmbl*
5'7
P. 561
(b) 1 + 2 s i n x c o s x
(c) 1 - 2 sin x cos x
(d) -1 -sinxcosx
(e) -1
12.
If y
+ sinxcosx
2 cot 22, then the number of vertical asymptotes
is equal to
over the interval
=
MATH 002-TO61 (MIDTERM EXAM)
13.
Page 7 of 13
3
5
If sin a = -, a lies in second quadrant, and cos ,O = -5
13'
lies in third quadrant, then sin - - a! P =
(;
14.
1MASTERI
P
+ )
If a wheel of radius 8 centimeters is rotating at 450 revolutions
per minute, then the linear speed of a point on the edge
of the wheel in centimeters per seconds is equal to
i.fl2OT
(b) 2407r
(c) 1107r
(d) 2207r
(e) 2 3 0 ~
MATH 002-TO61 (MIDTERM EXAM)
15.
Page 8 of 13
The line y = 3 intersects the graph of
37r
over the interval
67r) at
y
=
x
-2 csc ;
(-I,
/"
three points
(b) one point
(c)
twopoints
(d)
four points
I 4 p.529
k waqe
kc pnbt-
33,
mrr4
34,38) 41J
p.
(e) no point
16.
The reference angle 0') in radians, of the angle 0 = -1656"
is equal to
527
MATH 002-TO61 (MIDTERM EXAM)
17.
.
The expression
ipif 2 csc t
(b) 2sect
tan t
1 sect
+
+
I MASTER I
Page 9 of 13
+sect
tan t
simplifies to
SOP wmfle 4
P
p v a b t 4q
~
558
G 52 P 560
(c) 2 cot t
(d) 2 t a n t
(e) 2 sin t
18.
If the terminal side of an angle 0 lies on the line 3x
where x > 0, then the value of cot 0 cos 0 is
+
+ 49 = 0,
-.
MATH 002-TO61 (MIDTERM EXAM)
19.
I MASTER I
Page 10 of 13
Which one of the following is an odd function?
j d f (4=
3 cos x
~ e c j + o b k
\ 4~ g~ p~-s o &
x2tanx+cscx
(b) f(x) = x 3 + tan2x
+
(')
1 xcosx
f(x) = sinx + t a n x
(e) f (x) = x3 csc x
20.
+1
The exact value of the expression
2 cos
(
'4")
--
tan(240°) - h csc
is
see
&(3&
(b) 2 h
(4 h
(d)
-h
(e) - 2 h
($)
p r & i6
~5 d
66
kq4g
MATH 002-TO61 (MIDTERM EXAM)
21.
pGmq
Page 11 of 13
The range R and the period P of the function y
are given by
=-
[Hint: Sketch]
R = [-3,0], P = 2 n
see p'obl-
(c) R = [-3,0], P = 4 r
P=T
7r
(e) R = [-3,0], P = 2
22.
If L is the distance between the two points PI(cos 8, sin 8)
and P2(cos28,sin28), then L2 =
(b) 2+2sin6'
(c) 2+2cos38
(d) 3 - cos8
(e) 3 - cos 38
3 sin -
SSG 58
(b) R = [-3,3], P = 2 r
(d) R=[-3,0],
I I;
P 527
MATH 002-TO61 (MIDTERM EXAM) -
Page 12 of 13
23.
If, in the given figure, the length of AC
the length of BD is
24.
Ifthepoints (-1,3) and (2,81) lieonthegraphofthe
then b c =
exponential function f (x) = bx",
is 10 cm, then
+
pmmq
MATH 002-TO61 (MIDTERM EXAM)
Page 13 of 13
-
25.
+
If the given graph represents the function y = a tan(bx c)
over the interval (- 1,3), then the values of a, b and c
are given by
/Blr
7r
7r
a = -2, b = -, and c = -4
4
(b) a = 2 , b = -
7r
and c = 4'
4
7r
37r
7r
-2, b = - and c = -4'
4
(c) a
=
(d) a
= 2,
7r
7r
b = -- and c = -4
4'
(e) a = -2, b=47r, and c=-47r
p b l ~ l r l 50
p.
527