MATH002
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MAJOR EXAM II TERM 151
1) If a belt runs a pulley of radius 6 cm at 900 revolution per hour, then the
linear speed of the belt in centimeter per minute is
A)
180Δ
B)
3Δ
C)
30Δ
D)
45Δ
6
E)
45
ŜΔ
Sec. 6.2: Similer example 7, Page 563
2) The exact value of
A)
5 3
3
B)
- 5 3
3
C)
-
tan - śΔ + sec 11Δ
3
6
3
3
D)
3
3
E)
2+ 3
Sec. 6.2: Exercises 14 and 19, Page 564
is equal to
MATH002
MAJOR EXAM II TERM 151
3) The graph of
y = - 3 sin Δ x ,
2
with
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-4 K x K 4,
A)
is increasing on the interval [- 3, - 1 ]
B)
is decreasing on the interval [ 1, 3 ]
C)
has maximum value of 3 in the interval [- 4, - 2 ]
D)
has minimum value of - 3 in the interval [- 2, 0 ]
E)
intersects the y-axis at ( 0, 1 )
Sec. 6.3: Similar to exercises 37 and 38, Page 579
4) Which one of the following statements is FALSE about the function
f (x) = 1 + sin 2 Δx + Δ ?
4
2
A) The y-intercept of the function is (0, 1)
B) The vertical translation of the graph of the function is 1 unit up
2
C) The period of the function is 1
D) The phase shift of the function is 1 unit to the left
4
E) The amplitude of the function is 1
Sec. 6.4: Similar to exercise 55 and 56, Page 592
MATH002
5)
MAJOR EXAM II TERM 151
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If the graph in the adjacent figure represents the function
y = 3 + a tan bx over Δ/2 , 3Δ/2 , then
A)
3
2
B)
1
2
a+b=
C) - 1
2
D)
2
E)
1
Sec. 6.5: Exercise 28, Page 601
6) The given graph in the adjacent figure represents part of the graph of
the function
A)
y = sec ( x -ȱΔ/2 )
B)
y = csc ( x +ȱΔ/2 )
C)
y = csc ( x -ȱΔ/2 )
D)
y = sec ( x +ȱΔ )
E)
y = sec ( x -ȱΔ )
Sec. 6.6: Exercise 3, Page 609
MATH002
MAJOR EXAM II TERM 151
7) If tan ΅ = 1 and ΅ is in the third quadrant, then
2
A)
B)
-2- 5
5+2 5
C)
-2+ 5
D)
1- 5
E)
2+ 5
Sec. 7.1: Similar to exercises 85 and 86, Page 636
sin Ό
8) cos Ό +
1 + cos Ό
sin Ό
A)
csc Ό
B)
sec Ό
C)
tan Ό
D)
sin Ό
E)
cos Ό
=
Sec. 7.2: Similar to example 4, Page 639
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csc ΅ - cot ΅ =
MATH002
MAJOR EXAM II TERM 151
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9) (sin 2 x) (1 + cot x) + (cos 2 x) (1 - tan x) + cot 2 x =
A)
csc 2 x
B)
sec 2 x
C)
tan 2 x
D)
cot 2 x
E)
cos 2 x
Sec. 7.3: Exercise 76, Page 643
10)
If sin ΅ = 2 , ΅ is in quadrant I , and cos Ά = - 1 , Ά is in
5
10
quadrant II , then
A)
1
B)
5
6
C)
-1
D)
1
6
E)
1
5
tan (Ά - ΅) is equal to
Sec. 7.3: Similar to excercises 91 - 96, Page 657
MATH002
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MAJOR EXAM II TERM 151
11) The range of the function
A)
[- 1 - 2 , - 1 + 2 ]
B)
[- 1 , 1 ]
C)
[- 2 , - 1 + 2 ]
D)
[0, 1+ 2 ]
E)
[0, 1]
f (x) = - sin x - cos x - 1
Reduction Identity: Recitation exercises for Term 151
12) sin 202.5 o =
A)
-
2- 2
2
B)
-
2+ 2
2
1- 2
2
C)
D)
-
2- 2
2
E)
-
2+ 2
2
Sec. 7.4: Similar to example 9, Page 666
is
MATH002
MAJOR EXAM II TERM 151
13) If sec x =  5 and sin x < 0 , then cot x =
3
2
A)
- 1
2
B)
-2
C)
2
D)
1
2
E)
3
8
Sec. 7.4: Exercise 75-82, Page 683
14)
sin-1 sin ŜΔ =
5
A)
Δ
5
B)
Δ
5
C)
6Δ
5
D)
 6Δ
5
E)
4Δ
5
Sec. 7.5: Exercise 87-89, Page 725, Caution in page 688
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MATH002
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MAJOR EXAM II TERM 151
15) If 0 K x < 2Δ , then the sum of all the solutions of the equation
cos 2x = - cos x is equal to
A)
3Δ
B)
2Δ
C)
4Δ
D)
śΔ
2
E)
ŝΔ
2
Sec. 7.6: Exercise 81, Page 697
16) The number of solutions of the equation
o
o
interval [ 0 , 360 ) , is
A)
2
B)
4
C)
6
D)
3
E)
5
Sec. 7.6: Exercise 93, Page 697
csc 2 Ό = 2 sec Ό ,
2
over the
MATH002
MAJOR EXAM II TERM 151
17) If
arccos x + 2 arcsin 3 = Δ , then x =
2
A)
1
2
B)
- 1
2
C)
-
2
2
2
2
D)
E)
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-
3
2
Sec. 7.7: Similar to exercise 37, Page 705
18)
If the vector u has magnitude 8 and directional angle Δ , and vector
v = 4 i + 4 3 j , then the directional angle ΅ of the vector u + v
A)
΅ = ŘΔ
3
B)
΅ = 11Δ
6
C)
΅ = ŚΔ
3
D)
΅ = śΔ
6
E)
΅ = śΔ
3
Sec. 8.3: Similar to exercise 35, Page 756
is
MATH002
19)
MAJOR EXAM II TERM 151
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For the vectors s, u, v and w and the real number k , which one of the
following statements is FALSE ?
A)
s = 1, 1
B)
u· v = v· u
C)
u· (v+ w)= u· v+ u· w
D)
( ku ) · v = u · ( kv )
E)
u · u = |u| 2
is a unit vector
Sec. 8.3: Properties of dot product, Page 753
-1
20) If u > 0 , tan sin
A)
u 2
2
B)
2 u2
u2
C)
2 u2
2 +u2
D)
2 u2
u
E)
u
=
2
2 u
2
u
Sec. 7.5: Similar to exercise 105, Page 686