Download Right Circular - Mathematics - Exam and more Exams Mathematics in PDF only on Docsity!
MULTIPLE CHOICE: Circle the best choice on this exam paper.
- Simplify the difference quotient
f x h f x h
, if h ≠ 0 , for f ( x )= x − x^2.
A.
h
h x xh h h
f ( x h ) f ( x ) − 2 2 + 2 +^2
B. x h h
f x h f x = − −
C.
h
h x h
f ( x h ) f ( x ) 2 − 2 2
D. x h
f x h f x 1 2
E. x h h
f x h f x = − +
2. The volume V of a right circular cylinder of radius r and height h is V =π r h^2 ; the surface
area S of this cylinder is S = 2 π r^2 + 2 π r h. If the volume of this cylinder is 4 π cubic
meters, express the surface area S as a function of the radius r.
A.
r
Sr r
B. S ( r )= 2 π r 2 + 2 π rh
C.
r
r S r
D. 2
r
S r =
E. S ( r )=π r ( 2 − r^2 )
- For the function
x forx
x forx f x , as x → 0 +, f ( x )→_____?
A. 1
B. 5
C. -
D. f ( x )does not approach any value as x → 0 + E. none of these
- Solve the following inequality for x : ( x + 5 )( x − c )> 0 , c > 0.
A. (− 5 , c ) B. ( − ∞, − 5 ) ∪( c ,∞) C. ( − 5 ,∞) D. (− 5 , ∞) ∪( c ,∞) E. none of these
- The rational function
( )( ) ( )( )
f x
x r x s x r x
has which of the following characteristics?
x -intercept(s) hole horizontal asymptote vertical asymptotes
A. ( r , 0) and (s, 0) none y = 0 (^) X = r and x = ± 5 B. ( s , 0) x = r y = 0 (^) x = ± 5 C. ( s , 0) x = r y = 1 x = ± 5 D. ( r , 0) and ( s , 0) x = r none (^) x = ± 5 E. ( s , 0) none y = 1 x = 5
6. Which of the following angles is coterminal with θ
A. 120°
B. -120°
C. -60°
D. 60°
E. -240°
- The area cleared by an 18-inch windshield wiper is 90 π square inches. Find the distance the tip of the wiper travels.
A.
π inches
B. 5 π inches C. 10 π inches D. 90 π inches E. 180 π inches
- Find the exact value of ( π )
tan 6
cos 2
sin (^) −
−^.
A.
cos α+
B.
cos α−
C.
csc α−
D.
sin α−
E. none of these
- Which of the following is an equation, in the form y = a cos( bx + c ) for a function with
amplitude = 3, period = 8, and phase shift = 2?
A. y = (^) x −
cos 2
B. y = 3 cos(^8 x + 2 )
C. y = − (^) x −
cos
D. y = 3 cos(^8 x − 16 )
E. y = − (^) x −
cos
- Find the range of the graph of y = − 3 cos x + 1.
A. [-2, 1]
B. [-2, 4]
C. [1, 4]
D. [0, 2]
E. none of these
- A moving van has a 7-foot ramp off the back for loading. The angle the ramp makes with the ground is 34 ° 5 0 ′. To reduce the angle of elevation to a maximum of 25 ° , what is the shortest the ramp can be?
A. 9.38 feet B. 6.34 feet C. 10.44 feet D. 9.46 feet E. none of these
15. cos θ
is equivalent to which of the following?
A. (^ )
cos θ −sinθ
B. (^ )
cos θ +sinθ
C. ( 3 cosθ sin θ)
D. ( 3 cosθ sin θ)
E. (cos θ 3 sin θ)
16. Find the sum of all solutions to the following trigonometric equation over [ 0 2, π ).
cos 2 θ= − 2 − 5 sin θ
A. 3 π
B. 2.
C. π
D. 2 π
E.
17. If θ =
sin− 1 2
a , where 0 < a < 2, find tan( θ ).
A. tan( ) θ =
a 4 a^2
B. tan( ) θ =
4 − a^2 a
C. tan( ) θ
4 − a^2
D. tan( ) θ =
a a^2
E. tan( ) θ =
a^2
- Find the equations of the asymptotes for y^2 − 9 x^2 + 36 x − 45 = 0.
A. ( 2 ) 3
y = ± x −
B. y = ± 3 x + 2 C. y = ± 3 ( x − 2 )
D. 2 3
y = ± x −
E. none of these
- Write an equation in x and y for the given parametric equations.
x =cos t , y = 3 sec t
A.
x
y
B. y = 3 x
C. 3
x y =
D. 1
2 x^2 + y =
E. none of these
- Convert the equation x = 16 to polar form.
A. r = 16sec θ
B. r = 16csc θ
C. r = 4 sin θ
D. r = 4 sec θ
E. r = 16cos θ
OPEN RESPONSE: Show all work and place your answers in the box.
- Find all of the values of x , in the interval (^) [ 0 2, π ), which satisfy the equation
cot x sin x = − 3 sin x. Answer in exact form if applicable, else, round your answers to two decimal places.
