Download Point - Mathematics - Exam and more Exams Mathematics in PDF only on Docsity!
PART A: MULTIPLE CHOICE: Circle the best choice. Each question is worth 2 points.
- Let P = ( x, y ) be a point on the graph of y = x. Express the distance d from P to the point
(3, 0) as a function of x.
A. d x ( ) = (^ x − 3 ) 2 + y^2
B. d x ( ) = 2 x^2 − 6 x + 9 C. d x ( ) = x^2 − 5 x + 9 D. d x ( ) = x^2 + x + 9 E. None of these.
- f x
Ax x
2
3 2 15 has
A. no vertical asymptotes and a horizontal asymptote at y
A
B. vertical asymptotes at x = ± 5 and no horizontal asymptote. C. vertical asymptotes at x = ± 15 and a horizontal asymptote at y = 0.
D. vertical asymptotes at x = ± 5 and a horizontal asymptote at y =
E. None of these.
- The graph of which of the following functions has an x -intercept at (5, 0) and a hole at x = -2.
A. f x
x x x
B. f x
x x x
C. f x
x x x
D. f x
x x
E. None of these.
- Which of the following is equivalent to f x
x x
A. f ( ) x = − 2
B. f x
if x if x
C. f x
if x if x
D. f x
x if x x if x
E. None of these.
- Which one of the following angles is coterminal with
A. 60° B. 540° C. -240° D. -480° E. None of these
- Which of the following is equivalent to the expression sin x + cos x cot x?
A. 1 B. csc x C. sec x D. 2 sin x E. None of these.
7. For all θ, cos( − θ )+cosθ =
A. 0 B. 1 C. 2 cos θ D. cos 2 θ E. None of these.
- Which of the following has a period of
and a phase shift of p.
A. y = − cos 6( x − 6 p ) B. y = sin 3( x + 3 p ) C. y = tan( 6 x − 6 p ) D. y = − sin 6( x − p ) E. None of these.
- Find the exact value of 5
tan cos
^ π π
^
−^ −
^
4. Approximate, to the nearest 2 decimal places, all angles θ in the interval [ 0 2, π )that satisfy:
cos θ = −0 2316.
- Evaluate: cos −^1 cos
cos −^1 cos
- Evaluate: sin 2 tan
sin 2 tan
- Convert the polar equation r = −
cos θ 1
to simplest rectangular form.
PART C: Place your answers in the appropriate area. Each question is worth 4 points.
- Given g x x
find:
g x h g x h
( + ) − ( ) g x (^ h )^ g x (^ )
h
- Graph the given function. f x
x if x x if x
As x → 0 ,+ f ( ) x →_____.
- Two buildings on opposite sides of a street are 45 m apart. From the top of the taller building, which is 218 m high, the angle of depression to the top of the shorter building is 13 ° (^4 5) ′. Find the height of the shorter building.
Answer to the nearest meter.
6. Solve the following trigonometric equation over [ 0 360, °) :
9 sin θ− 4 = 5 cos 2 θ
θ =
Answer to the nearest degree.
- If tan θ = − 2 , where θ is in the fourth quadrant, find cos
π +θ.
cos
π +θ
^
- If sin θ =
, where
π < θ < π, find cos
θ 2
. cos
θ 2
Answer in exact, simplest form. No fractions in numerator or denominator.
- A ship travels for 3 hours at 18 mph in a direction N28°E. From its current direction, the ship then turns through an angle of 95° to the right and continues traveling at 18 mph. How long will it take before the ship reaches a point directly east of its starting point?
Answer to the nearest tenth of an hour.
- To find the distance between two points A and B , a surveyor chooses a point C that is 460 meters from A and 375 meters from B. If angle ACB has measure 54 ° 2 0 ′ , find the distance between A and B.
Answer to the nearest meter.
- An arch of a bridge is semielliptical. The base of the arch is 40 feet across, and the highest part of the arch is 12 feet above the horizontal roadway. Find the exact height of the arch 5 feet from the center of the base.
Answer in exact form.
- For the given equation, find the coordinates of the vertices and foci and equations for the asymptotes. Sketch the curve.
x^2 − 9 y^2 = 36 Vertices:
Foci:
Asymptotes:
x
y
