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Math 1113 Pre-Calculus Final Practice Summer 2008
Name: Last ___________________, First ______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use a calculator to find the value of the expression rounded to two decimal places.
- sin-^1
A) 14.48 B) 1.32 C) 75.52 D) 0.
- Find the smallest positive angle coterminal with (^) - 195 ° A) 15 ° B) 195 ° C) 165 ° D) 525 °
Solve the problem.
- A radio transmission tower is 220 feet tall. How long should a guy wire be if it is to be attached 6 feet from the top and is to make an angle of 30° with the ground? Give your answer to the nearest tenth of a foot. A) 440.0 ft B) 247.1 ft C) 428.0 ft D) 254.0 ft
Form a polynomial whose zeros and degree are given.
- Zeros: 2 , multiplicity 2; - 2 , multiplicity 2; degree 4 A) f(x) = x^4 + 4x^3 - 8x^2 + 8x - 16 B) f(x) = x^4 + 8x^2 + 16 C) f(x) = x^4 - 4x^3 + 8x^2 - 8x + 16 D) f(x) = x^4 - 8x^2 + 16
Find the vertex and axis of symmetry of the graph of the function.
- f(x) = - x^2 + 12x - 1 A) ( 12 , (^) - 1 ) ; x (^) = 12 B) ( 6 , 35 ) ; x (^) = 6 C) (- 6 , - 37 ) ; x = - 6 D) (- 6 , - 109 ) ; x = - 6
Form a polynomial whose zeros and degree are given.
- Zeros: (^) - 5 , multiplicity 2; 2 , multiplicity 1; degree 3 A) x^3 - 8x^2 + 5x (^) + 50 B) x^3 - 8x^2 - 20x (^) + 50 C) x^3 + 10x^2 + 5x (^) - 50 D) x^3 + 8x^2 + 5x (^) - 50
Find the vertical asymptotes of the rational function.
- F(x) = - x
x2^ + 5x + 4 A) x = - 1 B) x = - 1, x = 4 C) x = - 1, x = - 4 D) x = 1, x = - 4
Give the equation of the oblique asymptote, if any, of the function.
- f(x) = 2x
(^3) + 11x (^2) + 5x - 1 x2^ + 6x + 5 A) y = 0 B) y = 2x - 1 C) y = 2x D) y = 2x + 1
Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results.
- b = 4 , c = 8 , B = 80 ° A) one triangle B = 40°, A = 60°, a = 12
B) one triangle C = 39°, A = 61°, a = 14 C) one triangle C = 41°, A = 59°, a = 16
D) no triangle
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Simplify the trigonometric expression by following the indicated direction.
- Rewrite in terms of sine and cosine: cot x · tan x 10)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the expression.
- 1 cos+ sin θ^ θ + tan θ
A) sec θ B) cos θ + sin θ C) 1 D) sin^2 θ
- If the point (x, - .8) is on the unit circle in the third quadrant, what is x? A) - .6 B) .65 C) - .04 D) -.
Form a polynomial f(x) with real coefficients having the given degree and zeros.
- Degree: 3; zeros: (^) - 2 and 3 (^) + i. A) f(x) (^) = x^3 - 4x^2 - 10x (^) + 20 B) f(x) (^) = x^3 - 8x^2 + 2x (^) + 20 C) f(x) (^) = x^3 - 4x^2 - 2x (^) + 20 D) f(x) (^) = x^3 - 6x^2 - 10x (^) + 20
Find all zeros of the function and write the polynomial as a product of linear factors.
- f(x) = x^4 + 7x^3 + 16x^2 + 28x + 48 A) f(x) = (x - i 12 )(x + i 12 )(x - 2)(x +2) B) f(x) = (x - 4 )(x + 3 )(x - 2 )(x + 2 ) C) f(x) (^) = (x (^) - 1)(x (^) - 12 )(x (^) - 2 i)(x (^) + 2 i) D) f(x) (^) = (x (^) + 4 )(x (^) + 3 )(x (^) - 2 i)(x (^) + 2 i)
Find the length s. Round the answer to three decimal places.
s
40° 12 cm A) 8.378 cm B) 6.702 cm C) 9.216 cm D) 7.54 cm
- y = 94 cos (- 47 π x) Find the amplitude.
A) 49 π B) 72 C) 47 π D) (^94)
Graph the function.
- y = 4 tan 12 x
π 2 π^
3 π 2 2 π^
5 π 2 3 π
6 y
4
2
π 2 π^
3 π 2 2 π^
5 π 2 3 π
6 y
4
2
A)
π 2 π^
3 π 2 2 π^
5 π 2 3 π
6 y
4
2
π 2 π^
3 π 2 2 π^
5 π 2 3 π
6 y
4
2
B)
π 2 π^
3 π 2 2 π^
5 π 2 3 π
6 y
4
2
π 2 π^
3 π 2 2 π^
5 π 2 3 π
6 y
4
2
C)
π 2 π^
(^3) π 2 2 π^
(^5) π 2 3 π
6 y
4
2
π 2 π^
(^3) π 2 2 π^
(^5) π 2 3 π
6 y
4
2
D)
π 2 π^
(^3) π 2 2 π^
(^5) π 2 3 π
6 y
4
2
π 2 π^
(^3) π 2 2 π^
(^5) π 2 3 π
6 y
4
2
Find the phase shift.
- y = 2 sin( 3 πx - 2 ) A) 2 units to the right B) (^) 3π^2 units to the right
C) 2 units to the left D) 23 units to the left
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
- When light travels from one medium to anotherfrom air to water, for instanceit changes direction. (This is why a pencil, partially submerged in water, looks as though it is bent.) The angle of incidence θr is the angle in the first medium; the angle of refraction θr is the second medium. (See illustration.) Each medium has an index of refractionni and nr, respectivelywhich can be found in tables. Snell's law relates these quantities in the formula ni sinθi = nr sin θr Solving for θr, we obtain
θr = sin-^1
ni nr sin θi Find θr for air (ni = 1.0003), methylene iodide (nr = 1.74), and θi = 14.7°.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the equation on the interval 0 ≤ θ < 2 π.
- 2 sin^2 θ - 3 sin θ - 2 = 0 A) π 2 , 7π 6 , 1 1π 6 B) 4π 3 , 53 π C) 7π 6 , 1 1π 6 D) π 2 , 5π 6 , 76 π
Find the real zeros of the trigonometric function on the interval 0 ≤ x < 2π
- f(x) = 4 cos^2 x - 3 A) π 6 , 1 1π 6 B) π 3 , 2π 3 , 4π 3 , 53 π
C) π 3 , 53 π D) π 6 , 56 π , 7π 6 , 1 1π 6
Solve the triangle.
A) b = 9.44, A = 7.8°, C = 137.2° B) b = 8.44, A = 137.2°, C = 7.8° C) b = 7.44, A = 137.2°, C = 7.8° D) b = 8.44, A = 7.8°, C = 137.2°
Solve the problem.
- Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 23 mph in a direction 330°. The second sails at 34 mph in a direction 190°. Assuming that both boats maintain speed and heading, after 2 hours, how far apart are the boats? A) 107.4 mi B) 84.2 mi C) 90.3 mi D) 80.5 mi
- A painter needs to cover a triangular region 63 meters by 68 meters by 71 meters. A can of paint covers 70 square meters. How many cans will be needed? A) 14 cans B) 318 cans C) 3 cans D) 28 cans
Answer Key
Testname: MATH 1113 FINAL PRACTICE ALL
1) D
2) C
3) C
4) D
5) B
6) D
7) A
8) B
9) D
11) A
12) A
13) C
14) D
15) A
- 379 mi
- A
- C
- A
- A
- C
- D
- A
- B
- θr = 8.39°
- C
- D
- B
- 0, 1.
- C
- C
- C
- D
- A
- D
