Download 1.What Is The Solution Set For In The Interval A

1. What is the solution set for interval
A) {30°, 150°}
C) {30°, 330°}
in the
B) {60°, 120°}
D) {60°, 300°}
2. Solve the equation 2 tan C – 3 = 3 tan C – 4 algebraically for all values of C in the interval
0° C< 360°.
3. Find all values of in the interval 0° 360° that satisfy the equation sin 2 = sin .
4. Base your answer to the following question on Solve the
following equation algebraically for all values of in the
interval 0° 180°.
2 sin – 1 = 0
5. If 3x is the measure of a positive acute angle and cos 3x = sin 60°, find the value of x.
6. Find a value for in the interval 90° 270° that
satisfies the equation 2 sin + 1 = 0.
7. If sin (2x + 20)° = cos 40°, find x.
8. If cos (2x – 25)º = sin 55º, find the value of x.
9. If sin A = –1 and 0° A < 360°, find m A
10. Find, to the nearest degree, all values of x in the
interval 0º x 360º that satisfy the equation 2 sin2 x = 1 + sin x.
11. Express cos (sec – cos ), in terms of sin .
12. Prove the identity:
tan A + cot A = sec A csc A
13. Evaluate:
sin 300º cos 90º + cos 300º sin 90º
14. Using the formula for cos(x – y), find the exact value of
cos 15º in radical form if m x and m y = 30.
15. Express in radical form:
sin 90º cos 30º – cos 90º sin 30º
16. When and lies in Quadrat I and and lies in Quadrant II, what is ?
17. If tan A = and tan B = 3, express tan (A – B) as a
fraction in simplest form.
18. If sin A = , find cos 2A.
19. If tan A = , find the value of tan 2A.
20. If x is a positive acute angle and sin x = , find cos(2x
). 21. If tan A = and sin B =
and angles A and B are in Quadrant I, find the value of tan (A + B).
22. What is the numerical value of the product ?
23. The diagram below shows the plans for a cell phone tower. A guy wire attached to the top of the tower
makes an angle of 65 degrees with the ground. From a point on the ground 100 feet from the end of the
guy wire, the angle of elevation to the top of the tower is 32 degrees. Find the height of the tower, to the nearest foot.
24. The accompanying diagram shows the peak of a roof that is in the shape of an isosceles triangle. A base
angle of the triangle is 50º and each side of the roof is 20.4 feet. Determine, to the nearest tenth of a square
foot, the area of this triangular region.
25. In a triangle, two sides that measure 6 cm and 10 cm form an angle that measure 80°. Find, to the nearest
degree, the measure of the smallest angle in the triangle.
26. In DABC, a = 24, b = 36, and c = 30. Find m A to the
nearest tenth of a degree.
28. In the accompanying diagram of parallelogram ABCD,
m A = 30, AB = 10, and AD = 6. What is the area of
parallelogram ABCD?
27. The two sides and included angle of a parallelogram are
18, 22, and 60°. Find its exact area in
simplest form.
29. If a = 5, b = 7, and m A = 30, how many distinct
triangles can be constructed?
A) 1
B) 2
C) 3
D) 4
30. If a = 6, b = 5, and m A = 30, the number of distinct
triangles can be constructed is
A) 1
B) 2
C) 3
34. Which graph does not represent a function?
A)
D) 0
31. If m A = 30, a =
, and b = 6, the number of
triangles that can be constructed is
A) 1
C) 0
B) 2
D) an infinite number
32. Given the relation {(8,2), (3,6), (7,5), (k,4)}, which
value of k will result in the relation not being a
function?
A) 1
B) 2
C) 3
B)
D) 4
33. Which relation is not a function?
A) (x – 2) 2 + y 2 = 4
C) x + y = 4
B) x 2 + 4x + y = 4
D) xy = 4
C)
D)
35. Which function is one-to-one?
A) f(x) = |x|
C) f(x) = x 2
B) f(x) = 2 x
D) f(x) = sin x
36. If , what are its domain and range?
A) domain:
; range:
B) domain: C) domain: ; range: ; range: D) domain: ; range: 37. Base your answer to the following question on The accompanying graph shows the elevation of a certain
region in New York State as a hiker travels along a trail.
What is the domain of this function?
A) 1,000 x 1,500
C) 0 x 12
B) 1,000 y 1,500
D) 0 y 12
38. What is the domain of the function shown below?
40. The expression below is undefined when x equals
A) 0º
B) 30º
C) 45º
D) 60º
41. Which is not an element in the range of the function y = cos x?
A) 1
B) 2
C)
D) –
42.
A)
B)
C)
D)
A) –1 x 6
C) –2 x 5
B) –1 y 6
D) –2 y 5
39. What is the range of the function y = 2sin (3x)?
A) –1 y
C) –3 y
1
3
B) –2 y 2
D) all real numbers
all real numbers except 0
all real numbers except 3
all real numbers except 3 and –3
all real numbers
43. Base your answer to the following question on Find if
44. If f(x) = x 0 + x + x –1, find f(4).
45. What is the inverse of the function A)
B)
C)
D)
?
46. If p varies inversely as q, and p = 10 when q = , what
is the value of p when q = ?
A) 25
B) 15
C) 9
D) 4
47. The graphs of the equation xy = 16 and y = x are drawn
on the same set of axes. In which quadrant or quadrants
will they intersect?
A) I, only
C) I and III
B) I and II
D) II and IV
48. If R varies inversely as S, when S is doubled, R is
multiplied by
A)
B) 2
C)
D) 4
49. The inverse of e x is
A) log(x) B) ln(x) C) e –x
D) x
50. Solve for x: 4 3x = 8 (x+l)
51. If x = 5 a , then the value of 5x is
A) x + 1 B) 6 a
C) a + 5 D) 5 a + 1
52. Which value of k satisfies the equation 8 3k+4 = 4 2k–1?
A) –1
B)
C) –2
D)
53. The solution set of the equation A)
C)
is
B)
D)
54. The formula for continuously compounded interest is A
= Pert , where A is the amount of money in the account, P is the initial investment, r is the interest rate, and t is
the time in years. Using the formula, determine, to the nearest dollar, the
amount in the account after 8 years if $750 is invested
at an annual rate of 3%.
55. The number of bacteria present in a Petri dish can be modeled by the function N = 50e 3t, where N is the
number of bacteria present in the Petri dish after t hours. Using this model, determine, to the nearest
hundredth, the number of hours it will take for N to reach 30,700.
56. If log b x = y, then x equals
A) y • b
B)
C) y b
D) b y
57. If log b x = 3 log b p – (2 logb t + log b r), then the
value of x is
A)
B)
C)
D)
58. If , then log r can be represented by
A)
B)
C)
D)
59. The expression equivalent to
is
A)
B)
C)
D)
60. Banks use the formula A = P(1 + r) x when they
compound interest annually. If P represents the amount
of money invested and r represents the rate of interest,
which expression represents log A, where A represents
the amount of monet in the account after x years?
A)
B)
C)
D)
x log P + log (1 + r)
log P + x log (1 + r)
log P + x log 1 + r
log P + log x + log (1 + r)
61. If log 3 = a and log 5 = b, then log 45 is equal to
A) a 2 + b
C) 2ab
B) 2a + b
D) a 2b
62. If log 2 = A and log 3 = B, then log 6 is equal to
A) A + B B) A – B C) AB
D)
63. Solve algebraically for all values of x:
log (x + 4) (17x – 4) = 2
64. Solve for all values of x: log 4 (x 2 + 3x) – log 4 (x + 5)
= 1
66. The growth in the number of the people who own a new
computer can be modeled by the function y = 6(3.45 x ),
where y is the number of people in millions with a new
65. A colony of bacteria increases according to the equation
computer and x represents the number of years since
N(t) = N0ekt where N is the number of cells in the culture
2000. How many years, to the nearest thousandth of a
after a time t had passed (in hours), N0 is the initial
year, would it be until the number of people who own a
number of bacteria present, e is 2.7, and k is a positive
new computer reaches 700 million?
constant. If the constant is and the number of cells
67. The equation for interest compounded continuously is has tripled, how much time has passed, to the nearest
A = P(2.7)rt , where A = final amount of money, P =
hour?
original amount of money, r = the rate of interest, t =
time (in years).
To the nearest year, in approximately how many years
will Erin's money double if she starts out with $1000
and the interest rate is 5%?
Answer Key
MR22 Review2
1.
D
34.
D
2.
45 and 225
35.
B
3.
0, 60, 180, 300
36.
A
4.
30 and 150
37.
C
5.
10
38.
A
6.
210
39.
B
7.
15
40.
C
8.
30
41.
B
9.
270
42.
C
10.
90, 210, 330
43.
11.
sin2 44.
3
12.
45.
D
13.
46.
A
14.
47.
C
15.
48.
A
49.
B
16.
17.
_ 50.
1
51.
D
18.
52.
D
19.
53.
C
20.
54.
953
21.
55.
2.14
56.
D
57.
D
23 or 11.5
2
22.
58.
D
23.
88
59.
A
24.
204.9
60.
B
25.
33
61.
B
26.
41.4
62.
A
27.
198
63.
4 and 5
28.
30
64.
5 and –4
29.
B
65.
4 hours
30.
A
66.
3.843 years
31.
C
67.
14 years.
32.
C
33.
A