Name:______Date:______
Semester 2 Final Review
Use the Law of Sines to find the missing side of the triangle.
1.Find b.
2.Find the measure of given = 55°, = 44°, and b = 68.
3.Find the value of x for and. (The figure is not drawn to scale.)
4.Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth.
5.What is the height h of the parallelogram?
Not drawn to scale
6.You are planning to use a ceramic tile design in your new bathroom. The tiles are blue-and-white equilateral triangles. You decide to arrange the blue tiles in a hexagonal shape as shown. If the side of each tile measures 10 centimeters, what will be the exact area of each hexagonal shape?
Find the surface area of the cylinder in terms of .
7.
Find the volume of the given prism. Round to the nearest tenth if necessary.
8.
9.
Find the value of x. Round to the nearest tenth.
10.
11.
Find the value of x. If necessary, round your answer to the nearest tenth. The figures are not drawn to scale.
____12.The figure consists of a tangent and a secant to the circle.
A. / 24.1 / B. / 16.2 / C. / 261 / D. / 13.413.
14.The figure consists of a chord, a secant, and a tangent to the circle. Round to the nearest hundredth, if necessary.
15.AB = 11, BC = 8, and CD = 10
In the figure, and are tangent to circle O and bisects . The figure is not drawn to scale.
16.For = 49, find .
17.For = 48, find .
18.It costs a family $324 to buy a 10-ft-by-12-ft rug. At this rate, what will it cost them to buy a 15-ft-by-18-ft rug?
19.Find the value of w, then x. Round lengths of segments to the nearest tenth.
20.Find the probability that a point chosen at random from is on the segment .
21.In trapezoid PQRS, . Find the area of PQRS. Leave your answer in simplest radical form.
Not drawn to scale
____22.When designing a building, you must be sure that the building can withstand hurricane-force winds, which have a velocity of 74 mi/h or more. The formula gives the force F in pounds exerted by a wind blowing against a flat surface. A is the area of the surface in square feet, and v is the wind velocity in miles per hour. How much force is exerted by a wind blowing at 91 mi/h against the side of the building shown?
A. / about 6 tons / C. / about 11,025 tonsB. / about 55 tons / D. / about 20 tons
Find the value of x. Round the length to the nearest tenth.
23.
Find the area of the circle. Leave your answer in terms of .
24.
Find the area. The figure is not drawn to scale.
25.
26.
27.
28.What are the minor arcs of ?
The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second. The figures are not drawn to scale.
29.
30. is tangent to . If and, what is ?
The diagram is not to scale.
31.Find the exact area of the shaded region.
____32.Find the measures of the indicated angles in circle O. Which statement is NOTtrue? (The figure is not drawn to scale.)
A. / a = 53 / B. / b = 106 / C. / c = 73 / D. / d = 3733.A kite has diagonals 3.1 ft and 8 ft. What is the area of the kite?
Use the Law of Sines to find the missing angle of the triangle.
34.Find to the nearest tenth if , , and .
35.Find the measure of .
The figure is not drawn to scale.
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
36.
37.The volumes of two similar solids are 729 m and 125 m. The surface area of the larger solid is 324m. What is the surface area of the smaller solid?
Find the area of the trapezoid. Leave your answer in simplest radical form.
38.
39.
40.Find the volume of the composite space figure to the nearest whole number.
41.Each person in a group of college students was identified by graduating year and asked when he or she preferred taking classes: morning, afternoon, or evening. The results are shown in the table. Find the probability that the student preferred morning classes given he or she is a freshman. Round to the nearest thousandth.
Survey of Class TimesFreshman / Sophomore / Junior / Senior
Morning / 2 / 5 / 17 / 10
Afternoon / 19 / 20 / 15 / 2
Evening / 11 / 6 / 8 / 7
42.A pet store has two tanks of tropical fish. The first tank contains 6 blue fish and 2 yellow fish and the second tank contains 6 blue fish and 3 yellow fish. If Keisha randomly purchases a fish from each tank, what is the probability that both fish will be blue?
Find the length of the missing side. Leave your answer in simplest radical form.
43.
44.A local pizzeria offers 11 toppings for their pizzas and you can choose any 4 of them for one fixed price. How many different types of pizzas can you order with 4 toppings?
____45.Write the standard equation of the circle in the graph.
A. / (x + 3) + (y – 2) = 9 / C. / (x – 3) + (y + 2) = 18B. / (x – 3) + (y + 2) = 9 / D. / (x + 3) + (y – 2) = 18
46.Find the missing value to the nearest hundredth.
47.Given the regular hexagon, find the measure of each numbered angle.
48.and are diameters. Find the measure of . (The figure is not drawn to scale.)
49.In how many different orders can 15 basketball players be listed in a program?
50.What is the maximum volume of a pyramid that can fit inside a cube with a side length of 18 cm?
Find the circumference. Leave your answer in terms of .
51.
52.Find the center and radius of the circle with equation (x – 2) + (y – 6) = 9.
Use the Law of Cosines to find the missing angle.
53.In , g = 8 ft, h = 13 ft, and = 72°. Find . Round your answer to the nearest tenth.
54.Find , given a = 11, b = 12, and c = 17.
55.Find the measure of .
Use a trigonometric ratio to find the value of x. Round your answer to the nearest tenth.
56.
57.is tangent to circle O at A. If , what is mYAC? (The figure is not drawn to scale.)
Write the standard equation for the circle.
58.center (2, 8), r = 6
59.At a high school, 5 students volunteer for a committee. How many different 3-person committees can be chosen?
Find the area of the regular polygon. Give the answer to the nearest tenth.
60.hexagon with a radius of 5 in.
61.decagon with a side of 4 cm
62.Find the lateral area of the cone to the nearest whole number.
Not drawn to scale63.Lenny’s favorite radio station has this hourly schedule: news 11 min, commercials 3 min, music 46 min. If Lenny chooses a time of day at random to turn on the radio to his favorite station, what is the probability that he will hear the news?
64.A jewelry store buys small boxes in which to wrap items that they sell. The diagram below shows one of the boxes. Find the lateral area and the surface area of the box to the nearest whole number.
65.Viola drives 160 meters up a hill that makes an angle of 10 with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered?
66.is tangent to the circle at C. In the circle, . Find mBCP.
(The figure is not drawn to scale.)
67.In a survey of 200 people, 32% had a son, 33% had a daughter, and 16% had both a son and a daughter. What is the conditional probability that a person who has a son also has a daughter? Round to the nearest whole number.
68.What are the major arcs of that contain point J?
Determine whether each pair of actions results in independent or dependent events.
____69.Roll a standard number cube. Then pick a marble out of a bag.
A. / Independent; the roll will not affect the marble selection. / C. / Dependent; the roll will not affect the marble selection.B. / Independent; the roll will affect the marble selection. / D. / Dependent; the roll will affect the marble selection.
70.A drug trial is testing the effectiveness of two drugs. If 80 patients are given Drug A, 20 patients are given Drug B, and 90 patients are given a placebo, what is the probability that a patient will NOT be given a placebo?
71.The volume of a sphere is 2973 m. What is the surface area of the sphere to the nearest tenth?
72.Find the similarity ratio of a prism with the surface area of 64 ft to a similar prism with the surface area of 400 ft.
Find the value of x. If necessary, round your answer to the nearest tenth.O is the center of the circle. The figure is not drawn to scale.
73., , FG = 26, RS = 20, OP = 17
74.
Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.)
75. 129
76.Find the surface area of a sphere with a circumference of 115 mm. Round to the nearest tenth.
77.A conveyor belt carries supplies from the first floor to the second floor, which is 25 feet higher. The belt makes a 60° angle with the ground.
How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot.
If the belt moves at 75 ft/min, how long, to the nearest tenth of a minute, does it take the supplies to move to the second floor?
78.One-hundred students were allowed to re-take an exam for their math course. The probability distribution shows how studying for the latest exam affected their grade when compared with the first time they took the exam. What is the probability that a student who studied for the exam saw an increase in their exam grade? Round to the nearest thousandth.
Exam GradesStudied / Did Not Study / Totals
Raise in Grade / 0.52 / 0.04 / 0.56
No Raise in Grade / 0.06 / 0.38 / 0.44
Totals / 0.58 / 0.42 / 1
79.If , what is ?
80.In a college biology class, only half of the class earned a passing grade. Out of all the students, 30% studied and passed. What is the probability of someone having studied, given that they passed?
Find the surface area of the sphere with the given dimension. Leave your answer in terms of .
81.radius of 40 m
82.is tangent to circle O at C, , and . Find mDCE.
(The figure is not drawn to scale.)
83.Find the height of the cylinder.
84.A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249-foot-long shadow. Find the measure of to the nearest degree.
85.Allison is planning to cover the lateral surface of a large cylindrical garbage can with decorative fabric for a theme party. The can has a diameter of 3 feet and a height of 3.5 feet. How much fabric does she need? Round to the nearest square foot.
86.A parallelogram has sides measuring 23.8 m and 32.8 m. The height corresponding to the 23.8-m base is 9.6 m. Find the height, to the nearest tenth of a meter, corresponding to the 32.8-m base.
87.Suppose Q and R are independent events, and P(Q) = 0.74, P(R) = 0.27. Find P(Q and R).
88.Find the length of . Leave your answer in terms of .
89.Quilt squares are cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 4 inches long. What is the side length of each piece?
90.Find the angle of elevation of the sun from the ground when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree.
Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale.
91.
92.Find the area of the regular polygon. Round your answer to the nearest tenth.
93.and . Find mA. (The figure is not drawn to scale.)
94.Find the surface area of the cone in terms of .
95.Find the similarity ratio of a cube with volume 343 ft to a cube with volume 1728 ft.
96.Find the surface area of a conical grain storage tank that has a height of 43 meters and a diameter of 14 meters. Round the answer to the nearest square meter.
97.Find the area of the shaded region. Leave your answer in terms of and in simplest radical form.
Find the value of x. Round to the nearest degree.
98.
99.Find x in circle O. (The figure is not drawn to scale.)
100.A triangle has sides of lengths 21, 47, and 52. Is it a right triangle? Explain.
Semester 2 Final Review
Answer Section
1.40.6
2.96.68
3.20.5
4.x = 4.2, y = 3
5.32
6.150 cm2
7.360 in.
8.1386 ft
9.17 m
10.16.5
11.7.5
12.B
13.12.6
14.33.19
15.5.2
16.49
17.42
18.$729
19.w = 13.3, x = 10.2
20.
21.units2
22.A
23.783.2 m
24.2.4025 m2
25.
26.12.75 cm2
27.144.5 cm2
28.
29.and
30.120
31.
32.C
33.12.4 ft2
34.69.9
35.153
36.x = , y = 36
37.100 m
38.ft2
39.70 in.2
40.180 cm
41.0.063
42.
43. cm
44.330
45.B
46.32.23
47.
48.215
49.1,307,674,368,000
50.1944 cm
51. cm
52.center (2, 6); r = 3
53.35.9°
54. = 44.7°
55.
56.6.2 cm
57.70.5
58.(x – 2) + (y – 8) = 36
59.10
60.65.0 in.
61.123.1 cm
62.4712 m
63.
64.53 cm; 261 cm
65.157.6 m
66.44.5
67.50%
68.
69.A
70.
71.2144.8 m
72.2 : 5
73.18.9
74.15
75.51
76.4209.6 mm
77.29 ft; 0.4 min
78.0.897
79.
80.60%
81.6,400 m
82.51
83.2.4 in.
84.22
85.33 ft
86.7 m
87.0.1998
88.12 m
89.2
90.36
91.10.5 m
92.483.0 in.2
93.37
94.51 cm
95.7 : 12
96.1112 m
97.
98.34
99.21.5
100.no;