Download Semester 2 Final Review 3

H. Geometry
Name____________________________Period____Date_________
Semester 2 Final Review-1
Unit 5: Module 13 Review
1. The value for x is:
2. The value for x is:
8 2
o
x
o
o
20
x
1
3. The value for x is:
o
4. 4. The value for x is:
9
x
4
60°
x
60°
5. The value for x is:
6 3
60°
x
6. The ratio
8
represent the which relationship:
6
B
6 cm
10 cm
A
A) sin C
B) sin B
7. Which of the following is equal to cos 40◦
A) sin 50°
B) sin 40◦
C) tan C
C) tan 50◦
8. If cos Ɵ = sin ß then the two angles must be:
A) supplementary
B) complementary
9. Given the ratio
D) tan B
8 cm
C
D) cos 50◦
C) a linear pair
8
, which of the following is NOT equal to this
10
value?
CA
4
A) CB
B) 5
C) sin B
D) cos B
10. If cos Ɵ = sin ß then which of the following must be true?
a. A) Ɵ + ß = 180◦
B) Ɵ - ß = 90◦
C) ß = 90◦ - Ɵ
C
D) adjacent
A
8 cm
6 cm
10 cm
B
D) ß - Ɵ = 90◦
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H.Geometry
Semester Final Review 1
11. Julie has a large red apple in her hand that is 7 ft off the
ground. A blue bird sees the apple making a 55◦ between the
tree and the line of sight of the bird. If Julie is 15 ft from the
tree, how tall is the tree (round to the nearest foot)??
A) 19 ft
B) 20 ft
C) 28 ft
D) 24 ft
12. A 15 ft tree casts a 18 ft long shadow. What is the angle formed by the sun’s
rays and the ground to the nearest degree?
A) 60◦
B) 50◦
C) 40◦
D) 30◦
13. What is the height of this triangle?
8 cm
A) 4.92 cm
B) 6.30 cm
C) 10.24 cm
D) 11.03 cm
h
52°
14 cm
14. What is the area of the triangle?
A) 33.55 cm2
B) 57.68 cm2
34°
C) 67.10 cm2
D) 115.35 cm2
72°
8 cm
15 cm
True/False
15. In a right isosceles ∆, if the hypotenuse is 14 cm then one leg is 7 2 cm.
T or F
16. 10 2 , 10 2 and 20 could represent the three sides of a right isosceles triangle.
T or F
17. 5, 5 3 and 20 could represent the three sides of a 30◦, 60◦, 90◦
T or F
∆ triangle.
18. In right ∆ABC where C is a right angle, BC is adjacent to B.
T or F
19. For angles between 0◦ and 90◦ the cosine values are between 0 and 1.
T or F
20. In right triangles, the hypotenuse side is always smaller than the adjacent side.
T or F
21. The Sine ratio of 45◦ is equal to the Cosine ratio of 45◦.
T or F
22. sin (2x – 7) = cos (x + 13) when x = 28.
T or F
23. If cos Ɵ = sin ß, then ß = 90◦ - Ɵ
T or F
24. If you have two sides and an angle of a ∆, then you can determine the area.
T or F
25. Sin 45◦ = Cos 45◦
T or F
26. What is the area of a square that has a diagonal length of 12 2 cm?
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H.Geometry
Semester Final Review 1
27. Solve for the unknowns. Leave answers in reduced radical form.
A)
B)
C)
y
y
x
14 5
30°
30°
x
o
18 3
24 2
x = __________
y = __________
x = __________
y = __________
D)
y
30°
o
x
x
6
x = __________
x = __________
y = __________
28. Solve for the missing information. (Round all final answers to 1 decimal place)
a)
b)
c)
d)
12 cm
x
36°
x ≈ ____________
10 cm
63°
8 cm
11 cm
9 cm
θ°
Ɵ = ____________
θ°
x
x ≈ ____________
3 cm
Ɵ = ____________
29. Solve for the unknown.
a) sin (x + 18) = cos (45)
b) sin (2x – 15) = cos (x – 12)
c) sin (x)= cos (x)
1
2
d) sin ( x ) = cos ( x  3 )
5
5
e) sin (3x + 25) = cos (2x + 10)
3
f) sin ( x  12 )= cos (66)
4
30. A helicopter is hovering 200 ft in the air over a landing pad. If the
man sees the helicopter at an angle of elevation of 38◦, how far is
he from the landing pad (to the nearest foot)??
31.
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H.Geometry
Semester Final Review 1
32. Determine the area of the given triangles.
a)
b)
50°
h
30 cm
7 cm
h
118°
12 cm
29 cm
33. Determine the missing angle that makes the equation true.
a) sin 56◦ = cos _______ b) sin 12◦ = cos _______
c) cos 82◦ = sin _______
34. Round all sides and angles to the tenth place (1st decimal place).
a.)
b.)
c.)
d.)
4
H. Geometry
Name____________________________Period____Date_________
Semester 2 Final Review 2 - Unit 6: Module 15 Review
1. Determine the requested value(s).
a)
b)
c)
d)
x
1
2
151°
128°
52°
2
2
60°
1
1
1
77°
142°
74°
m1 = _______
m1 = _______
m1 = _______
m1 = _______
m2 = _______
m2 = _______
m2 = _______
𝑚 𝑥̂ = ________
2. Determine the requested value(s).
a)
b)
c)
d)
156°
74°
3
136°
88°
78°
2
2
1
1
m1 = _______
m2 = _______
m1 = _______
m2 = _______
m1 = _______
m2 = _______
m3 = _______
m1 = _______
m2 = _______
c)
d)
x
x
122°
2
48°
1
85°
1
2
1
3. Determine the requested value(s).
a)
b)
53°
31° 1
70°
2
121°
80°
1
1
110°
30°
x
122°
m1 = _______
m2 = _______
m1 = _______
𝑚 𝑥̂ = ________
m1 = _______
𝑚 𝑥̂ = ________
m1 = _______
𝑚 𝑥̂ = ________
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H.Geometry
4. Determine the requested value(s). (Lines that appear to be tangent are tangent.)
a)
b)
c)
1
Semester Final Review 2
d)
140°
1
30°
38°
65°
68°
x
x
1
48°
92°
92°
114°
m1 = _______
m1 = _______
𝑚 𝑥̂ = ________
m1 = _______
𝑚 𝑥̂ = ________
5. Determine the requested values.
a)
b)
c)
2
2
86°
d)
104°
2
2
1
68°
1
125°
106°
79°
1
1
m1 = _____ m2 =_____ m1 = _____ m2 = _____ m1 = _____ m2 =_____ m1 = _____ m2 = _____
6. Determine the arc measure.
Diagram for a – d
Diagram for e - h
̂
̂
108°
a) 𝑚𝐵𝐶 = ____________
e) 𝑚𝐴𝐶 = ____________
B
C
̂ = ____________
̂ = ____________
b) 𝑚𝐵𝐹𝐷
f) 𝑚𝐷𝐸𝐴
E
A
D
̂
̂ = ____________
c) 𝑚𝐴𝐹 = ____________
g) 𝑚𝐸𝐶
̂ = ____________
̂ = ____________
D
d) 𝑚𝐷𝐸
h) 𝑚𝐷𝐸𝐶
F 44°
123° G
B
A
F
E
C
7. Determine the value of x. (Lines that appear to be tangent are tangent.)
a)
b)
c)
d)
x = ____________ (1 dec.)
x = _____________ (1 dec.)
x = _____________ (2 dec.)
x = ____________ (2 dec.)
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H.Geometry
8. Solve for x ( AB and AD are tangent lines)
a)
b)
Semester Final Review 2
c)
D
D
12 cm
C
C
D
45°
B
C
77 cm
A
x
B
A
5x - 3
x2 - 3
13 cm
B
A
x = ____________
x = ____________
9. Using the diagram to the right complete the following.
a) Point ________ or ________ are in the interior of the circle.
b) Circle which of the following are chords AD AC
c) The diameter of circle Z is _____________.
d) How many radii are in this diagram? ___________
e) Point __________ is exterior to the circle.
f) How many chords are in this diagram? ____________
g) Name the tangent line ___________
h) Name the secant line ________
AB
AZ
x = ____________
H
A
BD
B
Z
G
D
C
̂ = 45° then the major arc from A to C would measure 215.
10. If 𝑚𝐴𝐶
T or F
11. A major arc has a measurement greater than 90.
T or F
̂ =180°
12. Points A, B, C, D, E & F (in that order) divide a circle into 6 congruent arcs, them 𝑚𝐶𝐹
T or F
13. Tangent line
14.
RM
intersects Circle T at M, then mRMT = 90.
T or F
AB and AG are tangents that intersect circle M at points B and G, then ABG is isosceles.
T or F
15. An inscribed triangle divides the circle into three arcs, 148, 200 and 12, then one
of the angles in the triangle is 74.
T or F
16. If the inscribed angle is 38, then the arc that it subtends is 19.
T or F
̂?
17. What is 𝑚𝐹𝐴𝐷
A
B
43°
32°
C
D
G
F
E
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H.Geometry
Semester Final Review 2
Module 16:
18. Approximately how many radians are there in one full circle?
19. Which of the following is not a true statement?
B.  radians = 180
A. 360 = 2 radians
20. What is the equivalent degree measure for
C. 1 =

D. 1 radian = 60
180
2
radians?
12
21. What is the equivalent radian measure for 200?
22. Convert the degree measures into radians. Leave answers as exact values in most reduced form.
a) 45
b) 36
c) 140
d) 300
23. Convert the following radian measures into degrees.
a)
11
6
b)
5
9
c)
23
12
d)
7
2
24. Determine the arc length. Leave
answers in exact form.
a) Central Angle of 30,
radius of 10 cm.
b) Central Angle of 24,
radius of 5 cm.
c) Central Angle of 270,
radius of 1 cm.
25. Determine the sector area. Leave answers in exact form.
a) Central Angle of 112,
b) Central Angle of 24,
radius of 10 cm.
radius of 8 cm.
c) Central Angle of 200,
radius of 5 cm.
26. Find the radius of a circle in which a central angle of 80 intercepts an arc length of 2cm?
27. If the arc length of a sector is
3
cm and its radius is 2 cm, then the central angle in radians is:
4
28. If the arc length of a sector is 24 cm and its radius is 8 cm, then the central angle in radians is:
4
then its radius is:
5
5
then its radius is:
8
29. If the area of circle sector is 40 cm2 and its central angle
30. If the area of circle sector is 5 cm2 and its central angle
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H.Geometry
31. Determine the arc length of the following.
a)
Semester Final Review 2
b)
5π
4
3π
2
3 cm
12 cm
Module 17:
32. Determine the center and radius of the given circles.
a)  x  7    y  10   81
Center (_____ , _____)
Radius = _______
b) 100   x  3  y 2
Center (_____ , _____)
Radius = _______
Center (_____ , _____)
Radius = _______
Center (_____ , _____)
Radius = _______
Center (_____ , _____)
Radius = _______
2
2
2
c)  x  9    y  2   1
2
2
d) 36   x  8    y  7 
2
2
e) x   y  1  4
2
2
33. Determine the center and radius of the given circles by completing the square.
x 2  y 2  4 x  14 y  17  0
ex)
a)
x2  y 2  4 x  16 y  52  0
x2  4 x  
  y 2  14 y     17
x 2  4 x   4    y 2  14 y   49    17  4  49
2
2
 x  2    y  7   36
Center (2,7)
Radius = 6 cm.
Center (_____ , _____)
b)
x  y  2 x  18 y  1  0
2
2
Center (_____ , _____)
d)
Radius = ______
x  14 x  y  2 y  50  0
2
2
Center (_____ , _____)
Radius = ______
c)
2
Center (_____ , _____)
e)
Radius = ______
x  10 x  y  16  0
2
Radius = ______
x  2 x  18   y  8x
2
2
Center (_____ , _____)
Radius = ______
5
H. Geometry
Name____________________________Period____Date_________
Semester 2 Final Review 3- Unit 7: Module 18
Find the volume of each prism. Round to the nearest tenth if necessary.
1.
2.
the oblique rectangular prism
the right triangular prism
3.a cube with edge length 0.75 m ___________________________________________________________
Find the volume of each cylinder. Give your answers both in terms
of  and rounded to the nearest tenth.
4.
5.
6. a cylinder with base circumference 18 ft and height 10 ft ________________________________
Describe the effect of each change on the volume of the given figure.
6.
7.
The dimensions are halved.
The dimensions are divided by 5.
Find the volume of each composite figure. Round to the nearest tenth.
8.
9.
Write each formula.
10. volume of a pyramid with base area B and height h
___________________________
11. volume of a square pyramid with base edge s and height h
___________________________
1
H.Geometry
Find the volume of each pyramid. Round to the nearest tenth.
12.
Semester Final Review 3
13.
rectangular pyramid
regular pentagonal pyramid
Find the volume of the composite figures.
14.
15.
Find the volume of each cone. Give your answers both in terms of and rounded to
the nearest tenth.
16.
17.
18.
19. a cone with diameter 15 yd and
height 10 yd
Find the volume of each composite figure. Round to the nearest tenth.
20.
2
H.Geometry
Find each measurement. Give your answers in terms of .
21.
Semester Final Review 3
22.
the volume of the sphere
the volume of the hemisphere
Module 19
Tell what kind of solid can be made from each net.
If there is no solid that can be made from the given net, write “none.”
23.
24.
_______________________
25.
_______________________
________________________
Name the shape of the cross section
produced by slicing each of these solids as described.
26. Vertical cross section of a cylinder _________________
27. Horizontal cross section of a square pyramid _________________
Find the surface area of each solid figure. Write the measures of the solid figures
on the corresponding parts of their nets. For cylinders, give answers in terms of .
28. Cube: ________ units2
29. Cylinder: ________ units2
30. Rectangular prism: ________ units2
31. Triangular prism: ________ units2
Height of base  25 units
3
H.Geometry
Semester Final Review 3
32. Cylinder: ________ units2
33. Triangular prism: ________ units2
Find the surface area of each composite figure. Show your work.
34. Cylinder on top of rectangular prism
________
units2
Find the surface area of each part of the solid figure. Add to find the total surface
area. For cones, give answers in terms of .
__________
mm2
What is the lateral surface area?
__________
mm2
What is the total surface area?
__________
mm2
36. What is the base area of the cone?
__________
ft2
What is the lateral surface area?
__________
ft2
What is the total surface area?
__________
ft2
35. What is the base area of the cone?
Find the surface area of each figure.
37. __________ in2
38. Slant Height is 12 in
__________
in2
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H.Geometry
Semester Final Review 3
Solve for the surface area.
Give surface areas in terms of .
39. Surface area  ______ mi2
40. Surface area  ______ m2
Module 20
State how each transformation affects the area.
41. The base of a parallelogram is multiplied by
3
.
4
________________________________________________________________________________________
42. A rectangle has length 12 yd and width 11 yd. The length is divided by 6.
________________________________________________________________________________________
43. A triangle has vertices A(2, 3), B(5, 2), and C(5, 4). The transformation is (x, y)  (x,
2y).
________________________________________________________________________________________
State how each transformation affects the perimeter or circumference and area.
44. The length and width of the rectangle are multiplied by
4
.
3
________________________________________________________________________________________
45. A triangle has base 1.5 m and height 6 m. Both base and height
are tripled.
________________________________________________________________________________________
1 1 
46. A circle with radius 2 has center (2, 2). The transformation is (x, y)   x, y  .
2 2 
________________________________________________________________________________________
State how each transformation affects the surface area and volume.
47. The dimensions of a rectangular prism are multiplied by a scale factor of 2.
________________________________________________________________________________________
5
H.Geometry
Semester Final Review 3
1
48. The dimensions of a right cylinder are multiplied by a scale factor of .
2
________________________________________________________________________________________
Find the population density.
49. Park rangers counted 7 coyotes over an area of 25 square miles.
________________________________________________________________________________________
50. A major metropolitan city has an average of 60,000 people visiting the city’s park during
peak hours. The city park is 3.41 km2.
________________________________________________________________________________________
51. About 50,000 full-grown Canadian geese were estimated to live in the state of
Minnesota in 1990. The state of Minnesota is about 86,000 square miles.
________________________________________________________________________________________
In Problems 4–6, state how the following changes will affect the population density.
52. Park rangers counted 7 coyotes over an area of 25 square miles. One of the coyotes
left the pack and is no longer in the area.
________________________________________________________________________________________
53. A major metropolitan city has an average of 60,000 people visit the city’s park during
peak hours. The city park is 3.41 km2. An outdoor concert is planned in the park and
40,000 additional people are expected to attend the concert.
________________________________________________________________________________________
54. About 50,000 full-grown Canadian geese were estimated to live in the state of Minnesota in
1990. The state of Minnesota is about 86,000 square miles. It is estimated that 62,000
goslings were produced and will become full-grown adults in 1991.
________________________________________________________________________________________
Find the population density.
55. Cardton City has a population of 2046. Its border can be modeled by a rectangle with
vertices A(1, 1), B(1, 1), C(1, 0), and D(1, 0), where each unit on the coordinate plane
represents 1 mile. Find the approximate population density of Cardton City.
In Problems 1–4, solve for the missing dimension of the figure.
56. A rectangular prism has a volume of 432 cubic feet. Two of the dimensions of the
rectangular prism are the same measure. The other dimension is equal to the sum of
the other two dimensions. What are the prism’s dimensions?
________________________________________________________________________________________
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H.Geometry
Semester Final Review 3
57. A cone’s height is six times greater than the measure of the cone’s radius. The volume
of the cylinder is 169.56 in3. What are the cone’s dimensions? Use 3.14 for .
________________________________________________________________________________________
58. A cube has a volume of 343 cubic centimeters. The length, width, and the height of
the figure are equal. What are the cube’s dimensions?
________________________________________________________________________________________
59. A circle has an area of 530.66 square inches. What is the circle’s radius? Use 3.14 for
.
________________________________________________________________________________________
60.
61.
7
H. Geometry
Name____________________________Period______
Semester 2 Final Review 4 - UNIT 8 – Module 22 and Module 23 Mixed Review Probability
1. When rolling two fair number cubes, what is the probability that the sum of the two cubes will not be even AND not
prime?
2. Ten marbles are placed in a jar. Of the 10 marbles, 3 are blue, 2 are red, 3 are green, 1 is orange, and 1 is yellow. The
10 marbles are randomly placed in a line. What is the probability that all marbles of the same color are next to each
other?
3. A class of 15 boys and 15 girls is putting together a random group of 3 students to do classroom chores. What is the
probability that at least 2 of the students are boys?
Use the sets below to find the indicated set for problems 4-7.
U = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = {1, 3, 5, 7, 9} B = {2, 4, 6, 8} C = {1, 2, 4, 5, 7, 9}
4. A ⋃C
5. B ⋂C
6. 𝐴𝑐
7. A ⋂B
8. A computer password can use all digits (0 –9) and all letters (a–z) that are case sensitive (upper and lower). How many
different permutations of 5-figure passwords are there if there is no repeated input?
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H.Geometry
Semester Final Review
9. Twenty-six tiles with the letters A through Z are placed face down on a table and mixed. (For the purpose of this
exercise assume that the letter Y is a vowel.) Five tiles are drawn in order. Compute the probability that only consonants
are selected.
10. The two-way table shows the results of a poll in a certain country that asked voters, sorted by political party,
whether they supported or opposed a proposed government initiative. Find the given probabilities.
a. P (no party or undecided)
b. P ((𝑝𝑎𝑟𝑡𝑦 𝐴 𝑜𝑟 𝑠𝑢𝑝𝑝𝑜𝑟𝑡)𝑐 )
11. Let H be the event that a coin flip lands with heads showing, and let T be the event that a flip lands with tails
showing. (Note that P(H) = P(T) = 0.5.) What is the probability that you will get heads at least once if you flip the coin ten
times? Explain your reasoning.
12. There are 8 girls and 6 boys on the student council. How many committees of 3 girls and 2 boys can be formed?
Show your work.
13. Find the probability that a black card drawn from the deck is a queen. (The deck is a standard one of 52 cards.)
2
H.Geometry
Semester Final Review
14. Jim rolled a set of two number cubes. If these are standard 6-sided number cubes, what is the probability of
obtaining 12? (That means the values of the top faces add up to 12.)
15. What is the probability that a diamond that is drawn from the deck is a queen?
16. What is the probability that a queen drawn is a diamond?
17. Isabelle believes that right- and left-footed soccer players are equally likely to score goals. She collected data from
260 players from a local soccer league. Using the following two-way frequency table, show that being right-footed and
scoring goals are independent events.
18. Jim has 2 blue, 2 green, and 2 black socks in his drawer. He picks out 2 socks, one after the other. Determine the
probability of him getting a matching pair of blue socks. Are these events Independent or Dependent?
19. You have a standard deck of 52 playing cards. You pick three cards in a row without replacement. What is the
probability that all three are aces? Now you replace the three cards, shuffle, and pick four cards in a row without
replacement. What is the probability that none are aces?
20. Lisa flipped the same coin twice. Determine the probability of the coin landing on tails on the second try.
3
H.Geometry
Semester Final Review
21. Lisa flipped the same coin three times. What is the probability she obtained all tails?
22. A jar contains 12 pennies, 5 nickels, and 18 quarters. You select 2 coins at random, one after the other. Does
selecting a nickel affect the probability of selecting another nickel? Does not selecting a dime affect the probability of
selecting a nickel? Find the probability of selecting 2 nickels.
23. Are the events independent? Choose Yes or No for each situation.
A. Picking a penny and a marble out of a jar of pennies and a jar of marbles.
Yes
No
B. Drawing cards from a deck to form a 4-card hand.
Yes
No
C. Choosing a color for a new shirt from a choice of red, yellow, or purple.
Yes
No
24. Of the boys running for School President, 2 are juniors and 3 are seniors. Of the girls who are running, 4 are juniors
𝟐
and 1 is a senior. Decide whether the situation has a probability of 𝟓.
Select Yes or No for A–C.
A. A girl wins.
Yes
No
B. A candidate who is a boy is a junior.
Yes
No
C. A candidate who is a junior is a boy.
Yes
No
25. You shuffle a standard deck of playing cards and deal one card. What is the probability that you deal an ace or a
club? Explain your reasoning.
4