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Final Exam – Unit 6 Study Guide

Total questions: 86

Worksheet time: 4hrs 3mins

Name
Class
Date
1.

Find the values of x and y.

a)

x = 13√2, y = 13

b)

x = 13, y = 13√2

c)

x = 13, y = 13

d)

x = 13√2, y = 13√2

2.

Find the values of x and y.

a)

x = 30√2, y = 30

b)

x = 30, y = 30√2

c)

x = 15√2, y = 15√2

d)

x = 15, y = 15√2

3.

Find the values of x and y.

a)

x = 6, y = 3√3

b)

x = 3√3, y = 3

c)

x = 3√3, y = 3√3

d)

x = 3√2, y = 6

4.

Find the values of x and y.

a)

x = 17, y = 17sqrt3

b)

x = 34, y = 17

c)

x = 17sqrt3, y = 17

d)

x = 17, y = 34

5.

Find the values of x and y.

a)

x = 10, y = 10

b)

x = 5, y = 5

c)

x = 10√2, y = 10√2

d)

x = 20, y = 20

6.

Find the values of x and y.

a)

x = 25, y = 25√3

b)

x = 25√3, y = 25

c)

x = 50, y = 25

d)

x = 25, y = 50

7.

Find the values of x and y.

a)

x = 2√7, y = 2√7

b)

x = 4√7, y = 4√7

c)

x = 2√14, y = 2√14

d)

x = 7, y = 7

8.

Find the values of x and y.

a)

x = 12, y = 24√3

b)

x = 24, y = 12√3

c)

x = 16√3, y = 8√3

d)

x = 12√3, y = 24

9.

Find the values of x and y.

a)

x = 33, y = 22√3

b)

x = 22√3, y = 22

c)

x = 11√3, y = 33

d)

x = 11, y = 11√3

10.

Find the values of x and y.

a)

x = 2, y = √3

b)

x = 3√2, y = 2√6

c)

x = 3, y = √6

d)

x = 3√2, y = 3

11.

Find the values of x and y.

a)

x = √10, y = 2√5

b)

x = 2√10, y = 2√5

c)

x = 2√5, y = √10

d)

x = √10, y = √10

12.

Find the values of x and y.

a)

x = 4√7, y = 4√21

b)

x = 2√21, y = 2√3

c)

x = 4√7, y = 4

d)

x = 2, y = 2√21

13.

In the given right triangle, find the values of a and b.

a)

A

b)

B

c)

C

d)

D

14.

In the given right triangle, find the values of x and y.

a)

A

b)

B

c)

C

d)

D

15.

In the given right triangle, find the values of a and b.

a)

A

b)

B

c)

C

d)

D

16.

In the given right triangle, find the values of x and y.

a)

A

b)

B

c)

C

d)

D

17.

In the given right triangle, find the values of u and v.

a)

A

b)

B

c)

C

d)

D

18.

In the given right triangle, find the values of u and v.

a)

A

b)

B

c)

C

d)

D

19.

Convert each measure to radians: 225°

a)

5π/4

b)

3π/4

c)

π/4

d)

7π/4

20.

Convert each measure to radians: 20°

a)

π/9

b)

π/4

c)

π/7

d)

π/5

21.

Convert each measure to radians: -255°

a)

-17π/12

b)

-15π/8

c)

17π/11

d)

-19π/12

22.

Convert each measure to radians: -140°

a)

-7π/9

b)

-7π/12

c)

-9π/5

d)

-7π/2

23.

Convert each measure to radians: 75°

a)

5π/12

b)

3π/8

c)

π/3

d)

2π/5

24.

Convert each measure to radians: -300°

a)

-5π/3

b)

-2π/3

c)

-π/2

d)

-π/3

25.

Convert each measure to degrees: 23π12\frac{23\pi}{12}

a)

345 degrees

b)

330 degrees

c)

360 degrees

d)

315 degrees

26.

Convert each measure to degrees: −31π36-\frac{31\pi}{36}

a)

-155°

b)

-160°

c)

-165°

d)

-170°

27.

Convert each measure to degrees: π12\frac{\pi}{12}

a)

15°

b)

30°

c)

45°

d)

60°

28.

Convert each measure to degrees: 5π9\frac{5\pi}{9}

a)

100°

b)

75°

c)

120°

d)

135°

29.

Convert each measure to degrees: −π2\frac{-\pi}{2}

a)

-90°

b)

-180°

c)

-45°

d)

-90°

30.

Convert each measure to degrees: 7π6\frac{7\pi}{6}

a)

210°

b)

180°

c)

150°

d)

120°

31.

Convert radian measure into degrees: −7π6-\frac{7\pi}{6}

a)

-210°

b)

-160°

c)

-230°

d)

190°

32.

Convert each degree measure into radians and each radian measure into degrees: −23π6-\frac{23\pi}{6}

a)

-690°

b)

-590°

c)

-790°

d)

-400°

33.

Convert each degree measure into radians and each radian measure into degrees: -30°

a)

-π/6

b)

-π/4

c)

-π/3

d)

-π/2

34.

Convert each degree measure into radians and each radian measure into degrees: -930°

a)

-35π/6

b)

37π/6

c)

-31π/6

d)

-41π/6

35.

Convert to radians: -210°

a)

-7π/6

b)

7π/6

c)

3π/2

d)

π

36.

Convert π/4 into degrees.

a)

45°

b)

90°

c)

30°

d)

60°

37.

Fill in the blank: cos 60° = ___

a)

1/2

b)

1/3

c)

1/4

d)

1

38.

Fill in the blank: cos 225° = ___

a)

-√2/2

b)

√2/2

c)

1/2

d)

-1/2

39.

Fill in the blank: tan 330° = ___

a)

1/sqrt3

b)

-sqrt3/3

c)

1

d)

0

40.

Fill in the blank: cos 30° = ___

a)

√3/2

b)

1/2

c)

1/√2

d)

2/√3

41.

Fill in the blank: sin 240° = ___

a)

sin 240° = -√3/2

b)

sin 240° = √3/2

c)

sin 240° = -1/2

d)

sin 240° = 1/2

42.

Fill in the blank: tan 210° = ___

a)

1/√3

b)

-√3

c)

√3

d)

-1/√3

43.

Fill in the blank: tan 30° = ___

a)

1/√3 or √3/3

b)

1

c)

√3

d)

0

44.

Fill in the blank: tan 0° = ___

a)

0

b)

1

c)

undefined

d)

infinity

45.

Fill in the blank: sin 45° = ___

a)

√2/2

b)

1/2

c)

√3/2

d)

1

46.

Fill in the blank: tan 7π/6 = ___

a)

1/√3

b)

√3/3

c)

√3/2

d)

√3

47.

Fill in the blank: cos 3π/4 = ___

a)

-√2/2

b)

√2/2

c)

0

d)

1

48.

Fill in the blank: sin π = ___

a)

0

b)

1

c)

-1

d)

Undefined

49.

Fill in the blank: sin π/6 = ___

a)

1/2

b)

1/3

c)

1/4

d)

1

50.

Fill in the blank: cos π = ___

a)

0

b)

-1

c)

1

d)

Undefined

51.

Fill in the blank: tan 3π/2 = ___

a)

0

b)

undefined

c)

1

d)

-1

52.

Find the exact value of cos −45°. Do NOT use a calculator!

a)

-sqrt(2)/2

b)

-1/2

c)

sqrt(2)/2

d)

-1

53.

Find the exact value of tan −240°. Do NOT use a calculator!

a)

-sqrt(3)

b)

-sqrt(3)

c)

-sqrt(3)/2

d)

-sqrt(3)/3

54.

Find the exact value of cos 45°. Do NOT use a calculator!

a)

√2/2

b)

1/2

c)

√3/2

d)

1

55.

Find the exact value of cos 225°. Do NOT use a calculator!

a)

-√2/2

b)

√2/2

c)

1/2

d)

-1/2

56.

Find the exact value of cos −240°. Do NOT use a calculator!

a)

-1/2

b)

1/2

c)

0

d)

-√3/2

57.

Find the exact value of tan 60°. Do NOT use a calculator!

a)

tan 60° = √3

b)

tan 60° = 1

c)

tan 60° = 0

d)

tan 60° = 1/√3

58.

Find the exact value of sin 45°. Do NOT use a calculator!

a)

sin 45° = √2/2

b)

sin 45° = 1/2

c)

sin 45° = √3/2

d)

sin 45° = 1

59.

Find the exact value of sin −225°. Do NOT use a calculator!

a)

-√2/2

b)

√2/2

c)

-1/2

d)

1/2

60.

Find the exact value of tan −60°. Do NOT use a calculator!

a)

tan(−60°) = −√3

b)

tan(−60°) = √3

c)

tan(−60°) = 1/√3

d)

tan(−60°) = 0

61.

Find the exact value of sin 225°. Do NOT use a calculator!

a)

-√2/2

b)

√2/2

c)

1/2

d)

-1/2

62.

Find the exact value of tan 5π3\frac{5\pi}{3} . Do NOT use a calculator!

a)

0

b)

sqrt3/3

c)

-sqrt3/3

d)

1

63.

Find the exact value of sin 4π3\frac{4\pi}{3} . Do NOT use a calculator!

a)

-sqrt3/2

b)

-1/2

c)

1/2

d)

sqrt3/2

64.

Using the diagram below, which of the following is an example of a radius?

a)

NP

b)

NL

c)

KL

d)

ML

65.
Question Image

For questions 1 – 10, match the term to the correct figure.

a)

radius

1.

B

b)

tangent

2.

D

c)

secant

3.

C

d)

chord

4.

A

e)

isosceles triangle

5.

J

66.
Question Image

For questions 1 – 10, match the term to the correct figure.

a)

right triangle

1.

K

b)

minor arc

2.

L

c)

major arc

3.

N

d)

inscribed angle

4.

E

e)

central angle

5.

F

67.

Find the area and circumference. Use Pi.

a)

Area: 216.42 m², Circumference: 52.15 m

b)

Area: 8.65 m², Circumference: 216.42 m

c)

Area: 52.15 m², Circumference: 10.42 m

d)

Area: 8.64 m², Circumference: 10.43 m

68.

Find the radius of a circle with a circumference of 106.81 centimeters.

a)

16.99 cm

b)

17.00 cm

c)

17.01 cm

d)

17.02 cm

69.

Find the diameter of a circle with an area of 95.03 square feet.

a)

30.25 feet

b)

5.5 feet

c)

11 feet

d)

60.5 feet

70.

Find the circumference of a circle with an area of 254.47 square inches. (Use Pi)

a)

56.52 inches

b)

50.24 inches

c)

60.28 inches

d)

56.55 inches

71.

What is the area of a circle with a circumference of 30π meters?

a)

75π square meters

b)

225π square meters

c)

150π square meters

d)

300π square meters

72.

Find each measure for parts a-f.

a)

a= 37°
b= 127°
c= 48°
e= 233°
f= 323°

b)

a= 39°
b= 137°
c= 58°
e= 233°
f= 323°

c)

a= 37°
b= 127°
c= 50°
e= 235°
f= 328°

d)

a= 37°
b= 130°
c= 48°
e= 233°
f= 322°

73.

Solve for x.

a)

x = 19

b)

x = 15

c)

x = 17

d)

x = 19

74.

Find measure of arc CD

a)

37°

b)

45°

c)

34°

d)

47°

75.

Identify the center and radius for the circle with the equation (x + 2)^2 + (y - 7)^2 = 16.

a)

Center: (-2, 7), Radius: 4

b)

Center: (2, -7), Radius: 16

c)

Center: (2, 7), Radius: 4

d)

Center: (-2, -7), Radius: 16

76.

Identify the center and diameter for the circle with the equation x^2 + (y + 6)^2 = 121. Center: ______, Diameter: ______

a)

Center: (0, -6), Diameter: 22

b)

Center: (0, 6), Diameter: 11

c)

Center: (0, -6), Diameter: 11

d)

Center: (0, 0), Diameter: 22

77.

Write the equation of the circle in standard form shown on the graph.

a)

(x+5)^2 + (y+1)^2 = 9

b)

(x+3)^2 + (y-2)^2 = 16

c)

(x+5)^2 + (y+1)^2 = 16

d)

(x+3)^2 + (y+2)^2 = 9

78.

Write the equation of the circle in standard form shown on the graph.

a)

x^2 + (y+2)^2 = 64

b)

(x+3)^2 + (y -2)^2 = 8

c)

(x+2)^2 + y^2 = 64

d)

(x+3)^2 + (y+2)^2 = 8

79.

Write an equation of the circle in standard form with the given characteristics: center: (-3, 4), radius: 7.

a)

(x + 3)^2 + (y - 4)^2 = 49

b)

(x - 3)^2 + (y + 4)^2 = 49

c)

(x + 3)^2 + (y + 4)^2 = 49

d)

(x - 3)^2 + (y - 4)^2 = 49

80.

Write an equation of the circle in standard form with the given characteristics: center: (-9, 0), diameter: 20.

a)

(x + 9)^2 + y^2 = 100

b)

(x - 9)^2 + y^2 = 25

c)

(x + 9)^2 + y^2 = 25

d)

(x - 9)^2 + y^2 = 100

81.

Write an equation of the circle in standard form with the given characteristics: center: (-7, -1), diameter: 9.

a)

(x + 7)^2 + (y + 1)^2 = 81

b)

(x - 7)^2 + (y - 1)^2 = 81

c)

(x + 7)^2 + (y + 1)^2 = 20.25

d)

(x - 7)^2 + (y - 1)^2 = 20.25

82.

What is the equation of the circle in standard form with the center at (12, 5) and radius √89?

a)

(x - 12)^2 + (y - 5)^2 = 89

b)

(x + 12)^2 + (y + 5)^2 = 89

c)

(x - 12)^2 + (y - 5)^2 = 89^2

d)

(x + 12)^2 + (y + 5)^2 = 89^2

83.

Write an equation of the circle in standard form with the given characteristics: center: (2, -2), circumference: 12π.

a)

(x - 2)^2 + (y + 2)^2 = 36

b)

(x - 2)^2 + (y + 2)^2 = 9

c)

(x + 2)^2 + (y - 2)^2 = 36

d)

(x + 2)^2 + (y - 2)^2 = 9

84.

Write an equation of the circle in standard form with the given characteristics: center: (0, 10), area: 225π.

a)

x^2 + (y - 10)^2 = 225

b)

x^2 + (y - 10)^2 = 225

c)

(x - 0)^2 + (y - 10)^2 = 22

d)

(x - 0)^2 + (y - 10)^2 = 25

85.

What is the equation of the circle in standard form with the given characteristics: center: (-4, 7), point on circle: (-1, 9)?

a)

(x + 4)^2 + (y - 7)^2 = 13

b)

(x + 4)^2 + (y - 7)^2 = 9

c)

(x + 4)^2 + (y - 7)^2 = 10

d)

(x + 4)^2 + (y - 7)^2 = 25

86.

Write an equation of the circle in standard form with the given characteristics: endpoints of diameter: (-18, -3) and (8, 11).

a)

(x + 5)^2 + (y - 4)^2 = 218

b)

(x - 5)^2 + (y + 4)^2 = 218

c)

(x - 5)^2 + (y - 4)^2 = 169

d)

(x + 5)^2 + (y + 4)^2 = 169

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