Free Printable Geometry B Review

1.

What is the value of X? Round to the nearest whole number.

2.

The measure of angle A is (a)

Choose from the below words

50 degrees

60 degrees

78 degrees

74 degrees

3.

Calculate the length of BC, rounded to the nearest whole number.

4.

Which trigonometric ratio is the ratio of the opposite side to the adjacent side?

a)

Tangent

b)

Secant

c)

Sine

d)

Cosine

5.

8.Solve for x

a)

3.85

b)

4.25

c)

3.35

d)

5.65

6.

Find the length of Side BC, rounded to the nearest whole number.

7.

In △EFD, e = 6.3 cm, m∠E = 68°, and d = 4 cm. Find the area to the nearest tenth of a square centimeter.

a)

15.2

b)

12.2

c)

13.8

d)

10.6

8.

In △ABC, c = 9.9 m, a = 17.2 m, and b = 11.7 m. Find m∠C. Round to the nearest tenth of a degree.

9.

Which Law would you use to solve for Angle B?

a)

Law of the Jungle

b)

Law of Cosines

c)

Law of the Gravity

d)

Law of Sines

10.

Find the area to the nearest tenth.

a)

19.2 m²

b)

17.1 m²

c)

13.5 m²

d)

16.5 m²

11.

What is Sin A?

a)

3/5

b)

5/3

c)

4/3

d)

4/5

12.

Use the Law of Cosines to find the value of X.

a)

41.7

b)

51.7

c)

61.7

d)

71.7

13.

Find AC

a)

12

b)

10

c)

23

d)

14

14.

1.What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

15.

Find x.

a)

$10$

b)

$\sqrt{3}$

c)

$5$

d)

$10\sqrt{3}$

16.

Find x.

a)

$4$

b)

$2$

c)

$\sqrt{3}$

d)

$2\sqrt{2}$

17.

I have been given the short leg in this 30-60-90 triangle. How do I find the long leg?

a)

Multiply 4 by 2

b)

Multiply 4 by $\sqrt{3}$

c)

Multiply 4 by $\sqrt{2}$

d)

Divide 4 by 2

18.

In this 30-60-90 triangle, x = (a) and y = (b) .

Choose from the below words

$6$

$3\sqrt{3}$

3

3\sqrt{2}

1.5

1.5\sqrt{3}

19.

In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...

a)

Multiply that leg by 2

b)

Use the same length for the second leg

c)

Multiply that leg by $\sqrt{2}$

d)

Divide that leg by $\sqrt{2}$

20.

Find x - the length of the hypotenuse of the triangle.

21.

Which set of sides would make a right triangle?

a)

4,5,6

b)

8,10,12

c)

5,12,13

d)

5,10,12

22.

What is the length of y in this 45-45-90 triangle?

a)

$8\sqrt{2}$

b)

$4\sqrt{2}$

c)

$4$

d)

$8$

23.

Given the triangle, find the area using the sine formula. Calculate to the nearest thousandth.

(a)

24.

Given the triangle, find the area using the sine formula. Calculate to the nearest thousandth.

(a)

25.

Solve for the misssing distance

a)

18.9

b)

19.5

c)

47

d)

27.5

26.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63 ft

b)

65 ft

c)

74 ft

d)

87 ft

27.

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.

a)

19 degrees

b)

45 degrees

c)

71 degrees

d)

138 degrees

28.

A drone is hovering at point W, 36 meters above the ground. It looks down at the base of a tree at an angle of 35°. What is the horizontal distance (BT) between the drone and the base of the tree? Round your answer to the nearest tenth of a meter.

(a)

29.

With φ as the reference angle, label the sides of the triangle.

a)

tan φ

b)

cos φ

c)

opposite

d)

adjacent

e)

hypotenuse

f)

sin φ

1

2

3

1)

2)

3)

30.

With θ as the reference angle, label the sides of the triangle.

a)

tan θ

b)

cos θ

c)

opposite

d)

adjacent

e)

hypotenuse

f)

sin θ

1

2

3

1)

2)

3)

31.

? = (a) degrees

32.

? = (a) degrees

33.

? = (a) degrees

34.

? = (a) degrees

35.

? = (a) degrees

36.

? = (a) degrees

37.

x = (a)

38.

Find the value of x

a)

10

b)

15

c)

12

d)

19

39.

Find x

a)

10

b)

5

c)

18

d)

9

40.

Find the value of x

a)

9

b)

10

c)

15

d)

14

41.

Find the value of x

a)

6

b)

13

c)

10

d)

9

42.

Find the value of x

a)

4

b)

18

c)

3

d)

9

43.

Find the value of x

a)

8

b)

13

c)

0

d)

3

44.

What is the value of x?

a)

22

b)

25

c)

15

d)

20

45.

Solve for x.

a)

4.3

b)

26

c)

13

d)

112

46.

Find the arc length. Leave your answer in terms of π.

a)

7/4π

b)

7/2π

c)

1/8π

d)

45π

47.

When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees. What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

a)

40

b)

35

c)

55

d)

69

48.

Find the measure of arc AB.

a)

17°

b)

34°

c)

68°

d)

136°

49.

Given that m∠AOB = 13π/18 and the radius is 8 cm, what is the length of arc AB?

a)

13π/8 cm

b)

52π/9 cm

c)

π/9 cm

d)

9π/52

50.

Find the area of the darkened sector.

a)

4248 m²

b)

7.9 m²

c)

2827.4 m²

d)

11.8 m²

51.

What is 5π/6 radians in degrees?

a)

180

b)

150

c)

360

d)

120

52.

What is 240 degrees in radians?

a)

π/3

b)

4π/3

c)

5π/3

d)

2π/3

53.

What is the area of the shaded sector?

a)

339.12 in²

b)

113.04 in²

c)

339.29 in²

d)

None of the above

54.

Match the following

a)

1.

Secant

b)

2.

Tangent

c)

3.

Chord

d)

4.

Diameter

e)

5.

Radius

55.

Match the following. The arrow is pointed at what part of the circle.

a)

1.

Central Angle

b)

2.

Inscribed Angle

c)

3.

Intercepted Arc

56.

Match the following.

a)

1.

Semicircle

b)

2.

Minor Arc

c)

3.

Major Arc

57.

Determine the measure of ∠NOP

a)

15°

b)

20°

c)

40°

d)

50°

58.

Solve for x.

a)

29

b)

33

c)

41.5

d)

50

59.

Drawing the inscribed circle of a triangle does NOT include which of the following steps?

a)

Bisecting the angles of the vertices

b)

Finding the incenter

c)

The radius is the perpendicular distance to each side from the incenter

d)

The radius is the distance from the incenter to the vertices

60.

Drawing the circumscribed circle of a triangle does NOT include which of the following steps?

a)

Perpendicularly bisecting each side

b)

Finding the circumcenter

c)

Bisecting the angle of each vertex

d)

The radius is the distance from the circumcenter to the vertices

61.

$\angle K=$

(a)

62.

Solve for x.

(a)

63.

Write the equation of a circle with center (7, 0) with radius 3.

64.

What are the coordinates of the center and the radius of the circle with equation:
(x - 4)² + (y - 3)² = 25 ?

a)

Center (4,3)
Radius = 5 units

b)

Center (4,3)
Radius = 25 units

c)

Center (-4,-3)
Radius = 25 units

d)

Center (-4,-3)
Radius = 5 units

65.

What is the equation of the circle?

66.

Is the point (3 , 5) inside, outside or on the circle with equation x² + y² = 9?

a)

Inside the Circle

b)

Outside the Circle

c)

On the Circle

67.

A circle has the equation x² + y² - 8x + 6y - 11 = 0. Write it in standard form.

68.

A circle has the equation x² + y² + 10x - 4y + 20 = 0. Write it in standard form.

a)

$(x-5)^2+(y+2)^2=9$

b)

$(x+5)^2+(y-2)^2=3$

c)

$(x+5)^2+(y-2)^2=9$

d)

$(x+5)^2+(y-2)^2=49$

69.

A circle has the equation x² + y² + 8x - 9 = 0. Write the equation in standard form.

70.

The focus is at (2,0) and the vertex is at (-4,0). What is the equation of the parabola?

71.

Which parabola has a vertex at

$(-3,0)$ ?

a)

$x=\frac{1}{8}(y+3)^2$

b)

$y=\frac{1}{8}(x+3)^2$

c)

$y=\frac{1}{8}(x-3)^2$

d)

$x=\frac{1}{8}(y-3)^2$

72.

Given the graph, what is the equation of the parabola?

73.

Given the graph, what is the equation of the parabola?

74.

What is the equation for axis of symmetry?

75.

$x=-\frac{1}{8}\left(y-4\right)^2-1$ What are the coordinates for the focus?

a)

$(1,4)$

b)

$(-1,6)$

c)

$(-1,2)$

d)

$(-3,4)$

76.

The vertex is halfway between the focus and directrix.

a)

true

b)

false

77.

What is the directrix of the parabola $y=\frac{1}{8}\left(x-4\right)^2-3$ ?

78.

What kind of construction is displayed in this picture?

a)

A circle inscribed in a hexagon

b)

A hexagon inscribed in a circle

c)

A hexagon

d)

A circle

79.

To inscribe a square inside a circle, first you must draw a diameter anywhere across the circle. What should your next step be?

a)

Construct a perpendicular bisector

b)

Draw a second diameter to the circle

c)

Construct a line tangent to the circle

d)

Set your compass the length of the radius.

80.

Which triangles are equilateral?

a)

$\Delta ABD$

b)

$\Delta EBA$

c)

$\Delta CDA$

d)

$\Delta EBC$

81.

The image shows the first step in what construction?

a)

inscribed triangle

b)

inscribed square

c)

tangent line

d)

secant line

82.

The steps shown are a part of the construction of which figure?

a)

square

b)

rectangle

c)

equilateral triangle

d)

regular hexagon

83.

Connecting every other point where the arcs intersect the circle will finish the construction of what polygon?

a)

equalateral triangle

b)

square

c)

hexagon

d)

rectangle

84.

Graph $y=\frac{1}{8}\left(x-3\right)^2-1$

85.

What is the total surface area of the triangular prism shown?

a)

468 in²

b)

540 in²

c)

576 in²

d)

700 in²

86.

Lateral surface area is ________________

a)

The area of just the bases of the prism/cylinder

b)

The area of all the faces of the prism cylinder

c)

The area of the sides of the prism/cylinder

87.

What is the area of the lateral faces?

a)

56 cm²

b)

80 cm²

c)

136 cm²

d)

96 cm²

88.

What 3D solid does this net create?

a)

Triangular Prism

b)

Triangular Pyramid

c)

Rectangular Pyramid

d)

Square Prism

89.

Match the following

a)

1.

Cylinder

b)

2.

Rectangular Prism

c)

3.

Triangular Prism

d)

4.

Triangular Pyramid

e)

5.

Square Pyramid

90.

Find the surface area of the trapezoidal prism

a)

214.94 cm²

b)

267.44 cm²

c)

322.84 cm²

d)

115.92 cm²

91.

Find the surface area of the cylinder with a radius 1 in. and a height 2 in.

a)

12.56 in²

b)

6.28 in²

c)

39.44 in²

d)

18.84 in²

92.

Which cylinder has the greater surface area?

a)

Cylinder A

b)

Cylinder B

93.

Find the surface area of the cylinder.

a)

471.24 cm²

b)

157.08 cm²

c)

314.16 cm²

d)

296.72 cm²

94.

Find the surface area of the pyramid.

a)

168 m²

b)

228 m²

c)

390 m²

d)

196 m²

95.

What is the surface area (in mm²) of this regular hexagonal prism? Round your answer to the nearest whole number.

96.

Match the following perimeter equations

a)

$2m+2n$

1.

parallelogram

b)

$ns$

2.

regular n-gon

c)

$2\pi r$

3.

circle

d)

$\left(3+\sqrt{3}\right)k$

4.

30-60-90 triangle

e)

$\left(2+\sqrt{2}\right)k$

5.

45-45-90 triangle

97.

Match the following area equations

a)

$bh$

1.

parallelogram

b)

$\left(\frac{b_1+b_2}{2}\right)h$

2.

trapezoid

c)

$\pi r^2$

3.

circle

d)

$\frac{bh}{2}$

4.

triangle

e)

$\frac{d_1\cdot d_2}{2}$

5.

kite

98.

Find the area of the regular polygon

a)

172.0 in²

b)

170.0 in²

c)

17.2 in²

d)

50 in²

99.

Find the area.

100.

Find the surface area. Use 3.14 for pi.

a)

252.58 yd²

b)

163.2 yd²

c)

365.50 yd²

d)

157.2 yd²

101.

Find the surface area. Use 3.14 for pi.

a)

117.88

b)

113.04

c)

46.38

d)

68.72

102.

What is the surface area of this pyramid? Round your answer to the nearest whole cm².

103.

Find the surface area of the figure.

a)

1,520.53 $cm^2$

b)

760.27 $cm^2$

c)

379.94 $cm^2$

d)

759.88 $cm^2$

104.

Find the surface area of the sphere.

a)

314.16 in²

b)

314 in²

c)

166.67 in²

d)

521.24 in²

105.

What is the equation to find the length of the apothem of a regular polygon?

a)

$a=\frac{s}{2\tan\left(\frac{180\degree}{n}\right)}$

b)

$a=\frac{ps}{4\tan\left(\frac{180\degree}{n}\right)}$

c)

$\frac{nsa}{2}$

d)

$a=\frac{ns}{2}$

106.

Which of the following equations can be used to find the area of a regular polygon?

a)

$A=\frac{nsa}{2}$

b)

$A=\frac{ps}{4\tan\left(\frac{180\degree}{n}\right)}$

c)

$A=\frac{d_1\cdot d_2}{2}$

d)

$A=\frac{s}{2\tan\left(\frac{180\degree}{n}\right)}$

e)

$A=\frac{ps}{2}$

107.