Georgia Online Formative Assessment Resource (GOFAR) G9-S ...chambleems.dekalb.k12.ga.us/Downloads/G9-Q1-GEO-SELECTED-77 … · A large picnic table is in the shape of a regular polygon

G9-S-GEO-Q1-77

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Date: ____________________________

Georgia Online Formative Assessment Resource (GOFAR)

Copyright © 2015by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 39 )

1. Amy drew a circle graph to represent the ages of people who were surveyed for a consumer group. Ofthose surveyed, 30% were over the age of 65. Which one of the following graphs best represents thesurvey results?

A)

B)

C)

D)



2. A square has two sides on the lines and It has a vertex at

What is the perimeter, in units, of the square?

A)18

B)36

C)44

D)52

3. Jennifer keeps a box under her bed to store clothes. The box is in the shape of a rectangular prism asshown in the figure below

Jennifer's sister, Molly, made a box that had the same height as Jennifer's box. Molly, however, realizedthat she could triple the length and double the width and it would still fit under her bed.

What is the ratio of the volume of Molly's box to the volume of Jennifer's box?

A)6:1

B)12:1

C)36:1

D)216:1

4. Which number is closest to the value ofxin the figure below?

A)0.424

B)1.060

C)1.250



D)1.378

5. In the figures shown below, is similar to .

What is the length of ?

A)2.0 cm

B)4.5 cm

C)12.5 cm

D)22.5 cm

6.Parallelogram is shown in this diagram.

Line segments are diagonals of parallelogram

· Point Jis the midpoint of

· Point Kis the midpoint of

· Point Lis the midpoint of



· Point Mis the midpoint of

Line segment is 12 centimeters long. What is the length of

A)6 cm

B)7 cm

C)8 cm

D)9 cm

7. Parallelogram is shown in this diagram.

Line segments are diagonals of parallelogram

· Point Jis the midpoint of

· Point Kis the midpoint of

· Point Lis the midpoint of

· Point Mis the midpoint of

The perimeter of parallelogram is 44 centimeters. What is the length of

A)5 cm

B)5.5 cm

C)10 cm

D)10.5 cm



8. In the figures shown below, is similar to .

What is the length of ?

A)2.0 cm

B)4.5 cm

C)12.5 cm

D)22.5 cm

9. In the triangle below, which list shows the angles from smallest to largest?

A)

B)

C)

D)

10. The sine of in this figure is



Which equation must be true?

A)

B)

C)

D)

11. This triangle has the measures shown.

Which measures shown in the triangle are equivalent to

A)

B)

C)

D)

12. The tangent of in this diagram is



The height of the mountain, z, is 1400 feet. Which equation must be true?

A)

B)

C)

D)

13. This diagram shows similar right triangles.


A)

B)

C)

D)

14. This is a right triangle.



Which expression is equivalent to

A)

B)

C)

D)

15. The tangent of in this triangle is


A)

B)

C)

D)

16. The measure of in right is Which equation must be true?

A)



B)

C)

D)

17. Angles 1, 2, 3, and 4 are marked in these similar right triangles.

Which measure is equivalent to

A)

B)

C)

D)

18. What is the value ofxin the triangle below?

A)

B)

C)

D)

19. Use this diagram and information to answer the question.



In the diagram, PQRS is a kite.

·

·

· = 24 inches

· = 36 inches

What is the length, to the nearest 0.01 inch, of

A)9.58 inches

B)15.03 inches

C)15.92 inches

D)19.94 inches

20. Use this diagram and information to answer the question.



Which is the best estimate of the ratio

A)

B)

C)

D)

21. This diagram shows the lengths of each side of a kite.

What is the value of w, to the nearest inch?



A)10 in

B)20 in

C)30 in

D)40 in

22. The angle of depression from a helicopter to the top of a monument is 16°, as shown in thisdiagram.

How far above the ground, to the nearest yard, is the helicopter?

A)798 yd.

B)828 yd.

C)2684 yd.

D)2860 yd.

23. A bridge is built across a stream as shown in this diagram.

The top of the bridge is 4 meters above the stream. Which equation can be used to find x, thelength, in meters, of the bridge?

A)



B)

C)

D)

24. A building casts a 50-foot shadow. The angle of elevation from the end of the shadow to thetop of the building is 69°.

What is the height, to the nearest foot, of the building?

A)19 ft.

B)47 ft.

C)54 ft.

D)130 ft.

25. Chords and are equidistant from center P in this circle.

Chord is 6 units long. Which statement MUST be true about the value of x?

A)It is 1.5.

B)It is between 1.5 and 4.5.

C)It is 4.5.

D)It is greater than 4.5.



26. The center of circle P is located at as shown on this coordinate plane.

Line m is tangent to circle P at

What is the equation of line m?

A)

B)

C)

D)

27. Circle O is inscribed inside quadrilateral PRST, as shown in this diagram.

· is tangent to circle O at point Q.



·

·

What is the perimeter of quadrilateral

A)80 in.

B)74 in.

C)68 in.

D)54 in.

28. The measure of is in this circle.

The measure of is What is the measure of

A)

B)

C)

D)

29. Segments KJ and KL are tangent to circle P.



What is the measure of

A)

B)

C)

D)

30. This diagram shows circle P with

What is the measure of

A)

B)

C)

D)

31. Points N, P, and Q lie on circle O, as shown in this diagram.



The measure of What is the measure of

A)

B)

C)

D)

32. Chord is congruent to chord in circle O, as shown.

What is the value of x?

A)54

B)36

C)27

D)24

33.

Beth made the following pie graph to represent her monthly budget.



What percentage of her budget does she spend on her rent and car combined?

A)50%

B)72%

C)90%

D)180%

34. A sector of a circle is created from a central angle with a measure of 60°. If the diameter ofthe circle is 6 inches, what is the area of the sector?

A)

B)

C)

D)

35. A new flower bed outside of a town hall is in the shape of a triangle. Two of the side lengthsare and

Which expression represents a possible length of the third side of the triangle?

A)

B)

C)

D)

36. Triangle the measures of its angles, and two of its side lengths are shown in thisdiagram.



Which expression could represent the length of

A)

B)

C)

D)

37. In this diagram, contains

Which statement MUST be true?

A)

B)

C)

D)

38. In the figure below, the diagonals of parallelogramABCDintersect at (5, 2).



What are the coordinates of pointC?

A)(7, 3)

B)(8, 3)

C)(9, 4)

D)(10, 4)

39. An electric company chose this design for its new logo.

What is the sum of the interior angles of the hexagon?

A)

B)

C)

D)

40. The measure of one exterior angle of a regular polygon is What is the sum of its interiorangles?

A)

B)

C)



D)

41. The exterior angles of a triangle have a ratio. What is the smallest exterior angle of thetriangle?

A)

B)

C)

D)

42. This diagram shows the shape of a city park.

What is the value of

A)20

B)42

C)50

D)56

43. A large picnic table is in the shape of a regular polygon. An interior angle of this tablemeasures

How many sides does the picnic table have?

A)6

B)8

C)10

D)12



44. Which pair of triangles MUST be congruent?

A)

B)

C)

D)

45. In this diagram, bisects

Which additional piece of information is NOT sufficient to prove



A)

B)

C)

D)

46. Which set of points is equidistant from the rays that form an angle?

A)perpendicular bisector

B)skew line

C)angle bisector

D)central angle

47. Which graph shows the relationship between the surface area and the volume of a sphere?

A)

B)



C)

D)

48. A trophy is shaped like a large golf ball. The diameter of the trophy is 8 inches.

What is the volume of the trophy?

A)

B)

C)

D)

49. The surface areas of the sphere and the cube shown in this diagram are the same.



What is the approximate volume of thesphere?

A)1000 cm3

B)1382 cm3

C)2000 cm3

D)2974 cm3

50. The vitamin represented in this diagram is in the shape of a cylinder with a half of a sphereon each end.

What is the volume, to the nearest cubic millimeter, of the vitamin?

A)

B)

C)

D)

51. A student used this equation to graph a circle.

The student then translated the circle 2 units up and 1 unit to the left. What is the equation ofthe translated circle?

A)

B)



C)

D)

52. This equation represents a circle that has been graphed on a coordinate plane.

What ordered pair represents the center of the circle?

A)

B)

C)

D)

53. Which equation represents a circle centered at the point on a coordinate plane?

A)

B)

C)

D)

54. A student made this graph of a circle.



Which equation represents the circle?

A)

B)

C)

D)

55. This equation represents a circle.

Which statement about the graph of the circle is correct?

A)The circle is centered at and has a radius of 12 units.

B)The circle is centered at and has a radius of 12 units.

C)The circle is centered at and has a radius of 144 units.

D)The circle is centered at and has a radius of 144 units.

56. Which equation of a line is perpendicular to the line given by the equation y = x – 6 ?

A)y = – x + 1



B)y = – x + 1

C)y = x + 1

D)y = x + 1

57. Which line is parallel to the liney= 2x+ 1?

A)y= -2x+ 1

B)y= - + 2

C)y= 2x+ 3

D)y= + 4

58. In the coordinate system below, to prove that segment is parallel to segment , whichof the following must be shown?

A)The length of is half the length of

B)The slope of equals the slope of

C)The length of equals the length of

D)The length of equals the length of

59. Sam began a construction with his compass and straightedge. The sketch shows the first steps in his construction.

Which construction is illustrated by the sketch?A)the midpoint of a line segment



B)an angle bisector of an acute angle

C)a bisector of a given line through a point on the line

D)the line perpendicular to a given line through a given point on the line

60. A circle is centered at and contains the point Which statement can be proven algebraicallywith the information given?A)The points and lie on the circle.

B)The perimeter of any isosceles right triangle inscribed in the circle is units.

C)Any right triangle with a vertex at and a hypotenuse that is less than 25 units will fit inside the circle.

D)The sum of the areas of two squares with side lengths of 3 units and 4 units is greater than the area ofthe circle.

61. A clock is designed in the shape of a regular dodecagon.

The perimeter of the dodecagon is 54 cm. By joining every other vertex of the dodecagon, a hexagon isformed. If each side of the hexagon is x cm long, what is the value of x to the nearest hundredth?A)6.36

B)7.79

C)8.69

D)9.32

62. The perpendicular bisector of chord is chord Which diagram shows chords and



A)

B)

C)

D)

63. An artist is using pieces of wire to make geometric shapes. Which three lengths could she useto make a triangle?

A)1-, 2-, and 3-inch pieces

B)1-, 2-, and 4-inch pieces

C)1-, 3-, and 4-inch pieces

D)2-, 3-, and 4-inch pieces

64. The body of this container is in the shape of a cylinder.



The top of the container is in the shape of half a sphere. What is the approximate amount ofspace inside the container?

A)49.5 cu. in.

B)56.5 cu. in.

C)226.2 cu. in.

D)282.7 cu. in.

65. This diagram represents the distance between a boat and a lighthouse.

Based on the diagram, which equation must be true?

A)

B)



C)

D)

66. Which pair of line segments could be contained in distinct parallel lines?

A)two radii of the same circle

B)two chords of the same circle

C)two diameters of the same circle

D)a radius and a diameter of the same circle

67. Triangles FGH and PQR are shown.

Which sequence of transformations on FGH could result in PQR ?

A)Reflection over a vertical line and translation up

B)Reflection over a horizontal line and translation down

C)Rotation 180 degrees and translation up

D)Rotation 180 degrees and translation down

68. Honmin is creating a graphic design. She draws a white dodecagon with a small gray isosceles trapezoidinside and labels it Figure 1. To complete her design, she performs these three transformations in order onthe preceding figure.

●Step 1: Reflection●Step 2: Rotation●Step 3: Reflection

Which sequence of figures could be Honmin’s design?



A)

B)

C)

D)

69. The focus of a parabola is and the directrix is Which equation represents the parabola?

A)

B)

C)

D)

70. Study the construction demonstrated in the diagram shown.



Which statement is the best description of the construction being demonstrated?

A)Line PQ is being constructed perpendicular to line AB.

B)Line AB, the perpendicular bisector of line PQ, is being constructed.

C)Line segment PQ is being constructed as the perpendicular bisector of line segment AB.

D)Segment bisector PQ is being constructed with twice the length of its original segment, AB.

71. In the figures shown, quadrilateral is a dilation of quadrilateral GHIJ. The perimeter of GHIJ is31.5 units.

Which statement is true of the quadrilaterals?

A)The quadrilaterals are similar figures because

B)The quadrilaterals are similar figures because they have congruent angle measures and their sides areproportional.

C)The quadrilaterals are similar figures because they have proportional sides and perimeters that have a

scale factor of



D)The quadrilaterals appear to be similar figures, but you are unable to prove this because the measures ofthe angles cannot be determined.

72. The picture shows Line segment FE will be drawn such that points F and E are on the triangle and

Which statement must be true?

A)

B)

C)

D)

73. Quadrilateral QRVT is drawn such that and is a diagonal.

Which theorem will prove that

A)Side-Side-Side Theorem

B)Side-Angle-Side Theorem



C)Angle-Side-Side Theorem

D)Angle-Angle-Side Theorem

74. In the figure shown, is similar to Let n represent the length, in centimeters, of

Which ratio represents the correct value of

A)

B)

C)

D)

75. The diagram shows the vertices of quadrilateral PQRS which lie on circle T.

Which conjecture can be proven to be true about quadrilateral PQRS?



A)Arc PS is congruent to arc QR.

B)The diagonals of PQRS intersect at point T.

C)The measures of are congruent.

D)The measures of are supplementary.

76.●Marble City has a population of 52,348 and covers an area of 125 square miles.

●Pebble City has the same population density as Marble City.

●The shape of Pebble City resembles a rectangle with a width of 11.8 miles and a length of x miles.

●The population of Pebble City is 85,312.Which measure is closest to the value of x?

A)11

B)17

C)36

D)77

77. The diagram shows a toy sphere that is made of stainless steel.

The volume of the toy is found by multiplying the thickness of the steel by the surface area. What is thethickness of the stainless steel?

A)0.375 cm

B)0.5 cm



C)0.67 cm

D)1.0 cm



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Georgia Online Formative Assessment Resource (GOFAR) G9-S ...chambleems.dekalb.k12.ga.us/Downloads/G9-Q1-GEO-SELECTED-77 … · A large picnic table is in the shape of a regular polygon