Geom Fin Exam Practice - Avery County Schools Multiple Choice ... the approximate length of chord LK? a. 17 in. b. 12 in. ... Sheila must spin a 7 on

Name: ________________________ Class: ___________________ Date: __________ ID: Practice

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Geom_Fin_Exam_Practice

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

G:1.01 Use the trignonometric ratios to model and solve problems involving right triangles.

1. Billy is 74 in. tall, and his shadow is 70 in. long. What is the approximate angle of elevation of the sun?a. 190

b. 430

c. 470

d. 710

2. A truck is at the top of a ramp as shown below.

Approximately how high above the ground is the truck?a. 4.45 mb. 3.59 mc. 1.95 md. 1.75 m

3. A right triangle is shown below.

What is the approximate value of h?a. 100 metersb. 115 metersc. 140 metersd. 173 meters

4. KM is an altitude of JKL, and KM ≅ JM . The measure of ∠LKM is 550 , and ML = 12 cm.

What is the approximate length of JK?a. 8.4 cmb. 11.9 cmc. 20.7 cmd. 24.2 cm

5. The angle of elevation from point G on the ground to the top of a flagpole is 20. Theheight of the flagpole is 60 feet.

Which equation could find the distance from point G to the base of the flagpole?

a. sin 200 = x60

b. sin 200 = 60x

c. tan 200 = 60x

d. tan 200 = x60

6. A mountain climber stands on level ground 300 m from the base of a cliff. The angle ofelevation to the top of the cliff is 580 . What is the approximate height of the cliff?a. 566 mb. 480 mc. 354 md. 187 m

Name: ________________________ ID: Practice

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7. A 20-foot ladder is leaning against a wall. The foot of the ladder is 7 feet from the base of the wall. What is the approximate measure of the angle the ladder forms with the ground?a. 70.70

b. 69.50

c. 20.50

d. 19.30

8. A ladder is leaning against the side of a building. The ladder is 30 feet long, and the angle between the ladder and the building is 150 . About how far is the foot of the ladder from thebuilding?a. 7.76 feetb. 8.04 feetc. 18.37 feetd. 28.98 feet

9. Susan is making a small cone out of paper. The cone has a radius of 13.2 cm, and the angle between the lateral surface and the base is 38.60 . The formula for the lateral area, s, of a cone is s = πrl, where r is the radius and l is the slant height. What is the cone’s approximate lateral area?a. 340 cm2

b. 430 cm2

c. 700 cm2

d. 800 cm2

10. A dead tree was struck by lightning, causing it to fall over at a point 10 ft up from its base.

If the fallen treetop forms a 400 angle with the ground, about how tall was the tree originally?a. 13 ft.b. 16 ft.c. 23 ft.d. 26 ft.

G:1.02 Use length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

11. What is the approximate area of a 700 sector of a circle with a radius of 8 inches?a. 5 in. 2

b. 10 in. 2

c. 39 in. 2

d. 156 in. 2

12. JK and LM are perpendicular diameters of a circle. They are each 12 inches long. What is the approximate length of chord LK?a. 17 in.b. 12 in.c. 10.4 in.d. 8.5 in.

13. The midpoint of PQ is R. R has coordinates −3,2,−1Ê

ËÁÁˆ¯̃̃ and P has coordinates 4,−6,−6Ê

ËÁÁˆ¯̃̃ .

What are the coordinates of Q?a. −10,10,4Ê

ËÁÁˆ¯̃̃

b. −3.5,4,2.5ÊËÁÁ

ˆ¯̃̃

c. 0.5,−2,−3.5ÊËÁÁ

ˆ¯̃̃

d. 11,−14,−11ÊËÁÁ

ˆ¯̃̃

Name: ________________________ ID: Practice

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14. A cone has a radius of 12 cm and a height of 9 cm. What is the approximate lateral surface area of the cone? (To calculate the lateral surface area, A, use the formula A = πrl, where r is the radius and l is the slant height.)a. 89 cm2

b. 123 cm2

c. 424 cm2

d. 565 cm2

15. A garden has the shape of an isosceles right triangle. The length of the hypotenuse is 24 feet. What is the area of the garden?a. 576 ft2

b. 288 ft2

c. 203 ft2

d. 144 ft2

16. The perimeter of a regular hexagon is 48 ft. What is the approximate area of this polygon?a. 288 ft2

b. 166 ft2

c. 96 ft2

d. 28 ft2

17. A plastic tray is shown below, with the dimensions labeled. The tray does not have a cover on top. The bottom and two of the sides are rectangles. The remaining two sides are congruent isosceles trapezoids.

What is the total area of the outer surface of the tray?a. 495 cm2

b. 584 cm2

c. 615 cm2

d. 975 cm2

18. A container in the shape of a rectangular prism has a base that measures 20 centimeters by 30 centimeters and has a height of 15 centimeters. The container is partially filled with water. A student adds more water to the container and notes that the water level rises 2.5 cm. What is the volume of the added water?a. 1,500 cm3

b. 3,600 cm3

c. 4,500 cm3

d. 9,000 cm3

19. Katie, a gardener, needs to put grass seeds on the triangle formed by the 3 roads below. Each side of the grass triangle is 350 ft long.

If one bag of seed covers 10,000 ft2 , how many bags will Katie need to buy?a. 5b. 6c. 7d. 8

20. What is the approximate surface area of a right hexagonal prism with a base perimeter of 96 meters and a height of 10 meters? (Use S = ap + ph, where a is the apothem of the base, p is the perimeter of the base, and h is the height of the prism.)a. 3,620 m2

b. 2,290 m2

c. 1,728 m2

d. 1,625 m2

Name: ________________________ ID: Practice

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21. The ratio of the height of the pyramid to the edge of the square base is 1.5 to 1. The height of the pyramid is 3 meters. What is the approximate length of the slant height of the pyramid?a. 4.4 mb. 3.2 mc. 2.8 md. 1.4 m

22. A rectangular prism is 40 ft by 38 ft by 15 ft. Shown below is the prism with a halfcylinder removed.

Approximately what volume of the original prism remains?a. 22,800 cubic feetb. 19,792 cubic feetc. 19,560 cubic feetd. 17,651 cubic feet

23. An apple pie is cut into six equal slices as shown below.

If the diameter of the pie is ten inches, what is the approximate arc length of one slice of pie?a. 1.67 in.b. 3.14 in.c. 5.24 in.d. 13.08 in.

24. A sign is shaped like an equilateral triangle.

If one side of the sign is 36 inches, what is the approximate area of the sign?a. 1,296 in.2

b. 648 in.2

c. 561 in.2

d. 108 in.2

25. An inflated round balloon with radius r = 50 centimeters holds approximately 523,600 cubic centimeters of air. When the balloon is

contracted such that the radius is 23 the original

size, what is the approximate volume of the partially deflated balloon?a. 1.94 × 104 cm3

b. 1.55 × 105 cm3

c. 1.75 × 105 cm3

d. 3.49 × 105 cm3

26. What is the approximate area of the trapezoid?

a. 83 cm2

b. 110 cm2

c. 128 cm2

d. 192 cm2

27. What is the approximate distance between the points 750, 900, 1,500Ê

ËÁÁˆ¯̃̃ and 950, 800, 550Ê

ËÁÁˆ¯̃̃?

a. 976 unitsb. 1,025 unitsc. 2,062 unitsd. 952,500 units

Name: ________________________ ID: Practice

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28. What is the ratio of the surface areas of two spheres with volumes of 64 cm3

and 125 cm3 ?a. 4 : 5b. 8 : 10c. 16 : 25d. 64 : 125

G:1.03 Use length, area, and volume to model and solve problems involving probability.

29. A rectangle contains two inscribed semicircles and a full circle, as shown below.

If a point is chosen at random inside the rectangle, what is the approximate probability that the point will also be inside the shaded region?a. 85%b. 79%c. 75%d. 50%

30. In order to win a game, Sheila must spin a 7 on the spinner below.

If the spinner is fair, what is the probability that she will spin a 7?

a. 112

b. 16

c. 310

d. 512

31. A number line is shown below.

Point P will be picked at random on EK. What is the probability that P will be on FK?

a. 46

b. 34

c. 45

d. 56

Name: ________________________ ID: Practice

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32. A cylinder with a height of 6 inches and a radius of 3 inches is inside a rectangular prism,as shown below.

A point inside the rectangular prism will be chosen randomly. What is the probabilitythat the point will also be inside the cylinder?a. 5.2%b. 7.9%c. 15.7%d. 23.6%

33. A point is randomly selected on XY . What is the probability that it will be closer to the midpoint of XY than to either X or Y?

a. 14

b. 13

c. 12

d. 34

34. A circle is inscribed in a square, as shown below.

If a point is randomly chosen inside the square, what is the approximate chance that the point lies outside the circle?a. 21%b. 27%c. 73%d. 79%

35. A cube is painted as shown. The three faces that are not seen are not painted.

If a point on the surface of the cube is randomly chosen, what is the probability that it will lie in the painted area?

a. 14

b. 13

c. 38

d. 12

Name: ________________________ ID: Practice

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36. A cube with edges 10 cm long is painted red. It is cut into smaller cubes with edges 2 cm long that are placed into a bag. One small cube is pulled out of the bag without looking. What is the probability of pulling out a cube with three of its faces painted red?

a. 4125

b. 8125

c. 225

d. 12125

37. To win a carnival game, Keisha must throw a dart and hit one of 25 circles in a dart board that is 4 feet by 3 feet. The diameter of each circle is 4 inches.

Approximately what is the probability that a randomly thrown dart that hits the board would also hit a circle?a. 18%b. 26%c. 63%d. 73%

G:2.01 Use logic and deductive reasoning to draw conclusions and solve problems.

38. Which statement is logically equivalent to the given statement?

If a quadrilateral is a rhombus, then it is a parallelogram.

a. If a quadrilateral is a parallelogram, then it is a rhombus.

b. If a quadrilateral is not a rhombus, then it is not a parallelogram.

c. If a quadrilateral is not a rhombus, then it is a parallelogram.

d. If a quadrilateral is not a parallelogram, then it is not a rhombus.

39. What is the inverse of the statement in the box?

If a polygon is regular, then it is convex.

a. If a polygon is not regular, then itis not convex.

b. If a polygon is convex, then it isregular.

c. If a polygon is not regular, then itis convex.

d. If a polygon is not convex, then itis not regular.

40. What is the converse of the statement in the box?

If today is Saturday, then there is no school today..

a. If there is no school today, then today is Saturday.

b. If there is school today, then today is not Saturday.

c. If today is not Saturday, then there is school today.

d. If today is not Saturday, then there is no school today.

Name: ________________________ ID: Practice

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41. The conditional statement “all 450 angles are acute angles” is true. Based on this conditional statement, which of the following can be concluded from the additional statement “the measure of ∠A is 450 ”?a. The complement of ∠A is not an acute angle.b. The supplement of ∠A is an acute angle.c. ∠A is an acute angle.d. ∠A is not an acute angle.

42. MNO is shown below.

Which statement about this triangle is true?a. m∠O > m∠Mb. m∠M > m∠Nc. m∠M < m∠Nd. m∠N < m∠O

43. What is the contrapositive of the statement below?

If a triangle is isosceles, then it has two congruent sides.

a. If a triangle does not have two congruent sides, then it is not isosceles.

b. If a triangle is isosceles, then it does not have two congruent sides.

c. If a triangle has two congruent sides, then it is isosceles.

d. If a triangle is not isosceles, then it does not have two congruentsides.

44. Which statement is the inverse of the statement in the box?

If a quadrilateral is a rectangle, then it is a parallelogram.

a. If a quadrilateral is not a parallelogram, then it is not a rectangle.

b. If a quadrilateral is a parallelogram, then it is a rectangle.

c. If a quadrilateral is not a rectangle, then it is not a parallelogram.

d. A quadrilateral is a rectangle if and only if it is a parallelogram.

45. Given:If there was lightning, then we did not swim.If there was lightning, then we did not jog.

Using either one or both of the given statements, which conclusion is valid?a. If we did not swim, then we did not jog.b. If we did not jog, then there was lightning.c. If we did swim, then we did not jog.d. If we did jog, then there was not lightning.

46. Given the statements:

Linear pairs are supplementary.∠1 and ∠2 are supplementary.

Using either one or both of the given statements, which conclusion is valid?a. ∠1 and ∠2 form a linear pair.b. Angles that are not supplemtary are not linear

pairs.c. ∠1 ≅ ∠2d. Supplementary angles are linear pairs.

Name: ________________________ ID: Practice

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G:2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs.

47. In the diagram below, j⊥m and k⊥m.

What is m∠1?a. 39b. 47c. 51d. 129

48. In the figure below, WY→⎯⎯⎯

bisects ∠VWZ, m∠VWY = 32, and m∠VWX = 117.

What is m∠ZWX ?a. 85b. 53c. 42.5d. 26.5

49. M is the midpoint of RS , RM = 3x + 1( ) , and MS = 4x − 2( ) . What is RS?a. 20b. 17c. 10d. 3

50. The slope of a line tangent to a circle is 25 .

What is the slope of the line that passes through the point of tangency and the center of the circle?

a. −52

b. −25

c. 25

d. 52

51. In the figure below, SR→⎯⎯

| | UV→⎯⎯⎯

.

What is m∠STU?a. 600

b. 900

c. 1200

d. 2400

52. OX→⎯⎯⎯

is the bisector of ∠WOZ, and OY→⎯⎯⎯

is the bisector of ∠XOZ.

If m∠YOZ = 26.5, what is m∠WOZ?a. 53.00

b. 79.50

c. 106.00

d. 132.50

Name: ________________________ ID: Practice

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53. Given ∠VYX is bisected by YW→⎯⎯⎯

, m∠VYX = 6r − 18( ) , and m∠VYW = 36. What is the value of r?a. 15b. 30c. 36d. 72

54. According to the map, the road connecting the cities of Oakton (O) and Ridgeton (R) intersects the road connecting Maple View (M) and Pineville (P).

If the roads intersect in the town of Forest Grove (F) in the diagram, which statement isalways true?a. MP = ROb. PF⊥OFc. ∠OFP ≅ ∠RFMd. ∠RFP ≅ ∠MFR

55. Given LP, LM = 3x + 1( ) , MN = 4x − 3( ) , NP = 6x − 5( ) , and LM ≅ NP.

What is the length of MP?a. 2b. 7c. 12d. 19

56. In the diagram below, MN⊥JL.

Which statement must be true?a. m∠PKN = m∠JKPb. m∠PKN = 900 + m∠JKPc. m∠PKN = 1800 − m∠JKPd. m∠PKN = 2700 − m∠JKP

57. Given: k Ä m Ä n

Which statement justifies the conclusion that ∠1 ≅ ∠2 ≅ ∠3?a. If k Ä m Ä n and are cut by transversal t, then

alternate interior angles are congruent.b. If k Ä m Ä n and are cut by transversal t, then

vertical angles are congruent.c. If k Ä m Ä n and are cut by transversal t, then

alternate exterior angles are congruent.d. If k Ä m Ä n and are cut by transversal t, then

corresponding angles are congruent.

Name: ________________________ ID: Practice

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58. In the diagram, GH Ä IJ .

If m∠GLK = 550 and m∠EFJ = 1200 , which is m∠KEF?a. 550

b. 600

c. 650

d. 700

59. Given RS→←⎯⎯

Ä TU→←⎯⎯

, m∠7 = 3x − 10( ) , and m∠3 = 2x + 5( ) .

What is m∠1?a. 1450

b. 750

c. 350

d. 150

60. ∠XYZ shown below has a measure of 8x + 12( ) 0 . The measure of ∠1 is 4x + 8( ) 0 , and the measure of ∠2 is 9x − 11( ) 0 .

What is the measure of ∠XYZ?a. 30

b. 200

c. 360

d. 600

61. In the drawing, what is the measure of angle y?

a. 400

b. 600

c. 800

d. 1000

Name: ________________________ ID: Practice

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62. Given m∠RQS = 12 x + 4, m∠SQT = 3

4 x − 6, and

m∠RQT = 2x − 47.

What is m∠RQS?a. 240

b. 340

c. 390

d. 600

Name: ________________________ ID: Practice

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G:2.03 Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs: a) Triangles b) Quadrilaterals c) Other Polygons d) Circles

63. Given: ABCD is an isosceles trapezoid. M is the midpoint of AB.Prove: DM ≅ CM

What is the missing statement and reason that completes the proof shown above?a. AD ≅ BC; the legs of an isosceles

trapezoid are congruent.c. AM ≅ BM ; the corresponding parts of

congruent triangles are congruent.b. ∠MAD ≅ ∠MBC ; the base angles of an

isosceles trapezoid are congruent.d. ∠ABC ≅ ∠DAB; if lines are parallel,

interior angles on the same side of a transversal are supplementary..

64. WXYZ is a parallelogram. If m∠W = 40, what is m∠Z?a. 40b. 50c. 140d. 150

65. What is the measure of an interior angle of a regular polygon with 16 sides?a. 22.50

b. 25.70

c. 157.50

d. 205.70

66. In the diagram below, PQ ≅ MQ and m∠M = 70.

What is m∠TQP?a. 70b. 110c. 140d. 150

Name: ________________________ ID: Practice

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67. Given parallelogram EFGH , what is the length of side EF?

a. 27b. 21c. 19d. 7

68. Circles P, Q, and R are shown below. The diameter of circle R is 22.

What is the length of PR?a. 25 c. 39b. 34 d. 50

69. Based on the coordinates E −2,−3ÊËÁÁ

ˆ¯̃̃ , F 3,−3Ê

ËÁÁˆ¯̃̃ ,

G 6,1ÊËÁÁ

ˆ¯̃̃ , H 3,5Ê

ËÁÁˆ¯̃̃ , I −2,5Ê

ËÁÁˆ¯̃̃ , and J 1,1Ê

ËÁÁˆ¯̃̃ , what best

describes polygon EFGHIJ?a. equilateral convexb. equilateral concavec. equiangular concaved. equiangular convex

70. Which parts must be congruent to prove PQR ≅ PSR by SAS?

a. ∠Q ≅ ∠S and QP ≅ SPb. ∠Q ≅ ∠S and QR ≅ SRc. ∠QRP ≅ ∠SRP and QP ≅ SPd. ∠QPR ≅ ∠SPR and QP ≅ SP

Name: ________________________ ID: Practice

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71. How long is EF?

a. 20 ftb. 25 ftc. 30 ftd. 35 ft

72. In circle O shown below, RS ≅ ST.

What kind of triangle is RST?a. rightb. acutec. obtused. scalene

73. Figure JKLM is a parallelogram.

What is the value of x?a. 650

b. 550

c. 450

d. 350

74. What is the measure of an interior angle of a regular hexagon?a. 450

b. 600

c. 1200

d. 1350

75. A regular octagon is inscribed in a circle. What is the degree measure of each arc joining the consecutive vertices?a. 400

b. 450

c. 540

d. 600

76. If KLMN is a rhombus, and m∠KLM = 80, what is the measure of ∠1?

a. 400

b. 500

c. 800

d. 900

77. The measure of each exterior angle of a regular polygon is 450 . How many sides does the polygon have?a. 4b. 5c. 8d. 9

78. In a hexagon, three angles have the same measure. The measure of each of the congruent angles is twice the measure of the fourth angle and is half the measure of the fifth angle. The sixth angle measures 1150 . What is the measure of the smallest angle?a. 410

b. 550

c. 1100

d. 1210

Name: ________________________ ID: Practice

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79. In the circle below, what is the value of x?

a. 4 unitsb. 6 unitsc. 7 unitsd. 9 units

80. In JKLM , JK⊥KL and JK Ä ML.

What is the area of the trapezoid?a. 120 sq cmb. 144 sq cmc. 164 sq cmd. 168 sq cm

81. A triangle has side lengths of 10 cm, 15 cm, and 20 cm. Which side lengths form the largest angle?a. 5 cm, 10 cmb. 10 cm, 15 cmc. 10 cm, 20 cmd. 15 cm, 20 cm

82. A gardener wants to enclose a circular garden with a square fence, as shown below.

If the circumference of the circular garden is about 48 feet, which of the following is the approximate length of fencing needed?a. 31 ft.b. 61 ft.c. 122 ft.d. 244 ft.

83. The vertices of a hexagon are 6,7ÊËÁÁ

ˆ¯̃̃ , 9,1Ê

ËÁÁˆ¯̃̃ ,

6,−4ÊËÁÁ

ˆ¯̃̃ , −1,−4Ê

ËÁÁˆ¯̃̃ , −6,1Ê

ËÁÁˆ¯̃̃ , and −1,7Ê

ËÁÁˆ¯̃̃ . Which best

describes the hexagon?a. nonregular and convexb. nonregular and concavec. regular and convexd. regular and concave

84. Jill wants to measure the width of a river. She marks distances as shown in the diagram.

Using this information, what is the approximate width of the river?a. 6.6 yardsb. 10 yardsc. 12.8 yardsd. 15 yards

85. The exterior angle of a base angle in an isosceles triangle is 1000 . What is the measure ofthe vertex angle?a. 200

b. 400

c. 600

d. 800

Name: ________________________ ID: Practice

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86. Right SRU is shown below.

What is the length of RS?a. 84b. 74c. 60d. 35

87. If PQRS is a rhombus, which statement must be true?

a. ∠PSR is a right angle.b. PR ≅ QSc. ∠PQR ≅ ∠QRSd. PQ ≅ QR

G:2.04 Develop and apply properties of solids to solve problems.

88. Which pattern would fold to make a pyramid with a square base?

a.

b.

c.

d. 89. A regular tetrahedron is a triangular pyramid.

What is the total surface area of a regular tetrahedron with base edges of 7 cm?a. 7 3 cm2

b. 14 3 cm2

c. 28 3 cm2

d. 49 3 cm2

90. Kevin’s teacher gave him the following pieces of cardboard.

2 equilateral triangles:

4 squares:

Which polyhedron can Kevin build using some or all of these pieces?a. a triangular prismb. a rectangular prismc. a triangular pyramidd. a square pyramid

91. A plane intersects a sphere that has a radius of 13 cm. The distance from the center of the sphere to the closest point on the plane is 5 cm. What is the radius of the circle that is the intersection of the sphere and the plane?a. 8 cmb. 10 cmc. 12 cmd. 13 cm

Name: ________________________ ID: Practice

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92. What is the best description of the solid figure shown below?

a. a regular polygonb. a convex polygonc. a regular polyhedrond. a nonregular polyhedron

93. What are the coordinates of vertex K for the cube shown below?

a. −3,3,0ÊËÁÁ

ˆ¯̃̃

b. −3,0,3ÊËÁÁ

ˆ¯̃̃

c. 0,3,−3ÊËÁÁ

ˆ¯̃̃

d. 3,−3,0ÊËÁÁ

ˆ¯̃̃

94. In the picture below, what are the coordinates of P?

a. 0,6,6ÊËÁÁ

ˆ¯̃̃

b. −6,0,6ÊËÁÁ

ˆ¯̃̃

c. −6,6,0ÊËÁÁ

ˆ¯̃̃

d. 6,−6,6ÊËÁÁ

ˆ¯̃̃

95. A spherical foam ball, 10 inches in diameter, is used to make a tabletop decoration for aparty. To make the decoration sit flat on the table, a horizontal slice is removed from thebottom of the ball, as shown below.

If the radius of the flat surface formed by the cut is 4 inches, what is the height of thedecoration?a. 10 in.b. 8 in.c. 6 in.d. 4 in.

Name: ________________________ ID: Practice

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96. What is the approximate surface area of a regular tetrahedron with edge length 12 cm?a. 166.3 sq cmb. 187.1 sq cmc. 249.4 sq cmd. 498.8 sq cm

97. Two tetrahedra are congruent. One tetrahedron is glued to the other so that the glued faces of the two tetrahedra completely cover each other, producing a new polyhedron. How many faces does the new polyhedron have?a. 6b. 7c. 8d. 9

98. The intersection of a sphere and a plane is a circle with a radius of 8 cm. If the sphere has a radius of 18 cm, how far is the plane from the center of the sphere?a. 16.12 cmb. 14.97 cmc. 10.00 cmd. 8.00 cm

99. A regular octahedron has eight faces that are congruent equilateral triangles. How many edges does a regular octahedron have?a. 12b. 16c. 17d. 24

G:3.01 Describe the transformation (translation, reflection, rotation, dilation) of polygons in the coordinate plane in simple algebraic terms.

100. A translation is applied to FGH , forming F ′G ′H ′. If the translation is described by x ′,y ′ÊËÁÁ

ˆ¯̃̃ = x + 2,y − 3Ê

ËÁÁˆ¯̃̃ ,

which graph shows the translation correctly?

a. c.

b. d.

Name: ________________________ ID: Practice

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101. GHI will be dilated by a scale factor of 3, resulting in G ′H ′I ′. What rule describes this transformation?

a. x ′,y ′ÊËÁÁ

ˆ¯̃̃ = 1

3 x, 13 y

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

b. x ′,y ′ÊËÁÁ

ˆ¯̃̃ = 3x,3yÊ

ËÁÁˆ¯̃̃

c. x ′,y ′ÊËÁÁ

ˆ¯̃̃ = x + 3,y + 3Ê

ËÁÁˆ¯̃̃

d. x ′,y ′ÊËÁÁ

ˆ¯̃̃ = x − 3,y − 3Ê

ËÁÁˆ¯̃̃

102. PQR, shown below, will be rotated clockwise 1800 about the origin.

Which rule describes the transformation?a. x ′,y ′Ê

ËÁÁˆ¯̃̃ = x,yÊ

ËÁÁˆ¯̃̃

b. x ′,y ′ÊËÁÁ

ˆ¯̃̃ = −x,yÊ

ËÁÁˆ¯̃̃

c. x ′,y ′ÊËÁÁ

ˆ¯̃̃ = x,−yÊ

ËÁÁˆ¯̃̃


ˆ¯̃̃ = −x,−yÊ

ËÁÁˆ¯̃̃

103. If SLM is rotated 1800 about the origin, what will be the coordinates for the image of M?

a. 5,5ÊËÁÁ

ˆ¯̃̃

b. 5,−5ÊËÁÁ

ˆ¯̃̃

c. −5,5ÊËÁÁ

ˆ¯̃̃

d. −5,−5ÊËÁÁ

ˆ¯̃̃

104. What is the rule for the transformation formed by a translation 2 units to the left and 3 units up followed by a 900 counterclockwise rotation?a. x″,y″Ê

ËÁÁˆ¯̃̃ = −3x,−2yÊ

ËÁÁˆ¯̃̃

b. x″,y″ÊËÁÁ

ˆ¯̃̃ = x − 2,y + 3Ê

ËÁÁˆ¯̃̃

c. x″,y″ÊËÁÁ

ˆ¯̃̃ = − y + 3Ê

ËÁÁˆ¯̃̃ ,x − 2Ê

ËÁÁ ˆ

¯˜̃

d. x″,y″ÊËÁÁ

ˆ¯̃̃ = − y − 2Ê

ËÁÁˆ¯̃̃ ,x + 3Ê

ËÁÁ ˆ

¯˜̃

Name: ________________________ ID: Practice

21

105. G ′H ′I ′ is the image of GHI after a transformation.

Which choice describes the transformation shown?a. reflection over the x − axisb. reflection over the y − axisc. x ′,y ′Ê

ËÁÁˆ¯̃̃ = x − 8,yÊ

ËÁÁˆ¯̃̃


ˆ¯̃̃ = x,y − 8Ê

ËÁÁˆ¯̃̃

106. In the diagram below, P′Q ′R′ is the image produced by applying a transformation to PQR.

Which rule describes the transformation?a. (x' ,y' ) = (x,y)b. (x' ,y' ) = (−x,−y)c. (x' ,y' ) = (−x,y)d. (x' ,y' ) = (x,−y)

107. Triangle PQR has vertices P −1,3ÊËÁÁ

ˆ¯̃̃ , Q 1,2Ê

ËÁÁˆ¯̃̃ , and

R −2,−1ÊËÁÁ

ˆ¯̃̃ . When PQR is reflected over the line

y = −2, what are the coordinates of P′?a. −1,−3Ê

ËÁÁˆ¯̃̃

b. −1,−7ÊËÁÁ

ˆ¯̃̃

c. −2,−2ÊËÁÁ

ˆ¯̃̃

d. −3,−3ÊËÁÁ

ˆ¯̃̃

108. P′Q ′R′ is the image produced aftet reflecting PQR across the y − axis. If P has coordinates

s,tÊËÁÁ

ˆ¯̃̃ , what are the coordinates of P′?

a. t,sÊËÁÁ

ˆ¯̃̃

b. s,−tÊËÁÁ

ˆ¯̃̃

c. −s,−tÊËÁÁ

ˆ¯̃̃

d. −s,tÊËÁÁ

ˆ¯̃̃

109. Point J p,qÊËÁÁ

ˆ¯̃̃ is a vertex of quadrilateral JKLM .

What are the coordinates of J ′ after JKLM is rotated 1800 about the origin?a. −p,−qÊ

ËÁÁˆ¯̃̃

b. −p,qÊËÁÁ

ˆ¯̃̃

c. p,−qÊËÁÁ

ˆ¯̃̃

d. q,−pÊËÁÁ

ˆ¯̃̃

110. The point G 2,−7ÊËÁÁ

ˆ¯̃̃ is transformed according to the

rule x ′,y ′ÊËÁÁ

ˆ¯̃̃ = x + 2,y − 3Ê

ËÁÁˆ¯̃̃ . The image G ′ of the

transformation is then reflected over the line y = x, resulting in point G ′. What are the coordinates of G″?a. 4,10Ê

ËÁÁˆ¯̃̃

b. 4,−10ÊËÁÁ

ˆ¯̃̃

c. −10,4ÊËÁÁ

ˆ¯̃̃

d. −4,10ÊËÁÁ

ˆ¯̃̃

Name: ________________________ ID: Practice

22

111. Point J p,qÊËÁÁ

ˆ¯̃̃ is a vertex of JKL. What are the

coordinates of J ′ after JKL is reflected across the line y = x?a. −p,−qÊ

ËÁÁˆ¯̃̃

b. p,−qÊËÁÁ

ˆ¯̃̃

c. q,−pÊËÁÁ

ˆ¯̃̃

d. q,pÊËÁÁ

ˆ¯̃̃

112. Point P′ is the image of point P after a counterclockwise rotation of 900 about the origin. If the coordinates of P′ are −7,3Ê

ËÁÁˆ¯̃̃ , what are the

coordinates of point P?a. −3,−7Ê

ËÁÁˆ¯̃̃

b. −3,7ÊËÁÁ

ˆ¯̃̃

c. 3,−7ÊËÁÁ

ˆ¯̃̃

d. 3,7ÊËÁÁ

ˆ¯̃̃

113. XYZ is dilated by a factor of 12. What is the ratio

of the area of XYZ to the area of its image, X ′Y ′Z′?

a. 4 :1b. 2 :1c. 1 :2d. 1 :4

Name: ________________________ ID: Practice

23

G3.02 Use matrix operations (addition, subtraction, multiplication, scalar multiplication) to describe the transformation of polygons in the coordinate plane.

114.

The vertex matrix for PQR is −2 2 3

−2 4 −3

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇.

The graph below shows PQR and its image, P′Q ′R′, after a transformation.

Which matrix expression produces the vertex matrix for P′Q ′R′?

a. 12

−2 2 3

−2 4 −3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b. 2 −2 2 3

−2 4 −3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c. 12

−4 4 6

−4 8 −6

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d. 2 −4 4 6

−4 8 −6

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

115. The vertex matrtix for JKL is −2 2 4

1 5 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇.

JKL is translated 2 units right and3 units up, resulting in J ′K ′L′. A translation of 4 units left and 1 unit up is applied to

J ′K ′L′, resulting in J ″K ″L″. Which matrix expression gives the vertex matrix for

J ″K ″L″?

a. −2 2 4

1 5 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

+ 2 2 2

3 3 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b. −2 2 4

1 5 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

+ −4 −4 −4

1 1 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c. −2 2 4

1 5 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

+ 2 2 2

2 2 2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d. −2 2 4

1 5 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

+ −2 −2 −2

4 4 4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

116. The vertex matrix for RST is −2 3 2

−3 −1 −4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇.

R′S ′T ′ is the image produced by translating RST 3 units left and 4 units up. What is the

vertex matrix for R′S ′T ′?

a. −5 0 −1

−7 −5 −8

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b. −5 0 −1

1 3 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c. 1 6 5

−7 −5 −8

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d. 1 6 5

1 3 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

Name: ________________________ ID: Practice

24

117. The vertex matrix for MNO is 5 0 8

−3 2 −4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇.

What is the vertex matrix for M ′N ′O ′, the image produced by reflecting MNO over the x-axis?

a. 5 0 8

−3 2 −4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b. 5 0 8

3 −2 4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c. −5 0 −8

3 −2 4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d. −5 0 −8

−3 2 −4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

118. In the diagram below, R′S ′T ′ is the image produced by applying a transformation to RST.

Which matrix calculation will give the vertex matrix for R′S ′T ′?

a. 2 2 4 3

5 4 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b. 12

4 8 6

10 8 2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c. 2 2 2

2 2 2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

+ 2 4 3

5 4 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d.

12

12

12

12

12

12

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

+ 4 8 6

10 8 2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

Name: ________________________ ID: Practice

25

119. NOP has vertices N 2,3ÊËÁÁ

ˆ¯̃̃ , O −1,4Ê

ËÁÁˆ¯̃̃ , and

P 3,−5ÊËÁÁ

ˆ¯̃̃ . Which matrix calculation is used to

determine the vertex matrix for the image N ′O ′P′ produced by a reflection across the

y-axis?

a. −1 0

0 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

2 −1 3

3 4 −5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b. 1 0

0 −1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

2 −1 3

3 4 −5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c. −1 0

0 −1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

2 −1 3

3 4 −5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d. 0 1

1 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

2 −1 3

3 4 −5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

120. DEF is reflected across the line y = x.

Which matrix multiplication shows how to find D ′E′F ′?

a. 1 0

0 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

4 5 6

1 3 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b. 0 1

1 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

4 5 6

1 3 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c. −1 0

0 −1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

4 5 6

1 3 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d. 0 −1

−1 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

4 5 6

1 3 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

121. Triangle MRT has vertices at M 3,8Ê

ËÁÁˆ¯̃̃ , R 7,−2Ê

ËÁÁˆ¯̃̃ ,

and T −5,−4ÊËÁÁ

ˆ¯̃̃ . If the triangle is to be translated by

the rule x ′,y ′ÊËÁÁ

ˆ¯̃̃ = x + 3,y − 2Ê

ËÁÁˆ¯̃̃ , which matirx

expression models the translation?

a. 3 7 −5

8 −2 −4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

+ 3 3 3

−2 −2 −2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b. 3 7 −5

8 −2 −4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

− −2 −2 −2

3 3 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c. 3 7 −5

8 −2 −4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

+ −2 −2 −2

3 3 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d. 3 7 −5

8 −2 −4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

− 3 3 3

−2 −2 −2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

Name: ________________________ ID: Practice

26

122. Which matrix calculation was used to transform

STU to S ′T ′U ′?

a. 0 −1

1 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

−7 −4 −3

0 2 8

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b. −1 0

0 −1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

−7 −4 −3

0 2 8

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c. −1 0

0 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

−7 −4 −3

0 2 8

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d. 0 −1

−1 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

−7 −4 −3

0 2 8

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

123. GHJ with vertex matrix −2 3 3

4 6 −2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇ is

dilated by a factor of 13. In the image G ′H ′J ′,

what are the coordinates of the vertex that lies in the second quadrant?

a. −73 , 13

3Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

b. −23 , 4

3Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

c. 1,−23

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

d. 1,2ÊËÁÁ

ˆ¯̃̃

124. The vertices of quadrilateral GHIJ are G −1,−1Ê

ËÁÁˆ¯̃̃ ,

H 3,−2ÊËÁÁ

ˆ¯̃̃ , I 2,4Ê

ËÁÁˆ¯̃̃ , and J −2,3Ê

ËÁÁˆ¯̃̃ . G ′H ′I ′J ′ is the

image produced by translating quadrilateral GHIJ 6 units to the left. Which matrix represents G ′H ′I ′J ′?

a. −7 −3 −4 −8

−7 −8 −2 −3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b. −7 −3 −4 −8

−1 −2 4 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c. −1 3 2 −2

−7 −8 −2 −3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d. 5 9 8 4

−1 −2 4 3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

125. M ′N ′O ′ is the image of MNO produced by

translating 3 units left and 1 unit up. The vertex

matrix for M ′N ′O ′ is −1 2 4

1 6 −3

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇. Which is

the vertex matrix for MNO?

a. 2 5 7

0 5 −4

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b. −4 −1 1

2 7 −2

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c. −2 1 3

4 9 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d. 0 3 5

−2 3 −6

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

Name: ________________________ ID: Practice

27

126. Polygon FGHI is represented by vertex matrix M .

M = 2 4 4 2

−2 −2 −5 −5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

Which multiplication would be used to reflect polygon FGHI across the x − axis?

a. 1 0

0 −1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

2 4 4 2

−2 −2 −5 −5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b. −1 0

0 1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

2 4 4 2

−2 −2 −5 −5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c. −1 0

0 −1

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

2 4 4 2

−2 −2 −5 −5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d. 0 −1

−1 0

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

2 4 4 2

−2 −2 −5 −5

È

Î


˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

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