Multiple Choice Practice

Multiple Choice

Identify the choice that best completes the statement or answers the question.

Use Pascal’s Triangle to expand the binomial.

____ 1.

a. b. c. d.

____ 2.

a. b. c. d.

____ 3.

a. b. c. d.

There are 220 students in the 11th grade at Silver High School. Ninety-five of the students are girls and 125 are boys.

The table below records the number of students that participate in after school activities.

____ 4. What is the probability that a student who participates in after school activities is a girl?

a.

c.

b.

d.

____ 5. What is the probability that a student who is a boy does not participate in after school activities?

a.

c.

b.

d.

____ 6. If the student is a girl, what is the probability that she does not participate in after school activities?

a.

c.

b.

d.

____ 7. A bag contains 4 blue chips, 5 red chips and 6 green chips. Nekisha draws two chips from the bag without replacement.

What is the probability that the second chip is blue if the first chip is green?

a.

c.

b.

d.

Find each element in Pascal’s Triangle.

____ 8.

a. 20 c. 15

b. 10 d. 35

Find the value of m.

____ 9.

a. 10 c. 12

b. 11 d. 15

____ 10. What is the total number of possible outcomes when you roll a die 4 times?

a. 1296 c. 24

b. 10 d. 6

____ 11. A spinner is numbered from 1 through 10 with each number equally likely to occur. What is the probability of obtaining a

number less than 2 or greater than 7 in a single spin?

a. 2

5

b. 1

2

c. 2

1

2

d. 3

10

____ 12. A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find P(red or blue).

a. 2

3

b. 3

2

c. 5

8

d. 3

4

____ 13. A coin is tossed 4 times. What is the probability of getting tails 2 times in a row?

a. 3

8

b. 1

2

c. 1

16

d. 1

8

Annabel conducted a census of the tenth grade students at her school. She asked each student about their daily sleep

habits and their overall alertness during the school day. Her results are displayed in the two-way table below.

____ 14. If a student sleeps between six to eight hours a night, what is the probability that they are generally alert during the school

day?

a. 0.06 c. 0.76

b. 0.56 d. 0.94

____ 15. Which statement can you conclude is true from the given information?

Given: is the perpendicular bisector of

I K

B

A

J

a. AJ = BJ c. IJ = JK

b. is a right angle. d. A is the midpoint of .

____ 16. Which statement is not necessarily true?

Given: is the bisector of

J L

E

D

K

a. DK = KE c. K is the midpoint of .

b. d. DJ = DL

____ 17. Find

1

2

3

4

Drawing not to scale

a. 37 b. 143 c. 27 d. 153

____ 18. Which statement is true?

a. are same-side angles.

b. are same-side angles.

c. are alternate interior angles.

d. are alternate interior angles.

____ 19. Find the value of k. The diagram is not to scale.

62°

45° k °

a. 17 b. 73 c. 118 d. 107

____ 20. Find the values of x, y, and z. The diagram is not to scale.

38°

56°

19°

x° y°z°

a. c.

b. d.

____ 21. Find the value of x. The diagram is not to scale.

105°

72°

x°

a. 33 b. 162 c. 147 d. 75

____ 22. Find the value of the variable. The diagram is not to scale.

114°

47°x°

a. 66 b. 19 c. 29 d. 43

____ 23. Judging by appearance, classify the figure in as many ways as possible.

•

•

•

•

|

|

|

|

a. rectangle, square, quadrilateral, parallelogram, rhombus

b. rectangle, square, parallelogram

c. rhombus, trapezoid, quadrilateral, square

d. square, rectangle, quadrilateral

____ 24. Judging by appearances, which figure is a trapezoid?

a.

c.

b.

d.

____ 25. LMNO is a parallelogram. If NM = x + 28 and OL = 5x + 8 find the value of x and then find NM and OL.

O N

L M

a. x = 5, NM = 35, OL = 33 c. x = 5, NM = 33, OL = 33

b. x = 7, NM = 35, OL = 35 d. x = 7, NM = 33, OL = 35

____ 26. For the parallelogram, if and find The diagram is not to scale.

3 4

2 1

a. 9 b. 17 c. 173 d. 163

____ 27. Find the values of the variables in the parallelogram. The diagram is not to scale.

x°

y°

z°

10229

a. c.

b. d.

____ 28. In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 4x – 5, and HE = 2y + 3. Find the values of x and y. The diagram is

not to scale.

D

FG

E

H

a. x = 6, y = 3 b. x = 2, y = 3 c. x = 3, y = 2 d. x = 3, y = 6

____ 29. Construct the line perpendicular to at point V.

T UV

a.

T UV

c.

T UV

b.

T UV

d.

T UV

____ 30. Are C, B, and A collinear? If so, name the line on which they lie.

A

B

C

D

a. Yes, they lie on the line AC.

b. No, the three points are not collinear.

c. Yes, they lie on the line BD.

d. Yes, they lie on the line AD.

____ 31. Given and , find and

a. 22 b. 11 c. 10 d. 25

____ 32. Justify the last two steps of the proof.

Given: and

Prove:

R

S T

U

Proof:

1. 1. Given

2. 2. Given

3. 3.

4. 4.

a. Symmetric Property of ; SAS c. Reflexive Property of ; SAS

b. Reflexive Property of ; SSS d. Symmetric Property of ; SSS

____ 33. Find the value of the variable if and The diagram is not to scale.

1 2

3 4

5 6

7 8

l

m

a. 1 b. 2 c. 3 d. –2

____ 34. What is the missing reason in the proof?

Given: parallelogram ABCD with diagonal

Prove:

D

BA

C

Statements Reasons

1. 1. Definition of parallelogram

2. 2. Alternate Interior Angles Theorem

3. 3. Definition of parallelogram

4. 4. Alternate Interior Angles Theorem

5. 5. Reflexive Property of Congruence

6. 6. ?

a. Reflexive Property of Congruence c. Alternate Interior Angles Theorem

b. ASA d. SSS

____ 35. Find the value of x. The diagram is not to scale.

T U

(3x – 50)° (7x )°

S

R

||

a. b. c. d. none of these

____ 36. Find the values of the variables and the lengths of the sides of this kite.

|

|

|| |

|

y – 2 x + 2

2x + 2 x + 11

a. x = 9, y = 13; 7, 15 c. x = 9, y = 13; 11, 20

b. x =13, y = 9; 7, 15 d. x =13, y = 9; 11, 11

____ 37. Find the values of a and b.The diagram is not to scale.

36° b°

113°a°

a. c.

b. d.

____ 38. ABCD is a parallelogram. If then The diagram is not to scale.

A B

D C

a. 66 b. 124 c. 114 d. 132

____ 39. WXYZ is a parallelogram. Name an angle congruent to

X

ZW

Y

N

a. b. c. d.

____ 40. Figure . Name a pair of corresponding sides?

a. b. c. d.

____ 41. The two rectangles are similar. Which is a correct proportion for corresponding sides?

x

8 m

4 m

12 m

a.

b.

c.

d.

Are the polygons similar? If they are, write a similarity statement and give the similarity ratio.

____ 42. In RST, RS = 10, RT = 15, and mR = 32. In UVW, UV = 12, UW = 18, and mU = 32.

a. ;

c. ;

b. ;

d. The triangles are not similar.

____ 43. In QRS, QR = 4, RS = 15, and mR = 36. In UVT, VT = 8, TU = 32, and mT = 36.

a. ;

c. ;

b. ;

d. The triangles are not similar.

____ 44. ABCD ~ WXYZ. AD = 6, DC = 3, and WZ = 59. Find YZ. The figures are not drawn to scale.

A

B

D

C

W

X

Z

Y

a. 118 b. 29.5 c. 21.7 d. 177

The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.

____ 45. The pentagons are similar.

16

4

6

8x – 3y – 2

a. x = 27, y = 4 c. x = 28, y = 5

b. x = 27, y = 5 d. x = 28, y = 4

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.

____ 46.

a. ; SAS c. ; SSS

b. ; SAS d. The triangles are not similar.

____ 47. Use the information in the diagram to determine the height of the tree to the nearest foot.

a. 80 ft b. 264 ft c. 60 ft d. 72 ft

____ 48. Use the Side-Splitter Theorem to find x, given that .

B

A

C

P Q

8

x 18

12

a. 12 b. 6 c. 20 d. 24

____ 49. Given: . Find the length of . The diagram is not drawn to scale.

B

A

C

P Q

6

12 18

a. 11 b. 12 c. 18 d. 9

____ 50. Find the values of x and y, given that and .

M

O

Py

x

9

1820

N

Q

a. x = 10; y = 25.5 c. x = 13; y = 25.5

b. x = 20; y = 17 d. x = 25.5; y = 10

Solve for x.

____ 51.

x

x + 5 x + 1

x – 2

>

>

a. 5 b. 2.5 c. 7.5 d. 10

____ 52.

4 5

x

Not drawn to scale

a. 20 b. 6 c. 2 5 d. 9

____ 53.

7 13

x

a. b. c. d.

____ 54. The widths of two similar rectangles are 16 cm and 14 cm. What is the ratio of the perimeters? Of the areas?

a. 8 : 7 and 64 : 49 c. 9 : 8 and 81 : 64 b. 9 : 8 and 64 : 49 d. 8 : 7 and 81 : 64

The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest whole

number.

____ 55. It costs a family $324 to buy a 10-ft-by-12-ft rug. At this rate, what will it cost them to buy a 15-ft-by-18-ft rug?

a. $729 b. $270 c. $388.80 d. $466.56

____ 56. The ramp shown below is used to move crates of fruit to loading docks of different heights. When the horizontal distance

AB is 12 meters, the height of the loading dock, BC, is 4 meters. What is the height of the loading dock DE?

a. 12 m b. 8 m c. 9 m d. 15 m

____ 57. The ladders shown below are standing against the wall at the same angle. How high up the wall does the longer ladder go?

(All measurements are in feet.)

x

30

24

10

a. 11.25 ft b. 12.5 ft c. 14 ft d. 26 ft

A scale drawing uses the scale 3 in. = 20 ft. Find the missing measure.

____ 58. 57 in. = ____ ft

a. 1,080 b. 340 c. 380 d. 190

____ 59. Find the length of arc AB.

a.

c.

b.

d.

____ 60. What is the measure of central angle in degrees?

a. 40° c. 30°

b. 45° d. 50°

____ 61. What is the measure of central angle in radians?

a.

c.

b.

d.

____ 62. What is the length of arc PQ?

a.

c.

b.

d.

____ 63. Grade 7 students were surveyed to determine how many hours a day they spent on various activities. The results are

shown in the circle graph below. Find the measure of each central angle in the circle graph.

a. Sleeping

b. Eating

a. 118.8°; 28.8° b. 108°; 28.8° c. 118.8°; 288° d. 59.4°; 288°

____ 64. Name the minor arc and find its measure.

C

B

A

D )115°

a. arc ADB; 30° b. arc AB; 115° c. arc ADB; 245° d. arc AB; 245°

____ 65. Name the major arc and find its measure.

C B

A

D)50°

a. arc ADB; 50 b. arc AB; 50 c. arc ADB; 310 d. arc AB; 310

Find the circumference. Leave your answer in terms of .

____ 66.

5.7 cm

a. cm b. cm c. cm d. cm

____ 67.

18 in.

a. in. b. in. c. in. d. in.

____ 68. Find the exact area of the shaded region.

a. c.

b. d. none of these

____ 69. is tangent to circle A at B and to circle D at C (not drawn to scale).

AB = 7, BC = 18, and DC = 5. Find AD to the nearest tenth.

A

B

C

D

a. 18.7 b. 18.1 c. 21.6 d. 19.3

____ 70. A chain fits tightly around two gears as shown. The distance between the centers of the gears is 20 inches. The radius of

the larger gear is 11 inches. Find the radius of the smaller gear. Round your answer to the nearest tenth, if necessary. The

diagram is not to scale.

19 inches

a. 17.2 inches b. 6.2 inches c. 11 inches d. 4.8 inches

Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

____ 71.

6

8

x

a. 8 b. 5 c. 6 d. 10

____ 72.

x

23

7

a. 21.9 b. 181.3 c. 24 d. 13.5

Use the diagram. is a diameter, and . The figure is not drawn to scale.

C

A

D

BP

____ 73. Find for = 66.

a. 73.5 b. 114 c. 132 d. 57

____ 74. Find m(arc BD) for m(arc AC) = 43.

a. 137° b. 133° c. 86° d. 47°

____ 75. m R = 22. Find m O. (The figure is not drawn to scale.)

O

N

Q

R a. 68 b. 22 c. 158 d. 44

____ 76. Given that DAB and DCB are right angles and m BDC = 41, what is the measure of arc CAD? (The figure is not

drawn to scale.)

A

D

C

B

a. 164 b. 303 c. 246 d. 262

____ 77. Find the measures of the indicated angles. Which statement is NOT true? (The figure is not drawn to scale.)

O

a bc

d

a. a = 53° b. b = 106° c. c = 73° d. d = 37°

____ 78. is tangent to circle O at C, m(arc AEC) = 279, and m ACE = 85. Find m DCE.

(The figure is not drawn to scale.)

C

A

E

O

B

D

a. 109 b. 97 c. 54.5 d. 48.5

____ 79. If m(arc BY) = 40, what is m YAC? (The figure is not drawn to scale.)

B

A

Y

O

C a. 140 b. 100 c. 70 d. 80

____ 80. In the circle, m(arc AD) = 94, and m D = 76. Find m DCQ.

(The figure is not drawn to scale.)

A

D

C

B

P

Q

a. 57 b. 95 c. 190 d. 114

____ 81. m(arc DE) = 96 and m(arc BC) = 67. Find m A. (The figure is not drawn to scale.)

D

A

E

C

B

a. 14.5 b. 62.5 c. 81.5 d. 29

____ 82. Find the value of x for m(arc AB) = 46 and m(arc CD) = 25. (The figure is not drawn to scale.)

C

A

D

B

O

x

a. 35.5 b. 58.5 c. 71 d. 21

____ 83. In the diagram below, quadrilateral ABCD has a circumscribed circle. What is the measure of ?

a. 152.5° c. 125°

b. 130° d. 122.5°

____ 84. What are the values of x and y?

a. x = 70°; y = 100° c. x = 90°; y = 80°

b. x = 130°; y = 40° d. x = 100°; y = 70°

____ 85. What is the measure of arc WZ?

a. 90° c. 110°

b. 70° d. 100°

____ 86. Quadrilateral ABCD is an inscribed quadrilateral. What is the value of x?

a. 95 c. 75

b. 85 d. 65

____ 87. What is the measure of arc RS?

a. 90° c. 110°

b. 100° d. 120°

____ 88. Quadrilateral PQRS is an inscribed quadrilateral. What is the value of x?

a. 49° c. 94°

b. 86° d. 105°

____

89.