Objective 1 - Winston-Salem/Forsyth County Schools



1) The angle of elevation from point G on the ground to the top of a flagpole is 20°. The height of the flagpole is 60feet.

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

A sin [pic] B sin [pic]

C tan [pic] D tan [pic]

2) A mountain climber stands on level ground 300 m from the base of a cliff. The angle of elevation to the top of the cliff is 58°. What is the approximate height of the cliff?

A 187 m B 354 m C 480 m D 566 m

3) 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 19.3° B 20.5° C 69.5° D 70.7°

4) 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 15°. About how far is the foot of the ladder from the building?

A 7.76 ft. B 8.04 ft. C 18.37 ft. D 28.98 ft.

5) 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 40° angle with the ground, about how tall was the tree originally?

A 13 ft

B 16 ft

C 23 ft

D 26 ft

6) A regular hexagon is inscribed in a circle. What is the degree measure of each arc joining the consecutive vertices?

A 40° B 45° C 54° D 60°

7) In the diagram, [pic] is the angle bisector of ∠ABC. If [pic],

what is [pic]?

A 30º B 40º

C 45º D 50º

8) In [pic]XYZ, W is between Y and Z. The coordinates are X(2, 3), Y(5, 0),Z(0, 0), and W(2, 0). What is [pic]?

A altitude

B angle bisector

C median

D perpendicular bisector of the side

9) It is given that [pic] and [pic]. Which reason

could be used to prove [pic]?

A side-angle-side B angle-side-angle

C side-side-side D side-side-angle

10) ABCD is a trapezoid with median [pic]. What is the length of [pic]?

A 5 units

B 7 units

C 9 units

D 10 units

11) [pic]ABC is an isosceles triangle with AB = BC and median [pic]. The perimeter of [pic]ABC is 60 units. What is AB?

A 10 units

B 15 units

C 20 units

D 40 units

12) A broadcast tower is located at point (-1, 3) on an xy-coordinate grid, where each unit is one mile. If its broadcast reaches only a 20-mile radius, what is the set of points where the broadcast is received by its listeners?

A [pic] B [pic]

C [pic] D [pic]

13) In [pic], Z is the midpoint of [pic] and Y is the midpoint of [pic]. If YZ = 21 and AB = (2x – 4), what is x?

A 7.25

B 12.5

C 23

D 46

14) 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 yards

B 10 yards

C 12.8 yards

D 15 yards

15) The exterior angle of a base angle in an isosceles triangle is 100°. What is the measure of the vertex angle?

A 20° B 40° C 60° D 80°

16) Write the equation for a circle that satisfies the given conditions: Center (7, –4), Radius 6.

A [pic] B [pic]

C [pic] D [pic]

17) Suppose you roll a pair of regular dice twice. What is the probability that you roll a sum of ten on the first roll and doubles on the second roll?

A [pic] B [pic] C [pic] D [pic]

18) Suppose that you roll a pair of dice and find the sum. Let event A be rolling a 3 on one of the die and event B be rolling a sum of 8. What is P(A|B)?

A [pic] B [pic] C [pic] D [pic]

19) Suppose you select a person at random from your school. Which of the following pairs of events are mutually exclusive?

A person is a teacher; person runs for the school track team

B person is male; person is taking a math class

C person is a junior; person has missed a day of school this year

D person has a younger sister; person likes pizza

20) Find unknown side lengths and angle

measures for triangle ABC.

21) An anthropologist examining the footprints made by a bipedal (two-footed) dinosaur finds that the dinosaur’s average pace was about 1.60 meters and average stride length was about 3.15 meters. Find the step angle x for this dinosaur.

22) a) An onlooker stands at the top of a cliff 119 meters above the water’s surface. With a

clinometer, she spots two ships due west. The angle of depression to each of the sailboats is 11°

and 16°. Calculate the distance between the two sailboats.

b) What is the distance from the onlooker’s eyes to each of the sailboats? What is the

difference of those distances?

23) Find the height of a tree to the nearest tenth if the angle of elevation of the sun is 28° and the shadow of the tree is 50 ft.

24) A box contains 30 glass objects, two of which have been cracked in shipping. If one of the objects is removed, what is the probability the object selected is not cracked?

A [pic] B [pic] C [pic] D [pic]

25) Tara wants to fix the location of a mountain by taking measurements

from two positions 3 miles apart. From the first position, the angle

between the mountain and the second position is 78o. From the second

position, the angle between the mountain and the first position is 53o.

How can Tara determine the distance of the mountain from each position,

and what is the distance from each position?

26) The equation [pic] is that of a circle with what center and what radius?

A center: (2, 4 ); radius: 4 B center: (–2, –4); radius: 4

C center: (2, 4); radius: 16 D center: (–2, –4);; radius: 16

27) There are six numbered balls in a bag, each with a different number from 12 to 6. If a ball is removed from the bag, what is the probability the number on it is prime?

A [pic] B [pic] C [pic] D [pic]

28) The names of two girls and five boys are written on slips of paper and placed in a box. Two names are drawn at random. What is the probability that two girls’ names are drawn?

A [pic] B [pic] C [pic] D) 1

29) A dance company is planning a program that will consist of one ballet, one tap, and one jazz routine. In its repertoire are five ballet, three jazz, and six tap routines. How many different programs are possible?

A 56 B 90 C 14 D 28

30) Selena has eight quarters, five dimes, and three nickels in her pocket. If one coin is selected at random, what is the probability that it will not be a quarter?

A [pic] B [pic] C [pic] D [pic]

31) Find the perimeter of the kite shown at the right if AP = 6, BP = 3, and DP = 12.

A [pic] B [pic]

C [pic] D [pic]

32) If AC = 10 in the figure at the right, find BD.

A [pic] B [pic]

C [pic] D [pic]

33) A 10-foot board is used as a ramp from a doorway down to the ground. If the vertical drop from the doorway to the ground is 9 inches, which expression gives the measure of the angle the ramp makes with the ground?

A [pic] B cos [pic] C [pic] D [pic]

34) What is an equation of the circle with center at (0, 3) and a diameter 6?

35) In[pic] below, if AC = 10, then AB is equal to what?

A [pic] C [pic]

B 8 D [pic]

36) The perpendicular bisectors of a triangle all pass through what point?______________________

37) The angle bisectors of a triangle are concurrent at a point called the _______________________

38) In the figure, [pic] and[pic] are right angles. If AB = 8, BC = 6, and CD = 4, what is the length of AD?

A 5 C [pic]

B [pic] D [pic]

39) A bag contains 3 green balls, 5 black balls, and 7 red balls. If two balls are removed at random and no ball is returned to the bag after the removal, what is the probability that the first ball is red and the second ball is black?

A [pic] B [pic] C [pic] D [pic]

40) In the diagram below, point M is the midpoint of [pic] and [pic]. Which triangle congruence theorem could be used to prove that [pic]?

A AAS

B ASA

C SAS

D SSA

41) Which of the following set of conditions will not ensure that [pic]?

A [pic] and [pic] B) [pic] and [pic]

C [pic], [pic], and [pic] D [pic]

42) Suppose that [pic] is an obtuse isosceles triangle. Which of the following statements is true?

A The circumcenter is equidistant from the three sides.

B The circumcenter is equidistant from the three vertices of [pic].

C The circumcenter is inside [pic].

D The incenter and the circumcenter of [pic] are the same point.

43) The incenter of a triangle is equidistant from the three _____________________ of the triangle.

44) The medians of a triangle are concurrent. Their common point is the _______________.

A orthocenter B circumcenter C incenter D centroid

45) Determine if each pair of triangles below are congruent. If they are congruent, write a congruence relation showing the correspondence between vertices and cite an appropriate congruence theorem to support your conclusion.

A B

C D

46) Your town is holding local elections. The town sets up three polling stations around the area that form a triangle. They decide to meet at the circumcenter of their locations. The circumcenter is equidistant from the three [pic] of the triangle formed by the polling stations.

A Angles B Sides C Vertices D Angle bisectors

47) An equilateral triangle has side lengths of 10. The length of its altitude is _____.

A 5 B [pic] C [pic] D [pic]

48) Which of the following cannot be the lengths of a [pic] triangle?

A [pic] 5, [pic] B [pic] [pic] [pic]

C 11, 22, [pic] D 3, [pic] [pic]

49) Solve for x to the nearest degree.

A 63 C 27

B 66 D 24

50) Write an equation for a circle with a radius of 2 units and center at (1, 3).

51) Write an equation for a circle given that the endpoints of the diameter are (-2, 7) and (4, -8).

52) Which parts must be congruent to prove [pic] by SAS?

A [pic] and [pic] P

B [pic] and [pic]

C [pic] and [pic]

D [pic] and [pic]

R

Q S

53) A truck is at the top of a ramp as shown below. Approximately how high above the ground is the truck?

A 4.45 m B 3.59 m

C 1.95 m D 1.75 m

54) a) What is A ∩ B?

b) What is by A [pic]B?

c) What is the complement of the set A[pic]B ?

55) If ∆DEF [pic] ∆PRS, which of these congruences must be true?

A [pic] B [pic] C [pic] D [pic]

56) Which theorem or postulate can be used to prove that ΔCAN is congruent to ΔBNA?

A SSS B ASA

C AAS D SAS

57) To prove the two triangles congruent by using the Angle-Side-Angle Congruence Postulate, what other piece of information is needed?

A [pic] B [pic]

C [pic] D [pic]

58) What theorem or postulate could be used to prove that ΔPAR is congruent to ΔSBN?

A SAS B SSS

C ASA D AAS

59) What is the image of P(1, 3) after the transformation [pic]?

A (1, 3) B (1, 6) C (2, 3) D (2, 6)

60) How would the transformation of QUAD to Q’U’A’D’ be described algebraically?

A (x, 2y)

B (-x, 2y)

C (-x, 3y)

D (3x, -y)

61) If a figure is reflected in the y-axis and then rotated 180º, it would be the same as which of the following transformations?

A reflection in the x-axis B rotation of 90° clockwise

C rotation of 180° D rotation of 270° clockwise

62) What are the coordinates of the image of (a, b) after a reflection over the x-axis?

A (-a, b) B (a, -b) C (-a, -b) D (a, b)

Use the following information to answer questions 63 - 64 below.

Patrick wanted to transform ΔPAT with vertices P(2, 6), A(-2, 4), and T(3, 1) so that the new

ΔP'A'T' would have vertices P'(-2, -6), A'(2, -4), and T'(-3, -1).

63) How would the transformation be described algebraically?

A (-x, y) B (-x, -y) C (y, -x) D (-y, x)

64) How would the transformation be described in words?

A It is a reflection over the x-axis. B It is a reflection over the y-axis.

C It is a rotation of 180°. D It is a rotation of 270°clockwise.

65) If [pic], then which statement is true?

A x = 7 B x = 4 C x = [pic] D x = 3

66) At the same time of day, a man who is 55 inches tall casts a 66-inch shadow and his son casts a 30-inch shadow. What is the height of the man’s son?

A 25 in. B 26 in. C 80 in. D 96 in.

67) A man who is standing 10 feet from a flagpole casts a 4 foot shadow. The man is 5 feet tall. What is the height of the flagpole?

A 11.2 ft. B 15 ft. C 17.5 ft. D 20 ft.

68) The shorter leg of a 30°-60°-90° triangle is 2.6 feet long. What is the perimeter?

A (5.2 + [pic] ft. B (5.2 + [pic] ft.

C (7.8 + [pic] ft. D (7.8 + [pic] ft.

69) A slide 6 meters long makes an angle of 45° with the ground. How high is the top of the slide above the ground?

A [pic] m B [pic] m C [pic] m D 3 m

70) A tree casts a 26-meter shadow when the angle of elevation of the sun measures 42°. To the nearest meter, how tall is the tree?

A 17 m B 19 m C 23 m D 25 m

71) A road in the foothills of the Blue Ridge Mountains rises 350 meters in a distance of 3,000 meters along the road. What is the measure of the angle that the road makes with the horizontal to the nearest degree?

A 5° B 7° C 9° D 83°

72) If the sine of an angle is about .7071, what is the measure of the angle to the nearest degree?

A 30° B 45° C 60° D 90°

73) What is the length, in units, of the missing side of the triangle below?

15

9

?

A 6 B 11 C 12 D 17

74) Find a to the nearest tenth.

B A 5.3 cm

B 5.7 cm

10 cm

A C 6.2 cm

32° D 8.5 cm

A C

75) Find the missing angle and side measures of [pic] given that m[pic],m[pic], and

CB = 19.

A m[pic], c = 21.4, b = 11 B m[pic], c = 21.9, b = 11

C m[pic], c = 21.9, b = 11 D m[pic], c = 21.9, b = 11

76) A telephone pole breaks and falls as shown. To the nearest foot, what was the original height of the pole?

A 19 ft.

B 20 ft.

C 21 ft.

7 ft.

D 22 ft.

12 ft.

77) How are the following triangles congruent?

A AAS B SAS

C ASA D SSS

78) How are the following triangles congruent?

A AAS B SAS

C ASA D SSS

79) How are the following triangles congruent?

A AAS B SAS

C ASA D SSS

80) How long is [pic]?

A 20 ft. B 25 ft.

C 30 ft. D 35 ft.

81) The measure of an angle is 30 more than four times the measure of its complement. What is the measure of the angle?

A 12 B 30 C 60 D 78

82) If (1 and (2 are interior angles on the same side of a transversal that cuts two parallel lines, what is the value of x?

A 3 B 26 C 43 D 43.5

83) According to the map below, 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 is always true?

A MP = RO

B [pic]

C [pic]

D [pic]

84) Which parts must be congruent to prove [pic] by SAS?

A [pic] and [pic]

B [pic] and [pic]

C [pic] and [pic]

D [pic] and [pic]

85) What are the images of F(2, –1) and G(5, –4) after the following transformations?

Reflection: in the x-axis

Translation: 3 units to the left

A [pic] B [pic]

C [pic] D [pic]

86) The vertices of ∆OPQ have coordinates O(0, 0), P(0, 6), and Q(7, 0). What are the

coordinates of [pic], the image of ∆OPQ, under a 90º clockwise rotation?

A [pic] B [pic]

C [pic] D [pic]

87) What are the coordinates of the reflection of M(7, 3) in the y–axis?

A [pic] B [pic] C [pic] D [pic]

88) In the graph below, [pic] is the image produced by applying a transformation to [pic]PQR.

Which rule describes the transformation?

A [pic]

B [pic]

C [pic]

D [pic]

89) A translation is applied to [pic]FGH, forming [pic]. If the translation is described by [pic] which graph shows the translation correctly?

A B

C D

90) Point [pic] is the image of point P after a counterclockwise rotation of 90° about the origin. If the coordinates of point [pic] are

(–7, 3) what are the coordinates of point P?

A (–3, –7) B (– 3, 7) C (3, –7) D (3, 7)

91) [pic]PQR, shown below, will be rotated clockwise 180° about the origin. 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)

92) Find the indicated measures for each triangle.

a) AB = __________________ C 28 m

[pic] B

AC = __________________

[pic]

A

b) [pic] ________________ P

[pic] ________________ 12 cm

12 cm

MK = __________________ K

[pic]

M

93) What is the probability of drawing a heart from a standard deck of cards on a second draw, given that a heart was drawn on the first draw and not replaced? Are these events independent or dependent?

-----------------------

U

B

A

7

5

4

3

2

1

8

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