ALLEN PARK HIGH SCHOOL - Weeblyaphsbrown.weebly.com/uploads/7/3/0/2/7302308/final_exam_review... · 35 Gus reflects an object twice. The first step is to reflect it over the line

Geometry Second Semester Review ____________

APHS/MATH

ALLEN PARK HIGH SCHOOL S e c o n d S e me s t e r R e v i e w

Geomet r y


APHS/MATH

5 10

x

12

13

5 10

8.0

4.9

x

1 The unit measures of the sides of a right triangle are shown below.

Find the exact measure of x.

A. 0.84

B. 1

C. 5

D. 25

2 The unit measures of the sides of a right triangle are shown below. Find the measure of the hypotenuse. Round to the nearest tenth.

A. 89.0

B. 9.3

C. 88.1

D. 9.4

3 Four vectors are graphed on the coordinate grid below.

6

4

2

5

D

C

B

A

Which vector is the result when the vectors (0, 2) and (1, 0) are added?

A. A B. B

C. C

D. D

4 Find the magnitude of 5,1m .

A. 26

B. 5

C. 1

D. 51


APHS/MATH

82

T

SRQ

5 Find the direction of 5,1m .

A. 101

B. 191

C. 11

D. 349

6 Consider the following statement.

“Regular polygons are convex.” Which is the converse of the given statement?

A. Regular polygons are not convex.

B. Polygons that are not regular are not convex.

C. If polygons are regular, then they are convex.

D. Convex polygons are regular.

7 Consider the following statement.

“Regular polygons are convex.”

Which is the negation of the given statement?

A. Regular polygons are not convex. B. Polygons that are not regular are not convex.

C. If polygons are regular, then they are convex.

D. Convex polygons are regular.

8 In the figure below, m QRT =82 . In RST , T is 6 greater than S .

What is the measure of T ?

A. 38

B. 52

C. 44

D. 46


APHS/MATH

XT

SR

Q

P

9 A circle has a diameter of 9 cm. What is the exact value of the area of this circle?

A. 20.25

B. 18

C. 81

D. 9

10 A circle has an area of 144 . What is the exact value of the circumference of this circle?

A. 24

B. 12

C. 24

D. 12

11 A circle has its center at the origin and one point on the circle is (4, 2). What is the measure of the radius of this circle?

A. 20

B. 2 5

C. 2 3

D. 24

12 In the figure, XP and XT are opposite rays.

If 2 14m PXQ a , 39m QXR , 2 5m RXS a , and 3 4m SXT a , find m RXS .

A. 22

B. 30

C. 49

D. 62


APHS/MATH

4

10

D C

BA

13 What is the exact length of the diagonal in the rectangle represented by the drawing below?

A. 20

B. 40

C. 14

D. 2 29

14 An isosceles right triangle has legs 5 in long. What is the length of the hypotenuse of this right

triangle?

A. 5 2

B. 5 3

C. 10 2

D. 10 3

15 An isosceles right triangle has a hypotenuse of 14 cm long. What is the length of each leg?

A. 7

B. 7 2

C. 14

D. 14 2

16 In PQR below, PQ PR and PS bisects QPR .

SQ R

P

If the length of QS is 2( 1)x units and SR is 4x units, what is the value of QR ?

A. 2

B. 6

C. 12

D. 14


APHS/MATH

C B

A

2 13

6

4

17 The unit measures of the sides of right ABC are shown below.

Which ratio represents the tangent of A ?

A. 2

3

B. 3

2

C. 12

13

D. 3 13

13

18 A ship is sighted from two radar stations 43 km apart. The angle between the line segment

joining the two stations ad the radar beam of the first station is 37 . The angle between the

line segment joining the two stations and the beam form the second station is 113 .

43 km

37radar station #1

ship

113

radar station #2

How far is the ship from the second station?

A. 43.0 km

B. 51.8 km

C. 30.0 km

D. 62.3 km


APHS/MATH

19 What is the exact value for the sine of a 30 angle?

A. 1

2

B. 3

3

C. 3

2

D. 2 3

3

20 The length of a rectangular garden is 30 ft more than 2 times its width. The area of the garden

is 2200 ft . What is the length of the garden?

A. 40 B. 110

C. 3 15

D. 5

21 The diagonals of a kite are 10 units and 5 5 3 units long. The longer diagonal bisects the

shorter diagonal, as shown in the diagram.

5 3

5 5

5

What is the perimeter of the kite?

A. 15 10 6

B. 15 5 3

C. 10 10 3

D. 20 10 2


APHS/MATH

(5x+30)30D C

BA

1

22 Which of the following properties is NOT always true for a rectangle?

A. All sides are congruent.

B. Opposite sides are parallel.

C. The diagonals are congruent.

D. The sum of the interior angles is 360 .

23 In the diagram below, ABCD is a parallelogram.

Find the value of x.

A. 0

B. 12

C. 24

D. 36

24 A regular decagon has 4 cm sides. Which is the closest to the area of this decagon?

A. 120 square cm

B. 123 square cm

C. 128 square cm

D. 132 square cm

25 Two regular octagons share a common side, as shown in the diagram below.

What is the measure of 1 in the diagram?

A. 88

B. 90

C. 45

D. 60


APHS/MATH

D

B

EF

C

A

A

BP

C

26 A square is inscribed in a circle shown below.

If the diagonal of the square measures 16 inches, what is the area of the shaded part of the

circle? A. (64 128 ) square inches

B. (128 64 )square inches

C. 256 square inches

D. 128 square inches

27 Chord AB passes through the center of circle C, and chord DE is perpendicular to AB at point

F. The diameter of the circle is 10 in, and the length of FE is 3 in.

What is the length of AF ?

A. 4

B. 6

C. 8

D. 9

28 In the diagram below, A, B, and C are on circle P.

Find the m CAB .

A. 45

B. 90

C. 135

D. 180


APHS/MATH

5 10

B

C

A

86

E

D C

BA

D C

BA

2 5

12

8

29 Points A and B are on circle C, as shown in the diagram below. The length of the hypotenuse

of ABC is 8 2 inches.

What are the circumference and area of circle C?

A. Circumference = 16 inches

Area = 64 square inches

B. Circumference = 8 2 inches


C. Circumference = 16 2 inches


D. Circumference = 8 inches


30 In parallelogram ABCD below, the length of AC is 8 units long and the length of EB is 6 units

long.

What is the area, in square units if ABCD?

A. 48 square units

B. 24 square units

C. 14 square units

D. Not enough information

31 The unit lengths of the sides of isosceles trapezoid ABCD are shown below.

Which expression shows the square unit area of the trapezoid as the sum of the areas of a

rectangle and two triangles? A. (4 8) (4 2)

B. (8 12) (2 2 5)

C. (4 8) (2 2 5)

D. (8 12) (2 4)


APHS/MATH

5

4

3

C B

A

159

12C B

A

156

8C B

A

106

12C B

A

109

4C B

A

25

25

32 Determine whether the pair of triangle is similar by the given information. Explain your answer.

A. Not similar B. Yes, SAS

C. Yes, AA

D. Yes, SSS

33

Which of the triangles is similar to the triangle above?

A. B.

C. D.


APHS/MATH

34 The vertices of quadrilateral ABCD are A (3, 4), B (4, 5), C (5, 3), and D (3, 0). A

transformation of quadrilateral ABCD to quadrilateral ' ' ' 'A B C D is defined as

( , ) ( 5, 3)T x y x y .

10

8

6

4

2

5 10D

C

B

A

After this transformation, B’ is the image of B. What are the coordinates of B’?

A. (4, 5)

B. (5, 3)

C. (10, 6)

D. (9, 8)

35 Gus reflects an object twice. The first step is to reflect it over the line 1y . Then Gus

completes the composite reflection by reflecting it over the line 1y . The net effect is a

translation of the object. Describe this translation.

A. ( , ) ( , )x y x y

B. ( , ) ( 4, )x y x y

C. ( , ) ( , 4)x y x y

D. ( , ) ( , 4)x y x y


APHS/MATH

36 A transformation maps ABC to ' ' 'A B C , as shown on the coordinate grid below.

Which of the following best describes this transformation?

A. reflection

B. translation

C. rotation

D. dilation

37 In the coordinate grid below, ABC is transformed to ' ' 'A B C

What is the scale factor for this dilation?

A. 1

3; reduction

B. 1

3; enlargement

C. 3; reduction

D. 3; enlargement


APHS/MATH

38 ABC and its image ' ' 'A B C are shown on the coordinate grid below.

Which best represents the mapping (T) from ABC onto ' ' 'A B C ?

A. : ( , ) 2, 2T x y x y

B. : ( , ) 2, 2T x y x y

C. : ( , ) ,3 3

x yT x y

D. : ( , ) 3 ,3T x y x y

39 Determine whether the quadrilateral is a parallelogram. Justify your answer.

A. No, the sides don’t add up to 180

B. No, all sides are not equal

C. Yes, the opposite sides are equal

D. Yes, the opposite sides are parallel

40 Find x so that the quadrilateral is a parallelogram.

A. 3

B. 7

C. 25

D. 13

41 Find the measure of K in the quadrilateral below.

A. 50

B. 115

C. 130

D. 65


APHS/MATH

42 Find the sum of the measures of the exterior angles of a regular dodecagon.

A. 1800

B. 150

C. 360

D. 30

43 Name the missing coordinates for the isosceles trapezoid.

A. (1, 3)

B. (c, b)

C. (a + d, c)

D. (b, c)

44 The ratio of the measures of three angles of a triangle are 5:7:8. Find the measure of each

angle of the triangle.

A. 9, 11, 12

B. 45, 63, 72

C. 30, 58, 92

D. Not enough information

45 The span of the Benjamin Franklin suspension bridge in Philadelphia, Pennsylvania, is 1750 feet. A model of the bridge has a span of 42 inches. What is the ratio of the span of the model to the span of the actual Benjamin Franklin Bridge?

A. 1

500

B. 3

125

C. 36

125

D. 7

1500


APHS/MATH

46 Determine whether the two triangles are similar. If so, calculate the length of AC .

A. The triangles are not similar.

B. The triangles are similar and AC = 4

C. The triangles are similar and AC = 2

D. The triangles are similar and AC = 14

47 Find x and y so that the quadrilateral is a parallelogram.

A. x = 45, y = 20

B. x = 6, y = 63

C. x = 7, y = 3

D. x = 6, y = 14

48 Determine which set of numbers can be the measures of the sides of a right triangle.

A. 3, 4, 6

B. 2 , 2, 3

C. 8, 9, 10

D. 4 3 , 4, 8

49 Calculate the value of x.

A. 4 11

B. 5 27

C. 3 15

D. 13

50 Use the figure below to determine the values of x and y.

A. x = 4, y = 9

B. x = 6, y = 6.5

C. x = 5, y = 7

D. x = 3, y = 8


APHS/MATH

51 Find MN if ,ABC MNP AD is an altitude of ABC , MQ is an altitude of MNP , AB = 24,

AD = 14, and MQ = 10.5.

A. 24

B. 32

C. 6.125

D. 18

52 The perimeter of an equilateral triangle is 30 centimeters. Find the length of an altitude of the

triangle.

A. 5 3

B. 5

C. 10

D. 5 2

53 Find cos B.

A. 3

4

B. 3

5

C. 4

5

D. 4

3

54 Find the measure of side g in EFG rounded to the nearest tenth if m G = 14, m E = 67, and

e = 14.

A. 4.1

B. 5.2

C. 3.7

D. 3.3


APHS/MATH

55 Calculate the measure of side c in ABC rounded to the nearest tenth.

A. 25.8

B. 27.9

C. 30.7

D. 32.3

56 Find the angle of elevation of the sun when a 6 – meter flagpole casts a 17 – meter shadow.

Round to the nearest tenth.

A. 19.4

B. 20.6

C. 69.3

D. 70.3

57 Find the value of x given the similar figures.

A. 32

B. 1

53

C. 1

133

D. 6

58 Find the value of x given the similar figures.

A. 20

B. 12

C. 3

D. 13.5


APHS/MATH

59 The drawing below illustrates two poles supported by wires. ,ABC GED AF CF , and

.FG GC DC Find the height of the pole .EC

A. 18 ft.

B. 10 ft.

C. 15 ft.

D. 22 ft.

60 Find the value of x.

A. 78 B. 90 C. 102 D. 156

61 Find the value of y.

A. 66 B. 57 C. 45 D. 21

62 Find the center of the circle whose equation is 2 2( 11) ( 7) 121x y .

A. (-11, 7) B. (11, 7) C. (121, 49) D. 11

63 Find the equation of circle P.

A. 2 2( 3) 4x y B. 2 2( 3) 2x y C. 2 2( 3) 2x y D. 2 2( 3) 4x y

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ALLEN PARK HIGH SCHOOL - Weeblyaphsbrown.weebly.com/uploads/7/3/0/2/7302308/final_exam_review... · 35 Gus reflects an object twice. The first step is to reflect it over the line