eoc final practice/review subject: mathematics,...

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EOC Final Practice/Review Subject: Mathematics, Grade: HS, Year Created: 2016

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Test

1) The side length of this square is . What is the radius of the circle?x

2) Segments AB and BC are tangent to circle P.

What is the value of ?x

82° 92°

88° 98°

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3) Segments and are radii of circle . CY CZ C

Chord is 5.6 centimeters long. What is the length of ?WZ XY

0.6 centimeters

1.4 centimeters

2.1 centimeters

2.8 centimeters

4) What is the length of on this circle? y

8 units 12 units

10 units 18 units

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5) Two circles the same center. Circle has a radius of units. Circle has a radius of units.have P p Q q

Which dilation could be used to prove that circles and are similar?P Q

Dilate circle by a scale factor of .P

Dilate circle by a scale factor of .Q

Dilate circle by a scale factor of × .P p q

Dilate circle by a scale factor of × .Q p q

6) Use the diagram to answer the question.

Angle is inscribed in circle . Angle circumscribes circle .AEC D ABC D

Which equation about the relationships in the circle is ?true

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7) Jenna translated this triangle according to the rule ( x3, + 2). – y

Which graph shows the result?

8) The location of point K after a translation is (-2, 3). Which rule describes this translation?

( – 3, + 6)x y ( , + 6)x y

( – 6, + 3)x y ( – 3, )x y

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9) Kevin drew square WXYZ on this grid.

Kevin translated the square 3 units along the axis and -1 unit alongx- the -axis. What are the new coordinates of the square? y

W' =(-5, 3)X'= (-1,3)Y'= (-1,-1)Z' = (-5,-1)

W' =(1, 1)X' = (5,1)Y' = (5,-3)Z' =(1, -3)

W' = (-3,5)X' = (1,5)Y' = (1,1)Z' = (-3,1)

W' = (-1,-1)X' = (3,-1)Y' = (3,-5)Z' = (-1,-5)

10) Bella transformed triangle ABC to make triangle A'B'C'.

Which transformation did Bella use?

reflection over the x -axis

reflection over the y -axis

translation 2 units down

translation 4 units down

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11) Jerome reflected this figure over the line = 2. y

Which graph shows the result?

12) Triangle Q'R'S' is a translation of triangle QRS.

Which transformation created triangle Q'R'S'?

translation 3 units left and 5 units up translation 3 units right and 5 units down

translation 5 units left and 3 units up translation 5 units right and 3 units down

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13) Jacob transformed quadrilateral FGHJ to F'G'H'J'.

Which transformation did Jacob use?

reflection across the -axisx

reflection across the -axisy

reflection across the line = 1x

reflection across the line = 1y

14) Ethan transformed quadrilateral ABCD to makequadrilateral A'B'C'D'.

Are quadrilaterals ABCD and A'B'C'D' congruent?Why or why not?

No, they are not congruent. ABCD wastranslated to form A'B'C'D'.

Yes, they are congruent. ABCD wastranslated to form A'B'C'D'.

No, they are not congruent. ABCD wasreflected to form A'B'C'D'.

Yes, they are congruent. ABCD wasreflected to form A'B'C'D'.

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15) Ethan is proving the Exterior Angle Theorem, which states that the measure of anexterior angle of a is equal to the sum of the measures of the two remotetriangle interior angles.

Given: Triangle on line segment ABC AD

Prove: m + m = m A B BCD

StatementReason

1. on line segment ABC AD 1. given

2. m + m + m = 180°A B BCA 2. Angle Sum Theorem

3. and form a linear pairBCA BCD 3. definition of a linear pair

4. and areBCA BCD supplementary.

4. If two angles form a linear pair,then they are supplementary.

5. ? 5. definition of supplementary angles

6. m + m + m = m +A B BCA BCA m BCD

6. substitution property of equality

7. m + m = m A B BCD 7. subtraction property of equality

What statement should Ethan Step 5 to complete the proof?add at

m =BCA m BCD

m <BCA m BCD

m +BCA m =BCD 90°

m +BCA m =BCD 180°

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16) Noah is a proof to show that opposite sides of parallelograms arewriting congruent.

Given: is a parallelogram. PQRS

Prove:

Which statement should Noah step 4?add at

17) What is the precise definition of an angle?

two rays that share a common endpoint

two line segments that share a common endpoint

the measure of an arc between two intersecting lines or line segments

one of the four intermediate spaces formed between two intersecting lines

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18) Use the graph to answer the question.

Olivia reflects the triangle over the -axis, then rotates itx 90° clockwise around the origin.

Which graph shows the resulting triangle?


Which transformation carries the trapezoid itself?onto

reflect over the line = –3x

reflect over the line = –3y

reflect over the line = 3x

reflect over the line = 3y

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20) Lucy draws a line on a coordinate plane.

Which transformation will result in a line perpendicular to Lucy’s line?always

reflect over the line = y x

rotate 270° clockwise around the origin

reflect over the -axis, and then reflect over the -axisx y

dilate by a factor of 2 with the origin as the center of dilation


What is the result of rotating the triangle 90°counterclockwise around the point (2, -1)?

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22) Rosa is proving this theorem:

Angles supplementary to the same angle congruent. are

Given: and are supplementary.

and are supplementary.

Prove:

The table shows the statements and reasons for Rosa’s proof, but they are out oforder.

What is the correct order for these statements and reasons?

3, 1, 5, 4,2

3, 5, 2, 1,4

3, 1, 5, 2,4

3, 5, 1, 2,4

23) A spherical marble has a diameter of 2 centimeters. What is the volume of the marble?

cubic centimeters

cubic centimeters

cubic centimeters

cubic centimeters

24) A waffle cone for ice cream has a diameter of 8 centimeters and a height of 12 centimeters. Whatis the volume of the cone, in cubic centimeters?

32 cubic centimeters




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25) What is the volume of this square pyramid?

18 cubic inches

54 cubic inches

108 cubic inches

324 cubic inches

26) A cone has a height of 45 centimeters and a radius of 6 centimeters. What is the estimate for thebest volume of the cone?



1,700 cubic centimeters

4,200 cubic centimeters

27) Which three-dimensional figure could have a rectangular cross-section?

cone

cylinder

tetrahedron

pentagonal pyramid

28) Which shape could be the intersection of a cone and a plane?not

circle

ellipse

parabola

rectangle

29) Claude has a piece of cheese in the shape of a cone. He uses a straight cut to slice off a smaller piece.Which shape could be one of the faces of Claude’s smaller piece of cheese?

ellipse

square

pentagon

parallelogram

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30) What is the name of the conic section shown by the shaded region?

circle

ellipse

parabola

hyperbola

31) A plane intersects this double cone in the center.

What is the description of the intersection?best

a point an ellipse

a circle a parabola

32) A plane intersects a cone such that the plane is parallel to the base of the cone. Which conic section isformed by this intersection?

a line

a circle

an ellipse

a parabola

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33) Use the diagram of the ice cream cone to answer the question.

The cone is completely filled with ice cream. There is a half sphere of ice cream on top.

What is the total volume of ice cream in cubic inches?

6.8 35.6

8.9 52.4


The rectangle is rotated around the dashed line.

What three-dimensional shape shows the path of this rotation?

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35) Monica graphed the line = 3 + 2. Janice graphs a second line that is parallel to Monica’s andy x passes through (-2, 0). What is the equation of Janice’s line?

= 3 + 6y x

= 3 – 6y x

= - – y x

= - + 2y x

36) What is the equation of the line that is perpendicular to this line and passes through (-6, -2)?

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37) Mario drew this line.

He wants to draw a second line that is parallel to the first and passes through (4,-5). What is the equation of Mario’s second line?

= –y x

8

= y x

+ 8

= - y x

–

= - y x

+

38) This graph represents the path of a ball rolling on a table.

A second ball rolls on the table parallel to the first ball. The path passes through (-2,1). What is the equation of the path of the second ball?

= 1y

= -2y

= 1x

= -2x

39)

The equation of line is = - – . What is the equation of the line that is perpendicular to line k y x k

and passes through (0, 0)?

= -8 y x

= -5 y x

= 5 y x

= 8 y x

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40) Which equation represents a line that passes through (9, 5) and is perpendicular to this line?

41) What is the equation of the line that is parallel to line and passes through (8,m -7)?

= - –y x 15

= - – 1y x

= – 15y x

= – 1y x

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42) Line contains thea points (-4, -2) and (-1,4). Line is parallel tob line but contains thea point (0, 2).

Which graph correctlyshows line ?b

43) Ron graphed 4 different lines that all had the same slope. Which statement describes Ron’scorrectly lines?

None of the lines intersect each other.

Exactly 2 lines intersect each other.

Exactly 3 lines intersect each other.

All of the lines intersect each other.

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44) This map shows the locations of the post office and the water department.

The fire station is located at point (0, 0). If the post office, fire station, and waterdepartment were connected to form a triangle, what would be the perimeter of thetriangle? Round your answer to the nearest tenth.

11.7units

18.4units

22.9units

38.3units

45) The equation of a circle is .x 2 + y 2 – 4 x + 2 y = 11

What are the coordinates of the center of the circle?

(–4, 2)

(–2, 1)

(2, –1)

(4, –2)

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46) Rita wants to prove or disprove that the point lies on the( , 4) –1 circle centered at and containing the point . Her(3, 1) (3, ) –4 reasoning is shown in the informal proof below.

1. If the distance from to is the same as the distance(3, ) –4 (3, 1)

from to , then lies on the circle. (3, ) –4 ( , 4) –1 ( , 4) –1

2. The distance from to is 5. (3, 1) (3, ) –4

3. The distance from to can be found using the(3, ) –4 ( , 4) –1

distance formula, as shown below.

4.

5.

6.

7.

8. 9. Therefore, does not lie on the circle. ( , 4) –1

What is the error in Rita’s reasoning?

In step 1, she comparesthe distances betweenthe wrong pairs of points.

In step 2, she incorrectlycalculates the distancebetween and (3, 1) (3, –4) .

In step 4, she makes asign error.

In step 5, she simplifiesincorrectly.


Nadia draws a line that is perpendicular to the line on the graph and goesthrough the point . (–6, –2)

What is the equation of Nadia’s line?

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48) Line segment is shown on the graph. AB

Emily draws point on the line so that the of AC to CB is 3 to 1. What are theC segment ratio coordinates of point C?

(-2, 2.5) (3, 0)

(-1, 2) (4, -0.5)


What is the perimeter of the triangle? Round to the nearest tenth.

19.1

22.4

29.6

31.4

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50) Bob is trying to describe a sphere to his little brother. Bob decides to go through his toys to findexamples of spheres. Which of the following would be a good representation of a sphere?not

a basketball

a baseball

a tennis ball

a football

51) Mr. Jones is trying to use a geometric shape to describe a tree trunk. Which shape would best describea tree trunk?

a cylinder

a sphere

a cube

a cone

52) Timmie just finished a roll of paper towels. What shape is the paper towel roll?

a cone

a sphere

a cube

a cylinder

53)The trunk of a pine tree will be cut up to make boards.

The trunk is 52 feet long.The base of the trunk is a circle 1.5 feet across.The trunk tapers gradually to a point at the top.

Which expression best models the volume of the trunk?

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54) Mr. Sanchez owns a square field. The side lengths are 0.9 kilometers. There are 1,980 prairie dogburrows in the field.

What is the approximate density of prairie dog burrows in burrows per square kilometer?

1,604

1,782

2,200

2,444

55) Apply a dilation with a scale factor of 3 to triangle ABC. Let the image be triangle A’B’C’. Which one ofthe following equations is true?

56) The coordinates for the endpoints of are L (-2, -3) and M (4, 5). is dilated by a scale factor of ( LM LM from center of dilation (3, -2) to form Segment . Which statement is true?1/ 2) L M not

is parallel to Segment .Segment L M LM

The length of Segment is twice the length of Segment .L M LM

The length of Segment is one-half the length of .L M Segment LM

The slope of is the same as the slope of .Segment L M Segment LM

57) The coordinates for the endpoints of are A (1, 3) and B (5, 0). is dilated by aSegment AB Segment AB scale factor of 3 with the origin as the center of dilation to create Segment . Which of the followingA B will be the slope of ?Segment A B

(3/ 4)

(4/ 3)

(- 3/ 4)

Slope of cannot be determined from the information provided.Segment A B

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58) Use the diagram of two triangles shown below to answer this question.

Triangles ACD and ABE are similar. What is equal to?x

30.0 cm

4.8 cm

14.4 cm

10.0 cm

59)

Triangles and are similar. ABC DEF

What is the measure of angle , rounded to the nearest tenth?C

25.8°

42.0°

64.1°

90.0°

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60) Triangle is similar to triangle . ABC DEF

What is the length of side ?FD

6 cm

12 cm

17 cm

18 cm

61) A 27-foot ladder leans against a building. It is 14 feet from the base of the building. What is themeasure of the angle formed by the ladder and the building rounded to the nearest tenth?

27.4°

31.2°

58.8°

62.6°

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62) How are these two triangles related?

congruent by side-side-side

congruent by side-angle-side

congruent by angle-side-angle

similar but not congruent

63) These triangles are similar.


6.00

6.25

9.00

10.50

64) Howard draws two similar triangles.

How long is the third side of the smaller triangle?

8 centimeters

9 centimeters

22 centimeters

24 centimeters

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65) Triangle is similar to triangle . XYZ LMN

How long is side ?MN

2 centimeters

4 centimeters

8 centimeters

16 centimeters

66) Ms. Castille is about 6 feet tall. At 3:00 her shadow is 8 feet long and the tree’s shadow 20 is feetP.M. long.

About how tall is the tree?

15 feet

18 feet

22 feet

24 feet

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67) Which fraction represents the value of cos ? x

68) What is the tangent of angle in this rectangle?x

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69) What is the sine of angle ?x

70) Triangle is a right triangle.PQR

What is tan , to the nearest hundredth?Q

0.60

0.75

0.80

1.33

71) Right triangle has leg with a length of 12 centimeters and leg with a length of 16FGH FG GH centimeters. To the nearest whole degree, what is the measure of angle ?GHF

37°

45°

53°

90°

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72) A 60-foot flagpole was placed in front of a post office, perpendicular to the ground. After many years,the flagpole began to lean. The distance from the top of the flagpole to the ground is now 50 feet.Which expression shows how to determine the angle the flagpole makes with the ground?

sin A =

cos A =

sin A =

cos A =

73) A cyclist pedals up a hill that has a 13° angle. If the cyclist pedals up the hill for 10 kilometers, what isthe change in her elevation, ?x

0.22 kilometer

2.2 kilometers

9.7 kilometers

45.0 kilometers

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74) Mr. Anderson bought a flagpole at a hardware store. He tilts the flagpole so it will fitthrough the doorway of the store.

What is the distance between the floor and the top of the doorway, rounded to thenearest tenth of a foot?

8 feet

13.2 feet

16.6 feet

22 feet

75) Maddie throws a baseball from third base to first base. The four 90-foot lines between the bases form asquare. Which number is the

best estimate of how far Maddie throws the baseball?

90 feet 130 feet

150 feet 180 feet

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76) Which fraction is equal to the cosine of ?x

77) This right triangle has side lengths , , and .r s t

What is the tangent of angle ?x

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78)

Use the diagram to answer the question.

What is the distance between Tavia’s house and the gas station in this diagram?

3.4 meters

3.6 meters

27.5 meters

29.2 meters

79) Javier built this skateboard ramp.

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

6 feet 8 feet

10 feet 12 feet

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80) What is the value of , rounded to the nearest tenth? x

2.6 centimeters

3.3 centimeters

5.3 centimeters

6.8 centimeters

81) What is the measure of angle , rounded to the nearest hundredth?x

23.96°

26.39°

63.61°

66.04°

82) Which measurement is closest to the value of ?x

0.11 foot

0.14 foot

3.6 feet

4.6 feet

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83) What is the measure of angle ? x

32.3°

39.2°

50.8°

63.2°

84) This list shows the lengths of the sides of a right triangle.

leg = 10 metersleg = 3 metersx hypotenuse = 26 meters


4

8

12

14

85) What is the perimeter of this right triangle?

300 millimeters

420 millimeters

720 millimeters

840 millimeters

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Which graph shows the line segment pictured above after

it has been dilated by a scale factor of with a center of

dilation of (2, 4)?

87) Caleb draws triangle ABC on the coordinate grid. Then he transforms triangle ABC, producing triangle . Triangles ABC and are similar, but not congruent. A'B'C' A'B'C'

Which transformation of triangle ABC could produce this result?

dilate by a factor of 3

reflect over the line = y x

rotate 180° around the origin

stretch vertically by a factor of 3

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Triangle is congruent to triangle . ABF EDF

What is the measure of angle ?FAE

28°

38°

56°

86°


The value of the tangent of angle is defined as . x

Which fact makes it possible to define the tangent of an angle?

The sum of the interior angles of a triangle equals 180°.

The angle and side measurements of congruent right triangles are equal.

All right triangles that share one congruent acute angle are similar, and therefore have equalside ratios.

For all right triangles that share one congruent acute angle, the other acute angle is alsocongruent.

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90) Use the triangle to answer the question.

Which equation shows a correct relationship of trigonometric functions?

91) The house shown below has a symmetrical roof.

What is the measure of the angle the roof makes at the peak (angle )?x

53.1°

73.7°

102.6°

106.3°

1. 2. 3.

92) The directions for constructing a figure inscribed in a circle are given below:

Given a circle, create a diameter.Construct a perpendicular bisector of the diameter.Draw line segments between the adjacent points on the circle generated by construction of thediameter and the perpendicular bisector.

Select the figure that would be constructed using these directions.

equilateral triangle

regular hexagon

right triangle

square

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93) Which of the following formulas would be most appropriate to calculate the volume of a water hose?

r 2 h

lwh

(4/ 3) r 3

(1/ 3) r 2h

94) A small rectangular pyramid-shaped metal object made of a single metal is found in an archaeologicaldig. Because of the metals available to the area’s inhabitants at the time, scientists believe the metalcould be either iron, lead, nickel, or silver. The weight of the object is 612.4 grams. The rectangularbase of the pyramid is 3 cm by 6 cm and the height is 9 cm. The density for each metal is shownbelow:

Iron: 7.874 grams/cm 3

Lead: 11.34 grams/cm 3

Nickel: 8.908 grams/cm 3

Silver: 10.49 grams/cm 3

Select the metal shown below that was used to construct the small rectangular pyramid-shaped metalobject found in the archaeological dig.

iron

lead

nickel

silver

95) Armando designs a suspension bridge. He makes this drawing to show its size.

After the bridge is built, Armando is asked to design another bridge. The second bridge needs to havea similar shape to Armando’s first bridge, but it only needs to be 184-feet long. How tall does thesecond bridge need to be?

32 feet

36 feet

40 feet

44 feet

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96) Use the triangle on the grid below to answer this question.

Triangle LMN is reflected across the Then it is reflected across the .x -axis. y -axis Finally, it is translated according to the rule . What are the final( x + 7, y + 3) coordinates of point M'?

(4, -4)

(-3, -7)

(10, 10)

(-10,-10)

97) Triangle is translated according to the rule .HJK

What are the coordinates of vertex after this translation?H

(-3, 3)

(-2, 1)

(1, -2)

(3, -3)

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98) Darnelle drew this figure and the accompanying equations.

+ + = 180 w x y + = 180 y z

Which equation also be true?must

+ = 180w z

– = y x w

+ + = 180w x z

+ = w x z


Which set of coordinates describes the transformations that map FGH to F'G'H' ?

( , ) ( – 6, – x y x y )

( , ) (– , –x y x y 2)

( , ) ( – 6, –x y x y 2)

( , ) ( – 6, –x y x y 8)

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100) Which statement explains why all circles are similar?

There are 360° in every circle.

The ratio of the circumference of a circle to its diameter is same for every circle.

The diameter of every circle is proportional to the radius.

The inscribed angle in every circle is proportional to the central angle.

I. II.

III. IV. V.

VI.

101) ABC is transformed to create A'B'C'. After the transformation, ABC A'B'C'. Which of the followingtransformations could have been used to create A'B'C' ?

( , ) ( + 3, )x y x y ( , ) (4 , 4 )x y x y ( , ) (– , )x y x y ( , ) ( , – )x y y x ( , ) (–2 , )x y x y ( , ) ( , )x y x y

I, II, V and VI only

II, III, IV, V, and VI only

III, IV, and V only

I, III, and IV only

102) Point A is located at (2, 1). The point is reflected over the line to obtain image point A'. What arey = –x the coordinates of point A'?

(–1, –2)

(–2, 1)

(1, 2)

(-2, –1)

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Zhan cut a drinking straw into three pieces (shown above) to investigate a triangle postulate. He movesthe straw pieces to make triangles that have been translated, rotated, and reflected from an originalposition. The end of one piece is always touching the end of another piece.

Which postulate could Zhan be investigating using only these straw pieces and no other tools?

The sum of the measures of the interior angles of all triangles is 180°.

If three sides of one triangle are congruent to three sides of a second triangle, then the trianglesare congruent.

The sum of the squares of the lengths of the two shorter sides of a triangle is equal to thesquare of the length of the longest side of a triangle.

If two sides and the included angle of one triangle are congruent to two sides and the includedangle of a second triangle, then the triangles are congruent.

104)Triangle is an isosceles triangle with congruent to . To prove that the baseLMN

angles and are congruent, is drawn such that point is the midpoint of asP shown in the diagram below. Complete the proof.

Given: in

is the midpoint of P

Prove:

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105) The triangle angle sum theorem states that the sum of the three interior angles of

a triangle is 180 degrees. Line is parallel to and passes through point .d C An incomplete proof is provided below the diagram.

Given: Line is parallel to d

Prove: 1 + 2 + 3 = 180 m m m

Which reason would be needed to complete this proof?

Correspondinganglestheorem

Same sideinterior anglestheorem

Alternateexterioranglestheorem

Alternateinterior anglestheorem

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106) Quadrilateral is a parallelogram. is a diagonal of the parallelogram. AnABCD Segment BD incomplete proof is provided below the diagram.

Given: Parallelogram ABCD

Prove: is congruent to . A C

Which statement and reason correctly complete this proof?

Statement: and

Reason: Alternate interior angles theorem

Statement: and

Reason: definition of parallelogram

Statement: and

Reason: definition of parallelogram

None of the above would properly completethe proof.

107) The diagonals of rectangle LMNP intersect at point Q.

Which method would be to use to prove that the diagonals bisect each other?best

LNM NLP by ASA

LNM NLP by SSS

LMQ NPQ by ASA

LQP NQM by SSS

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Daya is drawing a square inscribed in a circleusing a compass and a straightedge. Her first twosteps are shown.

Which is the step for Daya to do next?best

109) Use the figures to answer the question.

Sasha derived the formula for the volume ofa square pyramid. She started by dividing acube into 6 identical square pyramids. Thetop vertex of each pyramid meets at thecentral point in the cube, with the cube’sdiagonals as the edges.

= the volume of a pyramid; = side lengthV s of base, = height of pyramid h

The steps of Sasha’s work are shown. Step 1: 6V= s 3

Step 2: V= ( 1/ 6) s 3

Maggie also derived the formula for volumeof a square pyramid. Maggie’s result is . V= ( 1/ 3) s 2 h

The formulas derived by Sasha and Maggiecan both be used to correctly calculate thevolume of a square pyramid.

What are the best next steps for Sasha totake to prove that either formula can beused to find the volume of a squarepyramid?

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110) A square prism and a square pyramid have the same base area ( ), but the height of the squareBpyramid is twice the height of the prism.

If represents the height of the prism, find the formula that could be used to calculate the volume ofh the square pyramid.

V = Bh

V = 2hB

V = ( 1/ 3) B h

V = ( 2/ 3) B h

111) A square pyramid and a cone have the same base area. The volume of the cone is 100 cm , and the3

height of the cone is 15 cm. The height of the square pyramid is 24 cm.

Find the volume of the square pyramid to the nearest whole unit.

144 cm 3

160 cm 3

480 cm 3

2400 cm 3

112) The linear equation for a line that includes Segment RQ is 2 – = –3 . x y

If the perpendicular bisector of segment RQ passes through the point (0,8), find the linear equation ofthe perpendicular bisector.

– 2 = 16y x

2 + = 16y x

2 + = 8y x

– 2 = 8y x

113) Lauren graphed the linear equation . She wants to graph a line that is parallel to her original4y-3x=16 line and passes through the point (8, 6).

Which of the following would meet those criteria?

(4/ 3) y = x

y - ( 3/ 4) x = 3.5

- ( 3/ 4) y=x

y + ( 4/ 3) x=3.5

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Point is drawn on the line segment so that the ratio of to is 5 to 1.G FG GH

What are the coordinates of point ?G

(4, 4.6)

(4.5, 5)

(–5.5, –3)

(–5, –2.6)

115) Use the diagrams to answer the question.

Based on the two diagrams shown, which formula would be to use to estimate the volume of Citybest Park Pond?

V= r 2 h V= ( 1/ 3) Bh

V= ( 2/ 3) r 3 V= ( 1/ 3) r 2 h

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116) Brittany has designed four different birdcages, each with the same volume: a square pyramid, acylinder, a cone, and a sphere. The zoo wants to use one of Brittany’s designs but plans to change thevolume of the cage.

Find the design change that would result in the birdcage with the greatest volume.

Increase the area of the base of the square pyramid by a factor of ten.

Increase the height of the cylinder by a factor of ten.

Increase the radius of the cone by a factor of ten.

Increase the radius of a sphere by a factor of ten.

117) Juan wants to build a greenhouse in his back yard. He needs to maximize the ratio of floor area tostructure volume in order to provide the most room for plants while minimizing the area to be heated.

Find the description of the structure that best meets Juan’s criteria.

A hemisphere with a diameter of 12 feet

A cube with a side length of 12 feet

A cone with a diameter of 12 feet and a height of 10 feet

A square pyramid with a base side length of 12 feet and a height of 9 feet

118) Use the graph and flow chart to answer the question.

Kamal dilates triangle to get triangle . He knows that theABC A'B'C' triangles are similar because of the definition of similarity transformations.He wants to demonstrate the angle-angle similarity postulate by proving

and . Kamal makes this incomplete flow chartBAC B'A'C' ABC A'B'C' proof.

What reason should Kamal add at all of the question marks in order tocomplete the proof?

Two non-verticallines have the sameslope if and only ifthey are parallel.

Anglessupplementary tothe same angle orto congruent anglesare congruent.

If two parallel linesare cut by atransversal, theneach pair ofcorrespondingangles is congruent.

If two parallel linesare cut by atransversal, theneach pair ofalternate interiorangles is congruent.

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119) Adnan states if cos 30° 0.866, then sin 30° 0.866.

Which justification correctly explains whether or not Adnan is correct?

Adnan is correct because cos x° and sin x° are always equivalent in any right triangle.

Adnan is correct because cos x° and sin x° are only equivalent in a 30°-60°-90° triangle.

Adnan is incorrect because cos x° and sin (90 - x)° are always equivalent in any right triangle.

Adnan is incorrect because only cos x° and cos (90 - x)° are equivalent in a 30°-60°-90° triangle.

120) A six-sided number cube has numbers 1, 2, 3, 4, 5, and 6. Which of the following is another way todescribe the event of rolling an even number?

rolling a 2 or 4

rolling a 2 and 4 and 6

rolling a 1 or 3 or 5

not rolling a 1 or 3 or 5

121) A fair six-sided number cube (numbered 1-6) is rolled. If you know that the number rolled is odd, whatis the probability that it is either a 3 or a 5?

(1/ 6)

(2/ 6)

(2/ 3)

(2/ 2)

122) Given these probabilities:

, , , , , P ( A ) = ( 1/ 2) P ( B ) = ( 1/ 3) P ( C ) = ( 1/ 4) P ( A and B ) = ( 1/ 3) P ( A and C ) = ( 1/ 6) P ( B and C ) = ( 1/ 12)

Which pair of events represents independent events?

and A B

and A C

and B C

not enough information provided to determine independence

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123) A fair six-sided number cube (numbered 1-6) is rolled. If the number rolled is greater than 2, what is theprobability that the number rolled is less than 5?

(4/ 6)

(2/ 6)

(4/ 5)

(2/ 4)

124) A researcher is investigating a possible link between diabetes and leukemia. She collected data from113,572 people without diabetes and from 52,421 people with diabetes. The researcher wasspecifically looking for a large number of people with diabetes; therefore, the number of people withand without diabetes cannot be used to determine the prevalence of diabetes. Out of the113,572 people without diabetes, 13 had been diagnosed with leukemia. Out of the people withdiabetes, 6 had been diagnosed with leukemia. Based on this information, which of the followingstatements is true?

Diabetes and leukemia appear to be independent because .

Diabetes and leukemia are not independent because one group had 13 people with leukemiaand the other only had 6 people with leukemia.

Diabetes and leukemia are not independent because .

There is not enough information given to determine if diabetes and leukemia are independent.

125) The cafeteria manager surveys 100 randomly selected high school students to see if they would prefera traditional Thanksgiving meal on the Friday before Thanksgiving or if they would prefer a hamburgerand fries. Twenty-eight of the students surveyed are Juniors, and ten Juniors voted for a traditionalmeal. Sixty-one total students voted for the traditional meal.

If a student from the school is selected at random, what is the probability that the student is either aJunior or prefers a traditional Thanksgiving meal?

0.61

0.79

0.89

0.99


Which of the following statements about the independence of Juniors and selecting the traditional mealis most accurate?

Being a Junior and food selection independent events because .are 10 100 28 61

Being a Junior and food selection independent events because .are 10 28 61 100

Being a Junior and food selection independent events because .are not 10 100 28 61

Being a Junior and food selection independent events because .are not 10 28 61 100

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Copyright © 2013-2014 Data Recognition Corporation.


If a randomly selected student from the school chose the hamburger and fries, what is the probabilitythat the student is a Junior? not

72 100

39 100

21 39

21 72

128) Five hundred randomly selected Louisiana high school graduates who played football were surveyedand asked if they had sustained a concussion while playing football in high school. Of those surveyed,214 players reported having sustained a concussion at some point during high school. Which of thefollowing statements is true based on this data?

A randomly selected Louisiana high school graduate who played football has approximately a42.8% chance of having sustained a concussion in high school while playing football.

A randomly selected Louisiana high school graduate who has sustained a concussion hasapproximately a 42.8% chance of having been a football player in high school.

Exactly 42.8% of all high school graduates who played football in Louisiana have sustained aconcussion.

Exactly 42.8% of all high school graduates in Louisiana have sustained a concussion.

129) A six-sided number cube has numbers 1, 2, 3, 4, 5 and 6. Which of the following is another way todescribe the event of rolling an even number?

rolling a 2 or 4

rolling a 2 and 4 and 6

rolling a 1 or 3 or 5

not rolling a 1 or 3 or 5

eoc final practice/review subject: mathematics,...

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