The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (COMMON CORE )
Wednesday, August 17, 2016 — 8:30 to 11:30 a.m.
MODEL RESPONSE SET
Table of Contents
Question 25 . . . . . . . . . . . . . . . . . . . 2
Question 26 . . . . . . . . . . . . . . . . . . . 6
Question 27 . . . . . . . . . . . . . . . . . . 13
Question 28 . . . . . . . . . . . . . . . . . . 18
Question 29 . . . . . . . . . . . . . . . . . . 22
Question 30 . . . . . . . . . . . . . . . . . . 28
Question 31 . . . . . . . . . . . . . . . . . . 32
Question 32 . . . . . . . . . . . . . . . . . . 36
Question 33 . . . . . . . . . . . . . . . . . . 44
Question 34 . . . . . . . . . . . . . . . . . . 52
Question 35 . . . . . . . . . . . . . . . . . . 58
Question 36 . . . . . . . . . . . . . . . . . . 65
Question 25
25 Lines AE and BD are tangent to circles O and P at A, E, B, and D, as___
shown in the diagram below.
If AC:CE ⫽ 5:3, and BD ⫽ 56, determine and state the length of CD.
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[2]
Question 25
25 Lines AE and BD are tangent to circles O and P at A, E, B, and D, as___
shown in the diagram below.
If AC:CE ⫽ 5:3, and BD ⫽ 56, determine and state the length of CD.
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[3]
Question 25
25 Lines AE and BD are tangent to circles O and P at A, E, B, and D, as___
shown in the diagram below.
If AC:CE ⫽ 5:3, and BD ⫽ 56, determine and state the length of CD.
Score 1:
___
The student substituted incorrectly and found the length of CB.
Geometry (Common Core) – Aug. ’16
[4]
Question 25
25 Lines AE and BD are tangent to circles O and P at A, E, B, and D, as___
shown in the diagram below.
If AC:CE ⫽ 5:3, and BD ⫽ 56, determine and state the length of CD.
Score 0:
The student did not show enough relevant correct work to receive any credit.
Geometry (Common Core) – Aug. ’16
[5]
Question 26
26 In the diagram below, ABC has coordinates A(1,1), B(4,1), and C(4,5). Graph and label
A⬙B⬙C⬙, the image of ABC after the translation five units to the right and two units up
followed by the reflection over the line y ⫽ 0.
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[6]
Question 26
26 In the diagram below, ABC has coordinates A(1,1), B(4,1), and C(4,5). Graph and label
A⬙B⬙C⬙, the image of ABC after the translation five units to the right and two units up
followed by the reflection over the line y ⫽ 0.
y
C
A
Score 2:
B
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[7]
x
Question 26
26 In the diagram below, ABC has coordinates A(1,1), B(4,1), and C(4,5). Graph and label
A⬙B⬙C⬙, the image of ABC after the translation five units to the right and two units up
followed by the reflection over the line y ⫽ 0.
y
Score 1:
The student made an error by graphing the reflection and then the translation.
Geometry (Common Core) – Aug. ’16
[8]
Question 26
26 In the diagram below, ABC has coordinates A(1,1), B(4,1), and C(4,5). Graph and label
A⬙B⬙C⬙, the image of ABC after the translation five units to the right and two units up
followed by the reflection over the line y ⫽ 0.
Score 1:
The student made an error by translating five units to the left.
Geometry (Common Core) – Aug. ’16
[9]
Question 26
26 In the diagram below, ABC has coordinates A(1,1), B(4,1), and C(4,5). Graph and label
A⬙B⬙C⬙, the image of ABC after the translation five units to the right and two units up
followed by the reflection over the line y ⫽ 0.
Score 1:
The student made an error by reflecting over the y-axis.
Geometry (Common Core) – Aug. ’16
[10]
Question 26
26 In the diagram below, ABC has coordinates A(1,1), B(4,1), and C(4,5). Graph and label
A⬙B⬙C⬙, the image of ABC after the translation five units to the right and two units up
followed by the reflection over the line y ⫽ 0.
y
C
A
Score 1:
B
x
The student performed the sequence of transformations algebraically.
Geometry (Common Core) – Aug. ’16
[11]
Question 26
26 In the diagram below, ABC has coordinates A(1,1), B(4,1), and C(4,5). Graph and label
A⬙B⬙C⬙, the image of ABC after the translation five units to the right and two units up
followed by the reflection over the line y ⫽ 0.
Score 0:
The student graphed the sequence of transformations incorrectly.
Geometry (Common Core) – Aug. ’16
[12]
Question 27
27 A regular hexagon is rotated in a counterclockwise direction about its center. Determine and state
the minimum number of degrees in the rotation such that the hexagon will coincide with itself.
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[13]
Question 27
27 A regular hexagon is rotated in a counterclockwise direction about its center. Determine and state
the minimum number of degrees in the rotation such that the hexagon will coincide with itself.
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[14]
Question 27
27 A regular hexagon is rotated in a counterclockwise direction about its center. Determine and state
the minimum number of degrees in the rotation such that the hexagon will coincide with itself.
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[15]
Question 27
27 A regular hexagon is rotated in a counterclockwise direction about its center. Determine and state
the minimum number of degrees in the rotation such that the hexagon will coincide with itself.
Score 1:
The student found the measure of one interior angle of the hexagon.
Geometry (Common Core) – Aug. ’16
[16]
Question 27
27 A regular hexagon is rotated in a counterclockwise direction about its center. Determine and state
the minimum number of degrees in the rotation such that the hexagon will coincide with itself.
Score 0:
The student had a completely incorrect response.
Geometry (Common Core) – Aug. ’16
[17]
Question 28
28 In ___
the diagram of ABC shown below, use a compass and straightedge to construct the median
to AB . [Leave all construction marks.]
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[18]
Question 28
28 In ___
the diagram of ABC shown below, use a compass and straightedge to construct the median
to AB . [Leave all construction marks.]
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[19]
Question 28
28 In ___
the diagram of ABC shown below, use a compass and straightedge to construct the median
to AB . [Leave all construction marks.]
Score 1:
The student had a correct construction of a perpendicular bisector, but did not draw the
median.
Geometry (Common Core) – Aug. ’16
[20]
Question 28
28 In ___
the diagram of ABC shown below, use a compass and straightedge to construct the median
to AB . [Leave all construction marks.]
Score 0:
The student made a drawing that was not a construction.
Geometry (Common Core) – Aug. ’16
[21]
Question 29
29 Triangle MNP is the image of triangle JKL after a 120° counterclockwise rotation about point Q.
If the measure of angle L is 47° and the measure of angle N is 57°, determine the measure of
angle M. Explain how you arrived at your answer.
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[22]
Question 29
29 Triangle MNP is the image of triangle JKL after a 120° counterclockwise rotation about point Q.
If the measure of angle L is 47° and the measure of angle N is 57°, determine the measure of
angle M. Explain how you arrived at your answer.
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[23]
Question 29
29 Triangle MNP is the image of triangle JKL after a 120° counterclockwise rotation about point Q.
If the measure of angle L is 47° and the measure of angle N is 57°, determine the measure of
angle M. Explain how you arrived at your answer.
Score 1:
The student wrote a correct explanation, but the angle measure was incorrect.
Geometry (Common Core) – Aug. ’16
[24]
Question 29
29 Triangle MNP is the image of triangle JKL after a 120° counterclockwise rotation about point Q.
If the measure of angle L is 47° and the measure of angle N is 57°, determine the measure of
angle M. Explain how you arrived at your answer.
Score 1:
The student did not write an explanation.
Geometry (Common Core) – Aug. ’16
[25]
Question 29
29 Triangle MNP is the image of triangle JKL after a 120° counterclockwise rotation about point Q.
If the measure of angle L is 47° and the measure of angle N is 57°, determine the measure of
angle M. Explain how you arrived at your answer.
Score 1:
The student had an incomplete explanation.
Geometry (Common Core) – Aug. ’16
[26]
Question 29
29 Triangle MNP is the image of triangle JKL after a 120° counterclockwise rotation about point Q.
If the measure of angle L is 47° and the measure of angle N is 57°, determine the measure of
angle M. Explain how you arrived at your answer.
Score 0:
The student had a completely incorrect response.
Geometry (Common Core) – Aug. ’16
[27]
Question 30
30 A circle has a center at (1,–2) and radius of 4. Does the point (3.4,1.2) lie on the circle?
Justify your answer.
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[28]
Question 30
30 A circle has a center at (1,–2) and radius of 4. Does the point (3.4,1.2) lie on the circle?
Justify your answer.
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[29]
Question 30
30 A circle has a center at (1,–2) and radius of 4. Does the point (3.4,1.2) lie on the circle?
Justify your answer.
Score 1:
The student made a substitution error, but wrote an appropriate conclusion.
Geometry (Common Core) – Aug. ’16
[30]
Question 30
30 A circle has a center at (1,–2) and radius of 4. Does the point (3.4,1.2) lie on the circle?
Justify your answer.
Score 0:
The student had a completely incorrect response.
Geometry (Common Core) – Aug. ’16
[31]
Question 31
31 In the diagram below, a window of a house is 15 feet above the ground. A ladder is placed against
the house with its base at an angle of 75° with the ground. Determine and state the length of the
ladder to the nearest tenth of a foot.
15
ft
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[32]
Question 31
31 In the diagram below, a window of a house is 15 feet above the ground. A ladder is placed against
the house with its base at an angle of 75° with the ground. Determine and state the length of the
ladder to the nearest tenth of a foot.
15
ft
Score 2:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[33]
Question 31
31 In the diagram below, a window of a house is 15 feet above the ground. A ladder is placed against
the house with its base at an angle of 75° with the ground. Determine and state the length of the
ladder to the nearest tenth of a foot.
15
ft
75¡
Score 1:
The student had a correct equation, but solved it incorrectly.
Geometry (Common Core) – Aug. ’16
[34]
Question 31
31 In the diagram below, a window of a house is 15 feet above the ground. A ladder is placed against
the house with its base at an angle of 75° with the ground. Determine and state the length of the
ladder to the nearest tenth of a foot.
15
ft
Score 0:
The student did not show enough relevant correct work to receive any credit.
Geometry (Common Core) – Aug. ’16
[35]
Question 32
32 Using a compass and straightedge, construct and label A⬘B⬘C⬘, the image of ABC after a
dilation with a scale factor of 2 and centered at B. [Leave all construction marks.]
____
___
Describe the relationship between the lengths of AC and A⬘C⬘ .
Score 4:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[36]
Question 32
32 Using a compass and straightedge, construct and label A⬘B⬘C⬘, the image of ABC after a
dilation with a scale factor of 2 and centered at B. [Leave all construction marks.]
____
___
Describe the relationship between the lengths of AC and A⬘C⬘ .
Score 4:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[37]
Question 32
32 Using a compass and straightedge, construct and label A⬘B⬘C⬘, the image of ABC after a
dilation with a scale factor of 2 and centered at B. [Leave all construction marks.]
____
___
Describe the relationship between the lengths of AC and A⬘C⬘ .
Score 3:
The student had a correct construction, but the description was of a correct relationship
other than length.
Geometry (Common Core) – Aug. ’16
[38]
Question 32
32 Using a compass and straightedge, construct and label A⬘B⬘C⬘, the image of ABC after a
dilation with a scale factor of 2 and centered at B. [Leave all construction marks.]
____
___
Describe the relationship between the lengths of AC and A⬘C⬘ .
Score 2:
The student had a correct description, but no further correct work was shown.
Geometry (Common Core) – Aug. ’16
[39]
Question 32
32 Using a compass and straightedge, construct and label A⬘B⬘C⬘, the image of ABC after a
dilation with a scale factor of 2 and centered at B. [Leave all construction marks.]
____
___
Describe the relationship between the lengths of AC and A⬘C⬘ .
Score 2:
The student did not label A⬘ and C⬘ on the construction. The description was
incomplete.
Geometry (Common Core) – Aug. ’16
[40]
Question 32
32 Using a compass and straightedge, construct and label A⬘B⬘C⬘, the image of ABC after a
dilation with a scale factor of 2 and centered at B. [Leave all construction marks.]
____
___
Describe the relationship between the lengths of AC and A⬘C⬘ .
Score 1:
The student made an incorrect construction. The description was incomplete.
Geometry (Common Core) – Aug. ’16
[41]
Question 32
32 Using a compass and straightedge, construct and label A⬘B⬘C⬘, the image of ABC after a
dilation with a scale factor of 2 and centered at B. [Leave all construction marks.]
____
___
Describe the relationship between the lengths of AC and A⬘C⬘ .
Score 1:
The student wrote an incomplete description and the construction was missing.
Geometry (Common Core) – Aug. ’16
[42]
Question 32
32 Using a compass and straightedge, construct and label A⬘B⬘C⬘, the image of ABC after a
dilation with a scale factor of 2 and centered at B. [Leave all construction marks.]
____
___
Describe the relationship between the lengths of AC and A⬘C⬘ .
Score 0:
The construction and description were completely incorrect.
Geometry (Common Core) – Aug. ’16
[43]
Question 33
33 The grid below shows ABC and DEF.
y
E
x
F
A
D
B
C
Let A⬘B⬘C⬘ be the image of ABC after a rotation about point A. Determine and state the
location of B⬘ if the location of point C⬘ is (8,–3). Explain your answer.
Is DEF congruent to A⬘B⬘C⬘? Explain your answer.
Score 4:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[44]
Question 33
33 The grid below shows ABC and DEF.
y
E
x
F
A
D
B
C
Let A⬘B⬘C⬘ be the image of ABC after a rotation about point A. Determine and state the
location of B⬘ if the location of point C⬘ is (8,–3). Explain your answer.
Is DEF congruent to A⬘B⬘C⬘? Explain your answer.
Score 4:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[45]
Question 33
33 The grid below shows ABC and DEF.
y
E
x
F
A
D
B
C
Let A⬘B⬘C⬘ be the image of ABC after a rotation about point A. Determine and state the
location of B⬘ if the location of point C⬘ is (8,–3). Explain your answer.
Is DEF congruent to A⬘B⬘C⬘? Explain your answer.
Score 3:
The student wrote an incomplete explanation for why DEF is congruent to A⬘B⬘C⬘.
Geometry (Common Core) – Aug. ’16
[46]
Question 33
33 The grid below shows ABC and DEF.
y
E
x
F
A
D
B
C
Let A⬘B⬘C⬘ be the image of ABC after a rotation about point A. Determine and state the
location of B⬘ if the location of point C⬘ is (8,–3). Explain your answer.
Is DEF congruent to A⬘B⬘C⬘? Explain your answer.
Score 3:
The student wrote an incomplete explanation for why DEF is congruent to A⬘B⬘C⬘.
Geometry (Common Core) – Aug. ’16
[47]
Question 33
33 The grid below shows ABC and DEF.
y
E
x
F
A
D
B
C
Let A⬘B⬘C⬘ be the image of ABC after a rotation about point A. Determine and state the
location of B⬘ if the location of point C⬘ is (8,–3). Explain your answer.
Is DEF congruent to A⬘B⬘C⬘? Explain your answer.
Score 2:
The student wrote two incomplete explanations.
Geometry (Common Core) – Aug. ’16
[48]
Question 33
33 The grid below shows ABC and DEF.
y
E
x
F
A
D
B
C
Let A⬘B⬘C⬘ be the image of ABC after a rotation about point A. Determine and state the
location of B⬘ if the location of point C⬘ is (8,–3). Explain your answer.
Is DEF congruent to A⬘B⬘C⬘? Explain your answer.
Score 1:
The student wrote yes, but the explanation was incorrect. No further correct work was
shown.
Geometry (Common Core) – Aug. ’16
[49]
Question 33
33 The grid below shows ABC and DEF.
y
E
x
F
A
D
B
C
Let A⬘B⬘C⬘ be the image of ABC after a rotation about point A. Determine and state the
location of B⬘ if the location of point C⬘ is (8,–3). Explain your answer.
Is DEF congruent to A⬘B⬘C⬘? Explain your answer.
Score 1:
The student showed work to find (7,1), and wrote yes, but did not write any explanations.
Geometry (Common Core) – Aug. ’16
[50]
Question 33
33 The grid below shows ABC and DEF.
y
E
x
F
A
D
B
C
Let A⬘B⬘C⬘ be the image of ABC after a rotation about point A. Determine and state the
location of B⬘ if the location of point C⬘ is (8,–3). Explain your answer.
Is DEF congruent to A⬘B⬘C⬘? Explain your answer.
Score 0:
The student had a completely incorrect response.
Geometry (Common Core) – Aug. ’16
[51]
Question 34
34 As modeled below, a movie is projected onto a large outdoor screen. The bottom of the
60-foot-tall screen is 12 feet off the ground. The projector sits on the ground at a horizontal
distance of 75 feet from the screen.
60
12
␪
75
Determine and state, to the nearest tenth of a degree, the measure of ␪, the projection angle.
Score 4:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[52]
Question 34
34 As modeled below, a movie is projected onto a large outdoor screen. The bottom of the
60-foot-tall screen is 12 feet off the ground. The projector sits on the ground at a horizontal
distance of 75 feet from the screen.
60
12
␪
75
Determine and state, to the nearest tenth of a degree, the measure of ␪, the projection angle.
Score 4:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[53]
Question 34
34 As modeled below, a movie is projected onto a large outdoor screen. The bottom of the
60-foot-tall screen is 12 feet off the ground. The projector sits on the ground at a horizontal
distance of 75 feet from the screen.
60
12
␪
75
Determine and state, to the nearest tenth of a degree, the measure of ␪, the projection angle.
Score 3:
The student made a transcription error.
Geometry (Common Core) – Aug. ’16
[54]
Question 34
34 As modeled below, a movie is projected onto a large outdoor screen. The bottom of the
60-foot-tall screen is 12 feet off the ground. The projector sits on the ground at a horizontal
distance of 75 feet from the screen.
60
12
␪
75
Determine and state, to the nearest tenth of a degree, the measure of ␪, the projection angle.
Score 2:
The student made a conceptual error in using an obtuse triangle for right triangle
trigonometry.
Geometry (Common Core) – Aug. ’16
[55]
Question 34
34 As modeled below, a movie is projected onto a large outdoor screen. The bottom of the
60-foot-tall screen is 12 feet off the ground. The projector sits on the ground at a horizontal
distance of 75 feet from the screen.
Determine and state, to the nearest tenth of a degree, the measure of ␪, the projection angle.
Score 1:
The student determined only one angle of elevation.
Geometry (Common Core) – Aug. ’16
[56]
Question 34
34 As modeled below, a movie is projected onto a large outdoor screen. The bottom of the
60-foot-tall screen is 12 feet off the ground. The projector sits on the ground at a horizontal
distance of 75 feet from the screen.
60
12
␪
75
Determine and state, to the nearest tenth of a degree, the measure of ␪, the projection angle.
Score 0:
The student did not show enough correct work to receive any credit.
Geometry (Common Core) – Aug. ’16
[57]
Question 35
___
___
35 Given: Circle O, chords AB and CD intersect at E
C
A
O
E
D
B
Theorem: If two chords intersect in a circle, the product of the lengths of the segments of one
chord is equal to the product of the lengths of the segments of the other chord.
Prove this theorem by proving AE • EB ⫽ CE • ED.
Score 6:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[58]
Question 35
___
___
35 Given: Circle O, chords AB and CD intersect at E
C
A
O
E
D
B
Theorem: If two chords intersect in a circle, the product of the lengths of the segments of one
chord is equal to the product of the lengths of the segments of the other chord.
Prove this theorem by proving AE • EB ⫽ CE • ED.
Score 5:
___ ___ ___
___
The student did not include drawing chords AC, CB, BD, and AD in the proof.
Geometry (Common Core) – Aug. ’16
[59]
Question 35
___
___
35 Given: Circle O, chords AB and CD intersect at E
C
A
O
E
D
B
Theorem: If two chords intersect in a circle, the product of the lengths of the segments of one
chord is equal to the product of the lengths of the segments of the other chord.
Prove this theorem by proving AE • EB ⫽ CE • ED.
Score 4:
The student omitted one statement and reason, and another reason was incomplete.
Geometry (Common Core) – Aug. ’16
[60]
Question 35
___
___
35 Given: Circle O, chords AB and CD intersect at E
C
A
O
E
D
B
Theorem: If two chords intersect in a circle, the product of the lengths of the segments of one
chord is equal to the product of the lengths of the segments of the other chord.
Prove this theorem by proving AE • EB ⫽ CE • ED.
Score 3:
The student had three missing or incomplete statements.
Geometry (Common Core) – Aug. ’16
[61]
Question 35
___
___
35 Given: Circle O, chords AB and CD intersect at E
C
A
O
E
D
B
Theorem: If two chords intersect in a circle, the product of the lengths of the segments of one
chord is equal to the product of the lengths of the segments of the other chord.
Prove this theorem by proving AE • EB ⫽ CE • ED.
Score 2:
The student gave two correct relevant statements and reasons.
Geometry (Common Core) – Aug. ’16
[62]
Question 35
___
___
35 Given: Circle O, chords AB and CD intersect at E
C
A
O
E
D
B
Theorem: If two chords intersect in a circle, the product of the lengths of the segments of one
chord is equal to the product of the lengths of the segments of the other chord.
Prove this theorem by proving AE • EB ⫽ CE • ED.
Score 1:
The student correctly stated the vertical angles were congruent.
Geometry (Common Core) – Aug. ’16
[63]
Question 35
___
___
35 Given: Circle O, chords AB and CD intersect at E
C
A
O
E
D
B
Theorem: If two chords intersect in a circle, the product of the lengths of the segments of one
chord is equal to the product of the lengths of the segments of the other chord.
Prove this theorem by proving AE • EB ⫽ CE • ED.
Score 0:
The student had a completely incorrect response.
Geometry (Common Core) – Aug. ’16
[64]
Question 36
36 A snow cone consists of a paper cone completely filled with shaved ice and topped with a
hemisphere of shaved ice, as shown in the diagram below. The inside diameter of both the cone
and the hemisphere is 8.3 centimeters. The height of the cone is 10.2 centimeters.
8.3 cm
10.2 cm
The desired density of the shaved ice is 0.697 g/cm3, and the cost, per kilogram, of ice is $3.83.
Determine and state the cost of the ice needed to make 50 snow cones.
Score 6:
The student had a complete and correct response.
Geometry (Common Core) – Aug. ’16
[65]
Question 36
36 A snow cone consists of a paper cone completely filled with shaved ice and topped with a
hemisphere of shaved ice, as shown in the diagram below. The inside diameter of both the cone
and the hemisphere is 8.3 centimeters. The height of the cone is 10.2 centimeters.
8.3 cm
10.2 cm
The desired density of the shaved ice is 0.697 g/cm3, and the cost, per kilogram, of ice is $3.83.
Determine and state the cost of the ice needed to make 50 snow cones.
Score 5:
The student found the volume of a sphere and not a hemisphere.
Geometry (Common Core) – Aug. ’16
[66]
Question 36
36 A snow cone consists of a paper cone completely filled with shaved ice and topped with a
hemisphere of shaved ice, as shown in the diagram below. The inside diameter of both the cone
and the hemisphere is 8.3 centimeters. The height of the cone is 10.2 centimeters.
8.3 cm
10.2 cm
The desired density of the shaved ice is 0.697 g/cm3, and the cost, per kilogram, of ice is $3.83.
Determine and state the cost of the ice needed to make 50 snow cones.
Score 5:
The student used an incorrectly rounded total volume of one snow cone when computing
the mass.
Geometry (Common Core) – Aug. ’16
[67]
Question 36
36 A snow cone consists of a paper cone completely filled with shaved ice and topped with a
hemisphere of shaved ice, as shown in the diagram below. The inside diameter of both the cone
and the hemisphere is 8.3 centimeters. The height of the cone is 10.2 centimeters.
8.3 cm
10.2 cm
The desired density of the shaved ice is 0.697 g/cm3, and the cost, per kilogram, of ice is $3.83.
Determine and state the cost of the ice needed to make 50 snow cones.
Score 4:
The student determined the cost of the cone without the hemisphere.
Geometry (Common Core) – Aug. ’16
[68]
Question 36
36 A snow cone consists of a paper cone completely filled with shaved ice and topped with a
hemisphere of shaved ice, as shown in the diagram below. The inside diameter of both the cone
and the hemisphere is 8.3 centimeters. The height of the cone is 10.2 centimeters.
8.3 cm
10.2 cm
The desired density of the shaved ice is 0.697 g/cm3, and the cost, per kilogram, of ice is $3.83.
Determine and state the cost of the ice needed to make 50 snow cones.
Score 3:
The student found the volume of fifty snow cones, but no further correct work was shown.
Geometry (Common Core) – Aug. ’16
[69]
Question 36
36 A snow cone consists of a paper cone completely filled with shaved ice and topped with a
hemisphere of shaved ice, as shown in the diagram below. The inside diameter of both the cone
and the hemisphere is 8.3 centimeters. The height of the cone is 10.2 centimeters.
8.3 cm
10.2 cm
The desired density of the shaved ice is 0.697 g/cm3, and the cost, per kilogram, of ice is $3.83.
Determine and state the cost of the ice needed to make 50 snow cones.
Score 2:
The student made an error in determining the volume of the cone, but found an
appropriate mass of fifty snow cones. No further correct work was shown.
Geometry (Common Core) – Aug. ’16
[70]
Question 36
36 A snow cone consists of a paper cone completely filled with shaved ice and topped with a
hemisphere of shaved ice, as shown in the diagram below. The inside diameter of both the cone
and the hemisphere is 8.3 centimeters. The height of the cone is 10.2 centimeters.
8.3 cm
10.2 cm
The desired density of the shaved ice is 0.697 g/cm3, and the cost, per kilogram, of ice is $3.83.
Determine and state the cost of the ice needed to make 50 snow cones.
Score 1:
The student determined the volume of the cone.
Geometry (Common Core) – Aug. ’16
[71]
Question 36
36 A snow cone consists of a paper cone completely filled with shaved ice and topped with a
hemisphere of shaved ice, as shown in the diagram below. The inside diameter of both the cone
and the hemisphere is 8.3 centimeters. The height of the cone is 10.2 centimeters.
8.3 cm
10.2 cm
The desired density of the shaved ice is 0.697 g/cm3, and the cost, per kilogram, of ice is $3.83.
Determine and state the cost of the ice needed to make 50 snow cones.
Score 0:
The student did not show enough work to receive any credit.
Geometry (Common Core) – Aug. ’16
[72]
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