The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Thursday, January 26, 2017 — 9:15 a.m. to 12:15 p.m., only Student Name: _________________________________________________________ School Name: _______________________________________________________________ Print your name and the name of your school on the lines above. A separate answer sheet for Part I has been provided to you. Follow the instructions from the proctor for completing the student information on your answer sheet. This examination has four parts, with a total of 36 questions. You must answer all questions in this examination. Record your answers to the Part I multiple-choice questions on the separate answer sheet. Write your answers to the questions in Parts II, III, and IV directly in this booklet. All work should be written in pen, except for graphs and drawings, which should be done in pencil. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. The formulas that you may need to answer some questions in this examination are found at the end of the examination. This sheet is perforated so you may remove it from this booklet. Scrap paper is not permitted for any part of this examination, but you may use the blank spaces in this booklet as scrap paper. A perforated sheet of scrap graph paper is provided at the end of this booklet for any question for which graphing may be helpful but is not required. You may remove this sheet from this booklet. Any work done on this sheet of scrap graph paper will not be scored. When you have completed the examination, you must sign the statement printed at the end of the answer sheet, indicating that you had no unlawful knowledge of the questions or answers prior to the examination and that you have neither given nor received assistance in answering any of the questions during the examination. Your answer sheet cannot be accepted if you fail to sign this declaration. GEOMETRY (COMMON CORE) DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN. Notice… A graphing calculator, a straightedge (ruler), and a compass must be available for you to use while taking this examination. GEOMETRY ( COMMON CORE ) The possession or use of any communications device is strictly prohibited when taking this examination. If you have or use any communications device, no matter how briefly, your examination will be invalidated and no score will be calculated for you.
Transcript
The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (Common Core)Thursday, January 26, 2017 — 9:15 a.m. to 12:15 p.m., only
School Name: _______________________________________________________________
Print your name and the name of your school on the lines above.
A separate answer sheet for Part I has been provided to you. Follow theinstructions from the proctor for completing the student information on your answersheet.
This examination has four parts, with a total of 36 questions. You must answerall questions in this examination. Record your answers to the Part I multiple-choicequestions on the separate answer sheet. Write your answers to the questions inParts II, III, and IV directly in this booklet. All work should be written in pen,except for graphs and drawings, which should be done in pencil. Clearly indicatethe necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. Utilize the information provided for each question to determine youranswer. Note that diagrams are not necessarily drawn to scale.
The formulas that you may need to answer some questions in this examinationare found at the end of the examination. This sheet is perforated so you mayremove it from this booklet.
Scrap paper is not permitted for any part of this examination, but you may usethe blank spaces in this booklet as scrap paper. A perforated sheet of scrap graphpaper is provided at the end of this booklet for any question for which graphingmay be helpful but is not required. You may remove this sheet from this booklet.Any work done on this sheet of scrap graph paper will not be scored.
When you have completed the examination, you must sign the statement printedat the end of the answer sheet, indicating that you had no unlawful knowledge ofthe questions or answers prior to the examination and that you have neither givennor received assistance in answering any of the questions during the examination.Your answer sheet cannot be accepted if you fail to sign this declaration.
GEOMETRY (COMMON CORE)
DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.
Notice…
A graphing calculator, a straightedge (ruler), and a compass must be available for you to use whiletaking this examination.
GEOMETRY (COMMON CORE)
The possession or use of any communications device is strictly prohibited when taking this examination. If you have or use any communications device, no matter how briefly, your examinationwill be invalidated and no score will be calculated for you.
1 Which equation represents the line that passes through the point
(�2,2) and is parallel to y � x � 8?
(1) y � x (3) y � x � 3
(2) y � �2x � 3 (4) y � �2x � 3
2 In the diagram below, �ADE is the image of �ABC after a reflection
over the line AC followed by a dilation of scale factor centeredat point A.
Which statement must be true?
(1) m∠BAC � m∠AED (3) m∠DAE � m∠BAC
(2) m∠ABC � m∠ADE (4) m∠ACB � m∠DAB
3 Given �ABC � �DEF, which statement is not always true?
(1)
(2) m∠A � m∠D
(3) area of �ABC � area of �DEF
(4) perimeter of �ABC � perimeter of �DEF
12
12
B
A
C
D
E
AEAC
BC DF�
12
12
12
Use this space forcomputations.
Part I
Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partialcredit will be allowed. Utilize the information provided for each question to determine youranswer. Note that diagrams are not necessarily drawn to scale. For each statement or question,choose the word or expression that, of those given, best completes the statement or answersthe question. Record your answers on your separate answer sheet. [48]
Geometry (Common Core) – Jan. ’17 [2]
Use this space forcomputations.
4 In the diagram below, are midsegments of �ABC.
The perimeter of quadrilateral ADEF is equivalent to
(1) AB � BC � AC (3) 2AB � 2AC
(2) AB � AC (4) AB � AC
5 In the diagram below, if �ABE � �CDF and is drawn, thenit could be proven that quadrilateral ABCD is a
(1) square (3) rectangle
(2) rhombus (4) parallelogram
6 Under which transformation would �A�B�C�, the image of �ABC, notbe congruent to �ABC?
(1) reflection over the y-axis
(2) rotation of 90º clockwise about the origin
(3) translation of 3 units right and 2 units down
(4) dilation with a scale factor of 2 centered at the origin
B
D E
A F C
DE DF EF, , and
A D
E
B C
F
AEFC
12
12
Geometry (Common Core) – Jan. ’17 [3] [OVER]
Use this space forcomputations.7 The diagram below shows two similar triangles.
If tan � � , what is the value of x, to the nearest tenth?
(1) 1.2 (3) 7.6
(2) 5.6 (4) 8.8
8 A farmer has 64 feet of fence to enclose a rectangular vegetable garden. Which dimensions would result in the biggest area for thisgarden?
(1) the length and the width are equal
(2) the length is 2 more than the width
(3) the length is 4 more than the width
(4) the length is 6 more than the width
9 The diagram shows rectangle ABCD, with diagonal .
What is the perimeter of rectangle ABCD, to the nearest tenth?
(1) 28.4 (3) 48.0
(2) 32.8 (4) 62.4
A
CB
D
30°
12
BD
37
2.4
x
θ
Geometry (Common Core) –Jan. ’17 [4]
Geometry (Common Core) – Jan. ’17 [5] [OVER]
Use this space forcomputations.10 Identify which sequence of transformations could map pentagon
ABCDE onto pentagon A�B�C�D�E�, as shown below.
(1) dilation followed by a rotation
(2) translation followed by a rotation
(3) line reflection followed by a translation
(4) line reflection followed by a line reflection
11 A solid metal prism has a rectangular base with sides of 4 inches and6 inches, and a height of 4 inches. A hole in the shape of a cylinder,with a radius of 1 inch, is drilled through the entire length of the rectangular prism.
What is the approximate volume of the remaining solid, in cubicinches?
(1) 19 (3) 93
(2) 77 (4) 96
4 in
1 in4 in
6 in
A E
B D
C
D�B�
E�A�
C�
Geometry (Common Core) –Jan. ’17 [6]
12 Given the right triangle in the diagram below, what is the value of x,to the nearest foot?
(1) 11 (3) 18
(2) 17 (4) 22
13 On the graph below, point A(3,4) and with coordinates B(4,3)and C(2,1) are graphed.
What are the coordinates of B� and C� after undergoes a dilationcentered at point A with a scale factor of 2?
(1) B�(5,2) and C�(1,�2) (3) B�(5,0) and C�(1,�2)
(2) B�(6,1) and C�(0,�1) (4) B�(5,2) and C�(3,0)
�
���
����
BC
y
x
A
C
B
BC
Use this space forcomputations.
Geometry (Common Core) – Jan. ’17 [7] [OVER]
14 In the diagram of right triangle ADE below, .
Which ratio is always equivalent to the sine of ∠A?
(1) (3)
(2) (4)
15 In circle O, secants and are drawn from external point Asuch that points D, B, E, and C are on circle O. If AD � 8, AE � 6,and EC is 12 more than BD, the length of is
(1) 6 (3) 36
(2) 22 (4) 48
16 A parallelogram is always a rectangle if
(1) the diagonals are congruent
(2) the diagonals bisect each other
(3) the diagonals intersect at right angles
(4) the opposite angles are congruent
A C
B
E
D
BC DE||
BD
AECADB
ABAC
AEAD
BCAB
ADDE
Use this space forcomputations.
Geometry (Common Core) –Jan. ’17 [8]
17 Which rotation about its center will carry a regular decagon ontoitself?
(1) 54° (3) 198°
(2) 162° (4) 252°
18 The equation of a circle is x2 � y2 � 6y � 1 � 0. What are the coordinates of the center and the length of the radius of this circle?
(1) center (0,3) and radius �
(2) center (0,�3) and radius �
(3) center (0,6) and radius �
(4) center (0,�6) and radius �
19 Parallelogram ABCD has coordinates A(0,7) and C(2,1). Whichstatement would prove that ABCD is a rhombus?
(1) The midpoint of is (1,4).
(2) The length of is .
(3) The slope of is .
(4) The slope of is .
20 Point Q is on such that MQ:QN � 2:3. If M has coordinates (3,5)and N has coordinates (8,�5), the coordinates of Q are
(1) (5,1) (3) (6,�1)
(2) (5,0) (4) (6,0)
MN
35
35
2 2
2 2
AB 13
BD 13
BD 40
AC
Use this space forcomputations.
Geometry (Common Core) – Jan. ’17 [9] [OVER]
21 In the diagram below of circle O, GO � 8 and m∠GOJ � 60°.
What is the area, in terms of π, of the shaded region?
(1) (3)
(2) (4)
22 A circle whose center is the origin passes through the point (�5,12).Which point also lies on this circle?
(1) (10,3) (3)
(2) (�12,13) (4)
23 A plane intersects a hexagonal prism. The plane is perpendicular tothe base of the prism. Which two-dimensional figure is the cross section of the plane intersecting the prism?
(1) triangle (3) hexagon
(2) trapezoid (4) rectangle
24 A water cup in the shape of a cone has a height of 4 inches and amaximum diameter of 3 inches. What is the volume of the water inthe cup, to the nearest tenth of a cubic inch, when the cup is filledto half its height?
(1) 1.2 (3) 4.7
(2) 3.5 (4) 14.1
( , )�8 5 21
( , )11 2 12
203π 160
3π
43π 32
3π
G
JO
60°
8
Use this space forcomputations.
Geometry (Common Core) – Jan. ’17 [10]
25 Using a compass and straightedge, construct the line of reflection over which triangle RST reflectsonto triangle R�S�T�. [Leave all construction marks.]
S�
T�
R�
T
R
S
Part II
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correctnumerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [14]
Geometry (Common Core) – Jan. ’17 [11] [OVER]
26 The graph below shows �ABC and its image, �A�B�C�.
Describe a sequence of rigid motions which would map �ABC onto �A�B�C�.
y
x
B� C�
A�
A
C B
27 When instructed to find the length of in right triangle HJG, Alex wrote the equation
sin 28° � while Marlene wrote cos 62° � . Are both students’ equations correct?
Explain why.
28 In the diagram below, tangent and secant are drawn to circle O from external point D,
such that .
If m � 152°, determine and state m∠D.BC�
A
O
C
D
B
AC BC� ��
DA DBC
HJ20
HJ20
HJ
G J
H
20
28�
Geometry (Common Core) – Jan. ’17 [12]
Geometry (Common Core) – Jan. ’17 [13] [OVER]
29 In the diagram below, is parallel to , and intersects at A.
Prove: �GIA � �TNA
I
G
AT
N
GI NT IN GT
30 In the diagram below of isosceles triangle ABC, and angle bisectors , , and are drawn and intersect at X.
If m∠BAC � 50°, find m∠AXC.
B
E D
FA C
X
AB CB� AD BF CE
Geometry (Common Core) – Jan. ’17 [14]
Geometry (Common Core) – Jan. ’17 [15] [OVER]
31 In square GEOM, the coordinates of G are (2,�2) and the coordinates of O are (�4,2).Determine and state the coordinates of vertices E and M.
[The use of the set of axes below is optional.]
y
x
32 Triangle QRS is graphed on the set of axes below.
On the same set of axes, graph and label �Q�R�S�, the image of �QRS after a dilation with
a scale factor of centered at the origin.
Use slopes to explain why .Q R QR� � ||
32
y
x
S
R
Q
Part III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correctnumerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [12]
Geometry (Common Core) – Jan. ’17 [16]
Geometry (Common Core) – Jan. ’17 [17] [OVER]
33 Using a compass and straightedge, construct a regular hexagon inscribed in circle O below.Label it ABCDEF. [Leave all construction marks.]
If chords and are drawn, which type of triangle, according to its angles, would �FBC be?Explain your answer.
FB FC
O
34 A candle maker uses a mold to make candles like the one shown below.
The height of the candle is 13 cm and the circumference of the candle at its widest measure is31.416 cm. Use modeling to approximate how much wax, to the nearest cubic centimeter, isneeded to make this candle. Justify your answer.
Geometry (Common Core) – Jan. ’17 [18]
Geometry (Common Core) – Jan. ’17 [19] [OVER]
35 In quadrilateral ABCD, , , and and are perpendicular to diagonal at points F and E.
Prove: AE CF�
D C
A B
E
F
AB CD� AB CD|| BF DE AC
Part IV
Answer the 2 questions in this part. Each correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correctnumerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [12]
Geometry (Common Core) – Jan. ’17 [20]
36 New streetlights will be installed along a section of the highway. The posts for the streetlights willbe 7.5 m tall and made of aluminum. The city can choose to buy the posts shaped like cylindersor the posts shaped like rectangular prisms. The cylindrical posts have a hollow core, with aluminum 2.5 cm thick, and an outer diameter of 53.4 cm. The rectangular-prism posts have a hollow core, with aluminum 2.5 cm thick, and a square base that measures 40 cm on each side.
The density of aluminum is 2.7 g/cm3, and the cost of aluminum is $0.38 per kilogram.
If all posts must be the same shape, which post design will cost the town less?
How much money will be saved per streetlight post with the less expensive design?
Work space for question 36 is continued on the next page.
Scrap Graph Paper — This sheet will not be scored.
Scrap Graph Paper — This sheet will not be scored.Tear H
ereTear H
ere
Printed on Recycled Paper
GEOMETRY (COMMON CORE)GEOMETRY (COMMON CORE)
FOR TEACHERS ONLYThe University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (COMMON CORE)
Thursday, January 26, 2017 — 9:15 a.m. to 12:15 p.m., only
SCORING KEY AND RATING GUIDE
Mechanics of RatingThe following procedures are to be followed for scoring student answer papers for the
Regents Examination in Geometry (Common Core). More detailed information about scoring is provided in the publication Information Booklet for Scoring the RegentsExamination in Geometry (Common Core).
Do not attempt to correct the student’s work by making insertions or changes of anykind. In scoring the open-ended questions, use check marks to indicate student errors.Unless otherwise specified, mathematically correct variations in the answers will be allowed.Units need not be given when the wording of the questions allows such omissions.
Each student’s answer paper is to be scored by a minimum of three mathematics teachers. No one teacher is to score more than approximately one-third of the open-endedquestions on a student’s paper. Teachers may not score their own students’ answer papers.On the student’s separate answer sheet, for each question, record the number of creditsearned and the teacher’s assigned rater/scorer letter.
Schools are not permitted to rescore any of the open-ended questions on thisexam after each question has been rated once, regardless of the final exam score.Schools are required to ensure that the raw scores have been added correctly andthat the resulting scale score has been determined accurately.
Raters should record the student’s scores for all questions and the total raw score on thestudent’s separate answer sheet. Then the student’s total raw score should be converted to ascale score by using the conversion chart that will be posted on the Department’s web siteat: http://www.p12.nysed.gov/assessment/ on Thursday, January 26, 2017. Because scalescores corresponding to raw scores in the conversion chart may change from one administration to another, it is crucial that, for each administration, the conversion chart provided for that administration be used to determine the student’s final score. The student’sscale score should be entered in the box provided on the student’s separate answer sheet.The scale score is the student’s final examination score.
(1) . . . . . 3 . . . . .
(2) . . . . . 2 . . . . .
(3) . . . . . 1 . . . . .
(4) . . . . . 4 . . . . .
(5) . . . . . 4 . . . . .
(6) . . . . . 4 . . . . .
(7) . . . . . 2 . . . . .
(8) . . . . . 1 . . . . .
(9) . . . . . 2 . . . . .
(10) . . . . . 3 . . . . .
(11) . . . . . 2 . . . . .
(12) . . . . . 3 . . . . .
(13) . . . . . 1 . . . . .
(14) . . . . . 3 . . . . .
(15) . . . . . 2 . . . . .
(16) . . . . . 1 . . . . .
(17) . . . . . 4 . . . . .
(18) . . . . . 1 . . . . .
(19) . . . . . 3 . . . . .
(20) . . . . . 1 . . . . .
(21) . . . . . 4 . . . . .
(22) . . . . . 3 . . . . .
(23) . . . . . 4 . . . . .
(24) . . . . . 1 . . . . .
Updated information regarding the rating of this examination may be posted on the New York State Education Department’s web site during the rating period. Check this website at: http://www.p12.nysed.gov/assessment/ and select the link “Scoring Information” forany recently posted information regarding this examination. This site should be checkedbefore the rating process for this examination begins and several times throughout theRegents Examination period.
The Department is providing supplemental scoring guidance, the “Model Response Set,”for the Regents Examination in Geometry (Common Core). This guidance is intended to bepart of the scorer training. Schools should use the Model Response Set along with therubrics in the Scoring Key and Rating Guide to help guide scoring of student work. While not reflective of all scenarios, the Model Response Set illustrates how less common student responses to constructed-response questions may be scored. The Model Response Setwill be available on the Department’s web site at: http://www.nysedregents.org/geometrycc/.
If the student’s responses for the multiple-choice questions are being hand scored prior to beingscanned, the scorer must be careful not to make any marks on the answer sheet except to recordthe scores in the designated score boxes. Marks elsewhere on the answer sheet will interfere withthe accuracy of the scanning.
Part I
Allow a total of 48 credits, 2 credits for each of the following. Allow credit if the student has written the correct answer instead of the numeral 1, 2, 3, or 4.
I. General Principles for RatingThe rubrics for the constructed-response questions on the Regents Examination in Geometry (CommonCore) are designed to provide a systematic, consistent method for awarding credit. The rubrics are not tobe considered all-inclusive; it is impossible to anticipate all the different methods that students might useto solve a given problem. Each response must be rated carefully using the teacher’s professional judgmentand knowledge of mathematics; all calculations must be checked. The specific rubrics for each question mustbe applied consistently to all responses. In cases that are not specifically addressed in the rubrics, ratersmust follow the general rating guidelines in the publication Information Booklet for Scoring the RegentsExamination in Geometry (Common Core), use their own professional judgment, confer with other mathematics teachers, and/or contact the State Education Department for guidance. During each RegentsExamination administration period, rating questions may be referred directly to the Education Department.The contact numbers are sent to all schools before each administration period.
II. Full-Credit ResponsesA full-credit response provides a complete and correct answer to all parts of the question. Sufficient workis shown to enable the rater to determine how the student arrived at the correct answer.When the rubric for the full-credit response includes one or more examples of an acceptable method forsolving the question (usually introduced by the phrase “such as”), it does not mean that there are no additional acceptable methods of arriving at the correct answer. Unless otherwise specified, mathematicallycorrect alternative solutions should be awarded credit. The only exceptions are those questions that specify the type of solution that must be used; e.g., an algebraic solution or a graphic solution. A correctsolution using a method other than the one specified is awarded half the credit of a correct solution usingthe specified method.
III. Appropriate WorkFull-Credit Responses: The directions in the examination booklet for all the constructed-response questionsstate: “Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc.” The student has the responsibility of providing the correct answer and showing how that answerwas obtained. The student must “construct” the response; the teacher should not have to search through agroup of seemingly random calculations scribbled on the student paper to ascertain what method the student may have used.Responses With Errors: Rubrics that state “Appropriate work is shown, but…” are intended to be used withsolutions that show an essentially complete response to the question but contain certain types of errors,whether computational, rounding, graphing, or conceptual. If the response is incomplete; i.e., an equationis written but not solved or an equation is solved but not all of the parts of the question are answered, appropriate work has not been shown. Other rubrics address incomplete responses.
IV. Multiple ErrorsComputational Errors, Graphing Errors, and Rounding Errors: Each of these types of errors results in a 1-credit deduction. Any combination of two of these types of errors results in a 2-credit deduction. No morethan 2 credits should be deducted for such mechanical errors in a 4-credit question and no more than 3 credits should be deducted in a 6-credit question. The teacher must carefully review the student’s workto determine what errors were made and what type of errors they were.Conceptual Errors: A conceptual error involves a more serious lack of knowledge or procedure. Examplesof conceptual errors include using the incorrect formula for the area of a figure, choosing the incorrecttrigonometric function, or multiplying the exponents instead of adding them when multiplying terms withexponents.If a response shows repeated occurrences of the same conceptual error, the student should not be penalized twice. If the same conceptual error is repeated in responses to other questions, credit should bededucted in each response.For 4- and 6-credit questions, if a response shows one conceptual error and one computational, graphing, orrounding error, the teacher must award credit that takes into account both errors. Refer to the rubric forspecific scoring guidelines.
For each question, use the specific criteria to award a maximum of 2 credits. Unlessotherwise specified, mathematically correct alternative solutions should be awarded appropriate credit.
(28) [2] 48, and appropriate work is shown.
[1] Appropriate work is shown, but one computational error is made.
or
[1] Appropriate work is shown, but one conceptual error is made.
or
[1] m � 152 and m � 56 are stated, but no further correct work is shown.
or
[1] 48, but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
(29) [2] A complete and correct proof that includes a conclusion is written.
[1] Appropriate work is shown, but only one correct statement and reason arewritten.
or
[1] Appropriate work is shown, but one conceptual error is made.
[0] The “given” and/or the “prove” statements are written, but no further correctrelevant statements are written.
or
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
For each question, use the specific criteria to award a maximum of 4 credits. Unlessotherwise specified, mathematically correct alternative solutions should be awarded appropriate credit.
(33) [4] A correctly labeled construction of regular hexagon ABCDEF is drawn showingall appropriate arcs, right triangle, and an appropriate explanation is written.
[3] An appropriate construction of regular hexagon ABCDEF is drawn, right triangle, and an appropriate explanation is written, but one construction erroris made.
or
[3] A correct construction of a regular hexagon is drawn showing all appropriatearcs, right triangle, and an appropriate explanation is written, but the construction is not labeled or is labeled incorrectly.
or
[3] A correctly labeled construction of regular hexagon ABCDEF is drawn showingall appropriate arcs, and right triangle, but an appropriate explanation is notwritten or is incorrect.
[2] Appropriate work is shown, but one conceptual error is made. An appropriateanswer is stated, and an appropriate explanation is written.
or
[2] A correctly labeled construction of regular hexagon ABCDEF is drawn, butno further correct work is shown.
or
[2] Right triangle is stated, and an appropriate explanation is written, but theconstruction is not drawn or is drawn incorrectly.
[1] Appropriate work is shown to find the angles of �FBC, but no furthercorrect work is shown.
or
[1] All construction arcs are drawn, but no further correct work is shown.
[0] A drawing that is not an appropriate construction is drawn.
or
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
(35) [6] A complete and correct proof that includes a concluding statement is written.
[5] A proof is written that demonstrates a thorough understanding of the methodof proof and contains no conceptual errors, but one statement and/or reasonis missing or incorrect.
[4] A proof is written that demonstrates a good understanding of the method ofproof and contains no conceptual errors, but two statements and/or reasonsare missing or incorrect.
[3] A proof is written that demonstrates a good understanding of the method ofproof and contains no conceptual errors, but three statements and/or reasonsare missing or incorrect.
or
[3] A proof is written that demonstrates a good understanding of the method ofproof, but one conceptual error is made.
[2] A proof is written that demonstrates a method of proof, but one conceptualerror is made, and one statement and/or reason is missing or incorrect.
or
[2] Some correct relevant statements about the proof are made, but four statements and/or reasons are missing or incorrect.
[1] Only one or two correct relevant statements and reasons are written.
[0] The “given” and/or the “prove” statements are written, but no further correctrelevant statements are written.
or
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
Part IV
For each question, use the specific criteria to award a maximum of 6 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit.
(36) [6] Rectangular design, $19.06, and correct work is shown.
[5] Appropriate work is shown, but one computational or rounding error is made.
or
[5] Appropriate work is shown, but either rectangular design or the $19.06 difference is missing.
[4] Correct work is shown to find the cost of both post designs, but no further correct work is shown.
or
[4] Appropriate work is shown, but two or more computational or rounding errorsare made.
or
[4] Appropriate work is shown, but one conceptual error is made.
[3] Appropriate work is shown, but one conceptual error and one computationalor rounding error are made.
or
[3] Correct work is shown to determine the weight of both post designs, but nofurther correct work is shown.
or
[3] Correct work is shown to find the cost for one of the post designs, but no further correct work is shown.
[2] Appropriate work is shown, but one conceptual error and two or more computational errors are made.
or
[2] Appropriate work is shown, but two conceptual errors are made.
or
[2] Correct work is shown to determine the volumes for both post designs, but nofurther correct work is shown.
[1] Correct work is shown to determine the dimensions of the inner and outersolids, but no further correct work is shown.
or
[1] Correct work is shown to determine the volume of one post design, but no further correct work is shown.
or
[1] Rectangular design and $19.06, but no work or no correct work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correctresponse that was obtained by an obviously incorrect procedure.
Chart for Converting Total Test Raw Scores toFinal Examination Scores (Scale Scores)
Online Submission of Teacher Evaluations of the Test to the DepartmentSuggestions and feedback from teachers provide an important contribution to the test
development process. The Department provides an online evaluation form for State assessments. It contains spaces for teachers to respond to several specific questions and tomake suggestions. Instructions for completing the evaluation form are as follows:
1. Go to http://www.forms2.nysed.gov/emsc/osa/exameval/reexameval.cfm.
2. Select the test title.
3. Complete the required demographic fields.
4. Complete each evaluation question and provide comments in the space provided.
5. Click the SUBMIT button at the bottom of the page to submit the completed form.
The Chart for Determining the Final Examination Score for the January 2017 Regents Examination in Geometry (Common Core) will be posted on theDepartment’s web site at: http://www.p12.nysed.gov/assessment/ on Thursday,January 26, 2017. Conversion charts provided for previous administrations of the Regents Examination in Geometry (Common Core) must NOT be used to determine students’ final scores for this administration.
The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
GEOMETRY (COMMON CORE)Thursday, January 26, 2017 — 9:15 a.m. to 12:15 p.m.
Score 2: The student had a complete and correct response.
Geometry (Common Core) – Jan. ’17 [3]
25 Using a compass and straightedge, construct the line of reflection over which triangle RST reflectsonto triangle R�S�T�. [Leave all construction marks.]
S�
T�
R�
T
R
S
Question 25
Score 2: The student had a complete and correct response.
Geometry (Common Core) – Jan. ’17 [4]
25 Using a compass and straightedge, construct the line of reflection over which triangle RST reflectsonto triangle R�S�T�. [Leave all construction marks.]
S�
T�
R�
T
R
S
Question 25
Score 2: The student had a complete and correct response.
Geometry (Common Core) – Jan. ’17 [5]
25 Using a compass and straightedge, construct the line of reflection over which triangle RST reflectsonto triangle R�S�T�. [Leave all construction marks.]
S�
T�
R�
T
R
S
Question 25
Score 1: The student had a correct construction, but did not draw the line of reflection.
Geometry (Common Core) – Jan. ’17 [6]
25 Using a compass and straightedge, construct the line of reflection over which triangle RST reflectsonto triangle R�S�T�. [Leave all construction marks.]
S�
T�
R�
T
R
S
Question 25
Score 0: The student had a completely incorrect response.
Geometry (Common Core) – Jan. ’17 [7]
25 Using a compass and straightedge, construct the line of reflection over which triangle RST reflectsonto triangle R�S�T�. [Leave all construction marks.]
S�
T�
R�
T
R
S
Geometry (Common Core) – Jan. ’17 [8]
Question 26
Score 2: The student had a complete and correct response.
26 The graph below shows �ABC and its image, �A�B�C�.
Describe a sequence of rigid motions which would map �ABC onto �A�B�C�.
y
x
B� C�
A�
A
C B
Geometry (Common Core) – Jan. ’17 [9]
Question 26
Score 2: The student had a complete and correct response.
26 The graph below shows �ABC and its image, �A�B�C�.
Describe a sequence of rigid motions which would map �ABC onto �A�B�C�.
y
x
B� C�
A�
A
C B
Geometry (Common Core) – Jan. ’17 [10]
Question 26
Score 1: The student wrote an incorrect translation by translating in the wrong direction.
26 The graph below shows �ABC and its image, �A�B�C�.
Describe a sequence of rigid motions which would map �ABC onto �A�B�C�.
y
x
B� C�
A�
A
C B
Geometry (Common Core) – Jan. ’17 [11]
Question 26
Score 1: The student completed a correct sequence of rigid motions, but went from the imageto the pre-image.
26 The graph below shows �ABC and its image, �A�B�C�.
Describe a sequence of rigid motions which would map �ABC onto �A�B�C�.
y
x
B� C�
A�
A
C B
Geometry (Common Core) – Jan. ’17 [12]
Question 26
Score 0: The student’s description did not have enough detail to receive any credit.
26 The graph below shows �ABC and its image, �A�B�C�.
Describe a sequence of rigid motions which would map �ABC onto �A�B�C�.
y
x
B� C�
A�
A
C B
Geometry (Common Core) – Jan. ’17 [13]
Question 27
27 When instructed to find the length of in right triangle HJG, Alex wrote the equation
sin 28° � while Marlene wrote cos 62° � . Are both students’ equations correct?
Explain why.
HJ20
HJ20
HJ
G J
H
20
28�
Score 2: The student had a complete and correct response.
Geometry (Common Core) – Jan. ’17 [14]
Question 27
Score 2: The student had a complete and correct response.
27 When instructed to find the length of in right triangle HJG, Alex wrote the equation
sin 28° � while Marlene wrote cos 62° � . Are both students’ equations correct?
Explain why.
HJ20
HJ20
HJ
G J
H
20
28�
Geometry (Common Core) – Jan. ’17 [15]
Question 27
Score 1: The student wrote an incomplete explanation by not explaining why cos 62° and sin 28°are equal.
27 When instructed to find the length of in right triangle HJG, Alex wrote the equation
sin 28° � while Marlene wrote cos 62° � . Are both students’ equations correct?
Explain why.
HJ20
HJ20
HJ
G J
H
20
28�
Geometry (Common Core) – Jan. ’17 [16]
Question 27
Score 1: The student made an error by not considering complementary angles.
27 When instructed to find the length of in right triangle HJG, Alex wrote the equation
sin 28° � while Marlene wrote cos 62° � . Are both students’ equations correct?
Explain why.
HJ20
HJ20
HJ
G J
H
20
28�
Geometry (Common Core) – Jan. ’17 [17]
Question 27
Score 0: The student had a completely incorrect response.
27 When instructed to find the length of in right triangle HJG, Alex wrote the equation
sin 28° � while Marlene wrote cos 62° � . Are both students’ equations correct?
Explain why.
HJ20
HJ20
HJ
G J
H
20
28�
Geometry (Common Core) – Jan. ’17 [18]
Question 28
Score 2: The student had a complete and correct response.
28 In the diagram below, tangent and secant are drawn to circle O from external point D,
such that .
If m � 152°, determine and state m∠D.BC�
A
O
C
D
B
AC BC� ��
DA DBC
Geometry (Common Core) – Jan. ’17 [19]
Question 28
Score 1: The student showed appropriate work to find m and m , but no further correct workwas shown.
AC� AB�
28 In the diagram below, tangent and secant are drawn to circle O from external point D,
such that .AC BC� ��
DA DBC
If m � 152°, determine and state m∠D.BC�
Geometry (Common Core) – Jan. ’17 [20]
Question 28
Score 0: The student had a completely incorrect response.
28 In the diagram below, tangent and secant are drawn to circle O from external point D,
such that .
If m � 152°, determine and state m∠D.BC�
A
O
C
D
B
AC BC� ��
DA DBC
Geometry (Common Core) – Jan. ’17 [21]
Question 29
Score 2: The student had a complete and correct response.
29 In the diagram below, is parallel to , and intersects at A.
Prove: �GIA � �TNA
I
G
AT
N
GI NT IN GT
Geometry (Common Core) – Jan. ’17 [22]
Question 29
Score 2: The student had a complete and correct response.
29 In the diagram below, is parallel to , and intersects at A.
Prove: �GIA � �TNA
I
G
AT
N
GI NT IN GT
Geometry (Common Core) – Jan. ’17 [23]
Question 29
Score 2: The student had a complete and correct response.
29 In the diagram below, is parallel to , and intersects at A.GI NT IN GT
Prove: �GIA � �TNA
Geometry (Common Core) – Jan. ’17 [24]
Question 29
Score 1: The student wrote an incomplete reason for statement 4.
29 In the diagram below, is parallel to , and intersects at A.
Prove: �GIA � �TNA
I
G
AT
N
GI NT IN GT
Geometry (Common Core) – Jan. ’17 [25]
Question 29
Score 1: The student only had one relevant correct statement and reason.
29 In the diagram below, is parallel to , and intersects at A.GI NT IN GT
I
Prove: �GIA � �TNA
Geometry (Common Core) – Jan. ’17 [26]
Question 29
Score 0: The student did not show enough relevant correct work to receive any credit.
29 In the diagram below, is parallel to , and intersects at A.
Prove: �GIA � �TNA
I
G
AT
N
GI NT IN GT
Geometry (Common Core) – Jan. ’17 [27]
Question 29
Score 0: The student did not show enough relevant correct work to receive any credit.
29 In the diagram below, is parallel to , and intersects at A.GI NT IN GT
I
Prove: �GIA � �TNA
Geometry (Common Core) – Jan. ’17 [28]
Question 30
Score 2: The student had a complete and correct response.
30 In the diagram below of isosceles triangle ABC, and angle bisectors , , and are drawn and intersect at X.
If m∠BAC � 50°, find m∠AXC.
B
E D
FA C
X
AB CB� AD BF CE
Geometry (Common Core) – Jan. ’17 [29]
Question 30
Score 2: The student had a complete and correct response.
30 In the diagram below of isosceles triangle ABC, and angle bisectors , , and are drawn and intersect at X.
AB CB� AD BF CE
If m∠BAC � 50°, find m∠AXC.
Geometry (Common Core) – Jan. ’17 [30]
Question 30
Score 2: The student had a complete and correct response.
30 In the diagram below of isosceles triangle ABC, and angle bisectors , , and are drawn and intersect at X.
AB CB� AD BF CE
If m∠BAC � 50°, find m∠AXC.
Geometry (Common Core) – Jan. ’17 [31]
Question 30
Score 1: The student made one computational error.
30 In the diagram below of isosceles triangle ABC, and angle bisectors , , and are drawn and intersect at X.
If m∠BAC � 50°, find m∠AXC.
B
E D
FA C
X
AB CB� AD BF CE
Geometry (Common Core) – Jan. ’17 [32]
Question 30
Score 0: The student obtained the correct answer by an incorrect method.
30 In the diagram below of isosceles triangle ABC, and angle bisectors , , and are drawn and intersect at X.
If m∠BAC � 50°, find m∠AXC.
B
E D
FA C
X
AB CB� AD BF CE
Geometry (Common Core) – Jan. ’17 [33]
Question 31
Score 2: The student had a complete and correct response.
31 In square GEOM, the coordinates of G are (2,�2) and the coordinates of O are (�4,2).Determine and state the coordinates of vertices E and M.
[The use of the set of axes below is optional.]
y
x
Geometry (Common Core) – Jan. ’17 [34]
Question 31
Score 2: The student had a complete and correct response.
31 In square GEOM, the coordinates of G are (2,�2) and the coordinates of O are (�4,2).Determine and state the coordinates of vertices E and M.
[The use of the set of axes below is optional.]
y
x
Geometry (Common Core) – Jan. ’17 [35]
Question 31
Score 1: The student made an error in the order of the vertices of square GEOM.
31 In square GEOM, the coordinates of G are (2,�2) and the coordinates of O are (�4,2).Determine and state the coordinates of vertices E and M.
[The use of the set of axes below is optional.]
y
x
Geometry (Common Core) – Jan. ’17 [36]
Question 31
Score 0: The student had a completely incorrect response.
31 In square GEOM, the coordinates of G are (2,�2) and the coordinates of O are (�4,2).Determine and state the coordinates of vertices E and M.
[The use of the set of axes below is optional.]
y
x
Geometry (Common Core) – Jan. ’17 [37]
Question 32
Score 4: The student had a complete and correct response.
32 Triangle QRS is graphed on the set of axes below.
On the same set of axes, graph and label �Q�R�S�, the image of �QRS after a dilation with
a scale factor of centered at the origin.
Use slopes to explain why .Q R QR� � ||
32
y
x
S
R
Q
Geometry (Common Core) – Jan. ’17 [38]
Question 32
Score 4: The student had a complete and correct response.
32 Triangle QRS is graphed on the set of axes below.
On the same set of axes, graph and label �Q�R�S�, the image of �QRS after a dilation with
a scale factor of centered at the origin.32
y
x
S
R
Q
Use slopes to explain why .Q R QR� � ||
Geometry (Common Core) – Jan. ’17 [39]
Question 32
Score 4: The student had a complete and correct response.
32 Triangle QRS is graphed on the set of axes below.
On the same set of axes, graph and label �Q�R�S�, the image of �QRS after a dilation with
a scale factor of centered at the origin.32
y
x
S
R
Q
Use slopes to explain why .Q R QR� � ||
Geometry (Common Core) – Jan. ’17 [40]
Question 32
Score 3: The student made an error in stating the slope is .12
32 Triangle QRS is graphed on the set of axes below.
On the same set of axes, graph and label �Q�R�S�, the image of �QRS after a dilation with
a scale factor of centered at the origin.32
y
x
S
R
Q
Use slopes to explain why .Q R QR� � ||
Geometry (Common Core) – Jan. ’17 [41]
Question 32
Score 2: The student made an error in the transformation by translating �QRS instead of dilating �QRS.
32 Triangle QRS is graphed on the set of axes below.
On the same set of axes, graph and label �Q�R�S�, the image of �QRS after a dilation with
a scale factor of centered at the origin.32
y
x
S
R
Q
Use slopes to explain why .Q R QR� � ||
Geometry (Common Core) – Jan. ’17 [42]
Question 32
Score 1: The student transformed �QRS incorrectly and found the incorrect slope. The studentcorrectly interpreted that same slopes form parallel sides.
32 Triangle QRS is graphed on the set of axes below.
On the same set of axes, graph and label �Q�R�S�, the image of �QRS after a dilation with
a scale factor of centered at the origin.
Use slopes to explain why .Q R QR� � ||
32
y
x
S
R
Q
Geometry (Common Core) – Jan. ’17 [43]
Question 32
Score 1: The student found the appropriate slopes of and , but no further correct workwas shown.
Q R� �QR
32 Triangle QRS is graphed on the set of axes below.
On the same set of axes, graph and label �Q�R�S�, the image of �QRS after a dilation with
a scale factor of centered at the origin.
Use slopes to explain why .Q R QR� � ||
32
y
x
S
R
Q
Geometry (Common Core) – Jan. ’17 [44]
Question 32
Score 0: The student graphed the transformation incorrectly and wrote an incorrect explanation.
32 Triangle QRS is graphed on the set of axes below.
On the same set of axes, graph and label �Q�R�S�, the image of �QRS after a dilation with
a scale factor of centered at the origin.
Use slopes to explain why .Q R QR� � ||
32
y
x
S
R
Q
Geometry (Common Core) – Jan ’17 [45]
Question 33
Score 4: The student had a complete and correct response.
33 Using a compass and straightedge, construct a regular hexagon inscribed in circle O below.Label it ABCDEF. [Leave all construction marks.]
O
If chords and are drawn, which type of triangle, according to its angles, would �FBC be?Explain your answer.
FB FC
Geometry (Common Core) – Jan ’17 [46]
Question 33
Score 3: The student did not write an explanation.
33 Using a compass and straightedge, construct a regular hexagon inscribed in circle O below.Label it ABCDEF. [Leave all construction marks.]
O
If chords and are drawn, which type of triangle, according to its angles, would �FBC be?Explain your answer.
FB FC
Geometry (Common Core) – Jan ’17 [47]
Question 33
Score 3: The student wrote an incomplete explanation.
33 Using a compass and straightedge, construct a regular hexagon inscribed in circle O below.Label it ABCDEF. [Leave all construction marks.]
O
If chords and are drawn, which type of triangle, according to its angles, would �FBC be?Explain your answer.
FB FC
Geometry (Common Core) – Jan ’17 [48]
Question 33
Score 2: The student constructed and labeled the hexagon correctly, but no further correct workwas shown.
33 Using a compass and straightedge, construct a regular hexagon inscribed in circle O below.Label it ABCDEF. [Leave all construction marks.]
O
If chords and are drawn, which type of triangle, according to its angles, would �FBC be?Explain your answer.
FB FC
Geometry (Common Core) – Jan ’17 [49]
Question 33
Score 1: The student made a drawing that was not a construction. The triangle was correctlyidentified as a right triangle, but the explanation was missing.
33 Using a compass and straightedge, construct a regular hexagon inscribed in circle O below.Label it ABCDEF. [Leave all construction marks.]
O
If chords and are drawn, which type of triangle, according to its angles, would �FBC be?Explain your answer.
FB FC
Geometry (Common Core) – Jan ’17 [50]
Question 33
Score 0: The student made a drawing that was not a construction. The explanation was incorrectbecause �FBC cannot be identified according to the student's drawing.
33 Using a compass and straightedge, construct a regular hexagon inscribed in circle O below.Label it ABCDEF. [Leave all construction marks.]
O
If chords and are drawn, which type of triangle, according to its angles, would �FBC be?Explain your answer.
FB FC
Geometry (Common Core) – Jan ’17 [51]
Question 34
Score 4: The student had a complete and correct response.
34 A candle maker uses a mold to make candles like the one shown below.
The height of the candle is 13 cm and the circumference of the candle at its widest measure is31.416 cm. Use modeling to approximate how much wax, to the nearest cubic centimeter, isneeded to make this candle. Justify your answer.
Geometry (Common Core) – Jan ’17 [52]
Question 34
Score 3: The student divided the circumference by 3.14 instead of π.
34 A candle maker uses a mold to make candles like the one shown below.
The height of the candle is 13 cm and the circumference of the candle at its widest measure is31.416 cm. Use modeling to approximate how much wax, to the nearest cubic centimeter, isneeded to make this candle. Justify your answer.
Geometry (Common Core) – Jan ’17 [53]
Question 34
Score 2: The student use an incorrect method to find the radius.
34 A candle maker uses a mold to make candles like the one shown below.
The height of the candle is 13 cm and the circumference of the candle at its widest measure is31.416 cm. Use modeling to approximate how much wax, to the nearest cubic centimeter, isneeded to make this candle. Justify your answer.
Geometry (Common Core) – Jan ’17 [54]
Question 34
Score 1: The student used an incorrect method to find the radius and wrote the volume in termsof π.
34 A candle maker uses a mold to make candles like the one shown below.
The height of the candle is 13 cm and the circumference of the candle at its widest measure is31.416 cm. Use modeling to approximate how much wax, to the nearest cubic centimeter, isneeded to make this candle. Justify your answer.
Geometry (Common Core) – Jan ’17 [55]
Question 34
Score 0: The student did not show enough relevant correct work to receive any credit.
34 A candle maker uses a mold to make candles like the one shown below.
The height of the candle is 13 cm and the circumference of the candle at its widest measure is31.416 cm. Use modeling to approximate how much wax, to the nearest cubic centimeter, isneeded to make this candle. Justify your answer.
Geometry (Common Core) – Jan. ’17 [56]
Question 35
Score 6: The student had a complete and correct response.
35 In quadrilateral ABCD, , , and and are perpendicular to diagonal at points F and E.
Prove: AE CF�
D C
A B
E
F
AB CD� AB CD|| BF DE AC
Geometry (Common Core) – Jan. ’17 [57]
Question 35
Score 6: The student had a complete and correct response.
35 In quadrilateral ABCD, , , and and are perpendicular to diagonal at points F and E.
Prove: AE CF�
D C
A B
E
F
AB CD� AB CD|| BF DE AC
Geometry (Common Core) – Jan. ’17 [58]
Question 35
Score 5: The student did not write the given statements in the proof.
35 In quadrilateral ABCD, , , and and are perpendicular to diagonal at points F and E.
Prove: AE CF�
D C
A B
E
F
AB CD� AB CD|| BF DE AC
Geometry (Common Core) – Jan. ’17 [59]
Question 35
Score 4: The student had one missing statement and reason to prove step 3, and had an incompletereason in step 3.
35 In quadrilateral ABCD, , , and and are perpendicular to diagonal at points F and E.
Prove: AE CF�
D C
A B
E
F
AB CD� AB CD|| BF DE AC
Geometry (Common Core) – Jan. ’17 [60]
Question 35
Score 3: The student had one missing statement and reason to prove step 2, and two missingstatements and reasons to prove step 8.
35 In quadrilateral ABCD, , , and and are perpendicular to diagonal at points F and E.
Prove: AE CF�
D C
A B
E
F
AB CD� AB CD|| BF DE AC
Geometry (Common Core) – Jan. ’17 [61]
Question 35
Score 2: The student made a conceptual error by not proving that ABCD is a parallelogram, andone statement and reason were missing to prove step 4.
35 In quadrilateral ABCD, , , and and are perpendicular to diagonal at points F and E.
Prove: AE CF�
D C
A B
E
F
AB CD� AB CD|| BF DE AC
Geometry (Common Core) – Jan. ’17 [62]
Question 35
Score 1: Only one or two correct relevant statements and reasons are written.
35 In quadrilateral ABCD, , , and and are perpendicular to diagonal at points F and E.
Prove: AE CF�
D C
A B
E
F
AB CD� AB CD|| BF DE AC
Geometry (Common Core) – Jan. ’17 [63]
Question 35
Score 0: The student had a completely incorrect response.
35 In quadrilateral ABCD, , , and and are perpendicular to diagonal at points F and E.
Prove: AE CF�
D C
A B
E
F
AB CD� AB CD|| BF DE AC
Geometry (Common Core) – Jan. ’17 [64]
Question 36
36 New streetlights will be installed along a section of the highway. The posts for the streetlights willbe 7.5 m tall and made of aluminum. The city can choose to buy the posts shaped like cylindersor the posts shaped like rectangular prisms. The cylindrical posts have a hollow core, with aluminum 2.5 cm thick, and an outer diameter of 53.4 cm. The rectangular-prism posts have a hollow core, with aluminum 2.5 cm thick, and a square base that measures 40 cm on each side.
The density of aluminum is 2.7 g/cm3, and the cost of aluminum is $0.38 per kilogram.
If all posts must be the same shape, which post design will cost the town less?
How much money will be saved per streetlight post with the less expensive design?
Work space for question 36 is continued on the next page.
Geometry (Common Core) – Jan. ’17 [65]
Question 36
Score 6: The student had a complete and correct response.
Question 36 continued
Geometry (Common Core) – Jan. ’17 [66]
Question 36
36 New streetlights will be installed along a section of the highway. The posts for the streetlights willbe 7.5 m tall and made of aluminum. The city can choose to buy the posts shaped like cylindersor the posts shaped like rectangular prisms. The cylindrical posts have a hollow core, with aluminum 2.5 cm thick, and an outer diameter of 53.4 cm. The rectangular-prism posts have a hollow core, with aluminum 2.5 cm thick, and a square base that measures 40 cm on each side.
The density of aluminum is 2.7 g/cm3, and the cost of aluminum is $0.38 per kilogram.
If all posts must be the same shape, which post design will cost the town less?
How much money will be saved per streetlight post with the less expensive design?
Work space for question 36 is continued on the next page.
Geometry (Common Core) – Jan. ’17 [67]
Question 36
Score 5: The student only subtracted 2.5 cm once when finding the volume of the rectangularprism.
Question 36 continued
Geometry (Common Core) – Jan. ’17 [68]
Question 36
36 New streetlights will be installed along a section of the highway. The posts for the streetlights willbe 7.5 m tall and made of aluminum. The city can choose to buy the posts shaped like cylindersor the posts shaped like rectangular prisms. The cylindrical posts have a hollow core, with aluminum 2.5 cm thick, and an outer diameter of 53.4 cm. The rectangular-prism posts have a hollow core, with aluminum 2.5 cm thick, and a square base that measures 40 cm on each side.
The density of aluminum is 2.7 g/cm3, and the cost of aluminum is $0.38 per kilogram.
If all posts must be the same shape, which post design will cost the town less?
How much money will be saved per streetlight post with the less expensive design?
Work space for question 36 is continued on the next page.
Geometry (Common Core) – Jan. ’17 [69]
Question 36
Score 4: The student did not perform either conversion required by the problem.
Question 36 continued
Geometry (Common Core) – Jan. ’17 [70]
Question 36
36 New streetlights will be installed along a section of the highway. The posts for the streetlights willbe 7.5 m tall and made of aluminum. The city can choose to buy the posts shaped like cylindersor the posts shaped like rectangular prisms. The cylindrical posts have a hollow core, with aluminum 2.5 cm thick, and an outer diameter of 53.4 cm. The rectangular-prism posts have a hollow core, with aluminum 2.5 cm thick, and a square base that measures 40 cm on each side.
The density of aluminum is 2.7 g/cm3, and the cost of aluminum is $0.38 per kilogram.
If all posts must be the same shape, which post design will cost the town less?
How much money will be saved per streetlight post with the less expensive design?
Work space for question 36 is continued on the next page.
Geometry (Common Core) – Jan. ’17 [71]
Question 36
Score 3: The student found the cost for the rectangular prism post, but no further correct work wasshown.
Question 36 continued
Geometry (Common Core) – Jan. ’17 [72]
Question 36
36 New streetlights will be installed along a section of the highway. The posts for the streetlights willbe 7.5 m tall and made of aluminum. The city can choose to buy the posts shaped like cylindersor the posts shaped like rectangular prisms. The cylindrical posts have a hollow core, with aluminum 2.5 cm thick, and an outer diameter of 53.4 cm. The rectangular-prism posts have a hollow core, with aluminum 2.5 cm thick, and a square base that measures 40 cm on each side.
The density of aluminum is 2.7 g/cm3, and the cost of aluminum is $0.38 per kilogram.
If all posts must be the same shape, which post design will cost the town less?
How much money will be saved per streetlight post with the less expensive design?
Work space for question 36 is continued on the next page.
Geometry (Common Core) – Jan. ’17 [73]
Question 36
Score 2: The student’s procedure was correct, but contained multiple errors, such as using thediameter instead of the radius. The student stated an appropriate cost difference, but didnot identify which post design will cost less.
Question 36 continued
Geometry (Common Core) – Jan. ’17 [74]
Question 36
36 New streetlights will be installed along a section of the highway. The posts for the streetlights willbe 7.5 m tall and made of aluminum. The city can choose to buy the posts shaped like cylindersor the posts shaped like rectangular prisms. The cylindrical posts have a hollow core, with aluminum 2.5 cm thick, and an outer diameter of 53.4 cm. The rectangular-prism posts have a hollow core, with aluminum 2.5 cm thick, and a square base that measures 40 cm on each side.
The density of aluminum is 2.7 g/cm3, and the cost of aluminum is $0.38 per kilogram.
If all posts must be the same shape, which post design will cost the town less?
How much money will be saved per streetlight post with the less expensive design?
Work space for question 36 is continued on the next page.
Geometry (Common Core) – Jan. ’17 [75]
Question 36
Score 1: The student found the volume of only one post, and no further correct relevant work wasshown.
Question 36 continued
Geometry (Common Core) – Jan. ’17 [76]
Question 36
36 New streetlights will be installed along a section of the highway. The posts for the streetlights willbe 7.5 m tall and made of aluminum. The city can choose to buy the posts shaped like cylindersor the posts shaped like rectangular prisms. The cylindrical posts have a hollow core, with aluminum 2.5 cm thick, and an outer diameter of 53.4 cm. The rectangular-prism posts have a hollow core, with aluminum 2.5 cm thick, and a square base that measures 40 cm on each side.
The density of aluminum is 2.7 g/cm3, and the cost of aluminum is $0.38 per kilogram.
If all posts must be the same shape, which post design will cost the town less?
How much money will be saved per streetlight post with the less expensive design?
Work space for question 36 is continued on the next page.
Geometry (Common Core) – Jan. ’17 [77]
Question 36
Score 0: The student did not show enough relevant correct work to receive any credit.
The State Education Department / The University of the State of New York
Regents Examination in Geometry (Common Core) – January 2017Chart for Converting Total Test Raw Scores to Final Exam Scores (Scale Scores)
To determine the student’s final examination score (scale score), find the student’s total test raw score in the columnlabeled “Raw Score” and then locate the scale score that corresponds to that raw score. The scale score is thestudent’s final examination score. Enter this score in the space labeled “Scale Score” on the student’s answer sheet.
RawScore
ScaleScore
Performance Level
ScaleScore
Performance Level
Performance Level
(Use for the January 2017 exam only.)
Schools are not permitted to rescore any of the open-ended questions on this exam after each question hasbeen rated once, regardless of the final exam score. Schools are required to ensure that the raw scores havebeen added correctly and that the resulting scale score has been determined accurately.
Because scale scores corresponding to raw scores in the conversion chart change from one administration to another,it is crucial that for each administration the conversion chart provided for that administration be used to determine thestudent’s final score. The chart above is usable only for this administration of the Regents Examination in Geometry(Common Core).
