KIPP NYC College Prep - Spring Recess Packet

8/7/2019 KIPP NYC College Prep - Spring Recess Packet

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GEOMETRY

The University of the State of New York

REGENTS HIGH SCHOOL EXAMINATION

GEOMETRYTuesday, June 16, 20099:15 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.

This examination has four parts, with a total of 38 questions. You must answer

all questions in this examination. Record your answers to the Part I multiple-choicequestions, using a No. 2 pencil, on the separate answer sheet provided to you. Writeyour answers to the questions in Parts II, III, and IV directly in this test booklet. Allwork for Parts II, III, and IV should be written in pen, except graphs and drawings,which should be done in pencil. Clearly indicate the necessary steps, includingappropriate formula substitutions, diagrams, graphs, charts, etc.

The formulas that you may need to answer some questions iri this examinationare found at the end of the examination. This sheet is perforated so you may removeit 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 graph

paper is provided at the end of this booklet for any question for which graphing maybe helpful but is not required. You may remove this sheet from this booklet. Anywork 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 of thequestions or answers prior to the examination and that you have neither given norreceived assistance in answering any of the questions during the examination. Youranswer sheet cannot be accepted if you fail to sign this declaration.

Notice . . .

A graphing calculator, a straightedge (ruler), and a compass must be available for you to use whiletaking this examination.

The use of any communications device is strictly prohibited when taking thisexamination. If you use any communications device, no matter how briefly, yourexamination will be invalidated and no score will be calculated for you.

N

DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.

AH13IAIO30


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Part I

Answer all 28 questions in this part. Each correct answer will receive 2 credits. No partialcredit will be allowed. For each question, record your answer, using a No. 2 pencil, on the separateanswer sheet provided to you. [56]

1 Juliann plans on drawing AABC, where the measure of Z.A can rangefrom 50 to 60 and the measure of Z-B can range from 90 to 100,Given these conditions, what is the correct range of measures possiblefo r Z.C?

Use this space for

computations.

(1) 20 to 40'

(2) 30 to 50'

(3) 80 to 90

(4) 120 to 130'

2 In the diagram of AABC and ADEF below, AB = DE, LAand Z.B = Z.E.

D

Which method can be used to prove AABC

(1) SSS (3) ASA

(2) SAS (4) HL

ADEF?

Geometry - June '09 [2]


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3 In the diagram below, under which transform ation willAA'B'C" bethe image of A ABC?

Use this space forcomputations.

\ B

(1) rotation

(2) dilation

(3) translation(4 ) glide reflection

4 The lateralfaces of a regular pyramid are com posed of

(1) squares (3) congruent right triangles(2) rectangles (4 ) congruent isoscelestriangles

5 Point A is located at (4 ,image islocated at

(1) (-4,7)(2) (-4-7)

7). The point is reflected in thex-axis. Its

(3) (4,7)

(4) (7,-4)

Geometry - June *09 [3] [OVER]


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6 In the diagram of circle O below, chords AB and CD are parallel, andB D is a diameter of the circle.


If mA D = 60,what is m^CDB?

(1) 20 (3) 60

(2) 30 (4) 120

7 What is an equation of the line that passes through the point ( 2,5)

and is perpendicular to the line whose equation is y x + 5?

(1) y = 2x + 1 (3) y = 2x + 9

(2) y = -2r + 1 (4) y = -2x - 9



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8 After a composition of transformations,the coordinates A(4,2),B(4,6),and C(2,6) become A!'(- 2,-1), B"(-2,-3), and C"(-l,-3), as shown

' on the set ofaxes below.


Which composition of transformations was used?

(1 ) K 180 , D

(2) R D 090

(3)

(4) 90C

9 In an equilateral triangle, what is the difference between the sum ofthe exterior angles and the sum of the interior angles?

(1) 180 (3) 90

(2) 120 (4) 60



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Use this space for

10 What is ati equation of a circle with its center at ( 3,5)and a radius computations.of 4?/ '(1) (x - 3)2 + (y + 5)2 =16(2) (x + 3) 2 + (y - 5) 2 = 16

(3) (x - 3)2 + (y .+ 5) 2 - 4

(4 ) (x + 3)2 + (t /-5)2

=

11 In AABC,m^A = 95, mZ.B = 50, and mZ.C = 35. Which expressioncorrectly relates the lengths of the sides of this triangle?

(1) AB < BC < CA (3) AC < BC < AB

(2) AB < AC < BC (4) BC < AC < AB

12 In a coordinate plane, how many points are both 5 units from theorigin and 2 units from the x-axis?

(1) 1 (3) 3(2) 2 (4) 4

13 What is the contrapositive of the statement, "If I am tall, then I willbump m y head"?

(1) If I bump my head, then I am tall.

(2) If I do notbump m y head, then I am tall.

(3) If I am tall, then I will not bump my head.

(4 ) If I do not bump my head, then I am not tall.

Geometry-June'09 [6]


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14 In thediagram of AABC below, Jose found centroid P by constructingthe three medians. He measured CF and found it to be 6 inches.


A

ED

B

If PF = x, which equation can be used to find x?

(1) x + x = 6 (3) 3x + 2x = 62(2) 2x + x = 6 (4) x + - x x = 6

15 In the diagram below, the length of the legs AC and BC of righttriangle ABC are 6 cm and 8 cm, respectively. Altitude CD is drawnto the hypotenuse of AABC.

A

6 c m

xD

8cm B

What is the length ofAD to the nearest tenth of a centimeter?

(1) 3.6 (3) 6.4

(2) 6.0 (4) 4.0

Geometry - June '09 [7] [OVER.


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16 In the diagram below, tangent AB and secant ACD are drawn tocircle O from an external point A, AB = 8, andAC = 4.


D

What is the length of CD ?

(D 16(2) 13

(3) 12

(4) 10

17 In the diagram of AABC and AEDC below, AE and B D intersectat C, and Z.CAB = ZCED.

A

D

Which method can be used to show that AABC must be similar toAEDC?

(1) SAS

(2) AA

(3) SSS

(4 ) HL

Geometry - June *09 [8]


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18 Point P is on line m. What is the total number of planes that areperpendicular to line m and pass through point P?

' (1) 1 (3) 0(2) 2 (4) infinite


19 Square LMNO is shown in the diagram below.

What are the coordinates of the midpoint of diagonal LN ?

(3) (-213l)v w I ^ 2 2 ;\ /

(4) 2' 2

Geometry - June '09 [9] [OVER]


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20 Which graph represents a circle with the equation(x - 5)2 + (y + I) 2 = 9?


( i ) (3)

(2) (4)



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21 In the diagram below, a right circular cone has a diameter of 8 inchesarid a height of 12 inches.


8 inches

12 inches

What is the volume of the cone to the nearest cubic inch?

(1) 201

(2) 481

(3) 603

(4 ) 804

22 A circle is represented by the equation x2 + ( y + 3)2 = 13. Whatare the coordinates of the center of the circle and the length of theradius?

(1) (0,3) and 13(2) (0,3)andVl3

(3) (0,-3) and 13(4 ) (0,-3)andVl3

Geometry - June *09 t in [OVER]


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23 Given the system of equations:2 _f f "_ 'V*

yx

/v* B^.^. j/ji

The number of points of intersection is

(1) 1 (3) 3

(2) 2 (4) 0


24 Side PQ of APQR is extended through Q to point T. Which statement

is not always true?

(1 ) mZ.RQT > mZ-R (3) m/.RQT = m / _ P + m'Z.R

(2) m/,RQT>mP (4) mZ-RQT > m/.PQR

25 Which illustration shows the correct construction of an angle bisector?

( i ) (3)

(2) (4)



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Use this space for26 Which equation represents a line perpendicular to the line whose i computations.

equation is 2x + 3y = 12?

(1 ) 6y = -4x + 12 (3) 2y = -3x + 6

(4 ) 3y = -2x + 12

27 In AABC, point D is onAB, and point is onBC suchJthatDE AC.If DB = 2,DA = 7, and DE - 3, what is the length of AC"?

(1 ) 8 (3) 10.5

(2 ) 9 (4) 13.5 .

28 In three-dimensional space, two planes are parallel and a third planeintersects both of the parallel planes. The intersection of the planes is a

(1 ) plane (3) pair of parallel lines

(2 ) point (4 ) pair of intersecting lines

Geometry-June'09 [13] [OVER]


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Part II

Answer all 6 questions in this part. Each correct answer will receive 2 credits. Clearlyindicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. For all questions in this part, a correct numerical answer with no work shown willreceive only 1 credit. All answers should be written in pen, except for graphs and drawings,which should be done in pencil. [12]

29 In the diagram of AABC below, AB = 10, BC = 14, and AC = 16. Find the perimeter of thetriangle formed by connecting the midpoints of the sides of AABC.

10 14



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30 Using a compass and straightedge, construct a line that passes through point P and is perpendicularto line m. [Leave all construction marks.]

31 Find an equation of the line passing through the point (5,4) and parallel to the line whose equationis 2x + y = 3.



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32 The length ofAB is 3 inches. On the diagram below, sketch the points that are equidistant fromA and B and sketch the points that are 2 inches from A. Label with an X allpoints that satisfy bothconditions.

B



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33 Given: Two is an even integer or three is an even integer.

Determine the truth value of this disjunction. Justify your answer.



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34 In the diagram below, AABC ~ AEFG, m/_C = 4x + 30, and m/.G = 5x + 10. Determine thevalueof x.



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Part III

Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearlyindicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. For all questions in this part, a correct numerical answer with no work shown willreceive only 1 credit. All answers should be written in pen, except for graphs and drawings,which should be done in pencil. [12]

35 In the diagram below, circles X and Y have two tangents drawn to them from external point T. Thepoints of tangency are C, A, S, and E. The ratio of TA to AC is 1:3. If TS = 24, find the lengthofSE.

(Not drawn to scale)



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36 Triangle ABC has coordinates A( 6,2) , B( 3,6),and C(5,0). Find the perimeter of the triangle.Express your answer in simplest radical form. [The use of the grid below is optional.]



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37 The coordinates of the vertices of parallelogram AB CD are A(-2,2), B(3,5), C(4,2),andD(l,-l).State the coordinates of the vertices of parallelogram A"B"C"D"that result from the transformationr . T0 0. [The use of the set ofaxes below is optional. ]w-axis 2 , 3 L JT J



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Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicatethe necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.A correct numerical answer with no work shown will receive only 1 credit. The answer shouldbe written in pen. [6]

38 Given:AABC and AEDC, C is the midpoint of ED and AE

Prove: AB DE



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REGENTS EXAMINATION INGEOMETRY

TEST SAMPLERFALL 2008

The University o the State o New YorkTHE STATE EDUCATION DEPARTMENT

O f ce o Standards, Assessments and ReportingAlbany, New York 12234www.emsc.nysed.gov/osa/


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October 2008

Dear Colleagues:

Thank you or your support as we begin the second year o the transition to the new RegentsExaminations in mathematics. We are continuing to develop the new Regents Examination inGeometry, which will be administered or the f rst time in June 2009. That administration willbe the second step in the transition rom Mathematics A and Mathematics B to IntegratedAlgebra, Geometry, and Algebra 2/Trigonometry that will take place over the next two years.

The Regents Examination in Geometry is being developed to evaluate student achievemento the Mathematics Learning Standard 3 and the core curriculum, revised 2005. This RegentsExamination in Geometry Test Sampler consists o the types o questions, the ormatting, andthe scoring guides that are being developed or the examination. It also includes exampleso student work rom f eld tests. This Test Sampler may be printed and duplicated or use inclassroom instruction.

The Department is proud o its tradition o involving New York State teachers in a variety o curriculum guidance initiatives. Over the years, thousands o teachers have worked with us,and the expertise o diverse educators representing New Yorks diverse student population is

essential in guiding this important work.Through our Call or Expertise on the Departments web site,we encourage teachers to

become involved in test development and standard-setting activities . Please downloadand complete the Call or Expertise application oundat:

http://www.emsc.nysed.gov/ciai/call.htm

Thank you or all the work that you do on behal o the students in New York State.

Sincerely,

David Abrams

THE STATE EDUCATION DEPARTMENT/ THE UNIVERSITY OF THE STATE OF NEW YORK/ALBANY, NY 122

David Abrams, Assistant CommissionerOf ce of Standards, Assessment and Reporting


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Contents

Introduction ivGeneral Directions to the Student 1

Test Questions 2Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Part II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Part III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Part IV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Re erence Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Scrap Graph Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Sample Answer Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Scoring Guide 29

Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Part II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Part III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Part IV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Appendices 71Appendix A: Specif cations or the Regents Examination in Geometry . . . . . . . . . . . . . . 71Appendix B: Map to Learning Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Geometry Sampler Fall 08 iii


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Introduction

In March 2005, the Board o Regents adopted a new Learning Standard or Mathematics and issued arevised Mathematics Core Curriculum, resulting in the need or the development and phasing in o threenew Regents Examinations in mathematics: Integrated Algebra, Geometry, and Algebra 2/Trigonometry.These new Regents Examinations in mathematics will replace the current Regents Examinations inMathematics A and Mathematics B. Students must pass any one o these new commencement-level RegentsExaminations in order to ul ill the mathematics Regents Examination requirement or graduation. The

irst administration o the Regents Examination in Integrated Algebra took place in June 2008. The irstadministration will take place in June 2009 or the Regents Examination in Geometry and in June 2010 orthe Regents Examination in Algebra 2/Trigonometry. The Regents Examination in Geometry will be basedon the content o the Mathematics Core Curriculum (Revised 2005).

The Regents Examination in Geometry Test Sampler provides examples o the ormat and typeso questions that will comprise the operational examination. The scoring guide in the sampler includesexamples o student responses rom ield testing and the credit allowed or each response.

The re erence sheet included in the test sampler will also be provided as part o the operationalexamination booklet. A straightedge (ruler), a compass, and a graphing calculator must be available orthe exclusive use o each student taking the examination. For the operational examination, the memory o any calculator with programming capability must be cleared, reset, or disabled when students enter thetesting room. I the memory o a students calculator is password-protected and cannot be cleared, thecalculator must not be used. Students may not use calculators that are capable o symbol manipulationor that can communicate with other calculators through in rared sensors, nor may students use operatingmanuals, instruction or ormula cards, or other in ormation concerning the operation o calculators duringthe examination.

The sampler may be duplicated for use in your classroom.

Geometry Sampler Fall 08 iv


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The University of the State of New York

REGENTS HIGH SCHOOL EXAMINATION

GEOMETRY

TEST SAMPLERFALL 2008

GENERAL DIRECTIONS TO THE STUDENT

Answer all 38 questions in this examination. Write your answers to the Part I multiple-choice questions onthe separate answer sheet. No partial credit will be allowed on the multiple-choice section.

For Parts II, III, and IV, clearly indicate the necessary steps, including appropriate ormula substitutions,diagrams, graphs, charts, etc. For all questions in these parts, a correct numerical answer with no work shownwill receive only 1 credit.

A re erence sheet that you may need to answer some questions in this examination is included.

Scrap paper is not permitted or any part o this examination, but you may use the blank spaces in thisexamination as scrap paper. Scrap graph paper is provided at the end o this examination or any question owhich graphing may be help ul but is not required. Any work done on this sheet o scrap graph paper willnotbe scored. Write all your work in pen, except graphs and drawings, which should be done in pencil.

Note: A graphing calculator, a straightedge (ruler), and a compass must be available or you to use whiletaking this examination.

Geometry Sampler Fall 08 1


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Part I

Answer all 28 questions in this part. Each correct answer will receive 2 credits. No partialcredit will be allowed. For each question, write on the separate answer sheet the numeralpreceding the word or expression that best completes the statement or answers the question.


Use this space forcomputations.1 Isosceles trapezoid ABCD has diagonals

_ AC and

_ BD . I AC = 5x + 13 and BD = 11x 5, what is the value o x? (1) 28 (3) 3(2) 103 __ 4

(4) 1 __ 2

2 What is the negation o the statement The Sun is shining?

(1) It is cloudy.

(2) It is daytime.(3) It is not raining.(4) The Sun is not shining.

3 Triangle ABC has vertices A(1,3), B(0,1), and C(4,0). Under atranslation, A, the image point o A, is located at (4,4). Under thissame translation, point C is located at(1) (7,1) (3) (3,2)(2) (5,3) (4) (1,1)


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Use this space forcomputations.4 The diagram below shows the construction o the perpendicular

bisector o _

AB .

Which statement is not true?

(1) AC = CB (3) AC = 2AB(2) CB = 1 __ 2

AB (4) AC + CB = AB


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Use this space forcomputations.5 Which graph could be used to ind the solution to the ollowing

system o equations?y = x + 2

y = x2

x

y

x

y

(1) (3)

x

y

x

y

(2) (4)

6 Line k is drawn so that it is perpendicular to two distinct planes,P and R. What must be true about planes P and R?

(1) Planes P and R are skew.(2) Planes P and R are parallel.(3) Planes P and R are perpendicular.(4) Plane P intersects plane R but is not perpendicular to

plane R.


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Use this space forcomputations.7 The diagram below illustrates the construction o PS

parallel toRQ

through point P.

Which statement justi ies this construction?

(1) m1 = m2 (3)_PR

_RQ

(2) m1 = m3 (4)_PS

_RQ

8 The igure in the diagram below is a triangular prism.

Which statement must be true?

(1)_

DE _

AB (3)_

AD _

CE

(2)

_

AD

_

BC (4)

_

DE

_

BC


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Use this space forcomputations.9 The vertices o ABCare A(1,2), B(1,2), and C(6,0). Which

conclusion can be made about the angles o ABC?

(1) mA = mB (3) mACB= 90(2) mA = mC (4) mABC= 60

10 Given ABC with base _ AFEDC, median _ BF, altitude _ BD, and_ BE bisectsABC, which conclusion is valid?

(1) FAB ABF (3)_

CE _

EA (2) ABF CBD (4)

_ CF

_ FA


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Use this space forcomputations.11 In the diagram below, circle O has a radius o 5, and

CE = 2. Diameter_

AC is perpendicular to chord_

BD at E.

What is the length o _

BD ?

(1) 12 (3) 8

(2) 10 (4) 4

12 What is the equation o a line that passes through the point( 3,11) and is parallel to the line whose equation is 2x y = 4?(1) y = 2x + 5 (3) y = 1 __ 2

x + 25 __ 2

(2) y = 2x 5 (4) y = 1 __ 2 x 25 __ 2


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Use this space forcomputations.13 Line segment AB has endpoints A(2, 3) and B( 4,6). What are

the coordinates o the midpoint o _

AB ?(1) ( 2,3) (3) (1,3)

(2) ( 1,11 __ 2 ) (4) ( 3,41 __ 2 )

14 What are the center and radius o a circle whose equation is(x A)2 + (y B)2 = C?

(1) center = (A,B); radius = C(2) center = (A,B); radius = C(3) center = (A,B); radius =

__ C

(4) center = (A,B); radius = __

C

15 A rectangular prism has a volume o 3x 2 + 18x + 24. Its base hasa length o x + 2 and a width o 3. Which expression representsthe height o the prism?

(1) x + 4 (3) 3(2) x + 2 (4) x 2 + 6x + 8


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Use this space forcomputations.16 Lines k1 and k2 intersect at point E. Line m is perpendicular to

lines k1 and k2 at point E.

E

k 1

k 2

m

Which statement is always true?

(1) Lines k1 and k2 are perpendicular.(2) Line m is parallel to the plane determined by

lines k1 and k2.(3) Line m is perpendicular to the plane determined by

lines k1 and k2.(4) Line m is coplanar with linesk1 and k2.


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Use this space forcomputations.17 In the diagram below, PS is a tangent to circle O at point S,

PQR is a secant, PS = x, PQ = 3, and PR = x + 18.

R

QP

S

O

(Not drawn to scale)

What is the length o PS?(1) 6 (3) 3(2) 9 (4) 27

18 A polygon is trans ormed according to the rule: (x, y) (x + 2, y).Every point o the polygon moves two units in which direction?

(1) up (3) le t(2) down (4) right


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Use this space forcomputations.19 In the diagram below o ABC, D is a point on

_ AB ,

AC = 7, AD = 6, and BC = 18.

The length o _

DB could be

(1) 5 (3) 19(2) 12 (4) 25

20 The diameter o a circle has endpoints at ( 2,3) and (6,3). Whatis an equation o the circle?

(1) (x 2)2 + (y 3)2 = 16(2) (x 2)2 + (y 3)2 = 4

(3) (x + 2)2 + (y + 3)2 = 16(4) (x + 2)2 + (y + 3)2 = 4


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Use this space forcomputations.21 In the diagram below o PRT , Q is a point on

_ PR , S is a point

on_

TR,_

QS is drawn, andRPT RSQ.

Which reason justi ies the conclusion thatPRT ~SRQ ?

(1) AA (3) SAS(2) ASA (4) SSS

22 The lines 3y + 1 = 6x + 4 and 2y + 1 = x 9 are(1) parallel(2) perpendicular(3) the same line(4) neither parallel nor perpendicular

23 The endpoints o _

ABare A(3,2) and B(7,1). I _ ABis the result

o the trans ormation o _

AB under D T 4,32 what are thecoordinates o Aand B?

(1) A(2,10) andB(6,8)(2) A(1,5) and B(3,4)(3) A(2,7) and B(10,5)

(4) A(14 , 2) andB(22, 4)


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Use this space forcomputations.24 In the diagram below, circle A and circle B are shown.

What is the total number o lines o tangency that are common

to circle A and circle B? (1) 1 (3) 3(2) 2 (4) 4

25 In which triangle do the three altitudes intersect outside thetriangle?(1) a right triangle(2) an acute triangle(3) an obtuse triangle(4) an equilateral triangle

26 Two triangles are similar, and the ratio o each pair o corresponding sides is 2 : 1. Which statement regarding the two

triangles is not true? (1) Their areas have a ratio o 4 : 1.(2) Their altitudes have a ratio o 2 : 1.(3) Their perimeters have a ratio o 2 : 1.(4) Their corresponding angles have a ratio o 2 : 1.


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Use this space forcomputations.27 What is the measure o an interior angle o a regular octagon?

(1) 45 (3) 120 (2) 60 (4) 135

28 What is the slope o a line perpendicular to the line whoseequation is 5x + 3y = 8?

(1) 5 __ 3 (3) 3 __ 5

(2) 3 __ 5 (4) 5 __ 3


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Part II

Answer all 6 questions in this part. Each correct answer will receive 2 credits. Clearlyindicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. For all questions in this part, a correct numerical answer with no work shown willreceive only 1 credit. [12]


29 In the diagram below o right triangleACB, altitude_

CD intersects_

ABat D. I AD = 3 and DB = 4,ind the length o

_ CD in simplest radical orm.


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30 The vertices o ABCare A(3,2), B(6,1), and C(4,6). Identi y and graph a trans ormation o ABC such that its image,ABC, results in

_ AB AB .


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31 The endpoints o _

PQ are P(3,1) and Q(4,25). Find the length o _

PQ.


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32 Using a compass and straightedge, construct the bisector o the angle shown below. [Leave allconstruction marks.]


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33 The volume o a cylinder is 12,566.4 cm3. The height o the cylinder is 8 cm. Find the radius o thecylinder to the nearest tenth of a centimeter .

34 Write a statement that is logically equivalent to the statement I two sides o a triangle arecongruent, the angles opposite those sides are congruent.

Identi y the new statement as the converse, inverse, or contrapositive o the original statement.


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Part III

Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearlyindicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. For all questions in this part, a correct numerical answer with no work shown willreceive only 1 credit. [12]


35 On the set o axes below, graph and label

DEF with vertices at D(4,4), E(2,2), and F(8,2).I G is the midpoint o EF and H is the midpoint o DF, state the coordinates o G and H and labeleach point on your graph.

Explain why _

GH _

DE .


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36 In the diagram below o circleO, chords DF, DE, FG, and EG are drawn such thatm : m : m : m = 5 : 2 : 1 : 7DF FE EG GD

. Identi y one pair o inscribed angles that are congruentto each other and give their measure.


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37 A city is planning to build a new park. The park must be equidistant rom schoolA at (3,3) andschool B at (3, 5). The park also must be exactly 5 miles rom the center o town, which is located atthe origin on the coordinate graph. Each unit on the graph represents 1 mile.

On the set o axes below, sketch the compound loci and label with anX all possible locations or thenew park.


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Part IV

Answer the question in this part. The correct answer will receive 6 credits. Clearly indicatethe necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.For the question in this part, a correct numerical answer with no work shown will receive only1 credit. [6]


38 In the diagram below, quadrilateral ABCDis inscribed in circleO,

_

AB

_

DC , and diagonals

_

AC and_ BD are drawn.Prove that ACD BDC.


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Volume

Lateral Area ( L )

Surface Area

Cylinder

Pyramid

Right Circular Cone

Sphere

V Bh

where B is the area of the base

Right Circular Cylinder

Right Circular Cone

Sphere

V Bh


13

V Bh


13

V r 343

L 2 rh

SA 4 r 2

L

rl

where l is the slant height

Geometry Reference Sheet



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SAMPL

E1 . . . . . . . . . . . . . . . .

2 . . . . . . . . . . . . . . . .

3 . . . . . . . . . . . . . . . .

4 . . . . . . . . . . . . . . . .

5 . . . . . . . . . . . . . . . .

6 . . . . . . . . . . . . . . . .

7 . . . . . . . . . . . . . . . .

8 . . . . . . . . . . . . . . . .

9 . . . . . . . . . . . . . . . .

10 . . . . . . . . . . . . . . . .

11 . . . . . . . . . . . . . . . .

12 . . . . . . . . . . . . . . . .

13 . . . . . . . . . . . . . . . .

14 . . . . . . . . . . . . . . . .

15 . . . . . . . . . . . . . . .

16 . . . . . . . . . . . . . . . .

17 . . . . . . . . . . . . . . . .

18 . . . . . . . . . . . . . . . .

19 . . . . . . . . . . . . . . . .

20 . . . . . . . . . . . . . . . .

21 . . . . . . . . . . . . . . . .

22 . . . . . . . . . . . . . . .

23 . . . . . . . . . . . . . . . .

24 . . . . . . . . . . . . . . . .

25 . . . . . . . . . . . . . . . .

26 . . . . . . . . . . . . . . . .

27 . . . . . . . . . . . . . . . .

28 . . . . . . . . . . . . . . . .

Your answers for Parts II, III, and IV should be written in the test booklet.

The declaration below should be signed when you have completed the examination.I do hereby affirm, at the close of this examination, that I had no unlawful knowledge of the questions or answers prior to theexamination and that I have neither given nor received assistance in answering any of the questions during the examination.

Signature

The University of the State of New YorkREGENTS HIGH SCHOOL EXAMINATION

GEOMETRY TEST SAMPLERFall 2008

ANSWER SHEET

Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: Male Female Grade . . . . . . . .

Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Your answers to Part I should be recorded on this answer sheet.

Part I

Answer all 28 questions in this part.



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SAMPLE

GEOMETRY TEST SAMPLERRaters/Scorers Name

(minimum of three)


GEOMETRY TEST SAMPLER

Question MaximumCreditCreditsEarned

Raters/ScorersInitials

Part I 128 56

Part II 29 2

30 2

31 2

32 2

33 2

34 2

Part III 35 4

36 4

37 4

Part IV 38 6

MaximumTotal 86

Total RawScore

Checked by


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Logic and Reasoning Hansan

Use Every Digit Write up Instructions:

You must include each of the components listed below. You may work with your team to find the correct answer, but

you

are

each

responsible

for

your

own

write

up.

The

rubric

for

how

you

and

your

group

will

be

graded

is

on

the

back

of

this paper.

1) Explanation of the Problems

In your own words, describe the important elements of the problem. Write as if you were explaining this problem to

someone who has never been in this class and does not have any clue what we have been working on. Be sure you

include the constraints and what you are trying to achieve.

2) Problem solving strategies

What did you do to solve this problem? What were the paths you took that did not work out? This section should

include at least two mistakes you made early on in the process and what you learned from it. Focus on explaining your

thinking. This section should include diagrams that you used to solve the problem.

3) Final answer and justification

What is your final answer? How can you justify that your answer is correct? Be clear and explicit

4) Reflection

You need to write about what you are taking away from this problem. What did you learn from this problem? What

was difficult about the problem? What was easy for you? How did you work with your team? What did you contribute

to the team? What do I need to know about this problem for the future?

The final write up is due Wednesday April 27th, 2011. This will be an assessment grade and no late work will be accepted.


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Logic and Reasoning Hansan

Problem Solving : Use Every Digit

Teacher Name: Mr. Hansan

Student Name: ________________________________________

CATEGORY 4 3 2 1 Explanation Explanation is

detailed and clear. Explanation is clear.

Explanation is a little difficult to understand, but includes critical components.

Explanation is difficult to understand and is missing several components OR was not included.

Diagrams and Sketches

Diagrams and/or sketches are clear and greatly add to the reader's understanding of the procedure(s).

Diagrams and/or sketches are clear and easy to understand.

Diagrams and/or sketches are somewhat difficult to understand.

Diagrams and/or sketches are difficult to understand or are not used.

Neatness and Organization

The work is presented in a neat, clear, organized fashion that is easy to

read.

The work is presented in a neat and organized fashion that is usually easy to

read.

The work is presented in an organized fashion but may be hard to read at times.

The work appears sloppy and unorganized. It is hard to know what information goes

together.

Completion Write up includes all of the following: restatement of problems, problem solving process including mistakes, final answer, justification, reflection on the process.

All but one of the parts are completed.

All but two of the parts are completed.

Several of the problems are not completed.

Working with Others

Student was an engaged partner, listening to suggestions of others and working cooperatively throughout lesson.

Student was an engaged partner but had trouble listening to others and/or working cooperatively.

Student cooperated with others, but needed prompting to stay on task.

Student did not work effectively with others.


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Europea n Exp loration from 1400 to 1700 Workshee t

Spain France England Portugal

Reasons for Exploration

Obstacles to Exploration

Accomplishments/Regionsexplored and name of explorer

Impact of Exploration


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Unit 6: Kafka, Symbolism and Allegory

Spring Break AssignmentEnglish 10

Monday-TuesdayApril 18- 26, 2011

Reading Expectations:Read vii- xx of The Metamorphosis. Answer the questions in this packet.

Want up to 10 points extra credit on your critical lens? Read The Country Doctor and answer theattached questions.

Other Expectations:Complete your Twelfth Night final project. Descriptions attached again.


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Introduction: The Metamorphosis : The Monstrosity of Alienation

Answer the following questions in full sentences.

1. According to the writer, what aspects of Kafkas identity most likely caused his feelings of

marginalization within Czech society?_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

2. What are the two ways readers generally consider Gregors transformation in the story?_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

3. Describe Kafkas family life. Where was he born? What were his familys economic circumstances?How big was his family?

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

4. Describe Kafka as an individual. What was his profession?_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

5. What were the issues Kafka experienced with his health?_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________


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6. What famous text brought about the rise of socialism in Prague in the late 19 th/early 20 th century?_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

7. How were Jews treated in Prague in the late 19 th century?_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

8. Why, according to Camus, is Kafka not able to be considered existential ?_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________


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Ms. Wondwossen Name: ________________________________

Speech and Comp 9 April Break Homework

Background: When we come back from break, we will be starting a debate/argumentative writing unit. In order to get ready, spend some time brainstorming and outlining an essay using the organizer below. Once you have planned your response, you need to write a one page single spaced essay convincing the

reader of your point.

Task: Imagine that you have one opportunity to change a rule at KIPPNYCCP that you do not like. You

are writing a one page persuasive piece to be sent to Ms. Webb. You want to make such a strong case

for why the rule needs to change so that she might even change the rule for the school! The goal is for

you to identify a rule that you do not agree with, come up with a strong argument against it and support

your argument with reasonable and persuasive reasons.

What you will turn in on Wednesday May 4 th

Graphic Organizer Final typed draft

Your final draft should include (five paragraphs total):

Introduction with your claim/argument (underlined) Three body paragraphs with evidence to support your claim A conclusion

Your Body Paragraphs should have:

Topic sentence with states one reason why the rule should change Several supporting details for your point Concluding sentence.


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Name __________________________________________ 02 CW Cultural Diffusion Break Work April 12, 2011 Period ________ Global History/ Ms. Woods

Do Now: Explain 2 examples of cultural diffusion that we have discussed in Global History. _________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

Causes of Cultural Blending 1. ______________________________________ 2. _________________________________

3. ______________________________________ 4. _________________________________

Cultural Diffusion Project Part I

1. Choose 4 topics to research from the topics listed below. 2. Questions to answer: (on the graphic organizer provided)

a) How or why did this example of cultural diffusion occur? Did it happen because of migration, pursuit of

religious freedom or conversion, trade, or conquest? Explain your answer. b) Where did the culture begin and were did it diffuse to? (Be sure to include dates.) c) In what ways were things changed?

Part II Create a collage of pictures to show your examples of cultural diffusion. (2 4 pictures for each example)

Diffusion Topics

Architecture: arch, dome, column

Religion:

Tibetan Buddhism to Zen Buddhism Christianity in Africa, America Islam in Africa, America Protestantism to America (Puritans)

Government Rome: Republic found today in the United States (you could use NY state or local government as an example) Greece: Direct Democracy Be sure to explain how the governments are different.

Racial/Ethnic: Mestizo

Mulatto

Food: Columbian Exchange: (pg. 572) you can use any food pictured as an example of cultural diffusion. Explain how

the food became staples of diet for certain regions, ex. Potato to Ireland, Tomato to Italy, Sugar Cane to the Americas

Music: Spanish Flamenco, Celtic, Cajun, Afro Peruvian, Afro Cuban, Indian Bhangra, Caribbean Calypso, Brazilian Samba You could also focus on a specific instrument

DUE APRIL 28, 2011


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Project Outline Page

Four topics 1. _________________________________________

2. _________________________________________

3. _________________________________________

4. _________________________________________

Notes

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

Possible Pictures _________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________

_________________________________________________________________________________________________


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Name _________________________________________________

Cultural Diffusion

Blended Culture

How or Why? Beginning, Spread, Dates


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Spring Recess Assignments For Mathematics

All Exams can be found in your Green Booklet.

Pollock

Finish

January

2009

in

green

booklet

and

do

the

multiple

choice of June 2009

Cathcart Geometry and Integrated Algebra classes will complete the

Entire JUNE 2009 Regents. Please show work for all open ended

examples.

Leon Algebra Entire June 2009 Questions 31 39 on loose leaf

Trig Entire Test #1 Questions 28 39 on loose leaf

Hansan June 2009 Regents

Nelson June 2009 Regents and 2008 Fall Sampler

Documents

KIPP NYC College Prep - Spring Recess Packet