# TENTH YEAR MATHEMATICS

Size: px
Start display at page:

Transcription

2 Part I Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit will he allowed. Unless otherwise specified, answers may he left in terms of1t or in radical form. Write your answers in the spaces provided on the separate answer sheet. 1 In the accompanying diagram ofisosceles triangle ABC, AB BC and the measure of an exterior angle at B is Find mla. 4 In circle 0, chords AB and TR are eacb 5 centimeters from the center O. If mab = 73, find mtr. 5 The coordinates of the vertices of 6ABC are A(0,6), B(O,O), and C(8,0). Find the area of the triangle. A C -7 6 In the accompanyinagram, AB is tangent to circle 0 at A and macd 270. Find mlbad. 2 In the accompanying figure, AB Ii CD II EF with transversal BCE. If Ll\CB is a right angle and mlbac 60, find mlx. 3 In the accompanying diagram, 6DEF is inscribed in circle O. If mld = 70 and mdf = 130, find mlf. 7 In 6RST, mlr 50, mls = x + 5, and mlt = x 5. Which side of the triangle is the longest? 8 Point M is the midpoint of CD. The coordinates of Care (6, - 2) and the coordinates of Mare (0,0). Find the coordinates of point D. 9 The ratio of the areas of two similar triangles is 25:36. What is the ratio ofa pair ofcorresponding sides of these two triangles? 10 What is the slope of the line which passes through the points (-2,4) and (3,5)? Math. 10-June '85 [2]

3 11 In the accompanying diagram of 6RST, DE II ST, RDS, RET, mlr = 80, and mlrde = 40. Find mlt. R Directions (14-30): Write in the space provided on the separate answer sheet the number preceding the expression that best completes each statement or answers each question. 14 Congruent circles may be defined as circles with congruent (1) centers (3) central angles (2) chords (4) radii S T 15 Which is an equation ofthe locus ofpoints 3 units above the x-axis? (1) x 3 (3) Y = 3 (2) x = -3 (4)!I = In the accompanying diagram of circle 0, diameter AB is perpendicular to chord CD at E. If CD 8 and OE = 3, find the length of the radius of the circle. A E B 13 In the accompanying diagram, the radius OA of the larger circle is the diameter of the smaller circle. If OA 4, find the area of the shaded region in terms of 1T. o 16 In rhombus ABCD, the bisectors of LB and LC must be (1) parallel (3) perpendicular (2) oblique (4) congruent 17 Which is always a regular polygon? (1) rectangle (3) trapezoid (2) square (4) rhombus 18 The lengths of the sides of a right triangle are 6, 8, and 10. What is the tangent of the smallest angle of the triangle? 8 (1) + (3) 10 (2) 10 (4) 8 19 In a triangle whose angles measure 30, 60, and 90, the length of the hypotenuse is represented by 8a. The length of the side opposite the 60 angle is (1) 4a (3) 4aV2 (2) 4aV3 (4) V&l 20 In 6.4BC, mlc = 90 and D is any point on between A and C. Which statement must be true? (1) BD..L AC (3) BC > BD (2) CD > BC (4) BD > DC 21 If the area of a trapezoid is 32 and the altitude is 4, the sum of the bases is (1) 8 (3) 16 (2) 12 (4) 24 Math, 10-June '85 [3] [OVER1

4 22 In right triangle RST, angle bisectors RM, SN, and TV are drawn and intersect at point X. Which statement is true? R 26 If two circles with radii 2 and 5 are drawn such that the distance between their centers is 6, what is the maximum number of common tangents they may have? (1) 0 (3) 3 (2) 2 (4) 4 S----M T (1) Point X is the center of only the inscribed circle. (2) Point X is the center of only the circumscribed circle. (3) Point X is the center of both the inscribed circle and the circumscribed circle. (4) Point X is the center of neither the inscribed circle nor the circumscribed circle. 23 The measure of the central angle of a sector of a circle is If the radius of the circle is 6, the area of the sector is (1) 47T (3) 67r (2) 87r (4) 127T 24 The diagonals of parallelogram ABeD intersect at point E. IfDB = 4x + 2 and DE = x + 4, then the value of x is (1) 1 (3) 3 (2) 2- (4) Parallel lines e and mare 6 centimeters apart and P is a point on line e. The total number of points in the plane that are equidistant from e and m and also 3 centimeters from P is (1) 1 (3) 3 (2) 2 (4) 0 27 The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into two segments with lengths 10 and 3. The length of the altitude is (1) 7 (3) V100 (2) 13 (4) V30 28 The lines whose equations are x = 3 and y = 2x - 1 intersect at the point whose coordinates are (1) (3, -1) (3) (3,5) (2) (2,3) (4) (0, -1) 29 Given the statement: "If two triangles are congruent, then they are equal in area." Which of the following is true? (1) The statement is true but its inverse is false. (2) The statement is true and its inverse is true. (3) The statement is false and its inverse is false. (4) The statement is false but its inverse is true. 30 Which equation can not be derived from the pro. a r? portion b = -;. r + s (1) =!!.- (3) a + b r s b s (2) =!!.- (4)!!.- =!.. s r a r Math. lo-june '85 [4]

5 Answers to the following questions are to be written on paper provided by the school. Part II Answer four questions from this part. Show all work unless otherwise directed. 31 Prove either a or b but not both. 33 Given: CEB is tangent to circle 0 at B, a The measure ofan angle formed by two secants diameter BA II CD. Secants DFB and EFA is equal to one-half the difference of the intersect circle 0 at F. measures of the intercepted arcs. [10] OR b The square ofthe length ofthe hypotenuse ofa right triangle is equal to the sum ofthe squares of the lengths of the legs. [10] 32 Given: tangent CA and secant CDB are drawn to circle 0, chord AB == chord BD, and mlcad 30. A c BD AE Prove: -- = - CD BE [IOJ 34 Given: [).ABC, AB == BC, ED II AC, DC 1. AB, EF 1. BC, BCEA, and BFDC. B --. Find: a mad [2] b mlb [2] --. c mbd [2] d mlbac [2] e mlc [2] A c Prove: CE FD [10] GO RIGHT ON TO THE NEXT PAGE. Math. 10-June '85 [5] [OVER]

6 35 Given: PA and PB are tangent to the circle at A and B, respectively, R lies in the interior of the circle, AR and BR are drawn, and RP does not bisect LAPB. 36 A circle is inscribed in a regular polygon of 10 sides. The radius of the circle is 12. a Find the length of the apothem ofthe polygon. [2] b Find the length of a side of the polygon to the nearest tenth. [5] c Using the results from parts a and b, find the area of the polygon to the nearest integer. [3] R P Prove: R is not the center of the circle. [10] *37 Given: DABG with vertices A(O,O), B(8,3), and C(0,6). a Show that DABG is an isosceles triangle. [3] b Find the area of DABG. [3] c Write an equation of the line through G perpendicular to AB. [4] *This question is based on an optional topic in the syllabus. Math. 10-June '85 [6]

### TENTH YEAR MATHEMATICS

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION TENTH YEAR MATHEMATICS Tuesday, June 16,1987-1:15 to 4:15 p.m., only The last page of the booklet is the answer sheet. Fold the last

### TENTH YEAR MATHEMATICS

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION TENTH YEAR MATHEMATICS Thursday, January 26, 1989-1:1.5 to 4:1.5 p.m., only The last page of the booklet is the answer sheet. Fold

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 27, 2011 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Tuesday, January 28, 1992-9:15 a.m. to 12:15 p.m., only Notice... If your

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Wednesday, August 16, :30 to 11:30 a.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Wednesday, August 16, 000 8:30 to 11:30 a.m., only Notice... Scientific

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 17, 2011 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of

### 0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.

0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I,

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXMINTION GEOMETRY Thursday, January 26, 2012 9:15 a.m. to 12:15 p.m., only Student Name: Notice School Name: Print your name and the

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Tuesday, August 13, 2002 8:30 to 11:30 a.m., only Notice... Scientific

### 0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?

0113ge 1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? 1) XV ) WX 3) VW 4) NP 4 In the diagram below, under which transformation is A B C the image of ABC? In circle

### 0114ge. Geometry Regents Exam 0114

0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Tuesday, January 26, 1993-9:15 a.m. to 12:15 p.m., only Notice... Calculators

### 0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.

Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would

### 0609ge. Geometry Regents Exam AB DE, A D, and B E.

0609ge 1 Juliann plans on drawing ABC, where the measure of A can range from 50 to 60 and the measure of B can range from 90 to 100. Given these conditions, what is the correct range of measures possible

### 0612ge. Geometry Regents Exam

0612ge 1 Triangle ABC is graphed on the set of axes below. 3 As shown in the diagram below, EF intersects planes P, Q, and R. Which transformation produces an image that is similar to, but not congruent

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Friday, January 26, :15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Friday, January 26, 2001 9:15 a.m. to 12:15 p.m., only Notice... Scientific

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Friday, January 26, :15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXMINTION THREE-YER SEQUENCE FOR HIGH SCHOOL MTHEMTICS COURSE II Friday, January 26, 2001 9:15 a.m. to 12:15 p.m., only Notice... Scientific

### Indicate whether the statement is true or false.

PRACTICE EXAM IV Sections 6.1, 6.2, 8.1 8.4 Indicate whether the statement is true or false. 1. For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number.

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II

The University of the State of New York REGENTS HIGH SHOOL EXAMINATION THREE-YEAR SEQUENE FOR HIGH SHOOL MATHEMATIS OURSE II Tuesday, August 3, 2002 8:30 to :30 a.m., only Notice... Scientific calculators

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE III. Wednesday, June 21, :15 to 4:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Wednesday, June, 000 :5 to 4:5 p.m., only Notice... Scientific calculators

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE I. Wednesday, August 16, :30 to 11:30 a.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE I Wednesday, August 16, 2000 8:30 to 11:30 a.m., only Notice... Scientific

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Wednesday, June 19, 00 1:15 to 4:15 p.m., only Notice... Scientific calculators

### 1 What is the solution of the system of equations graphed below? y = 2x + 1

1 What is the solution of the system of equations graphed below? y = 2x + 1 3 As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. y = x 2 + 2x

### 0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism.

0610ge 1 In the diagram below of circle O, chord AB chord CD, and chord CD chord EF. 3 The diagram below shows a right pentagonal prism. Which statement must be true? 1) CE DF 2) AC DF 3) AC CE 4) EF CD

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Friday, June 0, 00 1:15 to 4:15 p.m., only Notice... Scientific calculators

### GEOMETRY. Part I. _,_ c. August 2010

GEOMETRY Part I nswer all 28 questions in this part. Each correct answer will receive,',"eliits. No partial credit will be allowed. For each question, write on the "pnce provided the numeral preceding

### Chapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in

Chapter - 10 (Circle) Key Concept * Circle - circle is locus of such points which are at equidistant from a fixed point in a plane. * Concentric circle - Circle having same centre called concentric circle.

### 0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.

0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation

### 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT.

1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would prove l m? 1) 2.5 2) 4.5 3)

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Wednesday, June 21, :15 to 4:15 p.m.

The University of the State of New York REGENTS HIGH SHOOL EXMINTION THREE-YER SEQUENE FOR HIGH SHOOL MTHEMTIS OURSE II Wednesday, June, 000 :5 to 4:5 p.m., only Notice... Scientific calculators must be

### Use this space for computations. 1 In trapezoid RSTV below with bases RS and VT, diagonals RT and SV intersect at Q.

Part I Answer all 28 questions in this part. Each correct answer will receive 2 credits. For each statement or question, choose the word or expression that, of those given, best completes the statement

### 0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?

0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB AC. The measure of B is 40. 1) a b ) a c 3) b c 4) d e What is the measure of A? 1) 40 ) 50 3) 70 4) 100

### 0811ge. Geometry Regents Exam

0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation

### COURSE II. From the digital collections of the New York State Library. THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS REGENTS HIGH SCHOOL EXAMINATION

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Tuesday, June 16, 1981-1:15 to 4:15 p.m., only The last page of the booklet

### ( ) ( ) Geometry Team Solutions FAMAT Regional February = 5. = 24p.

. A 6 6 The semi perimeter is so the perimeter is 6. The third side of the triangle is 7. Using Heron s formula to find the area ( )( )( ) 4 6 = 6 6. 5. B Draw the altitude from Q to RP. This forms a 454590

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B. Tuesday, January 26, :15 a.m. to 12:15 p.m.

MATHEMATICS B The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Tuesday, January 26, 2010 9:15 a.m. to 12:15 p.m., only Print Your Name: Print Your School s Name: Print

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE III. Friday, January 25, :15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Friday, January 5, 00 9:5 a.m. to :5 p.m., only Notice... Scientific calculators

### --- -._==--:--.AL-.- -'m"" _ 1/ \ \.. / 6 -6 \/4. ...v

10 Part Answer all 8 questions in this part. Each correct answer will receive credits. No partial credit will be allowed. For each question, write in the space provided the numeral preceding the word or

Triangles 1.In ABC right angled at C, AD is median. Then AB 2 = AC 2 - AD 2 AD 2 - AC 2 3AC 2-4AD 2 (D) 4AD 2-3AC 2 2.Which of the following statement is true? Any two right triangles are similar

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Tuesday, January 22, :15 to 4:15 p.m.

The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Tuesda, Januar, 00 1:15 to 4:15 p.m., onl Notice... Scientific calculators

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II

The University of the State of New York REGENTS HGH SCHOOL EXAMNATON THREE-YEAR SEQUENCE FOR HGH SCHOOL MATHEMATCS COURSE Thursday, June 17, 1993-9:1.5 a.m. to 12:15 p.m., only Notice... Calculators must

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Wednesday, June 21, :15 to 4:15 p.m.

The University of the State of New York REGENTS HIGH SHOOL EXMINTION THREE-YER SEQUENE FOR HIGH SHOOL MTHEMTIS OURSE II Wednesday, June, 000 :5 to 4:5 p.m., only Notice... Scientific calculators must be

### Unit 10 Geometry Circles. NAME Period

Unit 10 Geometry Circles NAME Period 1 Geometry Chapter 10 Circles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (10-1) Circles and Circumference

### SM2H Unit 6 Circle Notes

Name: Period: SM2H Unit 6 Circle Notes 6.1 Circle Vocabulary, Arc and Angle Measures Circle: All points in a plane that are the same distance from a given point, called the center of the circle. Chord:

### 0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?

0110ge 1 In the diagram below of trapezoid RSUT, RS TU, X is the midpoint of RT, and V is the midpoint of SU. 3 Which expression best describes the transformation shown in the diagram below? If RS = 30

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Tuesday, June 19, :15 a.m. to 12:15 p.m.

GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, June 19, 2018 9:15 a.m. to 12:15 p.m., only Student Name: School Name: The possession or use of any communications

### Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch

Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. in the parallelogram, each two opposite

### 0616geo. Geometry CCSS Regents Exam x 2 + 4x = (y 2 20)

0616geo 1 A student has a rectangular postcard that he folds in half lengthwise. Next, he rotates it continuously about the folded edge. Which three-dimensional object below is generated by this rotation?

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Thursday, June 20, 2002 :5 to 4:5 p.m., only Notice... Scientific calculators

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Thursday, June 20, 2002 :5 to 4:5 p.m., only Notice... Scientific calculators

### THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE II Thursday, January 22~ 1981-1:15 to 4:15 p.m., only The last page of the

### QUESTION BANK ON STRAIGHT LINE AND CIRCLE

QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,

### Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper.

Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. 12. What angle has the same measure as its complement? How do you know? 12. What is the

### JEFFERSON MATH PROJECT REGENTS AT RANDOM

JEFFERSON MATH PROJECT REGENTS AT RANDOM The NY Geometry Regents Exams Fall 2008-August 2009 Dear Sir I have to acknolege the reciept of your favor of May 14. in which you mention that you have finished

### 2016 State Mathematics Contest Geometry Test

2016 State Mathematics Contest Geometry Test In each of the following, choose the BEST answer and record your choice on the answer sheet provided. To ensure correct scoring, be sure to make all erasures

### Unit 1. GSE Analytic Geometry EOC Review Name: Units 1 3. Date: Pd:

GSE Analytic Geometry EOC Review Name: Units 1 Date: Pd: Unit 1 1 1. Figure A B C D F is a dilation of figure ABCDF by a scale factor of. The dilation is centered at ( 4, 1). 2 Which statement is true?

### 0116ge. Geometry Regents Exam RT and SU intersect at O.

Geometry Regents Exam 06 06ge What is the equation of a circle with its center at (5, ) and a radius of 3? ) (x 5) + (y + ) = 3 ) (x 5) + (y + ) = 9 3) (x + 5) + (y ) = 3 4) (x + 5) + (y ) = 9 In the diagram

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE I. Tuesday, June 20, :15 to 4:15 p.m., only

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE I Tuesday, June 0, 000 :5 to :5 p.m., only Notice... Scientific calculators

### Geometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems

Geometry Final Review Name: Per: Vocab Word Acute angle Adjacent angles Angle bisector Collinear Line Linear pair Midpoint Obtuse angle Plane Pythagorean theorem Ray Right angle Supplementary angles Complementary

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Thursday, August 13, 1992-8:30 to 11:30 a.m., only Notice... Calculators

### JEFFERSON MATH PROJECT REGENTS AT RANDOM

JEFFERSON MATH PROJECT REGENTS AT RANDOM The NY Geometry Regents Exams Fall 2008-January 2010 Dear Sir I have to acknolege the reciept of your favor of May 14. in which you mention that you have finished

### C=2πr C=πd. Chapter 10 Circles Circles and Circumference. Circumference: the distance around the circle

10.1 Circles and Circumference Chapter 10 Circles Circle the locus or set of all points in a plane that are A equidistant from a given point, called the center When naming a circle you always name it by

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE III. Friday, January 25, :15 a.m. to 12:15 p.m.

The Universit of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE III Frida, Januar 5, 00 9:5 a.m. to :5 p.m., onl Notice... Scientific calculators

### Geometry Final Exam REVIEW

Name: Class: _ Date: _ Geometry Final Exam 09-10 - REVIEW Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the perimeter and area of the parallelogram.

### (D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2

CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5

### Incoming Magnet Precalculus / Functions Summer Review Assignment

Incoming Magnet recalculus / Functions Summer Review ssignment Students, This assignment should serve as a review of the lgebra and Geometry skills necessary for success in recalculus. These skills were

### 21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle.

21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 22. Prove that If two sides of a cyclic quadrilateral are parallel, then

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE I. Tuesday, June 19, :15 to 4:15 p.m., only

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE I Tuesday, June 1, 2001 1:15 to 4:15 p.m., only Notice... Scientific calculators

### chapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?

chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "

### EOC Review MC Questions

Geometry EOC Review MC Questions Name Date Block You must show all work to receive full credit. - For every 5 answers that are correct, you may receive 5 extra points in the quiz category for a total of

### Chapter 10. Properties of Circles

Chapter 10 Properties of Circles 10.1 Use Properties of Tangents Objective: Use properties of a tangent to a circle. Essential Question: how can you verify that a segment is tangent to a circle? Terminology:

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE I. Tuesday, June 19, :15 to 4:15 p.m., only

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION THREE-YEAR SEQUENCE FOR HIGH SCHOOL MATHEMATICS COURSE I Tuesday, June 19, 2001 1:15 to 4:15 p.m., only Notice... Scientific calculators

### Name: Class: Date: c. WZ XY and XW YZ. b. WZ ZY and XW YZ. d. WN NZ and YN NX

Class: Date: 2nd Semester Exam Review - Geometry CP 1. Complete this statement: A polygon with all sides the same length is said to be. a. regular b. equilateral c. equiangular d. convex 3. Which statement

### Geometry Note Cards EXAMPLE:

Geometry Note Cards EXAMPLE: Lined Side Word and Explanation Blank Side Picture with Statements Sections 12-4 through 12-5 1) Theorem 12-3 (p. 790) 2) Theorem 12-14 (p. 790) 3) Theorem 12-15 (p. 793) 4)

### Proofs. by Bill Hanlon

Proofs by Bill Hanlon Future Reference To prove congruence, it is important that you remember not only your congruence theorems, but know your parallel line theorems, and theorems concerning triangles.

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name: School Name:

GEOMETRY The University of the State of New Yk REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Tuesday, June 16, 2009 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name of your

### VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)

BY:Prof. RAHUL MISHRA Class :- X QNo. VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CIRCLES Subject :- Maths General Instructions Questions M:9999907099,9818932244 1 In the adjoining figures, PQ

### NINTH YEAR MATHEMATICS

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION NINTH YEAR MATHEMATICS Wednesday, August 17, 1977-8:30 to 11:30 a.m., only The last page of the booklet is the answer sheet. Fold

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B. Tuesday, June 15, :15 a.m. to 12:15 p.m.

MATHEMATICS B The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Tuesday, June 5, 00 9:5 a.m. to :5 p.m., only Print Your Name: Print Your School s Name: Print your name

### LLT Education Services

8. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. (a) 4 cm (b) 3 cm (c) 6 cm (d) 5 cm 9. From a point P, 10 cm away from the

### Maharashtra State Board Class X Mathematics Geometry Board Paper 2015 Solution. Time: 2 hours Total Marks: 40

Maharashtra State Board Class X Mathematics Geometry Board Paper 05 Solution Time: hours Total Marks: 40 Note:- () Solve all questions. Draw diagrams wherever necessary. ()Use of calculator is not allowed.

### GEOMETRY (Common Core)

GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Tuesday, June 2, 2015 1:15 to 4:15 p.m., only Student Name: School Name: The possession

### Example 1: Finding angle measures: I ll do one: We ll do one together: You try one: ML and MN are tangent to circle O. Find the value of x

Ch 1: Circles 1 1 Tangent Lines 1 Chords and Arcs 1 3 Inscribed Angles 1 4 Angle Measures and Segment Lengths 1 5 Circles in the coordinate plane 1 1 Tangent Lines Focused Learning Target: I will be able

### Study Guide. Exploring Circles. Example: Refer to S for Exercises 1 6.

9 1 Eploring ircles A circle is the set of all points in a plane that are a given distance from a given point in the plane called the center. Various parts of a circle are labeled in the figure at the

### G.GPE.B.4: Quadrilaterals in the Coordinate Plane 2

Regents Exam Questions www.jmap.org Name: 1 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

### Midterm Review Packet. Geometry: Midterm Multiple Choice Practice

: Midterm Multiple Choice Practice 1. In the diagram below, a square is graphed in the coordinate plane. A reflection over which line does not carry the square onto itself? (1) (2) (3) (4) 2. A sequence

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

GEOMETRY The University of the State of New Yk REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 27, 2011 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name

### 2005 Palm Harbor February Invitational Geometry Answer Key

005 Palm Harbor February Invitational Geometry Answer Key Individual 1. B. D. C. D 5. C 6. D 7. B 8. B 9. A 10. E 11. D 1. C 1. D 1. C 15. B 16. B 17. E 18. D 19. C 0. C 1. D. C. C. A 5. C 6. C 7. A 8.

### Circles. II. Radius - a segment with one endpoint the center of a circle and the other endpoint on the circle.

Circles Circles and Basic Terminology I. Circle - the set of all points in a plane that are a given distance from a given point (called the center) in the plane. Circles are named by their center. II.

### Correlation of 2012 Texas Essential Knowledge and Skills (TEKS) for Algebra I and Geometry to Moving with Math SUMS Moving with Math SUMS Algebra 1

Correlation of 2012 Texas Essential Knowledge and Skills (TEKS) for Algebra I and Geometry to Moving with Math SUMS Moving with Math SUMS Algebra 1 ALGEBRA I A.1 Mathematical process standards. The student

### Topic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths

Topic 2 [312 marks] 1 The rectangle ABCD is inscribed in a circle Sides [AD] and [AB] have lengths [12 marks] 3 cm and (\9\) cm respectively E is a point on side [AB] such that AE is 3 cm Side [DE] is

Chapter 3 Cumulative Review Answers 1a. The triangle inequality is violated. 1b. The sum of the angles is not 180º. 1c. Two angles are equal, but the sides opposite those angles are not equal. 1d. The

### , The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY

, The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION... I I GEOMETRY i i Tuesday, June 19, 2018-9:15 a.m. to 12:15 p.m., only The possession or :use of any communications device is

### Due to the detail of some problems, print the contests using a normal or high quality setting.

General Contest Guidelines: Keep the contests secure. Discussion about contest questions is not permitted prior to giving the contest. Due to the detail of some problems, print the contests using a normal

### The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B. Tuesday, June 23, :15 to 4:15 p.m.

MATHEMATICS B The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Tuesday, June 23, 2009 1:15 to 4:15 p.m., only Print Your Name: Print Your School s Name: Print your

### Quads. 4. In the accompanying figure, ABCD is a parallelogram, m A = 2x + 35, and m C = 5x 22. Find the value of x.

Name: Date: 1. In the accompanying diagram of rhombus ACD, the lengths of the sides A and C are represented by 3x 4 and 2x + 1, respectively. Find the value of x. 4. In the accompanying figure, ACD is

### Name Score Period Date. m = 2. Find the geometric mean of the two numbers. Copy and complete the statement.

Chapter 6 Review Geometry Name Score Period Date Solve the proportion. 3 5 1. = m 1 3m 4 m = 2. 12 n = n 3 n = Find the geometric mean of the two numbers. Copy and complete the statement. 7 x 7? 3. 12

### Geometry Final Exam 2014 Study Guide. Name Date Block

Geometry Final Exam 014 Study Guide Name Date Block The final exam for Geometry will take place on June 5. The following study guide will help you prepare for the exam. Everything we have covered is fair