JEFFERSON MATH PROJECT REGENTS BY …...JEFFERSON MATH PROJECT REGENTS BY CHAPTER All 1165 NY Math A & B Regents Exam Questions from June 1999 to August 2005 Sorted by Prentice Hall

JEFFERSON MATH PROJECTREGENTS BY CHAPTER

All 1165 NY Math A & B Regents Exam Questions fromJune 1999 to August 2005 Sorted by Prentice Hall Chapter

GEOMETRY

www.jmap.org

Dear Sir

I have to acknolege the reciept of your favor of May 14. in which you mention that you have finished the6. first books of Euclid, plane trigonometry, surveying & algebra and ask whether I think a furtherpursuit of that branch of science would be useful to you. there are some propositions in the latter books ofEuclid, & some of Archimedes, which are useful, & I have no doubt you have been made acquainted withthem. trigonometry, so far as this, is most valuable to every man, there is scarcely a day in which he will notresort to it for some of the purposes of common life. the science of calculation also is indispensible as far asthe extraction of the square & cube roots; Algebra as far as the quadratic equation & the use of logarithmsare often of value in ordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; butnot to be indulged in by one who is to have a profession to follow for his subsistence. in this light I view theconic sections, curves of the higher orders, perhaps even spherical trigonometry, Algebraical operationsbeyond the 2d dimension, and fluxions. Letter from Thomas Jefferson to William G. Munford, Monticello, June 18, 1799.

TABLE OF CONTENTSGEOMETRY

PRENTICE HALL CHAPTERNUMBER OF

REGENTS QUESTIONSPAGE

1 Tools of Geometry 11 1

2 Investigating Geometric Figures 28 2

3 Transformations: Shapes in Motion 57 6

4 Triangle Relationships 73 15

5 Measuring in the Plane 52 24

6 Measuring in Space 19 31

7 Reasoning and Parallel Lines 8 34

8 Proving Triangles Congruent 7 36

9 Quadrilaterals 14 37

10 Similarity 15 40

11 Right Triangle Geometry 9 42

12 Chords, Secants, and Tangents 27 43

320

Math A & B Regents Exam Questions by Prentice Hall Chapter - Geometry Page 1www.jmap.org

GEOMETRY CHAPTER 1-6

NY LESSON 31. In the accompanying diagram of a construction,

what does PC represent?

[A] a median drawn to AB

[B] the bisector of ∠APB

[C] the perpendicular bisector of AB

[D] an altitude drawn to AB

2. Using only a ruler and compass, construct thebisector of angle BAC in the accompanyingdiagram.

3. Using only a compass and a straightedge,construct the perpendicular bisector of AB andlabel it c. [Leave all construction marks.]

4. On the accompanying diagram of ∆ABC , use acompass and a straightedge to construct amedian from A to BC .


5. Construct a triangle with sides of lengths a, b,and c, as shown below. Be sure the longest sideof your triangle lies on PQ and that point P isone of the triangle's vertices. [Show all arcsnecessary for a valid construction.]


NY LESSON 2

6. In the accompanying diagram, AB and CDintersect at E. If m AEC x∠ = −4 40 andm BED x∠ = + 50 , find the number of degrees in∠AEC.

7. ABsuur

and CDsuur

intersect at point E,m AEC x∠ = +6 20, and m DEB x∠ = 10 .What is the value of x?

[A] 2114

[B] 438

[C] 5 [D] 10

8. In the accompanying figure, two lines intersect,m t∠ = +3 6 30 , and m t∠ = −2 8 60. Find thenumber of degrees in m ∠ 4.

9. If the measure of an angle is represented by 2x,which expression represents the measure of itscomplement?

[A] 90 + 2x [B] 180 - 2x

[C] 90 - 2x [D] 88x

10. Two angles are complementary. One angle has ameasure that is five times the measure of theother angle. What is the measure, in degrees, ofthe larger angle?

11. The ratio of two supplementary angles is 2:7.What is the measure of the smaller angle?

[A] 14° [B] 40° [C] 20° [D] 10°

GEOMETRY CHAPTER 2-112. What is the measure of the largest angle in the

accompanying triangle?

[A] 46.5 [B] 41 [C] 83 [D] 56


13. In ∆ABC , the measure of ∠B is 21 less thanfour times the measure of ∠A , and the measureof ∠C is 1 more than five times the measure of∠A . Find the measure, in degrees, of eachangle of ∆ABC .

14. In the accompanying diagram of ∆BCD , ∆ABCis an equilateral triangle and AD = AB. What isthe value of x, in degrees?

15. In which of the accompanying figures aresegments XY and YZ perpendicular?

[A] figure 1, only [B] figure 2 only

[C] both figure 1 and figure 2

[D] neither figure 1 nor figure 2

16. In the accompanying diagram, ABCDsuuuuuur

is astraight line, and angle E in triangle BEC is a rightangle.

What does a° + d° equal?

[A] 270° [B] 180°

[C] 135° [D] 160°

17. In the accompanying diagram of ∆ABC , AB isextended to D, exterior angle CBD measures145°, and m C∠ = 75.

What is m CAB∠ ?

[A] 35 [B] 70 [C] 110 [D] 220

18. Triangle ABC, with side AC extended to D, isshown in the accompanying diagram. Ifm ABC∠ = 63 and m BCD∠ = 92 , what ism BAC∠ ?

19. In the accompanying diagram of ∆BCD ,m C m CDE∠ = ∠ =70 130, , and side BD isextended to A and to E. Find m CBA∠ .

20. Which phrase does not describe a triangle?

[A] acute scalene [B] isosceles right

[C] equilateral equiangular [D] obtuse right

21. In right triangle ABC, m C y∠ = −3 10,m B y∠ = + 40, and m A∠ = 90. What type ofright triangle is triangle ABC?

[A] isosceles [B] scalene

[C] equilateral [D] obtuse


GEOMETRY CHAPTER 2-222. What is the sum, in degrees, of the measures of

the interior angles of a stop sign, which is in theshape of an octagon?

[A] 1,880 [B] 1,440

[C] 1,080 [D] 360

23. The sum of the measures of the interior angles ofan octagon is

[A] 360° [B] 1,080°

[C] 540° [D] 180°

24. What is the sum, in degrees, of the measures ofthe interior angles of a pentagon?

[A] 900 [B] 540 [C] 180 [D] 360

25. The accompanying figure represents a section ofbathroom floor tiles shaped like regularhexagons.

What is the measure of angle ABC?

[A] 150° [B] 120°

[C] 90° [D] 60°

26. What is the measure, in degrees, of each exteriorangle of a regular hexagon?

[A] 120 [B] 45 [C] 60 [D] 135

27. Melissa is walking around the outside of abuilding that is in the shape of a regular polygon.She determines that the measure of one exteriorangle of the building is 60°. How many sidesdoes the building have?

[A] 6 [B] 12 [C] 9 [D] 3

28. A stop sign in the shape of a regular octagon isresting on a brick wall, as shown in theaccompanying diagram.

What is the measure of angle x?

[A] 60° [B] 45° [C] 135° [D] 120°

GEOMETRY CHAPTER 2-429. Which statement about quadrilaterals is true?

[A] All quadrilaterals are parallelograms.

[B] All quadrilaterals have four right angles.

[C] All quadrilaterals have equal sides.

[D] All quadrilaterals have four sides.

30. Which statement is not always true about aparallelogram?

[A] The diagonals are congruent.

[B] The opposite sides are congruent.

[C] The opposite sides are parallel.

[D] The opposite angles are congruent.

31. In a certain quadrilateral, two opposite sides areparallel, and the other two opposite sides are notcongruent. This quadrilateral could be a

[A] square [B] rhombus

[C] parallelogram [D] trapezoid


32. Al says, "If ABCD is a parallelogram, thenABCD is a rectangle." Sketch a quadrilateralABCD that shows that Al's statement is notalways true. Your sketch must show the lengthof each side and the measure of each angle forthe quadrilateral you draw.

33. The cross section of an attic is in the shape of anisosceles trapezoid, as shown in theaccompanying figure. If the height of the attic is 9feet, BC = 12 feet, and AD = 28 feet, find thelength of AB to the nearest foot.

GEOMETRY CHAPTER 2-534. The accompanying circle graph shows how the

Marino family spends its income each month.

What is the measure, in degrees, of the centralangle that represents the percentage of incomespent on food?

[A] 90 [B] 360 [C] 25 [D] 50

35. Mr. Smith's class voted on their favorite icecream flavors, and the results are shown in theaccompanying diagram. If there are 20 studentsin Mr. Smith's class, how many students chosecoffee ice cream as their favorite flavor?

36. The accompanying circle graph shows thefavorite colors of the 300 students in the ninthgrade. How many students chose red as theirfavorite color?


37. In a recent poll, 600 people were asked whetherthey liked Chinese food. A circle graph wasconstructed to show the results. The centralangles for two of the three sectors are shown inthe accompanying diagram. How many peoplehad no opinion?

38. In a class of 24 students, 10 have brown hair, 8have black hair, 4 have blond hair, and 2 havered hair. On the accompanying diagram,construct a circle graph to show the students' haircolor.

39. Nine hundred students were asked whether theythought their school should have a dress code. Acircle graph was constructed to show the results.The central angles for two of the three sectorsare shown in the accompanying diagram. Whatis the number of students who felt that the schoolshould have no dress code?

GEOMETRY CHAPTER 340. In the accompanying diagram, which

transformation changes the solid-line parabola tothe dotted-line parabola?

[A] rotation, only [B] translation

[C] line reflection, only

[D] line reflection or rotation

41. Which transformation does not always producean image that is congruent to the original figure?

[A] dilation [B] translation

[C] reflection [D] rotation

42. In the accompanying diagram, ∆ABC is similarto but not congruent to ∆A B C' ' ' . Whichtransformation is represented by ∆A B C' ' ' ?

[A] reflection [B] dilation

[C] rotation [D] translation


43. The transformation of ∆ABC to ∆AB C' ' isshown in the accompanying diagram.

This transformation is an example of a

[A] translation

[B] line reflection in point l[C] rotation about point A [D] dilation

44. The accompanying diagram shows atransformation.

Which transformation performed on figure 1resulted in figure 2?

[A] reflection [B] translation

[C] dilation [D] rotation

45. Which type of transformation is illustrated in theaccompanying diagram?

[A] dilation [B] rotation

[C] reflection [D] translation

46. A picture held by a magnet to a refrigerator slidesto the bottom of the refrigerator, as shown in theaccompanying diagram.

This change of position is an example of a

[A] reflection [B] rotation

[C] translation [D] dilation


47. As shown in the accompanying diagram, the starin position 1 on a computer screen transforms tothe star in position 2.

This transformation is best described as a

[A] line reflection [B] rotation

[C] dilation [D] translation

GEOMETRY CHAPTER 3-148. Which transformation is not an isometry?

[A] ry x= [B] T3 6, [C] R0 90, ° [D] D2

49. Which transformation is not an isometry?

[A] rotation [B] line reflection


50. Which transformation is a direct isometry?

[A] T2 5, [B] D2 [C] ry axis− [D] D−2

51. Which transformation is an opposite isometry?

[A] rotation of 90° [B] line reflection


52. Which transformation is an example of anopposite isometry?

[A] (x,y) → (y,-x) [B] (x,y) → (3x,3y)

[C] (x,y) → (x + 3,y - 6)

[D] (x,y) → (y,x)

53. Which transformation does not preserveorientation?

[A] dilation [B] translation

[C] reflection in the y-axis [D] rotation

54. If x = -3 and y = 2, which point on theaccompanying graph represents − −x y, ?b g

[A] P [B] Q [C] R [D] S

55. What is the image of point − −3 1,b g under areflection in the origin?

[A] (1, 3) [B] (3, 1)

[C] (-1, -3) [D] (-3, 1)

56. When the point 2 5,−b g is reflected in the x-axis,what are the coordinates of its image?

[A] (5, 2) [B] (-5, 2)

[C] (2, 5) [D] (-2, 5)


57. Triangle SUN has coordinates S(0,6), U(3,5),and N(3,0). On the accompanying grid, drawand label ∆SUN . Then, graph and state thecoordinates of ∆S U N' ' ' , the image of ∆SUNafter a reflection in the y-axis.

58. The coordinates of the endpoints of AB areA(0,2) and B(4,6). Graph and state thecoordinates of A’ and B’, the images of A and Bafter AB is reflected in the x-axis.

59. On the accompanying set of axes, draw thereflection of ABCD in the y-axis. Label and statethe coordinates of the reflected figure.

60. What are the coordinates of point P, the image ofpoint (3,-4) after a reflection in the line y = x?

[A] (-4,3) [B] (4,-3)

[C] (-3,4) [D] (3,4)

61. In the accompanying diagram of square ABCD,F is the midpoint of AB, G is the midpoint of

BC, H is the midpoint of CD, and E is themidpoint of DA.

Find the image of ∆EOA after it is reflected inline l.Is this isometry direct or opposite? Explain youranswer.


62. The graph below represents f(x).

Which graph best represents f(-x)?

[A] [B]

[C] [D]

GEOMETRY CHAPTER 3-263. The image of point (3,-5) under the translation

that shifts (x,y) to (x-1, y-3) is

[A] (-4,8) [B] (2,8)

[C] (2,-8) [D] (-3,15)

64. In the accompanying graph, if point P hascoordinates a b, ,b g which point has coordinates

− b a, ?b g

[A] A [B] B [C] D [D] C

65. If x = -2 and y = -1, which point on theaccompanying set of axes represents thetranslation x y x y, , ?b g b g→ + −2 3

[A] S [B] Q [C] T [D] R

66. What is the image of point (2,5) under thetranslation that shifts (x,y) to (x + 3, y - 2)?

[A] (5,3) [B] (0,3) [C] (0,8) [D] (5,8)

67. What is the image of (x, y) after a translation of 3units right and 7 units down?

[A] (x - 3, y + 7) [B] (x + 3, y + 7)

[C] (x - 3, y - 7) [D] (x + 3, y - 7)

68. A translation moves P(3,5) to P’(6,1). What arethe coordinates of the image of point (-3,-5)under the same translation?

[A] (-5,-3) [B] (0,-9)

[C] (-6,-1) [D] (-6,-9)

69. What are the coordinates of P', the image of P(-4, 0) under the translation (x - 3, y + 6)?

[A] (2,-3) [B] (-7,6)

[C] (1,6) [D] (7,-6)


70. The image of the origin under a certain translationis the point (2,-6). The image of point (-3,-2)under the same translation is the point

[A] ( , )−32

13

[B] (-1,-8)

[C] (-6,12) [D] (-5,4)

71. Two parabolic arches are to be built. Theequation of the first arch can be expressed asy x= − +2 9, with a range of 0 9≤ ≤y , and thesecond arch is created by the transformationT7 0, . On the accompanying set of axes, graph

the equations of the two arches. Graph the lineof symmetry formed by the parabola and itstransformation and label it with the properequation.

GEOMETRY CHAPTER 3-372. Point ′P is the image of point P(-3,4) after a

translation defined by T( , ).7 1− Which other

transformation on P would also produce ′P ?

[A] ry x=− [B] ry axis−

[C] R90° [D] R− °90

GEOMETRY CHAPTER 3-473. If the coordinates of point A are (-2,3), what is

the image of A under r Dy axis− o 3 ?

[A] (6,9) [B] (-6,-9)

[C] (5,6) [D] (9,-6)

74. What is the image of point (1,1) underr Rx axis− °o 0 90, ?

[A] (-1,1) [B] (1,1)

[C] (-1,-1) [D] (1,-1)

75. If f(x) = cos x, which graph represents f(x) underthe composition r ry axis x axis− −o ?

[A] [B]

[C] [D]

76. The graph of f(x) is shown in the accompanyingdiagram.

Which graph represents f x r rx axis y axis( ) ?

− −o

[A] [B]

[C] [D]


77. The accompanying graph represents the figure .

Which graph represents after a transformationdefined by r Ry x= °o 90 ?

[A] [B]

[C] [D]

78. a On the accompanying grid, graph the equation2 2 42y x= − in the interval − ≤ ≤3 3x andlabel it a.b On the same grid, sketch the image of a underT rx axis5 2,− −o and label it b.

79. Graph and label the following equations, a and b,on the accompanying set of coordinate axes.

a y x

b y x

:

: ( )

=

= − − +

2

24 3Describe the composition of transformationsperformed on a to get b.

80. On the accompanying grid, graph and label AB,where A is (0,5) and B is (2,0). Under thetransformation r r ABx axis y axis− −o ( ), A maps to

′′A and B maps to ′′B . Graph and label

′′ ′′A B . What single transformation would mapAB to ′′ ′′A B ?


GEOMETRY CHAPTER 3-581. Which graph is symmetric with respect to the y-

axis?

[A] [B]

[C] [D]

82. Which letter has point symmetry?

[A] B [B] A [C] W [D] H

83. Which letter has point symmetry, but not linesymmetry?

[A] H [B] T [C] S [D] X

84. Which letter below has point symmetry, but doesnot have line symmetry?

[A] N [B] E [C] H [D] A

85. Which shape does not have rotational symmetry?

[A] circle [B] square

[C] regular pentagon [D] trapezoid

86. Which geometric figure has one and only one lineof symmetry?

[A]

Rectangle

[B]

Square

[C]

Rhombus

[D]

Isoscelestrapezoid

87. Helen is using a capital H in an art design. TheH has

[A] two lines of symmetry and only one point ofsymmetry

[B] only one line of symmetry

[C] only two points of symmetry

[D] two lines of symmetry and two points ofsymmetry

88. Which diagram shows a dotted line that is not aline of symmetry?

[A] [B]

[C] [D]

89. Which letter demonstrates line symmetry but notpoint symmetry?

[A] H [B] T [C] N [D] S


90. Draw all the symmetry lines on the accompanyingfigure.

GEOMETRY CHAPTER 3-791. Triangle A'B'C' is the image of ∆ ABC under a

dilation such that A'B' = 3AB. Triangles ABCand A'B'C' are

[A] congruent but not similar

[B] similar but not congruent

[C] neither congruent nor similar

[D] both congruent and similar

92. On the accompanying set of axes, graph ∆ABCwith coordinates A(-1,2), B(0,6), and C(5,4).Then graph ∆A B C' ' ' , the image of ∆ABC aftera dilation of 2.

93. The coordinates of the endpoints of AB areA(2,6) and B(4,2). Is the image A B' ' ' ' thesame if it is reflected in the x-axis, then dilated by12

as the image is if it is dilated by 12

, then

reflected in the x-axis? Justify your answer.

94. In which quadrant would the image of point (5,-3) fall after a dilation using a factor of -3?

[A] II [B] III [C] IV [D] I


95. In the accompanying graph, the shaded regionrepresents set A of all points (x,y) such thatx y2 2 1+ ≤ . The transformation T maps point(x, y) to point (2x, 4y).

Which graph shows the mapping of set A by thetransformation T?

[A]

[B]

[C]

[D]

96. The graph of the function g(x) is shown on theaccompanying set of axes. On the same set ofaxes, sketch the image of g(x) under thetransformation D2 .

GEOMETRY CHAPTER 4-197. What is the smallest integer greater than 1 that is

both the square of an integer and the cube of aninteger?

[A] 64 [B] 9 [C] 8 [D] 36

98. Stan was trying to guess Melanie's age. She toldhim her age was an even number and a multipleof three. What could be Melanie's age?

[A] 12 [B] 16 [C] 15 [D] 10

99. Seth is thinking of a number between 20 and 30.The number is prime and not more than 2 awayfrom a perfect square. What is the number?


100. Frank, George, and Hernando are a plumber, acabinet maker, and an electrician, though notnecessarily in that order. Each can do all workappropriate to his own field, but no work in otherfields. Frank was not able to install a newelectric line in his home. Hernando was not ableto make cabinets. George is also a buildingcontractor who hired one of the other people todo his electrical work. Which statement must betrue?

[A] Frank is an electrician.

[B] Frank is a plumber.

[C] Hernando is an electrician.

[D] George is a cabinet maker.

101. John, Dan, Karen, and Beth went to a costumeball. They chose to go as Anthony andCleopatra, and Romeo and Juliet. John got thecostumes for Romeo and Cleopatra, but not hisown costume. Dan saw the costumes for Julietand himself. Karen went as Anthony. Bethdrove two of her friends, who were dressed asAnthony and Cleopatra, to the ball. Whatcostume did John wear?

102. At a school costume party, seven girls woremasks and nine boys did not. If there were 15boys at the party and 20 students did not wearmasks, what was the total number of students atthe party?

[A] 30 [B] 42 [C] 33 [D] 35

103. Mary says, "The number I am thinking of isdivisible by 2 or it is divisible by 3." Mary'sstatement is false if the number she is thinking ofis

[A] 6 [B] 15 [C] 8 [D] 11

104. Given the true statements: "Jason goes shoppingor he goes to the movies" and "Jason does not goto the movies." Which statement must also betrue?

[A] Jason stays home.

[B] Jason does not go shopping.

[C] Jason goes shopping.

[D] Jason does not go shopping and he does notgo to the movies.

105. The statement "x is not the square of an integerand x is a multiple of 3" is true when x is equal to

[A] 9 [B] 36 [C] 32 [D] 18

106. The statement "If x is divisible by 8, then it isdivisible by 6" is false if x equals

[A] 14 [B] 6 [C] 32 [D] 48

107. The statement "If x is prime, then it is odd" isfalse when x equals

[A] 2 [B] 4 [C] 3 [D] 1

108. The statement "x is divisible by 5 or x is divisibleby 4" is false when x equals

[A] 10 [B] 16 [C] 27 [D] 20

109. Given the true statement "John is not handsome"and the false statement "John is handsome orsmart." Determine the truth value for thestatement "John is smart."

110. Bob and Ray are describing the same number.Bob says, "The number is a positive even integerless than or equal to 20." Ray says, "The numberis divisible by 4." If Bob's statement is true andRay's statement is false, what are all the possiblenumbers?


111. Mark says, "The number I see is odd." Jan says,"That same number is prime." The teacher says,"Mark is correct or Jan is correct." Someintegers would make the teacher's statement truewhile other integers would make it false. Giveand explain one example of when the teacher'sstatement is true. Give and explain one exampleof when the teacher's statement is false.

112. What is the contrapositive of the statement "If Istudy, then I pass the test"?

[A] I pass the test if I study.

[B] If I do not study, then I do not pass the test.

[C] If I do not pass the test, then I do not study.

[D] If I pass the test, then I study.

113. Which statement is logically equivalent to "If it isSaturday, then I am not in school"?

[A] If I am in school, then it is not Saturday.

[B] If I am not in school, then it is Saturday.

[C] If it is not Saturday, then I am in school.

[D] If it is Saturday, then I am in school.

114. Which statement is logically equivalent to "If I didnot eat, then I am hungry"?

[A] If I did not eat, then I am not hungry.

[B] If I am hungry, then I did eat.

[C] If I am not hungry, then I did not eat.

[D] If I am not hungry, then I did eat.

115. Which statement is logically equivalent to "If Ieat, then I live"?

[A] If I live, then I eat.

[B] If I do not live, then I do not eat.

[C] If I eat, then I do not live.

[D] I live if and only if I eat.

116. Which statement is logically equivalent to "If atriangle is an isosceles triangle, then it has twocongruent sides"?

[A] If a triangle is an isosceles triangle, then itdoes not have two congruent sides.

[B] If a triangle is not an isosceles triangle, then ithas two congruent sides.

[C] If a triangle does not have two congruentsides, then it is not an isosceles triangle.

[D] If a triangle does not have two congruentsides, then it is an isosceles triangle.

117. Which statement is logically equivalent to "If theteam has a good pitcher, then the team has agood season"?

[A] If the team does not have a good pitcher,then the team does not have a good season.

[B] The team has a good pitcher and the teamdoes not have a good season.

[C] If the team does not have a good season,then the team does not have a good pitcher.

[D] If the team has a good season, then the teamhas a good pitcher.

118. Given the true statement: "If a person is eligible tovote, then that person is a citizen."Which statement must also be true?

[A] Marie is not eligible to vote; therefore, she isnot a citizen.

[B] Kayla is not a citizen; therefore, she is noteligible to vote.

[C] Juan is a citizen; therefore, he is eligible tovote.

[D] Morgan has never voted; therefore, he is nota citizen.


119. Which statement is logically equivalent to thestatement "If you are an elephant, then you donot forget"?

[A] If you are an elephant, then you forget.

[B] If you forget, then you are not an elephant.

[C] If you do not forget, then you are anelephant.

[D] If you do not forget, then you are not anelephant.

120. Which statement is the converse of "If the sum oftwo angles is 180°, then the angles aresupplementary"?

[A] If two angles are not supplementary, thentheir sum is not 180°.

[B] If the sum of two angles is not 180°, then theangles are supplementary.

[C] If two angles are supplementary, then theirsum is 180°.

[D] If the sum of two angles is not 180°, then theangles are not supplementary.

121. What is the converse of the statement "If it issunny, I will go swimming"?

[A] If it is not sunny, I will not go swimming.

[B] I will go swimming if and only if it is sunny.

[C] If I go swimming, it is sunny.

[D] If I do not go swimming, then it is not sunny.

122. Which statement is the converse of "If it is a 300ZX, then it is a car"?

[A] If it is not a 300 ZX, then it is not a car.

[B] If it is a car, then it is a 300 ZX.

[C] If it is a car, then it is not a 300 ZX.

[D] If it is not a car, then it is not a 300 ZX.

123. What is true about the statement "If two anglesare right angles, the angles have equal measure "and its converse "If two angles have equalmeasure then the two angles are right angles"?

[A] Both the statement and its converse arefalse.

[B] The statement is true but its converse isfalse.

[C] Both the statement and its converse are true.

[D] The statement is false but its converse istrue.

124. Given the statement: "If two lines are cut by atransversal so that the corresponding angles arecongruent, then the lines are parallel."What is true about the statement and itsconverse?

[A] The statement is false, but its converse istrue.

[B] The statement and its converse are bothfalse.

[C] The statement and its converse are bothtrue.

[D] The statement is true, but its converse isfalse.


125. Given the statement: "If two sides of a triangle arecongruent, then the angles opposite these sidesare congruent."

Given the converse of the statement: "If twoangles of a triangle are congruent, then the sidesopposite these angles are congruent."

What is true about this statement and itsconverse?

[A] Both the statement and its converse are true.

[B] Neither the statement nor its converse istrue.

[C] The statement is true but its converse isfalse.

[D] The statement is false but its converse istrue.

126. What is the converse of the statement "If it isSunday, then I do not go to school"?

[A] If I go to school, then it is not Sunday.

[B] If it is not Sunday, then I go to school.

[C] If I do not go to school, then it is Sunday.

[D] If it is not Sunday, then I do not go toschool.

127. What is the converse of the statement "If Aliciagoes to Albany, then Ben goes to Buffalo"?

[A] Alicia goes to Albany if and only if Ben goesto Buffalo.

[B] If Ben does not go to Buffalo, then Aliciadoes not go to Albany.

[C] If Alicia does not go to Albany, then Bendoes not go to Buffalo.

[D] If Ben goes to Buffalo, then Alicia goes toAlbany.

128. What is the inverse of the statement "If Mike didhis homework, then he will pass this test"?

[A] If Mike passes this test, then he did hishomework.

[B] If Mike did not do his homework, then hewill not pass this test.

[C] If Mike does not pass this test, then he didnot do his homework.

[D] If Mike does not pass this test, then he onlydid half his homework.

129. What is the inverse of the statement "If Julieworks hard, then she succeeds"?

[A] If Julie works hard, then she does notsucceed.

[B] If Julie does not work hard, then she doesnot succeed.

[C] If Julie does not succeed, then she does notwork hard.

[D] If Julie succeeds, then she works hard.

130. What is the inverse of the statement "If it is sunny,I will play baseball"?

[A] I will play baseball if and only if it is sunny.

[B] If I play baseball, then it is sunny.

[C] If I do not play baseball, then it is not sunny.

[D] If it is not sunny, I will not play baseball.

131. What is the inverse of the statement “If I do notbuy a ticket, then I do not go to the concert”?

[A] If I buy a ticket, then I go to the concert.

[B] If I buy a ticket, then I do not go to theconcert.

[C] If I go to the concert, then I buy a ticket.

[D] If I do not go to the concert, then I do notbuy a ticket.


GEOMETRY CHAPTER 4-2132. In isosceles triangle DOG, the measure of the

vertex angle is three times the measure of one ofthe base angles. Which statement about ∆DOGis true?

[A] ∆DOG is a right triangle.

[B] ∆DOG is an acute triangle.

[C] ∆DOG is an obtuse triangle.

[D] ∆DOG is a scalene triangle.

133. Dylan says that all isosceles triangles are acutetriangles. Mary Lou wants to prove that Dylan isnot correct. Sketch an isosceles triangle thatMary Lou could use to show that Dylan'sstatement is not true. In your sketch, state themeasure of each angle of the isosceles triangle.

134. In the accompanying diagram, ∆ABC and∆ABD are isosceles triangles withm CAB∠ = 50 and m BDA∠ = 55 . If AB=ACand AB=BD, what is m CBD∠ ?

135. Hersch says if a triangle is an obtuse triangle, thenit cannot also be an isosceles triangle. Using adiagram, show that Hersch is incorrect, andindicate the measures of all the angles and sidesto justify your answer.

136. Vertex angle A of isosceles triangle ABCmeasures 20° more than three times m B∠ . Findm C∠ .

137. Tina wants to sew a piece of fabric into a scarf inthe shape of an isosceles triangle, as shown in theaccompanying diagram.

What are the values of x and y?

[A] x = 69 and y = 69

[B] x = 90 and y = 48

[C] x = 42 and y = 96

[D] x = 96 and y = 42

138. The accompanying diagram shows two cables ofequal length supporting a pole. Both cables are14 meters long, and they are anchored to pointsin the ground that are 14 meters apart.

What is the exact height of the pole, in meters?

[A] 7 [B] 27 [C] 37 [D] 14

GEOMETRY CHAPTER 4-5139. In the accompanying diagram, ∆ABC is not

isosceles. Prove that if altitude BD were drawn,it would not bisect AC.


140. Given: ∆ABT CBTD CD, , and AB⊥

Write an indirect proof to show that AT is notperpendicular to CD.

GEOMETRY CHAPTER 4-6141. If the lengths of two sides of a triangle are 4 and

10, what could be the length of the third side?

[A] 14 [B] 16 [C] 8 [D] 6

142. If two sides of a triangle are 1 and 3, the thirdside may be

[A] 5 [B] 4 [C] 3 [D] 2

143. Which set can not represent the lengths of thesides of a triangle?

[A] {7,7,12} [B] {8,8,8}

[C] {4,5,6} [D] {5,5,11}

144. Which set could not represent the lengths of thesides of a triangle?

[A] {3,4,5} [B] {5,10,12}

[C] {7,9,11} [D] {2,5,9}

145. A plot of land is in the shape of rhombus ABCDas shown below.

Which can not be the length of diagonal AC?

[A] 24 m [B] 11 m [C] 4 m [D] 18 m

146. The direct distance between city A and city B is200 miles. The direct distance between city Band city C is 300 miles. Which could be thedirect distance between city C and city A?

[A] 350 miles [B] 550 miles

[C] 50 miles [D] 650 miles

147. Sara is building a triangular pen for her pet rabbit.If two of the sides measure 8 feet and 15 feet,the length of the third side could be

[A] 13 ft [B] 7 ft [C] 23 ft [D] 3 ft

148. José wants to build a triangular pen for his petrabbit. He has three lengths of boards alreadycut that measure 7 feet, 8 feet, and 16 feet.Explain why José cannot construct a pen in theshape of a triangle with sides of 7 feet, 8 feet,and 16 feet.

149. A box contains one 2-inch rod, one 3-inch rod,one 4-inch rod, and one 5-inch rod. What is themaximum number of different triangles that canbe made using these rods as sides?

[A] 4 [B] 3 [C] 2 [D] 1


150. An architect commissions a contractor toproduce a triangular window. The architectdescribes the window as ∆ABC , wherem A∠ = 50, BC = 10 inches, andAB = 12 inches. How many distinct trianglescan the contractor construct using thesedimensions?

[A] more than 2 [B] 2 [C] 1 [D] 0

151. Sam is designing a triangular piece for a metalsculpture. He tells Martha that two of the sidesof the piece are 40 inches and 15 inches, and theangle opposite the 40-inch side measures 120°.Martha decides to sketch the piece that Samdescribed. How many different triangles can shesketch that match Sam's description?

[A] 0 [B] 3 [C] 2 [D] 1

152. How many distinct triangles can be formed ifm A∠ = 30, side b = 12, and side a = 8?

[A] 1 [B] 3 [C] 2 [D] 0

153. A landscape designer is designing a triangulargarden with two sides that are 4 feet and 6 feet,respectively. The angle opposite the 4-foot sideis 30°. How many distinct triangular gardens canthe designer make using these measurements?

154. Main Street and Central Avenue intersect,making an angle measuring 34°. Angela lives atthe intersection of the two roads, and Caitlin liveson Central Avenue 10 miles from the intersection.If Leticia lives 7 miles from Caitlin, whichconclusion is valid?

[A] Leticia can live at only one location on MainStreet.

[B] Leticia cannot live on Main Street.

[C] Leticia can live at one of three locations onMain Street.

[D] Leticia can live at one of two locations onMain Street.

155. In ∆ABC, if AC = 12, BC = 11,andm A∠ = 30, angle C could be

[A] an obtuse angle, only

[B] an acute angle, only

[C] a right angle, only

[D] either an obtuse angle or an acute angle

156. What is the total number of distinct triangles thatcan be constructed if AC = 13, BC = 8, andm A∠ = 36 ?

[A] 2 [B] 1 [C] 0 [D] 3

GEOMETRY CHAPTER 4-7157. The distance between parallel lines l and m is

12 units. Point A is on line l . How many pointsare equidistant from lines l and m and 8 unitsfrom point A.

[A] 4 [B] 1 [C] 3 [D] 2

158. In the coordinate plane, what is the total numberof points 5 units from the origin and equidistantfrom both the x- and y-axes?

[A] 4 [B] 2 [C] 1 [D] 0

159. What is the total number of points equidistantfrom two intersecting straight roads and also 300feet from the traffic light at the center of theintersection?

[A] 4 [B] 0 [C] 2 [D] 1

160. How many points are equidistant from twoparallel lines and also equidistant from two pointson one of the lines?

[A] 2 [B] 3 [C] 4 [D] 1


161. In the accompanying diagram, line l1 is parallelto line l2 .

Which term describes the locus of all points thatare equidistant from line l1 and l2 ?

[A] line [B] point

[C] circle [D] rectangle

162. The locus of points equidistant from two sides ofan acute scalene triangle is

[A] an angle bisector [B] the third side

[C] an altitude [D] a median

163. If point P lies on line l, which diagramrepresents the locus of points 3 centimeters frompoint P?

[A]

[B]

[C]

[D]

164. Which equation represents the locus of all points5 units below the x-axis?

[A] x = 5 [B] x = -5

[C] y = -5 [D] y = 5

165. A treasure map shows a treasure hidden in apark near a tree and a statue. The map indicatesthat the tree and the statue are 10 feet apart. Thetreasure is buried 7 feet from the base of the treeand also 5 feet from the base of the statue. Howmany places are possible locations for thetreasure to be buried? Draw a diagram of thetreasure map, and indicate with an X eachpossible location of the treasure.

166. Maria's backyard has two trees that are 40 feetapart, as shown in the accompanying diagram.She wants to place lampposts so that the postsare 30 feet from both of the trees. Draw asketch to show where the lampposts could beplaced in relation to the trees. How manylocations for the lampposts are possible?

167. Steve has a treasure map, represented in theaccompanying diagram, that shows two trees 8feet apart and a straight fence connecting them.The map states that treasure is buried 3 feet fromthe fence and equidistant from the two trees.

a Sketch a diagram to show all the places wherethe treasure could be buried. Clearly indicate inyour diagram where the treasure could be buried.b What is the distance between the treasure andone of the trees?


168. A triangular park is formed by the intersection ofthree streets, Bridge Street, Harbor Place, andCollege Avenue, as shown in the accompanyingdiagram. A walkway parallel to Harbor Placegoes through the park. A time capsule has beenburied in the park in a location that is equidistantfrom Bridge Street and College Avenue and 5yards from the walkway. Indicate on thediagram with an X each possible location wherethe time capsule could be buried.

169. Point P is located on .ABsuur

a Describe the locus of points that are (1) 3 units from AB

suur

(2) 5 units from point Pb How many points satisfy both conditions inpart a?

GEOMETRY CHAPTER 5-1170. The Pentagon building in Washington, D.C., is

shaped like a regular pentagon. If the length ofone side of the Pentagon is represented by n + 2,its perimeter would be represented by

[A] 5n + 10 [B] 10n

[C] 5n + 2 [D] n + 10

171. If the area of a square garden is 48 square feet,what is the length, in feet, of one side of thegarden?

[A] 12 2 [B] 4 6

[C] 4 3 [D] 16 3

172. What is the area of a square whose perimeter isrepresented by 12x?

[A] 6 2x [B] 9 2x

[C] 12 2x [D] 144 2x

173. The length of a side of a square window inJessica's bedroom is represented by 2 1x − .Which expression represents the area of thewindow?

[A] 4 12x + [B] 4 4 12x x− +

[C] 4 4 12x x+ − [D] 2 12x +

174. The accompanying diagram shows a square withside y inside a square with side x.

Which expression represents the area of theshaded region?

[A] y2 [B] x 2

[C] x y2 2− [D] y x2 2−


175. In the accompanying figure, ACDH and BCEFare rectangles, AH = 2, GH = 3, GF = 4, andFE = 5.

What is the area of BCDG?

[A] 6 [B] 20 [C] 10 [D] 8

176. A farmer has a rectangular field that measures100 feet by 150 feet. He plans to increase thearea of the field by 20%. He will do this byincreasing the length and width by the sameamount, x. Which equation represents the areaof the new field?

[A] 2(100 + x) + 2(150 + x) = 15,000

[B] (100 + x)(150 + x) = 15,000

[C] (100 + 2x)(150 + x) = 18,000

[D] (100 + x)(150 + x) = 18,000

177. An engineer measured the dimensions for arectangular site by using a wooden pole ofunknown length x. The length of the rectangularsite is 2 pole measures increased by 3 feet, whilethe width is 1 pole measure decreased by 4 feet.Write an algebraic representation, in terms of x,for the perimeter of the site.

178. Jack is building a rectangular dog pen that hewishes to enclose. The width of the pen is 2yards less than the length. If the area of the dogpen is 15 square yards, how many yards offencing would he need to completely enclose thepen?

179. The area of the rectangular playground enclosureat South School is 500 square meters. Thelength of the playground is 5 meters longer thanthe width. Find the dimensions of theplayground, in meters. [Only an algebraicsolution will be accepted.]

180. Javon's homework is to determine the dimensionsof his rectangular backyard. He knows that thelength is 10 feet more than the width, and thetotal area is 144 square feet. Write an equationthat Javon could use to solve this problem. Thenfind the dimensions, in feet, of his backyard.

181. A rectangular park is three blocks longer than itis wide. The area of the park is 40 squareblocks. If w represents the width, write anequation in terms of w for the area of the park.Find the length and the width of the park.

182. Express both the perimeter and the area of therectangle shown in the accompanying diagram aspolynomials in simplest form.

183. Mr. Santana wants to carpet exactly half of hisrectangular living room. He knows that theperimeter of the room is 96 feet and that thelength of the room is 6 feet longer than the width.How many square feet of carpeting does Mr.Santana need?

184. Kerry is planning a rectangular garden that hasdimensions of 4 feet by 6 feet. Kerry wants one-half of the garden to have roses, and she saysthat the rose plot will have dimensions of 2 feetby 3 feet. Is she correct? Explain.


185. Keesha wants to tile the floor shown in theaccompanying diagram. If each tile measures 1foot by 1 foot and costs $2.99, what will be thetotal cost, including an 8% sales tax, for tiling thefloor?

186. In the figure below, the large rectangle, ABCD, isdivided into four smaller rectangles. The area ofrectangle AEHG x= 5 , the area of rectangleGHFB x= 2 2 , the area of rectangleHJCF x= 6 , segment AG = 5, and segment AE= x.

a Find the area of the shaded region.b Write an expression for the area of therectangle ABCD in terms of x.

187. A rectangular garden is going to be planted in aperson's rectangular backyard, as shown in theaccompanying diagram. Some dimensions of thebackyard and the width of the garden are given.Find the area of the garden to the nearestsquare foot.

188. Mr. James wanted to plant a garden that wouldbe in the shape of a rectangle. He was given 80feet of fencing to enclose his garden. He wantsthe length to be 10 feet more than twice thewidth. What are the dimensions, in feet, for arectangular garden that will use exactly 80 feet offencing?

189. In the accompanying diagram, the perimeter ofis equal to the perimeter of square ABCD. If thesides of the triangle are represented by 4x + 4,5x - 3, and 17, and one side of the square isrepresented by 3x, find the length of a side of thesquare.


190. A homeowner wants to increase the size of arectangular deck that now measures 15 feet by20 feet, but building code laws state that ahomeowner cannot have a deck larger than 900square feet. If the length and the width are to beincreased by the same amount, find, to thenearest tenth, the maximum number of feet thatthe length of the deck may be increased in sizelegally.

191. Chad had a garden that was in the shape of arectangle. Its length was twice its width. Hedecided to make a new garden that was 2 feetlonger and 2 feet wider than his first garden. If xrepresents the original width of the garden, whichexpression represents the difference between thearea of his new garden and the area of theoriginal garden?

[A] x x2 3 2+ + [B] 8

[C] 6 4x + [D] 2 2x

192. A small, open-top packing box, similar to ashoebox without a lid, is three times as long as itis wide, and half as high as it is long. Eachsquare inch of the bottom of the box costs$0.008 to produce, while each square inch ofany side costs $0.003 to produce.Write a function for the cost of the box describedabove.Using this function, determine the dimensions of abox that would cost $0.69 to produce.

GEOMETRY CHAPTER 5-2193. What is the perimeter of an equilateral triangle

whose height is 2 3 ?

[A] 6 [B] 12 [C] 6 3 [D] 12 3

194. Sean knows the length of the base, b, and thearea, A, of a triangular window in his bedroom.Which formula could he use to find the height, h,of this window?

[A] h A b= 2b gb g [B] hAb

=2

[C] hA

b=

2 [D] h A b= −2

195. If the midpoints of the sides of a triangle areconnected, the area of the triangle formed is whatpart of the area of the original triangle?

[A] 38

[B] 13

[C] 12

[D] 14

196. On the accompanying set of axes, graph andlabel the following lines:

y

x

y x

=

= −

= +

5

454

5

Calculate the area, in square units, of the triangleformed by the three points of intersection.


197. Mr. Gonzalez owns a triangular plot of land BCDwith DB = 25 yards and BC = 16 yards. Hewishes to purchase the adjacent plot of land inthe shape of right triangle ABD, as shown in theaccompanying diagram, with AD = 15 yards. Ifthe purchase is made, what will be the totalnumber of square yards in the area of his plot ofland, ∆ACD?

198. The plan of a parcel of land is represented bytrapezoid ABCD in the accompanying diagram.If the area of ∆ABE is 600 square feet, find theminimum number of feet of fence needed tocompletely enclose the entire parcel of land,ABCD.

199. The plot of land illustrated in the accompanyingdiagram has a perimeter of 34 yards. Find thelength, in yards, of each side of the figure. Couldthese measures actually represent the measuresof the sides of a triangle? Explain your answer.

200. On the accompanying grid, draw and labelquadrilateral ABCD with points A(1,2), B(6,1),C(7,6), and D(3,7). On the same set of axes,plot and label quadrilateral A’B’C’D’, thereflection of quadrilateral ABCD in the y-axis.Determine the area, in square units, ofquadrilateral A’B’C’D’.

GEOMETRY CHAPTER 5-4201. A garden in the shape of an equilateral triangle

has sides whose lengths are 10 meters. What isthe area of the garden?

[A] 25 2m [B] 50 2m

[C] 25 3 2m [D] 50 3 2m

GEOMETRY CHAPTER 5-6202. A picnic table in the shape of a regular octagon is

shown in the accompanying diagram. If thelength of AE is 6 feet, find the length of one sideof the table to the nearest tenth of a foot, andfind the area of the table's surface to the nearesttenth of a square foot.


GEOMETRY CHAPTER 5-7203. What is the approximate circumference of a

circle with radius 3?

[A] 7.07 [B] 18.85

[C] 9.42 [D] 28.27

204. What is the diameter of a circle whosecircumference is 5?

[A] 52π

[B] 2 5.π

[C] 2 52

.π

[D] 5π

205. A wheel has a radius of 5 feet. What is theminimum number of complete revolutions that thewheel must make to roll at least 1,000 feet?

206. To measure the length of a hiking trail, a workeruses a device with a 2-foot-diameter wheel thatcounts the number of revolutions the wheelmakes. If the device reads 1,100.5 revolutionsat the end of the trail, how many miles long is thetrail, to the nearest tenth of a mile?

207. Every time the pedals go through a 360° rotationon a certain bicycle, the tires rotate three times.If the tires are 24 inches in diameter, what is theminimum number of complete rotations of thepedals needed for the bicycle to travel at least 1mile?

[A] 12 [B] 561 [C] 281 [D] 5,280

208. Ileana buys a large circular pizza that is dividedinto eight equal slices. She measures along theouter edge of the crust from one piece and finds

it to be 512

inches. What is the diameter of the

pizza to the nearest inch?

[A] 14 [B] 4 [C] 8 [D] 7

209. A ball is rolling in a circular path that has a radiusof 10 inches, as shown in the accompanyingdiagram. What distance has the ball rolled whenthe subtended arc is 54°? Express your answerto the nearest hundredth of an inch.

210. Cities H and K are located on the same line oflongitude and the difference in the latitude ofthese cities is 9°, as shown in the accompanyingdiagram. If Earth's radius is 3,954 miles, howmany miles north of city K is city H along arcHK? Round your answer to the nearest tenthof a mile.

211. Kathy and Tami are at point A on a circular trackthat has a radius of 150 feet, as shown in theaccompanying diagram. They runcounterclockwise along the track from A to S, adistance of 247 feet. Find, to the nearestdegree, the measure of minor arc AS.


212. The accompanying diagram shows the path of acart traveling on a circular track of radius 2.40meters. The cart starts at point A and stops atpoint B, moving in a counterclockwise direction.What is the length of minor arc AB, over whichthe cart traveled, to the nearest tenth of ameter?

GEOMETRY CHAPTER 5-8213. If the circumference of a circle is 10π inches,

what is the area, in square inches, of the circle?

[A] 100π [B] 25π

[C] 10π [D] 50π

214. In the accompanying diagram, right triangle ABCis inscribed in circle O, diameter AB = 26, andCB = 10. Find, to the nearest square unit, thearea of the shaded region.

215. As shown in the accompanying diagram, radiostation KMA is increasing its radio listeningradius from 40 miles to 50 miles. How manyadditional square miles of listening area, to thenearest tenth, will the radio station gain?

216. Virginia has a circular rug on her square livingroom floor, as represented in the accompanyingdiagram. If her entire living room floor measures100 square feet, what is the area of the part ofthe floor covered by the rug?

217. In the accompanying diagram, a circle with radius4 is inscribed in a square.

What is the area of the shaded region?

[A] 16 8− π [B] 16 16− π

[C] 64 16− π [D] 64 8π π−


218. If asphalt pavement costs $0.78 per square foot,determine, to the nearest cent, the cost of pavingthe shaded circular road with center O , anoutside radius of 50 feet, and an inner radius of36 feet, as shown in the accompanying diagram.

219. A target shown in the accompanying diagramconsists of three circles with the same center.The radii of the circles have lengths of 3 inches, 7inches, and 9 inches.

a What is the area of the shaded region to thenearest tenth of a square inch?b To the nearest percent, what percent of thetarget is shaded?

220. Mr. Petri has a rectangular plot of land withlength = 20 feet and width = 10 feet. He wantsto design a flower garden in the shape of a circlewith two semicircles at each end of the centercircle, as shown in the accompanying diagram.He will fill in the shaded area with wood chips. Ifone bag of wood chips covers 5 square feet,how many bags must he buy?

221. The circumference of a circular plot of land isincreased by 10%. What is the best estimate ofthe total percentage that the area of the plotincreased?

[A] 21% [B] 10% [C] 31% [D] 25%

GEOMETRY CHAPTER 6-1222. Which piece of paper can be folded into a

pyramid?

[A] [B]

[C] [D]


GEOMETRY CHAPTER 6-2223. A roll of candy is shown in the accompanying

diagram.

The shape of the candy is best described as a

[A] cone [B] rectangular solid

[C] pyramid [D] cylinder

GEOMETRY CHAPTER 6-3224. Triangle ABC represents a metal flag on pole

AD, as shown in the accompanying diagram. Ona windy day the triangle spins around the pole sofast that it looks like a three-dimensional shape.

Which shape would the spinning flag create?

[A] cone [B] pyramid

[C] right circular cylinder [D] sphere

GEOMETRY CHAPTER 6-4225. A box in the shape of a cube has a volume of 64

cubic inches. What is the length of a side of thebox?

[A] 4 in [B] 21 3. in

[C] 8 in [D] 16 in

226. Which diagram represents the figure with thegreatest volume?

[A] [B]

[C] [D]

227. The volume of a cube is 64 cubic inches. Its totalsurface area, in square inches, is

[A] 16 [B] 48 [C] 96 [D] 576

228. A storage container in the shape of a rightcircular cylinder is shown in the accompanyingdiagram.

What is the volume of this container, to thenearest hundredth?

[A] 50265. in3 [B] 25133. in3

[C] 5655. in3 [D] 12566. in3

229. A cardboard box has length x - 2, width x + 1,and height 2x.a Write an expression, in terms of x, torepresent the volume of the box.b If x = 8 centimeters, what is the number ofcubic centimeters in the volume of the box?


230. Deborah built a box by cutting 3-inch squaresfrom the corners of a rectangular sheet ofcardboard, as shown in the accompanyingdiagram, and then folding the sides up. Thevolume of the box is 150 cubic inches, and thelonger side of the box is 5 inches more than theshorter side. Find the number of inches in theshorter side of the original sheet of cardboard.

231. The volume of a rectangular pool is 1,080 cubicmeters. Its length, width, and depth are in theratio 10:4:1. Find the number of meters in eachof the three dimensions of the pool.

232. A fish tank with a rectangular base has a volumeof 3,360 cubic inches. The length and width ofthe tank are 14 inches and 12 inches,respectively. Find the height, in inches, of thetank.

233. The dimensions of a brick, in inches, are 2 by 4by 8. How many such bricks are needed to havea total volume of exactly 1 cubic foot?

234. Tina's preschool has a set of cardboard buildingblocks, each of which measures 9 inches by 9inches by 4 inches. How many of these blockswill Tina need to build a wall 4 inches thick, 3feet high, and 12 feet long?

235. Tamika has a hard rubber ball whosecircumference measures 13 inches. She wants tobox it for a gift but can only find cube-shapedboxes of sides 3 inches, 4 inches, 5 inches, or 6inches. What is the smallest box that the ball willfit into with the top on?

236. In the accompanying diagram, a rectangularcontainer with the dimensions 10 inches by 15inches by 20 inches is to be filled with water,using a cylindrical cup whose radius is 2 inchesand whose height is 5 inches. What is themaximum number of full cups of water that canbe placed into the container without the wateroverflowing the container?

237. As shown in the accompanying diagram, thelength, width, and height of Richard's fish tankare 24 inches, 16 inches, and 18 inches,respectively. Richard is filling his fish tank withwater from a hose at the rate of 500 cubic inchesper minute. How long will it take, to the nearestminute, to fill the tank to a depth of 15 inches?


238. A rectangular piece of cardboard is to be formedinto an uncovered box. The piece of cardboardis 2 centimeters longer than it is wide. A squarethat measures 3 centimeters on a side is cut fromeach corner. When the sides are turned up toform the box, its volume is 765 cubiccentimeters. Find the dimensions, in centimeters,of the original piece of cardboard.

GEOMETRY CHAPTER 6-8239. At a school fair, the spinner represented in the

accompanying diagram is spun twice.

What is the probability that it will land in sectionG the first time and then in section B the secondtime?

[A] 12

[B] 116

[C] 18

[D] 14

240. A square dartboard is represented in theaccompanying diagram. The entire dartboard isthe first quadrant from x = 0 to 6 and from y = 0to 6. A triangular region on the dartboard isenclosed by the graphs of the equations y = 2, x= 6, and y = x. Find the probability that a dartthat randomly hits the dartboard will land in thetriangular region formed by the three lines.

GEOMETRY CHAPTER 7-1241. In the accompanying figure, what is one pair of

alternate interior angles?

[A] ∠4 and ∠6 [B] ∠6 and ∠8

[C] ∠1 and ∠2 [D] ∠4 and ∠5


242. In the accompanying diagram, lines a and b areparallel, and lines c and d are transversals.

Which angle is congruent to angle 8?

[A] 5 [B] 6 [C] 4 [D] 3

243. In the accompanying diagram, parallel lines ABsuur

and CDsuur

are intersected by transversal EFsuur

atpoints G and H, respectively,m AGH x∠ = +15 , and m GHD x∠ = 2 .

Which equation can be used to find the value ofx?

[A] 2x(x + 15) = 0 [B] 2x + x + 15 = 180

[C] 2x = x + 15 [D] 2x + x + 15 = 90

244. The accompanying diagram shows a footballplayer crossing the 20-yard line at an angle of30° and continuing along the same path.

What is the measure of angle B, where the playercrosses into the end zone?

[A] 30° [B] 60° [C] 150° [D] 180°

245. The accompanying diagram shows two parallelstreets, Main Street and Brooks Road,intersected by Jay Street. The obtuse angle thatJay Street forms with Brooks Road is three timesthe measure of the acute angle that Jay Streetforms with Main Street.

What is the measure of the acute angle formed byJay Street and Main Street?

[A] 90° [B] 135° [C] 45° [D] 60°

246. In the accompanying diagram, parallel lines ABand CD are intersected by transversal EF atpoints X and Y, and m FYD∠ = 123 . Findm AXY∠ .

247. In the accompanying diagram, line m is parallel toline p, line t is a transversal, m a x∠ = +3 12 ,and m b x∠ = +2 13 . Find the value of x.


248. Two parallel roads, Elm Street and Oak Street,are crossed by a third, Walnut Street, as shownin the accompanying diagram. Find the numberof degrees in the acute angle formed by theintersection of Walnut Street and Elm Street.


249.

GEOMETRY CHAPTER 8-6250. In the accompanying diagram of ∆ABC,

AB AC≅ , BD BA=13

, and CE CA=13

.

Triangle EBC can be proved congruent totriangle DCB by

[A] HL ≅ HL [B] SSS ≅ SSS

[C] SAS ≅ SAS [D] ASA ≅ ASA


251. In the accompanying diagram, CA AB⊥ ,

ED DF⊥ , ED AB , CB BF≅ , AB ED≅

and m CAB m FDE∠ = ∠ = 90.

Which statement would not be used to prove∆ ∆ABC DEF≅ ?

[A] SAS ≅ SAS [B] HL ≅ HL

[C] AAS ≅ AAS [D] SSS ≅ SSS


252. In the accompanying diagram of parallelogramABCD, DE BF≅ .

Triangle EGC can be proved congruent totriangle FGA by

[A] HL ≅ HL [B] AAA ≅ AAA

[C] AAS ≅ AAS [D] SSA ≅ SSA

253. In the accompanying diagram, HK bisects ILand ∠ ≅ ∠H K.

What is the most direct method of proof thatcould be used to prove ∆ ∆HIJ KLJ≅ ?

[A] AAS ≅ AAS [B] ASA ≅ ASA

[C] HL ≅ HL [D] SAS ≅ SAS

254. Which condition does not prove that twotriangles are congruent?

[A] SSS ≅ SSS [B] SSA ≅ SSA

[C] ASA ≅ ASA [D] SAS ≅ SAS

255. Which statements could be used to prove that∆ABC and ∆ ′ ′ ′A B C are congruent?

[A] ∠ ≅ ∠ ′A A , ∠ ≅ ∠ ′B B , and ∠ ≅ ∠ ′C C

[B] AB A B≅ ′ ′, ∠ ≅ ∠ ′A A , and ∠ ≅ ∠ ′C C

[C] AB A B≅ ′ ′, BC B C≅ ′ ′, and ∠ ≅ ∠ ′A A

[D] ∠ ≅ ∠ ′A A , AC A C≅ ′ ′, and BC B C≅ ′ ′

GEOMETRY CHAPTER 9-1256. In the accompanying diagram of parallelogram

ABCD, diagonals AC and DB intersect at E,AE = 3x - 4, and EC = x + 12.

What is the value of x?

[A] 40 [B] 8 [C] 20 [D] 16

257. In the accompanying diagram of parallelogramABCD, m A x∠ = +( )2 10 and m B x∠ = 3 .Find the number of degrees in m B∠ .

GEOMETRY CHAPTER 9-2258. Prove that the diagonals of a parallelogram bisect

each other.

259. Given: parallelogram ABCD, diagonal AC, and

ABE

Prove: m m∠ > ∠1 2


260. In the accompanying diagram of ABCD, wherea b≠ , prove ABCD is an isosceles trapezoid.

GEOMETRY CHAPTER 9-3261. Which quadrilateral must have diagonals that are

congruent and perpendicular?

[A] parallelogram [B] rhombus

[C] trapezoid [D] square

262. In the accompanying diagram of rectangleABCD, m BAC x∠ = +3 4 andm ACD x∠ = + 28 .

What is m CAD∠ ?

[A] 12 [B] 37 [C] 50 [D] 40

263. In rectangle ABCD, AC x= +3 15 andBD x= −4 5. Find the length of AC.

GEOMETRY CHAPTER 9-6264. Ashanti is surveying for a new parking lot shaped

like a parallelogram. She knows that three of thevertices of parallelogram ABCD are A(0,0),B(5,2), and C(6,5). Find the coordinates ofpoint D and sketch parallelogram ABCD on theaccompanying set of axes. Justify mathematicallythat the figure you have drawn is a parallelogram.

265. Given: A(1,6), B(7,9), C(13,6), and D(3,1)Prove: ABCD is a trapezoid. [The use of theaccompanying grid is optional.]


266. Quadrilateral KATE has vertices K(1,5), A(4,7),T(7,3), and E(1,-1).a Prove that KATE is a trapezoid. [The use ofthe grid is optional.]b Prove that KATE is not an isosceles trapezoid.

267. The coordinates of quadrilateral ABCD are A(-1,-5), B(8,2), C(11,13), and D(2,6). Usingcoordinate geometry, prove that quadrilateralABCD is a rhombus. [The use of the grid isoptional.]

268. The coordinates of quadrilateral JKLM are J(1,-2), K(13,4), L(6,8), and M(-2,4). Prove thatquadrilateral JKLM is a trapezoid but not anisosceles trapezoid. [The use of the grid isoptional.]

269. Jim is experimenting with a new drawing programon his computer. He created quadrilateralTEAM with coordinates T(-2,3), E(-5,-4), A(2,-1), and M(5,6). Jim believes that he has createda rhombus but not a square. Prove that Jim iscorrect. [The use of the grid is optional.]


GEOMETRY CHAPTER 10-1270. A triangle has sides whose lengths are 5, 12, and

13. A similar triangle could have sides withlengths of

[A] 3, 4, and 15 [B] 6, 8, and 10

[C] 10, 24, and 26 [D] 7, 24, and 25

271. The accompanying diagram shows two similartriangles.

Which proportion could be used to solve for x?

[A] 32 1215x

= [B] 3212

15=

x

[C] 249

15=

x[D] x

249

15=

272. The Rivera family bought a new tent for camping.Their old tent had equal sides of 10 feet and afloor width of 15 feet, as shown in theaccompanying diagram.

If the new tent is similar in shape to the old tentand has equal sides of 16 feet, how wide is thefloor of the new tent?

273. The accompanying diagram shows a section ofthe city of Tacoma. High Road, State Street,and Main Street are parallel and 5 miles apart.Ridge Road is perpendicular to the three parallelstreets. The distance between the intersection ofRidge Road and State Street and where therailroad tracks cross State Street is 12 miles.What is the distance between the intersection ofRidge Road and Main Street and where therailroad tracks cross Main Street?

274. Fran's favorite photograph has a length of 6inches and a width of 4 inches. She wants tohave it made into a poster with dimensions thatare similar to those of the photograph. Shedetermined that the poster should have a lengthof 24 inches. How many inches wide will theposter be?

GEOMETRY CHAPTER 10-5275. The perimeter of ∆A B C' ' ' , the image of

∆ABC , is twice as large as the perimeter of∆ABC . What type of transformation has takenplace?

[A] reflection [B] rotation



276. Delroy's sailboat has two sails that are similartriangles. The larger sail has sides of 10 feet, 24feet, and 26 feet. If the shortest side of thesmaller sail measures 6 feet, what is the perimeterof the smaller sail?

[A] 15 ft [B] 100 ft [C] 60 ft [D] 36 ft

277. Two triangles are similar. The lengths of thesides of the smaller triangle are 3, 5, and 6, andthe length of the longest side of the larger triangleis 18. What is the perimeter of the largertriangle?

[A] 18 [B] 14 [C] 42 [D] 24

278. The perimeter of an equilateral triangle variesdirectly as the length of a side. When the lengthof a side is doubled, the perimeter of the triangleis

[A] doubled [B] divided by 3

[C] multiplied by 3 [D] halved

279. In the accompanying diagram of equilateral

triangle ABC, DE = 5 and DE AB .

If AB is three times as long as DE, what is theperimeter of quadrilateral ABED?

[A] 20 [B] 30 [C] 35 [D] 40

280. On a scale drawing of a new school playground,a triangular area has sides with lengths of 8centimeters, 15 centimeters, and 17 centimeters.If the triangular area located on the playgroundhas a perimeter of 120 meters, what is the lengthof its longest side?

[A] 24 m [B] 51 m

[C] 40 m [D] 45 m

281. The ratio of the corresponding sides of twosimilar squares is 1 to 3. What is the ratio of thearea of the smaller square to the area of thelarger square ?

[A] 16: [B] 19: [C] 13: [D] 1 3:

282. The lengths of the sides of two similar rectangularbillboards are in the ratio 5:4. If 250 square feetof material is needed to cover the largerbillboard, how much material, in square feet, isneeded to cover the smaller billboard?

283. If the circumference of a circle is doubled, thediameter of the circle

[A] is doubled [B] is multiplied by 4

[C] increases by 2 [D] remains the same

GEOMETRY CHAPTER 10-6284. If the length of a rectangular prism is doubled, its

width is tripled, and its height remains the same,what is the volume of the new rectangular prism?

[A] double the original volume

[B] six times the original volume

[C] triple the original volume

[D] nine times the original volume


GEOMETRY CHAPTER 11-3285. At Mogul's Ski Resort, the beginner's slope is

inclined at an angle of 12.3°, while the advancedslope is inclined at an angle of 26.4°. If Rudyskis 1,000 meters down the advanced slopewhile Valerie skis the same distance on thebeginner's slope, how much longer was thehorizontal distance that Valerie covered?

[A] 977.0 m [B] 895.7 m

[C] 231.6 m [D] 81.3 m

GEOMETRY CHAPTER 11-5286. Two tow trucks try to pull a car out of a ditch.

One tow truck applies a force of 1,500 poundswhile the other truck applies a force of 2,000pounds. The resultant force is 3,000 pounds.Find the angle between the two applied forces,rounded to the nearest degree.

287. One force of 20 pounds and one force of 15pounds act on a body at the same point so thatthe resultant force is 19 pounds. Find, to thenearest degree, the angle between the twooriginal forces.

288. Two equal forces act on a body at an angle of80°. If the resultant force is 100 newtons, findthe value of one of the two equal forces, to thenearest hundredth of a newton.

GEOMETRY CHAPTER 11-6289. Gregory wants to build a garden in the shape of

an isosceles triangle with one of the congruentsides equal to 12 yards. If the area of his gardenwill be 55 square yards, find, to the nearesttenth of a degree, the three angles of thetriangle.

290. The accompanying diagram shows the floor planfor a kitchen. The owners plan to carpet all ofthe kitchen except the "work space," which isrepresented by scalene triangle ABC. Find thearea of this work space to the nearest tenth of asquare foot.

291. Two sides of a triangular-shaped pool measure16 feet and 21 feet, and the included anglemeasures 58°. What is the area, to the nearesttenth of a square foot, of a nylon cover thatwould exactly cover the surface of the pool?

292. The triangular top of a table has two sides of 14inches and 16 inches, and the angle between thesides is 30°. Find the area of the tabletop, insquare inches.

293. A landscape architect is designing a triangulargarden to fit in the corner of a lot. The corner ofthe lot forms an angle of 70°, and the sides of thegarden including this angle are to be 11 feet and13 feet, respectively. Find, to the nearestinteger, the number of square feet in the area ofthe garden.

GEOMETRY CHAPTER 12-1294. What is the greatest possible number of points of

intersection of a triangle and a circle?

[A] 3 [B] 6 [C] 2 [D] 4


295. In the coordinate plane, the points (2,2) and(2,12) are the endpoints of a diameter of a circle.What is the length of the radius of the circle?

[A] 7 [B] 10 [C] 5 [D] 6

296. a On the set of axes provided below, sketch acircle with a radius of 3 and center at (2,1) andalso sketch the graph of the line 2 8x y+ = .

b What is the total number of points ofintersection of the two graphs?

297. On the accompanying grid, graph a circle whosecenter is at (0,0) and whose radius is 5.Determine if the point (5,-2) lies on the circle.

298. Which equation represents a circle whose centeris (3,-2)?

[A] x y− + + =2 3 42 2b g b g[B] x y− + + =3 2 42 2b g b g[C] x y+ + − =2 3 42 2b g b g[D] x y+ + − =3 2 42 2b g b g

299. Which equation represents the locus of points 4units from the origin?

[A] x y+ = 16 [B] x y2 2 16+ =

[C] x y2 2 4+ = [D] x = 4

300. What is the total number of points of intersectionin the graphs of the equations x y2 2 16+ = andy = 4?

[A] 0 [B] 2 [C] 1 [D] 3

301. The graph of the equation x y2 2 4+ = can bedescribed as a

[A] circle with its center at the origin and aradius of 2

[B] circle with its center at the origin and aradius of 4

[C] line passing through points (0,2) and (2,0)

[D] parabola with its vertex at (0,2)


302. John uses the equation x y2 2 9+ = to representthe shape of a garden on graph paper.a Graph x y2 2 9+ = on the accompanying grid.

b What is the area of the garden to the nearestsquare unit?

303. Solve the following system of equationsalgebraically or graphically:

x y2 2 25+ =3 4 0y x− =

[The use of the accompanying grid is optional.]

GEOMETRY CHAPTER 12-2304. Kimi wants to determine the radius of a circular

pool without getting wet. She is located at pointK, which is 4 feet from the pool and 12 feet fromthe point of tangency, as shown in theaccompanying diagram.

What is the radius of the pool?

[A] 20 ft [B] 32 ft

[C] 16 ft [D] 4 10 ft

305. In the accompanying diagram of circle O, PA isdrawn tangent to the circle at A. Place B on PAanywhere between P and A and draw OA, OP,and OB. Prove that OB is not perpendicular toPA.


GEOMETRY CHAPTER 12-3306. An overhead view of a revolving door is shown

in the accompanying diagram. Each panel is 1.5meters wide.

What is the approximate width of d, the openingfrom B to C?

[A] 1.50 m [B] 3.00 m

[C] 1.73 m [D] 2.12 m

307. A toy truck is located within a circular play area.Alex and Dominic are sitting on oppositeendpoints of a chord that contains the truck.Alex is 4 feet from the truck, and Dominic is 3feet from the truck. Meira and Tamara are sittingon opposite endpoints of another chordcontaining the truck. Meira is 8 feet from thetruck. How many feet, to the nearest tenth of afoot, is Tamara from the truck? Draw a diagramto support your answer.

GEOMETRY CHAPTER 12-4308. A regular hexagon is inscribed in a circle. What

is the ratio of the length of a side of the hexagonto the minor arc that it intercepts?

[A] 3π

[B] π6

[C] 6π

[D] 36

309. Given: chords AB and CD of circle O intersectat E, an interior point of circle O; chords ADand CB are drawn.

Prove: (AE)(EB) = (CE)(ED)

310. The new corporate logo created by the designengineers at Magic Motors is shown in theaccompanying diagram.

If chords BA and BC are congruent and

mBC)

= 140, what is m B∠ ?

[A] 280 [B] 80 [C] 40 [D] 140

311. In the accompanying diagram, the length of

ABC)

is 32π radians.

What is m ABC∠ ?

[A] 45 [B] 36 [C] 53 [D] 72


312. The accompanying diagram shows a child's spintoy that is constructed from two chordsintersecting in a circle. The curved edge of thelarger shaded section is one-quarter of thecircumference of the circle, and the curved edgeof the smaller shaded section is one-fifth of thecircumference of the circle.

What is the measure of angle x?

[A] 72° [B] 108° [C] 40° [D] 81°

313. The accompanying diagram represents circularpond O with docks located at points A and B.From a cabin located at C, two sightings aretaken that determine an angle of 30° for tangentsCAuuur

and .CBuuur

What is m CAB∠ ?

[A] 60 [B] 30 [C] 75 [D] 150

314. An architect is designing a park with an entrancerepresented by point C and a circular gardenwith center O, as shown in the accompanyingdiagram. The architect plans to connect threepoints on the circumference of the garden, A, B,and D, to the park entrance, C, with walkwaysso that walkways CA and CB are tangent to thegarden, walkway DOEC is a path through thecenter of the garden, ¼ ¼: 3:2,mADB mAEB = BC= 60 meters, and EC = 43.6 meters.Find the measure of the angle between walkwaysCA and CB.Find the diameter of the circular garden, to thenearest meter.

315. A small fragment of something brittle, such aspottery, is called a shard. The accompanyingdiagram represents the outline of a shard from asmall round plate that was found at anarchaeological dig.

If BCuuur

is a tangent to »AC at B and

m ABC∠ = 45, what is the measure of »AC , theoutside edge of the shard?

[A] 45° [B] 90° [C] 135° [D] 225°

316. Point P lies outside circle O, which has adiameter of AOC . The angle formed by tangentPA and secant PBC measures 30°. Sketch theconditions given above and find the number ofdegrees in the measure of minor arc CB.


317. In the accompanying diagram, cabins B and Gare located on the shore of a circular lake, andcabin L is located near the lake. Point D is adock on the lake shore and is collinear withcabins B and L. The road between cabins G andL is 8 miles long and is tangent to the lake. Thepath between cabin L and dock D is 4 mileslong.

What is the length, in miles, of BD?

[A] 8 [B] 4 [C] 24 [D] 12

318. The accompanying diagram shows a circularmachine part that has rods PT and PARattached at points T, A, and R, which are locatedon the circle; º » »: : 1:3:5;mTA mAR RTm = RA =12 centimeters; and PA = 5 centimeters.

Find the measure of ∠P, in degrees, and find the

length of rod PT, to the nearest tenth of acentimeter.

319. Given circle O with diameter GOAL; secants

HUG and HTAM intersect at point H;» » º: : 7:3:2;mGM mML LTm = and chord GU ≅

chord UT. Find the ratio of m UGL∠ tom H∠ .

GEOMETRY CHAPTER 12-6320. The accompanying diagram shows a semicircular

arch over a street that has a radius of 14 feet. Abanner is attached to the arch at points A and B,such that AE = EB = 5 feet. How many feetabove the ground are these points of attachmentfor the banner?

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JEFFERSON MATH PROJECT REGENTS BY …...JEFFERSON MATH PROJECT REGENTS BY CHAPTER All 1165 NY Math A & B Regents Exam Questions from June 1999 to August 2005 Sorted by Prentice Hall