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JEFFERSON MATH PROJECTREGENTS AT RANDOM

All 689 NY Math A Regents Exam Questionsfrom June 1999 to August 2005 at Random

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Dear Sir

I have to acknolege the reciept of your favor of May 14. in which you mention that you have finishedthe 6. first books of Euclid, plane trigonometry, surveying & algebra and ask whether I think afurther pursuit of that branch of science would be useful to you. there are some propositions in thelatter books of Euclid, & some of Archimedes, which are useful, & I have no doubt you have beenmade acquainted with them. trigonometry, so far as this, is most valuable to every man, there is scarcelya day in which he will not resort to it for some of the purposes of common life. the science of calculationalso is indispensible as far as the extraction of the square & cube roots; Algebra as far as thequadratic equation & the use of logarithms are often of value in ordinary cases: but all beyond these isbut a luxury; a delicious luxury indeed; but not to be indulged in by one who is to have a profession tofollow for his subsistence. in this light I view the conic sections, curves of the higher orders, perhapseven spherical trigonometry, Algebraical operations beyond the 2d dimension, and fluxions. Letter from Thomas Jefferson to William G. Munford, Monticello, June 18, 1799.

Math A Regents Exam Questions at Random Page 1www.jmap.org

1. Seth is thinking of a number between 20 and30. The number is prime and not more than 2away from a perfect square. What is thenumber?

[1]

2. Which graph is symmetric with respect to they-axis?

[2]

[A] [B]

[C] [D]

3. The area of the rectangular playgroundenclosure at South School is 500 squaremeters. The length of the playground is 5meters longer than the width. Find thedimensions of the playground, in meters.[Only an algebraic solution will be accepted.]

[3]

4. In the coordinate plane, what is the totalnumber of points 5 units from the origin andequidistant from both the x- and y-axes?

[4]

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

5. If x ≠ 0, then xx

2 3

5 1000c h

⋅ is equivalent to

[5]

[A] 1000x [B] 0[C] 1000+ x [D] 1000

6. A triangle has sides whose lengths are 5, 12,and 13. A similar triangle could have sideswith lengths of

[6]

[A] 7, 24, and 25 [B] 10, 24, and 26

[C] 6, 8, and 10 [D] 3, 4, and 15

7. Joe is holding his kite string 3 feet above theground, as shown in the accompanyingdiagram. The distance between his hand anda point directly under the kite is 95 feet. Ifthe angle of elevation to the kite is 50°, findthe height, h, of his kite, to the nearest foot.

[7]

8. Solve for all values of x that satisfy the

equation xx x+

=+35

7.

[8]

9. Expressed in decimal notation, 4 726 10 3. × −

is

[9]

[A] 0.004726 [B] 0.04726

[C] 472.6 [D] 4,726

10. Solve for x: x x2 3 40 0+ − =

[10]


11. In the accompanying diagram, the perimeterof ∆MNO is equal to the perimeter of squareABCD. If the sides of the triangle arerepresented by 4x + 4, 5x - 3, and 17, and oneside of the square is represented by 3x, findthe length of a side of the square.

[11]

12. Juan has a cellular phone that costs $12.95per month plus 25¢ per minute for each call.Tiffany has a cellular phone that costs $14.95per month plus 15¢ per minute for each call.For what number of minutes do the two planscost the same?

[12]

13. If the probability that it will rain on Thursday

is 56

, what is the probability that it will not

rain on Thursday?

[13]

[A] 1 [B] 16

[C] 56

[D] 0

14. Ninety percent of the ninth grade students atRichbartville High School take algebra. If180 ninth grade students take algebra, howmany ninth grade students do not takealgebra?

[14]

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

yx

y x

== −

= +

54

54

5

Calculate the area, in square units, of thetriangle formed by the three points ofintersection.

[15]

16. In bowling leagues, some players are awardedextra points called their "handicap." The"handicap" in Anthony's league is 80% of thedifference between 200 and the bowler'saverage. Anthony's average is 145. What isAnthony's "handicap"?

[16]

17. The expression ( )( )x z xy z2 3 2 is equivalent to

[17]

[A] x y z4 2 5 [B] x y z2 2 3

[C] x y z3 2 4 [D] x y z3 3 4


18. If the number represented by n-3 is an oddinteger, which expression represents the nextgreater odd integer?

[18]

[A] n - 5 [B] n - 1 [C] n - 2 [D] n + 1

19. The party registration of the voters inJonesville is shown in the table below.

If one of the registered Jonesville voters isselected at random, what is the probabilitythat the person selected is not a Democrat?

[19]

[A] 0.600 [B] 0.333

[C] 0.667 [D] 0.400

20. 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 thedog pen is 15 square yards, how many yardsof fencing would he need to completelyenclose the pen?

[20]

21. What point is the intersection of the graphs ofthe lines 2x - y = 3 and x + y = 3?

[21]

[A] (3, 3) [B] (1, 2)

[C] (2, 1) [D] (3, 0)

22. At Ron's Rental, a person can rent a big-screen television for $10 a month plus a one-time "wear-and-tear" fee of $100. At Josie'sRental, the charge is $20 a month and anadditional charge of $20 for delivery with no"wear-and-tear" fee.a If c equals the cost, write one equationrepresenting the cost of the rental for mmonths at Ron's Rental and one equationrepresenting the cost of the rental for mmonths at Josie's Rental.b On the accompanying grid, graph and labeleach equation.c From your graph, determine in whichmonth Josie's cost will equal Ron's cost.

[22]


23. A certain state is considering changing thearrangement of letters and numbers on itslicense plates. The two options the state isconsidering are:Option 1: three letters followed by a four-digit number with repetition of both lettersand digits allowedOption 2: four letters followed by a three-digit number without repetition of eitherletters or digits[Zero may be chosen as the first digit of thenumber in either option.]Which option will enable the state to issuemore license plates? How many moredifferent license plates will that option yield?

[23]

24. The accompanying diagram shows atransformation.

Which transformation performed on figure 1resulted in figure 2?

[24]

[A] dilation [B] reflection

[C] translation [D] rotation

25. Which ratio represents cos A in theaccompanying diagram of ∆ABC ?

[25]

[A] 1213

[B] 125

[C] 135

[D] 513

26. Expressed in its simplest form,( )( ) ( )3 2 43 2 4x y x is equivalent to

[26]

[A] 24 7 2x y [B] 48 12 2x y

[C] 48 7 2x y [D] 24 12 2x y

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

[27]

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

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

28. The ratio of the corresponding sides of twosimilar squares is 1 to 3. What is the ratio ofthe area of the smaller square to the area ofthe larger square ?

[28]

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

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

[29]

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

30. The statement "x is divisible by 5 or x isdivisible by 4" is false when x equals

[30]

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

31. If the midpoints of the sides of a triangle areconnected, the area of the triangle formed iswhat part of the area of the original triangle?

[31]

[A] 13

[B] 38

[C] 14

[D] 12


32. Factor completely: 5 802n −

[32]

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

What is m CAD∠ ?

[33]

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

34. Connor wants to compare Celsius andFahrenheit temperatures by drawing aconversion graph. He knows that− ° = − °40 40C F and that 20 68° = °C F. Onthe accompanying grid, construct theconversion graph and, using the graph,determine the Celsius equivalent of 25°F.

[34]

35. Jamie is 5 years older than her sister Amy. Ifthe sum of their ages is 19, how old is Jamie?

[35]

[A] 12 [B] 5 [C] 14 [D] 7

36. In a school building, there are 10 doors thatcan be used to enter the building and 8stairways to the second floor. How manydifferent routes are there from outside thebuilding to a class on the second floor?

[36]

[A] 18 [B] 80 [C] 1 [D] 10

37. Solve the following system of equationsalgebraically or graphically:

x y2 2 25+ =3 4 0y x− =

[The use of the accompanying grid isoptional.]

[37]

38. The set of integers {3,4,5} is a Pythagoreantriple. Another such set is

[38]

[A] {6,12,13} [B] {8,15,17}

[C] {6,7,8} [D] {6,8,12}


39. The image of point (3,-5) under thetranslation that shifts (x,y) to (x-1, y-3) is

[39]

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

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

40. Parking charges at Superior Parking Garageare $5.00 for the first hour and $1.50 for eachadditional 30 minutes. If Margo has $12.50,what is the maximum amount of time she willbe able to park her car at the garage?

[40]

[A] 6 12

hours [B] 2 12

hours

[C] 6 hours [D] 3 12

hours

41. A line segment on the coordinate plane hasendpoints (2,4) and (4,y). The midpoint ofthe segment is point (3,7). What is the valueof y?

[41]

[A] 5 [B] -2 [C] 10 [D] 11

42. 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 thearea of the new field?

[42]

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

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

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

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

43. As shown in the accompanying diagram, thelength, width, and height of Richard's fishtank are 24 inches, 16 inches, and 18 inches,respectively. Richard is filling his fish tankwith water from a hose at the rate of 500cubic inches per minute. How long will ittake, to the nearest minute, to fill the tank to adepth of 15 inches?

[43]

44. The expression 0 62 103. × is equivalent to

[44]

[A] 0.062 [B] 6 2 104. ×

[C] 62,000 [D] 6 2 102. ×

45. A 10-foot ladder is to be placed against theside of a building. The base of the laddermust be placed at an angle of 72° with thelevel ground for a secure footing. Find, to thenearest inch, how far the base of the laddershould be from the side of the building andhow far up the side of the building the ladderwill reach.

[45]

46. The value of !3!7 is

[46]

[A] 4 [B] 7 [C] 24 [D] 840


47. A roll of candy is shown in the accompanyingdiagram.

The shape of the candy is best described as a

[47]

[A] pyramid [B] rectangular solid

[C] cone [D] cylinder

48. If point P lies on line , which diagramrepresents the locus of points 3 centimetersfrom point P?

[48]

[A]

[B]

[C]

[D]

49. The quotient of − ≠155

08

2

xx

x, , is

[49]

[A] −10 6x [B] − 3 4x

[C] −10 4x [D] − 3 6x

50. In the accompanying diagram of aconstruction, what does PC represent?

[50]

[A] the perpendicular bisector of AB

[B] an altitude drawn to AB

[C] a median drawn to AB

[D] the bisector of ∠APB

51. Sue bought a picnic table on sale for 50% offthe original price. The store charged her 10%tax and her final cost was $22.00. What wasthe original price of the picnic table?

[51]

52. The line 3 2 12x y− = has

[52]

[A] a slope of 3 and a y-intercept of -2

[B] a slope of − 32

and a y-intercept of 6

[C] a slope of 32

and a y-intercept of -6

[D] a slope of -3 and a y-intercept of -6


53. Bob and Ray are describing the same number.Bob says, "The number is a positive eveninteger less than or equal to 20." Ray says,"The number is divisible by 4." If Bob'sstatement is true and Ray's statement is false,what are all the possible numbers?

[53]

54. The accompanying diagram shows a box-and-whisker plot of student test scores on lastyear's Mathematics A midterm examination.

What is the median score?

[54]

[A] 71 [B] 62 [C] 81 [D] 92

55. Linda paid $48 for a jacket that was on salefor 25% of the original price. What was theoriginal price of the jacket?

[55]

[A] $192 [B] $96 [C] $72 [D] $60

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

[56]

57. Solve for x: x x2 3 28 0+ − =

[57]

58. If r = 2 and s = -7, what is the value ofr s− ?

[58]

[A] 5 [B] 9 [C] -9 [D] -5

59. The expression 27 12+ is equivalent to

[59]

[A] 13 3 [B] 39

[C] 5 6 [D] 5 3

60. The distance between parallel lines and mis 12 units. Point A is on line . How manypoints are equidistant from lines and m and8 units from point A.

[60]

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

61. The formula C F= −59

32( ) can be used to

find the Celsius temperature (C) for a givenFahrenheit temperature (F). What Celsiustemperature is equal to a Fahrenheittemperature of 77°?

[61]

[A] 171° [B] 25° [C] 8° [D] 45°

62. Which graph represents the equation x = 2?

[62]

[A] [B]

[C] [D]


63. Which ordered pair is the solution of thefollowing system of equations?

3 2 42 2 24

x yx y+ =

− + =

[63]

[A] (2,-5) [B] (-4,8)

[C] (2,-1) [D] (-4,-8)

64. Tom throws a ball into the air. The balltravels on a parabolic path represented by theequation h t t= − +8 402 , where h is theheight, in feet, and t is the time, in seconds.a On the accompanying set of axes, graph theequation from t= 0 to t = 5 seconds, includingall integral values of t from 0 to 5.

b What is the value of t at which h has itsgreatest value?

[64]

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

[65]

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

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

66. A tree casts a shadow that is 20 feet long.The angle of elevation from the end of theshadow to the top of the tree is 66°.Determine the height of the tree, to thenearest foot.

[66]

67. Seth bought a used car that had been driven20,000 miles. After he owned the car for 2years, the total mileage of the car was 49,400.Find the average number of miles he droveeach month during those 2 years.

[67]

68. A rocket is launched from the ground andfollows a parabolic path represented by theequation y x x= − +2 10 . At the same time, aflare is launched from a height of 10 feet andfollows a straight path represented by theequation y x= − +10. Using theaccompanying set of axes, graph theequations that represent the paths of therocket and the flare, and find the coordinatesof the point or points where the pathsintersect.

[68]


69. The expression 50 32+ is equivalent to

[69]

[A] 6 [B] 9 2 [C] 18 [D] 82

70. Sal has a small bag of candy containing threegreen candies and two red candies. Whilewaiting for the bus, he ate two candies out ofthe bag, one after another, without looking.What is the probability that both candies werethe same color?

[70]

71. Which geometric figure has one and only oneline of symmetry?

[71]

[A]

Square

[B]

Rectangle

[C]

Rhombus

[D]

Isoscelestrapezoid

72. Two numbers are in the ratio 2:5. If 6 issubtracted from their sum, the result is 50.What is the larger number?

[72]

[A] 55 [B] 35 [C] 40 [D] 45

73. Katrina hikes 5 miles north, 7 miles east, andthen 3 miles north again. To the nearest tenthof a mile, how far, in a straight line, is Katrinafrom her starting point?

[73]

74. The coordinates of the midpoint of AB are(2,4), and the coordinates of point B are (3,7).What are the coordinates of point A? [Theuse of the accompanying grid is optional.]

[74]

75. On a bookshelf, there are five differentmystery books and six different biographies.How many different sets of four books canEmilio choose if two of the books must bemystery books and two of the books must bebiographies?

[75]

76. What is the value of 3 2− ?

[76]

[A] -9 [B] −19

[C] 19

[D] 9

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

[77]


78. If x > 0, the expression x xd id i2 is

equivalent to

[78]

[A] x 2 [B] x2 2

[C] 2x [D] 2x

79. In the accompanying diagram, line 1 isparallel to line 2 .

Which term describes the locus of all pointsthat are equidistant from line 1 and 2 ?

[79]

[A] rectangle [B] point

[C] line [D] circle

80. The accompanying circle graph shows howthe Marino family spends its income eachmonth.

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

[80]

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

81. Ben had twice as many nickels as dimes.Altogether, Ben had $4.20. How manynickels and how many dimes did Ben have?

[81]

82. How many different five-member teams canbe made from a group of eight students, ifeach student has an equal chance of beingchosen?

[82]

[A] 6,720 [B] 56 [C] 336 [D] 40

83. If point (-1,0) is on the line whose equation isy x b= +2 , what is the value of b?

[83]

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

84. Which expression is equivalent to6 02 1023. × ?

[84]

[A] 60 2 1021. × [B] 0 602 1021. ×

[C] 602 1021× [D] 6020 1021×

85. A hockey team played n games, losing four ofthem and winning the rest. The ratio ofgames won to games lost is

[85]

[A] 4n

[B] n4

[C] n − 44

[D] 44n −

86. If n represents an odd number, whichcomputation results in an answer that is aneven number?

[86]

[A] 2 1× −n [B] 3 1× +n[C] 2 1× +n [D] 3 2× −n


87. Which linear equation represents the data inthe accompanying table?

[87]

[A] d = 1.50c + 20.00 [B] d = 1.50c

[C] d = 20.00c + 1.50 [D] d = 21.50c

88. Walter is a waiter at the Towne Diner. Heearns a daily wage of $50, plus tips that areequal to 15% of the total cost of the dinnershe serves. What was the total cost of thedinners he served if he earned $170 onTuesday?

[88]

89. If the length of a rectangular prism isdoubled, its width is tripled, and its heightremains the same, what is the volume of thenew rectangular prism?

[89]

[A] double the original volume

[B] nine times the original volume

[C] six times the original volume

[D] triple the original volume

90. The dimensions of a brick, in inches, are 2 by4 by 8. How many such bricks are needed tohave a total volume of exactly 1 cubic foot?

[90]

91. A doughnut shop charges $0.70 for eachdoughnut and $0.30 for a carryout box.Shirley has $5.00 to spend. At most, howmany doughnuts can she buy if she also wantsthem in one carryout box?

[91]

92. On February 18, from 9 a.m. until 2 p.m., thetemperature rose from -14°F to 36°F. Whatwas the total increase in temperature duringthis time period?

[92]

[A] 32° [B] 36° [C] 50° [D] 22°

93. In the accompanying figure, what is one pairof alternate interior angles?

[93]

[A] ∠4 and ∠6 [B] ∠6 and ∠8

[C] ∠1 and ∠2 [D] ∠4 and ∠5

94. Shoe sizes and foot length are related by theformula S = 3F - 24, where S represents theshoe size and F represents the length of thefoot, in inches.a Solve the formula for F.b To the nearest tenth of an inch, how long

is the foot of a person who wears a size 10 12

shoe?

[94]


95. In the accompanying diagram of equilateraltriangle ABC, DE = 5 and DE AB .

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

[95]

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

96. The sum of the ages of the three Romanobrothers is 63. If their ages can berepresented as consecutive integers, what isthe age of the middle brother?

[96]

97. If x ≠ 0, the expression x xx

2 2+ is equivalent

to

[97]

[A] 2 [B] 4 [C] x + 2 [D] 3x

98. Arielle has a collection of grasshoppers andcrickets. She has 561 insects in all. Thenumber of grasshoppers is twice the numberof crickets. Find the number of each type ofinsect that she has.

[98]

99. Which is a rational number?

[99]

[A] π [B] 5 9 [C] 8 [D] 6 2

100. What are the factors of x x2 10 24− − ?

[100]

[A] (x - 12)(x + 2) [B] (x - 4)(x - 6)

[C] (x - 4)(x + 6) [D] (x + 12)(x - 2)

101. The expression3 2 7 6 4 32 2x xy x xy+ + − − +c h c h is equivalent

to

[101]

[A] − − +3 2 42x xy [B] 3 6 42x xy− −

[C] − + +3 6 42x xy [D] 3 2 42x xy− +

102. The telephone company has run out of seven-digit telephone numbers for an area code. Tofix this problem, the telephone company willintroduce a new area code. Find the numberof new seven-digit telephone numbers thatwill be generated for the new area code ifboth of the following conditions must be met:o The first digit cannot be a zero or a one.o The first three digits cannot be theemergency number (911) or the number usedfor information (411).

[102]

103. The operation element @ is determined by thefollowing table:

What is the identity element of this operation?

[103]

[A] c [B] a, only

[C] a and b [D] b, only


104. As seen in the accompanying diagram, aperson can travel from New York City toBuffalo by going north 170 miles to Albanyand then west 280 miles to Buffalo.

a If an engineer wants to design a highwayto connect New York City directly to Buffalo,at what angle, x, would she need to build thehighway? Find the angle to the nearestdegree.b To the nearest mile, how many mileswould be saved by traveling directly fromNew York City to Buffalo rather than bytraveling first to Albany and then to Buffalo?

[104]

105. In his will, a man leaves one-half of hismoney to his wife, one-half of what is thenleft to his older child, and one-half of what isthen left to his younger child. His twocousins divide the remainder equally, eachreceiving $2,000. What was the total amountof money in the man's will?

[105]

[A] $32,000 [B] $16,000

[C] $40,000 [D] $24,000

106. What is the identity element for in theaccompanying table?

[106]

[A] r [B] u [C] s [D] t

107. Steve has a treasure map, represented in theaccompanying diagram, that shows two trees8 feet apart and a straight fence connectingthem. The map states that treasure is buried 3feet from the fence and equidistant from thetwo trees.

a Sketch a diagram to show all the placeswhere the treasure could be buried. Clearlyindicate in your diagram where the treasurecould be buried.b What is the distance between the treasureand one of the trees?

[107]

108. Find all negative odd integers that satisfy thefollowing inequality:

− + ≤3 1 17x

[108]

109. Cole's Ice Cream Stand serves sixteendifferent flavors of ice cream, three types ofsyrup, and seven types of sprinkles. If an icecream sundae consists of one flavor of icecream, one type of syrup, and one type ofsprinkles, how many different ice creamsundaes can Cole serve?

[109]

[A] 10,836 [B] 3 [C] 336 [D] 26

110. Which statement is logically equivalent to "IfI eat, then I live"?

[110]

[A] If I live, then I eat.

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

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

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


111. The students in Woodland High School'smeteorology class measured the noontemperature every schoolday for a week.Their readings for the first 4 days wereMonday, 56°; Tuesday, 72°; Wednesday, 67°;and Thursday, 61°. If the mean (average)temperature for the 5 days was exactly 63°,what was the temperature on Friday?

[111]

112. In the figure below, the large rectangle,ABCD, is divided into four smaller rectangles.The area of rectangle AEHG x= 5 , the area ofrectangle GHFB x= 2 2 , the area of rectangleHJCF x= 6 , segment AG = 5, and segmentAE = x.

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

[112]

113. In isosceles triangle DOG, the measure of thevertex angle is three times the measure of oneof the base angles. Which statement about∆DOG is true?

[113]

[A] ∆DOG is an obtuse triangle.

[B] ∆DOG is a scalene triangle.

[C] ∆DOG is a right triangle.

[D] ∆DOG is an acute triangle.

114. What is the solution set of m m2 3 10 0− − = ?

[114]

[A] {2,-5} [B] {3,-10}

[C] {5,-2} [D] {3,10}

115. Which point is in the solution set of thesystem of inequalities shown in theaccompanying graph?

[115]

[A] (2, 4) [B] (-4, 1)

[C] (4, -1) [D] (0, 4)

116. Alexandra purchases two doughnuts and threecookies at a doughnut shop and is charged$3.30. Briana purchases five doughnuts andtwo cookies at the same shop for $4.95. Allthe doughnuts have the same price and all thecookies have the same price. Find the cost ofone doughnut and find the cost of one cookie.

[116]

117. What is the slope of the line whose equationis 2y = 5x + 4?

[117]

[A] 5 [B] 25

[C] 52

[D] 2


118. In the accompanying diagram, whichtransformation changes the solid-line parabolato the dotted-line parabola?

[118]

[A] rotation, only

[B] line reflection or rotation

[C] line reflection, only [D] translation

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

[119]

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

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

120. The accompanying histogram shows theheights of the students in Kyra's health class.

What is the total number of students in theclass?

[120]

[A] 15 [B] 209 [C] 5 [D] 16

121. The perimeter of an equilateral triangle variesdirectly as the length of a side. When thelength of a side is doubled, the perimeter ofthe triangle is

[121]

[A] doubled [B] halved

[C] multiplied by 3 [D] divided by 3

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

This transformation is an example of a

[122]

[A] rotation about point A

[B] dilation [C] translation

[D] line reflection in point

123. Frank, George, and Hernando are a plumber,a cabinet maker, and an electrician, thoughnot necessarily in that order. Each can do allwork appropriate to his own field, but nowork in other fields. Frank was not able toinstall a new electric line in his home.Hernando was not able to make cabinets.George is also a building contractor whohired one of the other people to do hiselectrical work. Which statement must betrue?

[123]

[A] Frank is an electrician.

[B] Hernando is an electrician.

[C] Frank is a plumber.

[D] George is a cabinet maker.


124. Draw all the symmetry lines on theaccompanying figure.

[124]

125. If 9x + 2a = 3a - 4x, then x equals

[125]

[A] a [B] a13

[C] − a [D] 512a

126. In which list are the numbers in order fromleast to greatest?

[126]

[A] 13, , 3.2, 33

π [B] 13.2, , 3 , 33

π

[C] 13.2, 3 , 3,3

π [D] 13, 3.2, , 33

π

127. If a is an odd number, b an even number, andc an odd number, which expression willalways be equivalent to an odd number?

[127]

[A] a bcb g [B] ac bb g0

[C] ac bb g2 [D] ac bb g1

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

[128]

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

129. What is the value of x y2 42− , if x = 4 and

y = −3?

[129]

[A] -2 [B] 14 [C] 10 [D] 2

130. 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∠ ?

[130]

131. Jeremy's bedroom has two doors leading intothe hallway. His house has four doors leadingto the outside. Using the doorways, in howmany different ways can Jeremy leave hisroom and go outside?

[131]

[A] 5 [B] 6 [C] 8 [D] 4

132. Which property of real numbers is illustratedby the equation − + =3 3 0

[132]

[A] associative property of addition

[B] additive inverse

[C] commutative property of addition

[D] additive identity


133. Which expression represents the number ofyards in x feet?

[133]

[A] x3

[B] 12x [C] x12

[D] 3x

134. The expression − − 7 is equivalent to

[134]

[A] 0 [B] 1 [C] -7 [D] 7

135. The scores on a mathematics test were 70, 55,61, 80, 85, 72, 65, 40, 74, 68, and 84.Complete the accompanying table, and usethe table to construct a frequency histogramfor these scores.

[135]

136. Tanisha and Rachel had lunch at the mall.Tanisha ordered three slices of pizza and twocolas. Rachel ordered two slices of pizza andthree colas. Tanisha's bill was $6.00, andRachel's bill was $5.25. What was the priceof one slice of pizza? What was the price ofone cola?

[136]

137. On a map, 1 centimeter represents 40kilometers. How many kilometers arerepresented by 8 centimeters?

[137]

[A] 320 [B] 280 [C] 48 [D] 5

138. If one factor of 56 424 3 2 6x y x y− is 14 2 3x y ,what is the other factor?

[138]

[A] 4 32 2x y xy− [B] 4 32 3x y xy−

[C] 4 32 2x y− [D] 4 32 3x y−

139. What is the measure, in degrees, of eachexterior angle of a regular hexagon?

[139]

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

140. If 3(x - 2) = 2x + 6, the value of x is

[140]

[A] 12 [B] 0 [C] 20 [D] 5

141. If t t t2 < < , then t could be

[141]

[A] −14

[B] 14

[C] 4 [D] 0


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

[142]

[A] 5 [B] 21 14

[C] 4 38

[D] 10

143. A storage container in the shape of a rightcircular cylinder is shown in theaccompanying diagram.

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

[143]

[A] 5655. in3 [B] 502 65. in3

[C] 12566. in3 [D] 25133. in3

144. If x and y are defined as indicated by theaccompanying table, which equation correctlyrepresents the relationship between x and y?

[144]

[A] y = 2x + 3 [B] y = x + 2

[C] y = 2x + 2 [D] y = 2x - 3

145. Bob and Laquisha have volunteered to serveon the Junior Prom Committee. The names oftwenty volunteers, including Bob andLaquisha, are put into a bowl. If two namesare randomly drawn from the bowl withoutreplacement, what is the probability thatBob's name will be drawn first and Laquisha'sname will be drawn second?

[145]

[A] 120

120⋅ [B] 2

20!

[C] 220

[D] 120

119⋅

146. The Excel Cable Company has a monthly feeof $32.00 and an additional charge of $8.00for each premium channel. The Best CableCompany has a monthly fee of $26.00 andadditional charge of $10.00 for each premiumchannel. The Horton family is decidingwhich of these two cable companies tosubscribe to.a For what number of premium channels willthe total monthly subscription fee for theExcel and Best Cable companies be the same?b The Horton family decides to subscribe to2 premium channels for a period of one year. (1) Which cable company should theysubscribe to in order to spend less money? (2) How much money will the Hortonssave in one year by using the less expensivecompany?

[146]

147. If − + =2 3 7x and 3 1 5x y+ = + , the value ofy is

[147]

[A] 10 [B] 0 [C] −10 [D] 1


148. A hotel charges $20 for the use of its diningroom and $2.50 a plate for each dinner. Anassociation gives a dinner and charges $3 aplate but invites four nonpaying guests. Ifeach person has one plate, how many payingpersons must attend for the association tocollect the exact amount needed to pay thehotel?

[148]

[A] 40 [B] 60 [C] 20 [D] 44

149. Determine the distance between point A(-1,-3)and point B(5,5). Write an equation of theperpendicular bisector of AB . [The use ofthe accompanying grid is optional.]

[149]

150. There were 100 more balcony tickets thanmain-floor tickets sold for a concert. Thebalcony tickets sold for $4 and the main-floortickets sold for $12. The total amount of salesfor both types of tickets was $3,056.a Write an equation or a system of equationsthat describes the given situation. Define thevariables.b Find the number of balcony tickets thatwere sold.

[150]

151. Given: 9911

164 196, ,

Identify the expression that is a rationalnumber and explain why it is rational.

[151]

152. When Tony received his weekly allowance,he decided to purchase candy bars for all hisfriends. Tony bought three Milk Chocolatebars and four Creamy Nougat bars, whichcost a total of $4.25 without tax. Then herealized this candy would not be enough forall his friends, so he returned to the store andbought an additional six Milk Chocolate barsand four Creamy Nougat bars, which cost atotal of $6.50 without tax. How much dideach type of candy bar cost?

[152]

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

[153]

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

[154]

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


155. The operation * for the set {p,r,s,v} isdefined in the accompanying table. What isthe inverse element of r under the operation*?

[155]

[A] s [B] p [C] v [D] r

156. If x = -4 and y = 3, what is the value ofx y− 3 2 ?

[156]

[A] -13 [B] -31 [C] -23 [D] -85

157. 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 theplayer crosses into the end zone?

[157]

[A] 30° [B] 60° [C] 180° [D] 150°

158. Sterling silver is made of an alloy of silverand copper in the ratio of 37:3. If the massof a sterling silver ingot is 600 grams, howmuch silver does it contain?

[158]

[A] 200 g [B] 555 g

[C] 450 g [D] 48.65 g

159. As shown in the accompanying diagram, thestar in position 1 on a computer screentransforms to the star in position 2.

This transformation is best described as a

[159]

[A] dilation [B] translation

[C] rotation [D] line reflection

160. In the accompanying graph, if point P hascoordinates a b, ,b g which point hascoordinates −b a, ?b g

[160]

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

161. Selena and Tracey play on a softball team.Selena has 8 hits out of 20 times at bat, andTracey has 6 hits out of 16 times at bat.Based on their past performance, what is theprobability that both girls will get a hit nexttime at bat?

[161]

[A] 48320

[B] 1436

[C] 1 [D] 3140


162. A boy got 50% of the questions on a testcorrect. If he had 10 questions correct out of

the first 12, and 14

of the remaining questions

correct, how many questions were on the test?

[162]

[A] 26 [B] 24 [C] 16 [D] 28

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

[163]

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

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

164. Which number is irrational?

[164]

[A] 23

[B] 9 [C] 0.3333 [D] 8

165. TOP Electronics is a small business with fiveemployees. The mean (average) weeklysalary for the five employees is $360. If theweekly salaries of four of the employees are$340, $340, $345, and $425, what is thesalary of the fifth employee?

[165]

166. When 3 2 12x x− + is subtracted from2 7 52x x+ + , the result will be

[166]

[A] x x2 9 4− − [B] − + +x x2 5 6

[C] x x2 5 6+ + [D] − + +x x2 9 4

167. The number 8 375 10 3. × − is equivalent to

[167]

[A] 0.0008375 [B] 8,375

[C] 0.008375 [D] 0.08375

168. Ramón rented a sprayer and a generator. Onhis first job, he used each piece of equipmentfor 6 hours at a total cost of $90. On hissecond job, he used the sprayer for 4 hoursand the generator for 8 hours at a total cost of$100. What was the hourly cost of each pieceof equipment?

[168]

169. 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 andB after AB is reflected in the x-axis.

[169]

170. The direct distance between city A and city Bis 200 miles. The direct distance between cityB and city C is 300 miles. Which could bethe direct distance between city C and city A?

[170]

[A] 350 miles [B] 550 miles

[C] 650 miles [D] 50 miles

171. The expression 15 - 3[2 + 6(-3)] simplifies to

[171]

[A] -33 [B] 192 [C] -45 [D] 63


172. If the mass of a proton is 167 10 24. × − gram,what is the mass of 1,000 protons?

[172]

[A] 167 10 23. × − [B] 167 10 22. × −

[C] 167 10 21. × − [D] 167 10 27. × −

173. The sum of 3 4 22x x+ − and x x2 5 3− + is

[173]

[A] 4 12x x− − [B] 4 12x x+ −

[C] 4 12x x− + [D] 4 12x x+ +

174. The sum of 3 25

0x

x+ ≠, , is

[174]

[A] 1x

[B] 2 155

xx+

[C] 2 155

xx++

[D] 55x +

175. What is true about the statement "If twoangles are right angles, the angles have equalmeasure " and its converse "If two angleshave equal measure then the two angles areright angles"?

[175]

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

[B] Both the statement and its converse aretrue.

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

[D] Both the statement and its converse arefalse.

176. Which equation could represent therelationship between the x and y values shownin the accompanying table?

[176]

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

[C] y x= + 2 [D] y x= 2

177. Ramón said that the set of integers is notclosed for one of the basic operations(addition, subtraction, multiplication, ordivision). You want to show Ramón that hisstatement is correct.For the operation for which the set of integersis not closed, write an example using:o a positive even integer and a zeroo a positive and a negative even integero two negative even integersBe sure to explain why each of your examplesillustrates that the set of integers is not closedfor that operation.

[177]

178. The volume of a cube is 64 cubic inches. Itstotal surface area, in square inches, is

[178]

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


179. The accompanying diagram is an example ofwhich type of graph?

[179]

[A] box-and-whisker plot

[B] stem-and-leaf plot

[C] histogram [D] bar graph

180. A ship on the ocean surface detects a sunkenship on the ocean floor at an angle ofdepression of 50°. The distance between theship on the surface and the sunken ship on theocean floor is 200 meters. If the ocean flooris level in this area, how far above the oceanfloor, to the nearest meter, is the ship on thesurface?

[180]

181. A certain car comes in three body styles witha choice of two engines, a choice of twotransmissions, and a choice of six colors.What is the minimum number of cars a dealermust stock to have one car of every possiblecombination?

[181]

[A] 42 [B] 13 [C] 72 [D] 36

182. If rain is falling at the rate of 2 inches perhour, how many inches of rain will fall in xminutes?

[182]

[A] 2x [B] 30x

[C] x30

[D] 60x

183. What is the measure of the largest angle in theaccompanying triangle?

[183]

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

184. John uses the equation x y2 2 9+ = torepresent the shape of a garden on graphpaper.a Graph x y2 2 9+ = on the accompanyinggrid.

b What is the area of the garden to thenearest square unit?

[184]


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

[185]

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

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

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

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

186. A straw is placed into a rectangular box thatis 3 inches by 4 inches by 8 inches, as shownin the accompanying diagram. If the strawfits exactly into the box diagonally from thebottom left front corner to the top right backcorner, how long is the straw, to the nearesttenth of an inch?

[186]

187. Factor completely: 3 15 422x x+ −

[187]

188. The statement "x is not the square of aninteger and x is a multiple of 3" is true when xis equal to

[188]

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

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

[189]

[A] (-6,-9) [B] (-5,-3)

[C] (0,-9) [D] (-6,-1)

190. In the accompanying diagram, ∆ABC issimilar to but not congruent to ∆A B C' ' ' .Which transformation is represented by∆A B C' ' ' ?

[190]

[A] translation [B] dilation

[C] reflection [D] rotation

191. In the accompanying diagram, parallel linesAB and CD are intersected by transversalEF at points X and Y, and m FYD∠ = 123 .Find m AXY∠ .

[191]

192. 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 inthe shape of a triangle with sides of 7 feet, 8feet, and 16 feet.

[192]


193. Sara is building a triangular pen for her petrabbit. If two of the sides measure 8 feet and15 feet, the length of the third side could be

[193]

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

194. If 2ax - 5x = 2, then x is equivalent to

[194]

[A] 22 5a −

[B] 2 52+ aa

[C] 7 2− a [D] 15a −

195. Nine hundred students were asked whetherthey thought their school should have a dresscode. A circle graph was constructed to showthe results. The central angles for two of thethree sectors are shown in the accompanyingdiagram. What is the number of students whofelt that the school should have no dresscode?

[195]

196. What is the value of 6 3 103 10

8

4

. ××

in scientific

notation?

[196]

[A] 21 10 4. × − [B] 21 10 2. × −

[C] 21 102. × [D] 21 104. ×

197. The distance from Earth to the imaginaryplanet Med is 17 107. × miles. If a spaceshipis capable of traveling 1,420 miles per hour,how many days will it take the spaceship toreach the planet Med? Round your answer tothe nearest day.

[197]

198. If 3x is one factor of 3 92x x− , what is theother factor?

[198]

[A] x + 3 [B] x x2 6−[C] x − 3 [D] 3x

199. Which equation represents the locus of allpoints 5 units below the x-axis?

[199]

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

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

200. During each marking period, there are fivetests. If Vanita needs a 65 average to passthis marking period and her first four gradesare 60, 72, 55, and 80, what is the lowestscore she can earn on the last test to have apassing average?

[200]

[A] 65 [B] 100 [C] 80 [D] 58

201. A box in the shape of a cube has a volume of64 cubic inches. What is the length of a sideof the box?

[201]

[A] 16 in [B] 8 in

[C] 4 in [D] 21 3. in


202. The solution set for the equation 652 =− xxis

[202]

[A] {-2,3} [B] {1,-6}

[C] {-1,6} [D] {2,-3}

203. Which diagram shows a dotted line that is nota line of symmetry?

[203]

[A] [B]

[C] [D]

204. The product of 2 3x and 6 5x is

[204]

[A] 12 8x [B] 12 15x

[C] 10 8x [D] 10 15x

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

[205]

[A] 4 4 12x x+ − [B] 2 12x +

[C] 4 4 12x x− + [D] 4 12x +

206. A car dealer has 22 vehicles on his lot. If 8 ofthe vehicles are vans and 6 of the vehicles arered, and 10 vehicles are neither vans nor red,how many red vans does he have on his lot?

[206]

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

[207]

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

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

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

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

208. There are 30 students on a school bus. Ofthese students, 24 either play in the schoolband or sing in the chorus. Six of the studentsplay in the school band but do not sing in thechorus. Fourteen of the students sing in thechorus and also play in the school band. Howmany students on the school bus sing in thechorus but do not play in the band?

[208]

209. A ribbon 56 centimeters long is cut into twopieces. One of the pieces is three timeslonger than the other. Find the lengths, incentimeters, of both pieces of ribbon.

[209]

210. There were seven students running in a race.How many different arrangements of first,second, and third place are possible?

[210]

211. A 12-foot tree casts a 16-foot shadow. Howmany feet tall is a nearby tree that casts a 20-foot shadow at the same time?

[211]


212. If 385 106. × is divided by 385 104× , theresult is

[212]

[A] 385 1010. × [B] 385 104. ×

[C] 1 [D] 0 01.

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

[213]

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

214. Which expression is a factor of n n2 3 54+ − ?

[214]

[A] n + 9 [B] n + 6

[C] n2 9+ [D] n − 9

215. Solve the following system of equationsalgebraically.y x x= + −2 4 2y x= +2 1

[215]

216. Two angles are complementary. One anglehas a measure that is five times the measureof the other angle. What is the measure, indegrees, of the larger angle?

[216]

217. A school district offers hockey andbasketball. The result of a survey of 300students showed:120 students play hockey, only 90 students play basketball, only 30 students do not participate in either sportOf those surveyed, how many students playboth hockey and basketball?

[217]

218. Sara's telephone service costs $21 per monthplus $0.25 for each local call, and long-distance calls are extra. Last month, Sara'sbill was $36.64, and it included $6.14 in long-distance charges. How many local calls didshe make?

[218]

219. Which piece of paper can be folded into apyramid?

[219]

[A] [B]

[C] [D]

220. John, Dan, Karen, and Beth went to a costumeball. They chose to go as Anthony andCleopatra, and Romeo and Juliet. John gotthe costumes for Romeo and Cleopatra, butnot his own costume. Dan saw the costumesfor Juliet and himself. Karen went asAnthony. Beth drove two of her friends, whowere dressed as Anthony and Cleopatra, tothe ball. What costume did John wear?

[220]

221. How many different three-member teams canbe selected from a group of seven students?

[221]

[A] 5,040 [B] 35 [C] 1 [D] 210

222. If a and b are both odd integers, whichexpression must always equal an odd integer?

[222]

[A] a b⋅ [B] a b+ [C] a b− [D] ab


223. The Rivera family bought a new tent forcamping. Their old tent had equal sides of 10feet and a floor width of 15 feet, as shown inthe accompanying diagram.

If the new tent is similar in shape to the oldtent and has equal sides of 16 feet, how wideis the floor of the new tent?

[223]

224. Seventy-eight students participate in one ormore of three sports: baseball, tennis, andgolf. Four students participate in all threesports; five play both baseball and golf, only;two play both tennis and golf, only; and threeplay both baseball and tennis, only. If sevenstudents play only tennis and one plays onlygolf, what is the total number of students whoplay only baseball?

[224]

[A] 12 [B] 44 [C] 56 [D] 60

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

[225]

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

226. Mr. Smith's class voted on their favorite icecream flavors, and the results are shown inthe accompanying diagram. If there are 20students in Mr. Smith's class, how manystudents chose coffee ice cream as theirfavorite flavor?

[226]

227. Three times as many robins as cardinalsvisited a bird feeder. If a total of 20 robinsand cardinals visited the feeder, how manywere robins?

[227]

[A] 5 [B] 15 [C] 10 [D] 20

228. Which is an irrational number?

[228]

[A] 3 [B] 9 [C] 34

[D] 3.14

229. The solution set for the equationx x2 2 15 0− − = is

[229]

[A] {5,3} [B] {-5,-3}

[C] {5,-3} [D] {-5,3}


230. A group of 148 people is spending five daysat a summer camp. The cook ordered 12pounds of food for each adult and 9 pounds offood for each child. A total of 1,410 poundsof food was ordered.a Write an equation or a system of equationsthat describes the above situation and defineyour variables.b Using your work from part a, find: (1) the total number of adults in the group (2) the total number of children in thegroup

[230]

231. Which type of transformation is illustrated inthe accompanying diagram?

[231]

[A] rotation [B] translation

[C] dilation [D] reflection

232. The school cafeteria offers five sandwichchoices, four desserts, and three beverages.How many different meals consisting of onesandwich, one dessert, and one beverage canbe ordered?

[232]

[A] 3 [B] 12 [C] 60 [D] 1

233. In the accompanying diagram, line m isparallel to line p, line t is a transversal,m a x∠ = +3 12 , and m b x∠ = +2 13 . Find thevalue of x.

[233]

234. The angle of elevation from a point 25 feetfrom the base of a tree on level ground to thetop of the tree is 30°. Which equation can beused to find the height of the tree?

[234]

[A] tan3025

°=x [B] sin 30

25°=

x

[C] cos3025

°=x [D] 30 252 2 2+ = x

235. Which quadrilateral must have diagonals thatare congruent and perpendicular?

[235]

[A] trapezoid [B] rhombus

[C] parallelogram [D] square

236. If (x - 4) is a factor of x x w2 0− − = , then thevalue of w is

[236]

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

237. Which expression is a factor of x x2 2 15+ −

[237]

[A] (x - 5) [B] (x - 3)

[C] (x + 3) [D] (x + 15)


238. Which phrase does not describe a triangle?

[238]

[A] obtuse right [B] isosceles right

[C] equilateral equiangular

[D] acute scalene

239. In a telephone survey of 100 households, 32households purchased Brand A cereal and 45purchased Brand B cereal. If 10 householdspurchased both items, how many of thehouseholds surveyed did not purchase eitherBrand A or Brand B cereal?

[239]

240. The inequality 12

3 2 6x x+ < − is equivalent

to

[240]

[A] x < 6 [B] x < − 56

[C] x > − 56

[D] x > 6

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

[241]

242. The accompanying diagram shows a squarewith side y inside a square with side x.

Which expression represents the area of theshaded region?

[242]

[A] y x2 2− [B] x y2 2−

[C] y2 [D] x2

243. Hersch says if a triangle is an obtuse triangle,then it cannot also be an isosceles triangle.Using a diagram, show that Hersch isincorrect, and indicate the measures of all theangles and sides to justify your answer.

[243]

244. Which inequality is true if x = 304148..

, y = 1.99

+ 0.33, and z = 13 3.b g ?

[244]

[A] y < x < z [B] y < z < x

[C] x < y < z [D] x < z < y

245. Seth has one less than twice the number ofcompact discs (CDs) that Jason has. Raoulhas 53 more CDs than Jason has. If Sethgives Jason 25 CDs, Seth and Jason will havethe same number of CDs. How many CDsdid each of the three boys have to begin with?

[245]


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

[246]

247. If x + y = 9x + y, then x is equal to

[247]

[A] 8 [B] y [C] 0 [D] 15

y

248. What is the sum, in degrees, of the measuresof the interior angles of a stop sign, which isin the shape of an octagon?

[248]

[A] 360 [B] 1,080

[C] 1,880 [D] 1,440

249. The accompanying diagram shows the graphsof a linear equation and a quadratic equation.

How many solutions are there to this systemof equations?

[249]

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

250. The expression 50 can be simplified to

[250]

[A] 2 25 [B] 5 10

[C] 5 2 [D] 25 2

251. M is the midpoint of AB . If the coordinatesof A are (-1,5) and the coordinates of M are(3,3), what are the coordinates of B?

[251]

[A] (2,8) [B] (7,1)

[C] (-5,7) [D] (1,4)

252. Which expression is equivalent to x−4 ?

[252]

[A] x4 [B] − 4x [C] 14x

[D] 0

253. Mary chooses an integer at random from 1 to6. What is the probability that the integer shechooses is a prime number?

[253]

[A] 56

[B] 36

[C] 46

[D] 26

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

[254]

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

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

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

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


255. If asphalt pavement costs $0.78 per squarefoot, determine, to the nearest cent, the costof paving the shaded circular road with centerO , an outside radius of 50 feet, and an innerradius of 36 feet, as shown in theaccompanying diagram.

[255]

256. The perimeter of ∆A B C' ' ' , the image of∆ABC , is twice as large as the perimeter of∆ABC . What type of transformation hastaken place?

[256]

[A] reflection [B] dilation

[C] rotation [D] translation

257. The Grimaldis have three children born indifferent years.a Draw a tree diagram or list a sample spaceto show all the possible arrangements of boyand girl children in the Grimaldi family.b Using your information from part a, what isthe probability that the Grimaldis have threeboys?

[257]

258. A person standing on level ground is 2,000feet away from the foot of a 420-foot-tallbuilding, as shown in the accompanyingdiagram. To the nearest degree, what is thevalue of x?

[258]

259. Mr. Petri has a rectangular plot of land withlength = 20 feet and width = 10 feet. Hewants to design a flower garden in the shapeof a circle with two semicircles at each end ofthe center circle, as shown in theaccompanying diagram. He will fill in theshaded area with wood chips. If one bag ofwood chips covers 5 square feet, how manybags must he buy?

[259]


260. Construct a stem-and-leaf plot listing thescores below in order from lowest to highest.15, 25, 28, 32, 39, 40, 43, 26, 50, 75, 65, 19,55, 72, 50

[260]

261. Factor completely: 3 272x −

[261]

[A] 3 3 2x −b g [B] 3 272x −c h[C] 3 3 3x x+ −b gb g [D] 3 3 9x x+ −b gb g

262. If the area of a square garden is 48 squarefeet, what is the length, in feet, of one side ofthe garden?

[262]

[A] 16 3 [B] 12 2

[C] 4 3 [D] 4 6

263. In the accompanying diagram, x representsthe length of a ladder that is leaning against awall of a building, and y represents thedistance from the foot of the ladder to thebase of the wall. The ladder makes a 60°angle with the ground and reaches a point onthe wall 17 feet above the ground. Find thenumber of feet in x and y.

[263]

264. The mean (average) weight of three dogs is38 pounds. One of the dogs, Sparky, weighs46 pounds. The other two dogs, Eddie andSandy, have the same weight. Find Eddie'sweight.

[264]

265. If a girl 1.2 meters tall casts a shadow 2meters long, how many meters tall is a treethat casts a shadow 75 meters long at thesame time?

[265]

266. Which polynomial is the quotient of6 9 3

3

3 2x x xx

+ + ?

[266]

[A] 6 92x x+ [B] 2 32x x+

[C] 2 3 12x x+ + [D] 2 3x +


267. Which equation represents a line parallel tothe line y = 2x - 5?

[267]

[A] y x= −5 2 [B] y x= − −12

5

[C] y x= +2 5 [D] y x= − −2 5

268. The senior class is sponsoring a dance. Thecost of a student disk jockey is $40, andtickets sell for $2 each. Write a linearequation and, on the accompanying grid,graph the equation to represent therelationship between the number of ticketssold and the profit from the dance. Then findhow many tickets must be sold to break even.

[268]

269. A cake recipe calls for 1.5 cups of milk and 3cups of flour. Seth made a mistake and used5 cups of flour. How many cups of milkshould he use to keep the proportions correct?

[269]

[A] 1.75 [B] 2 [C] 2.25 [D] 2.5

270. A fair coin is thrown in the air four times. Ifthe coin lands with the head up on the firstthree tosses, what is the probability that thecoin will land with the head up on the fourthtoss?

[270]

[A] 0 [B] 116

[C] 18

[D] 12

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

[271]

[A] increases by 2 [B] is multiplied by 4

[C] remains the same

[D] is doubled

272. Javon's homework is to determine thedimensions of his rectangular backyard. Heknows that the length is 10 feet more than thewidth, and the total area is 144 square feet.Write an equation that Javon could use tosolve this problem. Then find thedimensions, in feet, of his backyard.

[272]

273. The profits in a business are to be shared bythe three partners in the ratio of 3 to 2 to 5.The profit for the year was $176,500.Determine the number of dollars each partneris to receive.

[273]

274. The graphs of the equations y x x= + −2 4 1and y x+ =3 are drawn on the same set ofaxes. At which point do the graphs intersect?

[274]

[A] (-2, 1) [B] (1, 4)

[C] (1, -2) [D] (-2, -5)


275. The following set of data represents thescores on a mathematics quiz:58, 79, 81, 99, 68, 92, 76, 84, 53, 57, 81, 91,77, 50, 65, 57, 51, 72, 84, 89Complete the frequency table below and, onthe accompanying grid, draw and label afrequency histogram of these scores.

[275]

276. Express both the perimeter and the area of therectangle shown in the accompanyingdiagram as polynomials in simplest form.

[276]

277. In Jackson County, Wyoming, license platesare made with two letters (A through Z)followed by three digits (0 through 9). Theplates are made according to the followingrestrictions:o the first letter must be J or W, and thesecond letter can be any of the 26 letters inthe alphabeto no digit can be repeatedHow many different license plates can bemade with these restrictions?

[277]

278. Which equation illustrates the distributiveproperty?

[278]

[A] 5(a + b) = 5a + 5b

[B] a + b = b + a [C] a + 0 = a

[D] a + (b + c) = (a + b) + c

279. Simplify: 9 159 25

2

2 2

x xyx y

−−

[279]

280. In the accompanying diagram ofparallelogram ABCD, m A x∠ = +( )2 10 andm B x∠ = 3 . Find the number of degrees inm B∠ .

[280]


281. The expression 5 6 2

8

x yx y

is equivalent to

[281]

[A]14

35xy [B] yx 25

[C]2

5x

y [D] 3145 yx

282. Fran's favorite photograph has a length of 6inches and a width of 4 inches. She wants tohave it made into a poster with dimensionsthat are similar to those of the photograph.She determined that the poster should have alength of 24 inches. How many inches widewill the poster be?

[282]

283. The expression x − 6 2b g is equivalent to

[283]

[A] x x2 12 36− + [B] x2 36+

[C] x x2 12 36+ + [D] x2 36−

284. The product of 3 2x y and − 4 3xy is

[284]

[A] −12 2 3x y [B] 12 3 4x y

[C] −12 3 4x y [D] 12 2 3x y

285. Rosario and Enrique are in the samemathematics class. On the first five tests,Rosario received scores of 78, 77, 64, 86, and70. Enrique received scores of 90, 61, 79, 73,and 87. How much higher was Enrique'saverage than Rosario's average?

[285]

[A] 4 points [B] 3 points

[C] 2 points [D] 15 points

286. What is the value of ?2 3−

[286]

[A] -6 [B]61 [C]

81 [D] -8

287. A triangular park is formed by theintersection of three streets, Bridge Street,Harbor Place, and College Avenue, as shownin the accompanying diagram. A walkwayparallel to Harbor Place goes through thepark. A time capsule has been buried in thepark in a location that is equidistant fromBridge Street and College Avenue and 5yards from the walkway. Indicate on thediagram with an X each possible locationwhere the time capsule could be buried.

[287]

288. The weights of all the students in grade 9 arearranged from least to greatest. Whichstatistical measure separates the top half ofthis set of data from the bottom half?

[288]

[A] mean [B] average

[C] median [D] mode

289. A deli has five types of meat, two types ofcheese, and three types of bread. How manydifferent sandwiches, consisting of one typeof meat, one type of cheese, and one type ofbread, does the deli serve?

[289]

[A] 10 [B] 75 [C] 30 [D] 25


290. Which letter has point symmetry?

[290]

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

291. Tara buys two items that cost d dollars each.She gives the cashier $20. Which expressionrepresents the change she should receive?

[291]

[A] 20 - 2d [B] 20 + 2d

[C] 2d - 20 [D] 20 - d

292. Rashawn bought a CD that cost $18.99 andpaid $20.51, including sales tax. What wasthe rate of the sales tax?

[292]

[A] 2% [B] 3% [C] 5% [D] 8%

293. A wheel has a radius of 5 feet. What is theminimum number of complete revolutionsthat the wheel must make to roll at least 1,000feet?

[293]

294. In the set of positive integers, what is thesolution set of the inequality 2x - 3 < 5?

[294]

[A] {0, 1, 2, 3, 4} [B] {1, 2, 3}

[C] {0, 1, 2, 3} [D] {1, 2, 3, 4}

295. What is the solution set of the equation3 34 24 02x x− − = ?

[295]

[A] − 2 6,l q [B] − 6 2,l q[C] −RST

UVW23

12, [D] −RSTUVW12 2

3,

296. A fair coin is tossed three times. What is theprobability that the coin will land tails up onthe second toss?

[296]

[A] 23

[B] 12

[C] 34

[D] 13

297. Tamika has a hard rubber ball whosecircumference measures 13 inches. She wantsto box it for a gift but can only find cube-shaped boxes of sides 3 inches, 4 inches, 5inches, or 6 inches. What is the smallest boxthat the ball will fit into with the top on?

[297]

298. The accompanying figure represents a sectionof bathroom floor tiles shaped like regularhexagons.

What is the measure of angle ABC?

[298]

[A] 120° [B] 90°

[C] 150° [D] 60°

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

[299]

[A] {4,5,6} [B] {8,8,8}

[C] {5,5,11} [D] {7,7,12}

300. How many different three-member teams canbe formed from six students?

[300]

[A] 120 [B] 216 [C] 20 [D] 720


301. In a game, each player receives 5 cards from adeck of 52 different cards. How manydifferent groupings of cards are possible inthis game?

[301]

[A] 5! [B] 52 5C [C] 52 5P [D] 525

!!

302. The manufacturer of Ron's car recommendsthat the tire pressure be at least 26 pounds persquare inch and less than 35 pounds persquare inch. On the accompanying numberline, graph the inequality that represents therecommended tire pressure.

[302]

303. Paul orders a pizza. Chef Carl randomlychooses two different toppings to put on thepizza from the following: pepperoni, onion,sausage, mushrooms, and anchovies. If Paulwill not eat pizza with mushrooms, determinethe probability that Paul will not eat the pizzaChef Carl has made.

[303]

304. Tina's preschool has a set of cardboardbuilding blocks, each of which measures 9inches by 9 inches by 4 inches. How many ofthese blocks will Tina need to build a wall 4inches thick, 3 feet high, and 12 feet long?

[304]

305. A rectangular garden is going to be planted ina person's rectangular backyard, as shown inthe accompanying diagram. Somedimensions of the backyard and the width ofthe garden are given. Find the area of thegarden to the nearest square foot.

[305]

306. A painting that regularly sells for a price of$55 is on sale for 20% off. The sales tax onthe painting is 7%. Will the final total cost ofthe painting differ depending on whether thesalesperson deducts the discount beforeadding the sales tax or takes the discount aftercomputing the sum of the original price andthe sales tax on $55?

[306]

307. 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 isthinking of is

[307]

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

308. The lengths of the sides of two similarrectangular billboards are in the ratio 5:4. If250 square feet of material is needed to coverthe larger billboard, how much material, insquare feet, is needed to cover the smallerbillboard?

[308]


309. Which equation illustrates the distributiveproperty of multiplication over addition?

[309]

[A] 6(3a + 4b) = (3a + 4b)6

[B] 6(3a + 4b) = 6(4b + 3a)

[C] 6(3a + 4b) = 18a + 24b

[D] 6(3a + 4b) = 18a + 4b

310. The ninth graders at a high school are raisingmoney by selling T-shirts and baseball caps.The number of T-shirts sold was three timesthe number of caps. The profit they receivedfor each T-shirt sold was $5.00, and the profiton each cap was $2.50. If the students made atotal profit of $210, how many T-shirts andhow many caps were sold?

[310]

311. The formula for changing Celsius (C)temperature to Fahrenheit (F) temperature is

F C= +95

32 . Calculate, to the nearest

degree, the Fahrenheit temperature when theCelsius temperature is -8.

[311]

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

[312]

[A] 14° [B] 40° [C] 20° [D] 10°

313. Which expression must be added to 3x - 7 toequal 0?

[313]

[A] 0 [B] 3x + 7

[C] -3x - 7 [D] -3x + 7

314. What is the slope of line shown in theaccompanying diagram?

[314]

[A] −34

[B] −43

[C] 34

[D] 43

315. The accompanying graph shows the amountof water left in Rover's water dish over aperiod of time.

How long did Rover wait from the end of hisfirst drink to the start of his second drink ofwater?

[315]

[A] 30 sec [B] 60 sec

[C] 10 sec [D] 75 sec

316. What is the approximate circumference of acircle with radius 3?

[316]

[A] 9.42 [B] 7.07

[C] 28.27 [D] 18.85


317. In the addition table for a subset of realnumbers shown below, which number is theinverse of 3? Explain your answer.

[317]

318. If the instructions for cooking a turkey state"Roast turkey at 325° for 20 minutes perpound," how many hours will it take to roast a20-pound turkey at 325°?

[318]

319. What is the additive inverse of 23

?

[319]

[A] −32

[B] 13

[C] −23

[D] 32

320. What is the slope of the line whose equationis 3 4 16 0x y− − = ?

[320]

[A] 3 [B] 34

[C] -4 [D] 43

321. A factory packs CD cases into cartons for amusic company. Each carton is designed tohold 1,152 CD cases. The Quality ControlUnit in the factory expects an error of lessthan 5% over or under the desired packingnumber. What is the least number and themost number of CD cases that could bepacked in a carton and still be acceptable tothe Quality Control Unit?

[321]

322. The midpoint M of line segment AB hascoordinates (-3,4). If point A is the origin,(0,0), what are the coordinates of point B?[The use of the accompanying grid isoptional.]

[322]

323. Mr. Yee has 10 boys and 15 girls in hismathematics class. If he chooses two studentsat random to work on the blackboard, what isthe probability that both students chosen aregirls?

[323]

324. Which diagram represents the figure with thegreatest volume?

[324]

[A] [B]

[C] [D]


325. The probability that the Cubs win their first

game is 13

. The probability that the Cubs win

their second game is 37

. What is the

probability that the Cubs win both games?

[325]

[A] 1621

[B] 67

[C] 17

[D] 25

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

[326]

327. Which equation represents a circle whosecenter is (3,-2)?

[327]

[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

328. The expression 90 40 8 18⋅ − ⋅simplifies to

[328]

[A] 22.9 [B] 864 [C] 48 [D] 3,456

329. Two trains leave the same station at the sametime and travel in opposite directions. Onetrain travels at 80 kilometers per hour and theother at 100 kilometers per hour. In howmany hours will they be 900 kilometersapart?

[329]

330. For which value of x is the expression xx−+

72

undefined?

[330]

[A] -2 [B] 0 [C] 2 [D] 7

331. In the accompanying diagram, a circle withradius 4 is inscribed in a square.

What is the area of the shaded region?

[331]

[A] 16 8− π [B] 64 16− π

[C] 64 8π π− [D] 16 16− π

332. Juan has three blue shirts, two green shirts,seven red shirts, five pairs of denim pants,and two pairs of khaki pants. How manydifferent outfits consisting of one shirt andone pair of pants are possible?

[332]

[A] 130 [B] 84 [C] 420 [D] 19


333. Currently, Tyrone has $60 and his sister has$135. Both get an allowance of $5 eachweek. Tyrone decides to save his entireallowance, but his sister spends all of herseach week plus an additional $10 each week.After how many weeks will they each havethe same amount of money?[The use of the grid is optional.]

[333]

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

[334]

335. A company manufactures bicycles andskateboards. The company's daily productionof bicycles cannot exceed 10, and its dailyproduction of skateboards must be less thanor equal to 12. The combined number ofbicycles and skateboards cannot be more than16. If x is the number of bicycles and y is thenumber of skateboards, graph on theaccompanying set of axes the region thatcontains the number of bicycles andskateboards the company can manufacturedaily.

[335]

336. Simplify: 50 2 4r s

[336]

337. One of the factors of 4 92x − is

[337]

[A] (x - 3) [B] (x + 3)

[C] (2x + 3) [D] (4x - 3)


338. The NuFone Communications Company mustrun a telephone line between two poles atopposite ends of a lake, as shown in theaccompanying diagram. The length andwidth of the lake are 75 feet and 30 feet,respectively.

What is the distance between the two poles, tothe nearest foot?

[338]

[A] 105 [B] 81 [C] 45 [D] 69

339. If the length of the legs of a right triangle are5 and 7, what is the length of the hypotenuse?

[339]

[A] 74 [B] 2 6

[C] 2 3 [D] 2

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

[340]

341. What is the sum of 75 and ?283

[341]

[A] 760 [B] 711

[C] 79 [D] 358

342. An architect is designing a museumentranceway in the shape of a parabolic archrepresented by the equation y x x= − +2 20 ,where 0 20≤ ≤x and all dimensions areexpressed in feet. On the accompanying setof axes, sketch a graph of the arch anddetermine its maximum height, in feet.

[342]

343. The expression yx−

12

is equivalent to

[343]

[A] 22y x

x− [B] x y

x− 22

[C] yx−−

12

[D] 12− yx

344. Which expression is equaivalent to x y− ⋅1 2 ?

[344]

[A] xy2 [B] yx

2

[C] xy2 [D] xy−2


345. The accompanying diagram shows twoparallel streets, Main Street and Brooks Road,intersected by Jay Street. The obtuse anglethat Jay Street forms with Brooks Road isthree times the measure of the acute angle thatJay Street forms with Main Street.

What is the measure of the acute angleformed by Jay Street and Main Street?

[345]

[A] 45° [B] 60° [C] 135° [D] 90°

346. In a class of 450 students, 300 are taking amathematics course and 260 are taking ascience course. If 140 of these students aretaking both courses, how many students arenot taking either of these courses?

[346]

[A] 30 [B] 110 [C] 40 [D] 140

347. Which ordered pair is not in the solution setof y x> +2 1?

[347]

[A] (1,6) [B] (2,5) [C] (3,8) [D] (1,4)

348. In a survey of 400 teenage shoppers at a largemall, 240 said they shopped at Abernathy's,210 said they shopped at Bongo Republic,and 90 said they shopped at both stores. Howmany of the teenage shoppers surveyed didnot shop at either store?

[348]

349. Which number is in the solution set of theinequality 5x + 3 > 38?

[349]

[A] 6 [B] 7 [C] 5 [D] 8

350. The Pentagon building in Washington, D.C.,is shaped like a regular pentagon. If thelength of one side of the Pentagon isrepresented by n + 2, its perimeter would berepresented by

[350]

[A] n + 10 [B] 10n

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

351. Which statement is logically equivalent to "Ifit is Saturday, then I am not in school"?

[351]

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

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

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

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

352. Which set could not represent the lengths ofthe sides of a triangle?

[352]

[A] {5,10,12} [B] {7,9,11}

[C] {2,5,9} [D] {3,4,5}

353. In a hockey league, 87 players play on sevendifferent teams. Each team has at least 12players. What is the largest possible numberof players on any one team?

[353]

[A] 21 [B] 15 [C] 13 [D] 14

354. Which equation represents a line that isperpendicular to the line whose equation is− = +2 3 7y x ?

[354]

[A] y x= −23

3 [B] y x= + 7

[C] y x= −32

3 [D] 2 3 3y x= −


355. Solve the following system of equationsalgebraically or graphically for x and y:

y x x= + −2 2 1y x= +3 5

For an algebraic solution, show your workhere .For a graphic solution, show your work here.

[355]

356. The world population was 4.2 billion peoplein 1982. The population in 1999 reached 6billion. Find the percent of change from 1982to 1999.

[356]

357. If 0.0347 is written by a scientist in the form347 10. × n , the value of n is

[357]

[A] 2 [B] -2 [C] -3 [D] 3

358. Which equation illustrates the multiplicativeidentity element?

[358]

[A] x x⋅ =1 [B] x x− = 0

[C] x x+ =0 [D] xx⋅ =1 1

359. Bob and Latoya both drove to a baseballgame at a college stadium. Bob lives 70miles from the stadium and Latoya lives 60miles from it, as shown in the accompanyingdiagram. Bob drove at a rate of 50 miles perhour, and Latoya drove at a rate of 40 milesper hour. If they both left home at the sametime, who got to the stadium first?

[359]

360. The expression ( ) ( )x x x x2 25 2 6 7 3− − − − − −is equivalent to

[360]

[A] 7 12 52x x− − [B] 7 2 12x x+ +

[C] 7 2 12x x− + [D] 7 2 52x x+ −

361. Which statement about quadrilaterals is true?

[361]

[A] All quadrilaterals have four sides.

[B] All quadrilaterals have four right angles.

[C] All quadrilaterals have equal sides.

[D] All quadrilaterals are parallelograms.


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

[362]

[A] figure 1, only

[B] both figure 1 and figure 2

[C] neither figure 1 nor figure 2

[D] figure 2 only

363. 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?

[363]

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

[364]

[A] 100 ft [B] 36 ft

[C] 15 ft [D] 60 ft

365. There are four students, all of differentheights, who are to be randomly arranged in aline. What is the probability that the talleststudent will be first in line and the shorteststudent will be last in line?

[365]

366. Alan, Becky, Jesus, and Mariah are fourstudents in the chess club. If two of thesestudents will be selected to represent theschool at a national convention, how manycombinations of two students are possible?

[366]

367. When Kimberly bought her new car, shefound that there were 72 different ways hercar could be equipped. Her choices includedfour choices of engine and three choices oftransmission. If her only other choice wascolor, how many choices of color did shehave?

[367]

[A] 60 [B] 6 [C] 65 [D] 12

368. Maria's backyard has two trees that are 40feet apart, as shown in the accompanyingdiagram. She wants to place lampposts sothat the posts are 30 feet from both of thetrees. Draw a sketch to show where thelampposts could be placed in relation to thetrees. How many locations for the lamppostsare possible?

[368]

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

[369]


370. The exact average of a set of six test scores is92. Five of these scores are 90, 98, 96, 94,and 85. What is the other test score?

[370]

[A] 86 [B] 89 [C] 92 [D] 91

371. The expression 2 43 2⋅ is equivalent to

[371]

[A] 27 [B] 212 [C] 86 [D] 85

372. The accompanying diagram shows twosimilar triangles.

Which proportion could be used to solve forx?

[372]

[A] 32 1215x

= [B] 3212

15=

x

[C] 249

15=

x[D] x

249

15=

373. An addition table for a subset of real numbersis shown below. Which number is the identityelement? Explain your answer.

[373]

374. Dylan says that all isosceles triangles areacute triangles. Mary Lou wants to prove thatDylan is not correct. Sketch an isoscelestriangle that Mary Lou could use to show thatDylan's statement is not true. In your sketch,state the measure of each angle of theisosceles triangle.

[374]

375. The amount of time, t, in seconds, it takes anobject to fall a distance, d, in meters, is

expressed by the formula t d=

4 9..

Approximately how long will it take an objectto fall 75 meters?

[375]

[A] 2.34 sec [B] 7.7 sec

[C] 0.26 sec [D] 3.9 sec

376. The tickets for a dance recital cost $5.00 foradults and $2.00 for children. If the totalnumber of tickets sold was 295 and the totalamount collected was $1,220, how manyadult tickets were sold? [Only an algebraicsolution can receive full credit.]

[376]

377. Mr. Perez owns a sneaker store. He bought350 pairs of basketball sneakers and 150 pairsof soccer sneakers from the manufacturers for$62,500. He sold all the sneakers and made a25% profit. If he sold the soccer sneakers for$130 per pair, how much did he charge forone pair of basketball sneakers?

[377]

378. Given the true statement "John is nothandsome" and the false statement "John ishandsome or smart." Determine the truthvalue for the statement "John is smart."

[378]


379. Which table does not show an example ofdirect variation?

[379]

[A] [B]

[C] [D]

380. In the accompanying diagram, a rectangularcontainer with the dimensions 10 inches by15 inches by 20 inches is to be filled withwater, using a cylindrical cup whose radius is2 inches and whose height is 5 inches. Whatis the maximum number of full cups of waterthat can be placed into the container withoutthe water overflowing the container?

[380]

381. Mark says, "The number I see is odd." Jansays, "That same number is prime." Theteacher says, "Mark is correct or Jan iscorrect." Some integers would make theteacher's statement true while other integerswould make it false. Give and explain oneexample of when the teacher's statement istrue. Give and explain one example of whenthe teacher's statement is false.

[381]

382. How many different 4-letter arrangements canbe formed using the letters of the word"JUMP," if each letter is used only once?

[382]

[A] 24 [B] 12 [C] 16 [D] 4

383. If one-half of a number is 8 less than two-thirds of the number, what is the number?

[383]

[A] 32 [B] 24 [C] 48 [D] 54

384. Point P is located on .ABa Describe the locus of points that are (1) 3 units from AB (2) 5 units from point Pb How many points satisfy both conditions inpart a?

[384]

385. For which value of x is the expression 3 64

xx−−

undefined?

[385]

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

386. How many different outfits consisting of ahat, a pair of slacks, and a sweater can bemade from two hats, three pairs of slacks, andfour sweaters?

[386]

[A] 24 [B] 9 [C] 12 [D] 29

387. The approximate number of seconds in a yearis 32,000,000. When this number is writtenin scientific notation, the numerical value ofthe exponent is

[387]

[A] 7 [B] -7 [C] 8 [D] 6


388. Brett was given the problem: "Evaluate2 52x + when x = 3." Brett wrote that theanswer was 41. Was Brett correct? Explainyour answer.

[388]

389. At a school fair, the spinner represented in theaccompanying diagram is spun twice.

What is the probability that it will land insection G the first time and then in section Bthe second time?

[389]

[A] 116

[B] 18

[C] 12

[D] 14

390. If Laquisha can enter school by any one ofthree doors and the school has two staircasesto the second floor, in how many differentways can Laquisha reach a room on thesecond floor? Justify your answer by drawinga tree diagram or listing a sample space.

[390]

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

[391]

[A] 2 52

.π

[B] 5π

[C] 52π

[D] 2 5.π

392. A wall is supported by a brace 10 feet long, asshown in the diagram below. If one end ofthe brace is placed 6 feet from the base of thewall, how many feet up the wall does thebrace reach?

[392]

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

[393]

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

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

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

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

394. What is the inverse of the statement "If Mikedid his homework, then he will pass thistest"?

[394]

[A] If Mike does not pass this test, then hedid not do his homework.

[B] If Mike does not pass this test, then heonly did half his homework.

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

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


395. 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 studentsat the party?

[395]

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

396. There are 28 students in a mathematics class.

If 14

of the students are called to the guidance

office, 13

of the remaining students are called

to the nurse, and, finally, 12

of those left go to

the library, how many students remain in theclassroom?

[396]

397. Amy tossed a ball in the air in such a way thatthe path of the ball was modeled by theequation y x x= − +2 6 . In the equation, yrepresents the height of the ball in feet and xis the time in seconds.a Graph y x x= − +2 6 for 0 6≤ ≤x on thegrid provided below.

b At what time, x, is the ball at its highestpoint?

[397]

398. The following data consists of the weights, inpounds, of 30 adults:195, 206, 100, 98, 150, 210, 195, 106, 195,168, 180, 212, 104, 195, 100,216, 195, 209, 112, 99, 206, 116, 195, 100,142, 100, 135, 98, 160, 155Using the data, complete the accompanyingcumulative frequency table and construct acumulative frequency histogram on the gridbelow.

[398]

399. In Ms. Wright's English class, 16 students arein band, 7 students play sports, 3 studentsparticipate in both activities, and 9 studentsare not in band and do not play sports. Howmany students are in Ms. Wright's Englishclass?

[399]

[A] 29 [B] 26 [C] 7 [D] 10


400. In a class of 50 students, 18 take music, 26take art, and 2 take both art and music. Howmany students in the class are not enrolled ineither music or art?

[400]

[A] 6 [B] 16 [C] 8 [D] 24

401. A bookshelf contains six mysteries and threebiographies. Two books are selected atrandom without replacement.a What is the probability that both books aremysteries?b What is the probability that one book is amystery and the other is a biography?

[401]

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

[402]

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

403. The sum of 18 and 72 is

[403]

[A] 3 10 [B] 9 2

[C] 6 3 [D] 90

404. Given the true statement: "If a person iseligible to vote, then that person is a citizen."Which statement must also be true?

[404]

[A] Morgan has never voted; therefore, he isnot a citizen.

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

[C] Juan is a citizen; therefore, he is eligibleto vote.

[D] Kayla is not a citizen; therefore, she isnot eligible to vote.

405. Which numbers are arranged from smallest tolargest?

[405]

[A] π,722,14.3,1.9

[B] 1.9,,722,14.3 π

[C]722,,14.3,1.9 π

[D]722,14.3,,1.9 π

406. The number of people on the school board isrepresented by x. Two subcommittees withan equal number of members are formed, one

with 23

5x − members and the other with x4

members. How many people are on theschool board?

[406]

[A] 20 [B] 4 [C] 12 [D] 8


407. Helen is using a capital H in an art design.The H has

[407]

[A] two lines of symmetry and two points ofsymmetry

[B] two lines of symmetry and only one pointof symmetry

[C] only one line of symmetry

[D] only two points of symmetry

408. What is the contrapositive of the statement "IfI study, then I pass the test"?

[408]

[A] If I do not study, then I do not pass thetest.

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

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

[D] I pass the test if I study.

409. What is the sum, in degrees, of the measuresof the interior angles of a pentagon?

[409]

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

410. Which inequality is represented in theaccompanying graph?

[410]

[A] − ≤ ≤3 4x [B] − < <3 4x[C] − ≤ <3 4x [D] − < ≤3 4x

411. Solve for x: 2(x - 3) = 1.2 - x

[411]

412. What is the multiplicative inverse of 34

?

[412]

[A] −34

[B] −43

[C] 43

[D] -1

413. The expression 2 50 2− is equivalent to

[413]

[A] 2 48 [B] 10

[C] 49 2 [D] 9 2

414. In the time trials for the 400-meter run at thestate sectionals, the 15 runners recorded thetimes shown in the table below.

a Using the data from the frequency column,draw a frequency histogram on the gridprovided below.

b What percent of the runners completed thetime trial between 52.0 and 53.9 seconds?

[414]


415. Which number below is irrational?49

20 121, ,

Why is the number you chose an irrationalnumber?

[415]

416. The mass of an orchid seed is approximately0.0000035 gram. Written in scientificnotation, that mass is equivalent to 35 10. .× n

What is the value of n?

[416]

[A] -5 [B] -6 [C] -7 [D] -8

417. How many different 6-letter arrangements canbe formed using the letters in the word“ABSENT,” if each letter is used only once?

[417]

[A] 720 [B] 46,656 [C] 36 [D] 6

418. Which number has the greatest value?

[418]

[A] 1.5 [B] π2

[C] 2 [D] 123

419. Which equation illustrates the distributiveproperty for real numbers?

[419]

[A] 1 1 1 13 2 2 3+ = + [B] 3 0 3+ =

[C] -3(5 + 7) = (-3)(5) + (-3)(7)

[D] (1.3 0.07) 0.63=1.3 (0.07 0.63)× × × ×

420. The accompanying diagram shows a flagpolethat stands on level ground. Two cables, rand s, are attached to the pole at a point 16feet above the ground. The combined lengthof the two cables is 50 feet. If cable r isattached to the ground 12 feet from the baseof the pole, what is the measure of the angle,x, to the nearest degree, that cable s makeswith the ground?

[420]

421. After an ice storm, the following headlineswere reported in the Glacier County Times:Monday: Ice Storm Devastates County - 8out of every 10 homes lose electrical powerTuesday: Restoration Begins - Power

restored to 12

of affected homes

Wednesday: More Freezing Rain - Powerlost by 20% of homes that had power onTuesdayBased on these headlines, what fractionalportion of homes in Glacier County hadelectrical power on Wednesday?

[421]

422. Which equation represents a line that isparallel to the line whose equation is2 3 12x y+ = ?

[422]

[A] 6 4 2y x− = [B] 4 6 2x y− =

[C] 6 4 2x y+ = − [D] 6 4 2y x+ =


423. If bx K− =2 , then x equals

[423]

[A] Kb− 2 [B] 2 − K

b

[C] Kb+ 2 [D] K

b+ 2

424. In the accompanying diagram of ∆ABC , ABis extended to D, exterior angle CBDmeasures 145°, and m C∠ = 75.

What is m CAB∠ ?

[424]

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

425. Triangle A'B'C' is the image of ∆ ABC undera dilation such that A'B' = 3AB. TrianglesABC and A'B'C' are

[425]

[A] both congruent and similar

[B] congruent but not similar

[C] neither congruent nor similar

[D] similar but not congruent

426. How many times larger than 14

x is 5x ?

[426]

[A] 45

[B] 9 [C] 20 [D] 54

427. The ages of five children in a family are 3, 3,5, 8, and 18. Which statement is true for thisgroup of data?

[427]

[A] median > mean [B] median = mode

[C] mean > median [D] mode > mean

428. What is the value of n in the equation0 6 10 36. ( ) . ?n + =

[428]

[A] -0.4 [B] -4 [C] 4 [D] 5

429. Tori computes the value of 8 95× in her headby thinking 8 100 5 8 100 8 5( ) .− = × − ×Which number property is she using?

[429]

[A] distributive [B] commutative

[C] associative [D] closure

430. Perform the indicated operation and expressthe result in simplest terms:

xx

xx+

÷−3

392

[430]

431. In ∆ABC , the measure of ∠B is 21 less thanfour times the measure of ∠A , and themeasure of ∠C is 1 more than five times themeasure of ∠A . Find the measure, indegrees, of each angle of ∆ABC .

[431]


432. The accompanying diagram shows the resultsof a survey asking which sports the membersof the Key Club watch on television.

Which statement or statements are true?I The most watched sport is tennis.II The least watched sport is baseball.III More Key Club members watch tennisthan football.

[432]

[A] I, only [B] I and II, only

[C] II and III, only [D] II, only

433. Which statement is the converse of "If thesum of two angles is 180°, then the angles aresupplementary"?

[433]

[A] If two angles are supplementary, thentheir sum is 180°.

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

[C] If the sum of two angles is not 180°, thenthe angles are supplementary.

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

434. If x ab

b4

0 0− = ≠, , then x is equal to

[434]

[A]b

a4

[B]ba4

− [C]b

a4

− [D]ba4

435. a On the set of axes provided below, sketch acircle with a radius of 3 and center at (2,1)and also sketch the graph of the line2 8x y+ = .

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

[435]

436. The sum of Scott's age and Greg's age is 33years. If Greg's age is represented by g,Scott's age is represented by

[436]

[A] 33g [B] g + 33

[C] g - 33 [D] 33 - g

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

[437]


438. What is the area of a square whose perimeteris represented by 12x?

[438]

[A] 12 2x [B] 9 2x

[C] 6 2x [D] 144 2x

439. The number 156 10 2. × − is equivalent to

[439]

[A] 0.0156 [B] 156

[C] 0.156 [D] 0.00156

440. Which equation is an illustration of theadditive identity property?

[440]

[A] x x+ =0 [B] x x⋅ =1

[C] x x− = 0 [D] xx⋅ =1 1

441. Megan decides to go out to eat. The menu atthe restaurant has four appetizers, three soups,seven entrees, and five desserts. If Megandecides to order an appetizer or a soup, andone entree, and two different desserts, howmany different choices can she make?

[441]

442. On an English examination, two studentsreceived scores of 90, five students received85, seven students received 75, and onestudent received 55. The average score onthis examination was

[442]

[A] 79 [B] 76 [C] 77 [D] 75

443. At a concert, $720 was collected for hot dogs,hamburgers, and soft drinks. All three itemssold for $1.00 each. Twice as many hot dogswere sold as hamburgers. Three times asmany soft drinks were sold as hamburgers.The number of soft drinks sold was

[443]

[A] 360 [B] 480 [C] 120 [D] 240

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

[444]

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

[B] The statement and its converse are bothtrue.

[C] The statement and its converse are bothfalse.

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

445. Alexi's wallet contains four $1 bills, three $5bills, and one $10 bill. If Alexi randomlyremoves two bills without replacement,determine whether the probability that thebills will total $15 is greater than theprobability that the bills will total $2.

[445]


446. The accompanying Venn diagram shows thenumber of students who take various courses.All students in circle A take mathematics. Allin circle B take science. All in circle C taketechnology. What percentage of the studentstake mathematics or technology?

[446]

447. In a certain quadrilateral, two opposite sidesare parallel, and the other two opposite sidesare not congruent. This quadrilateral could bea

[447]

[A] rhombus [B] trapezoid

[C] parallelogram [D] square

448. A fish tank with a rectangular base has avolume of 3,360 cubic inches. The length andwidth of the tank are 14 inches and 12 inches,respectively. Find the height, in inches, of thetank.

[448]

449. Kerry is planning a rectangular garden thathas dimensions of 4 feet by 6 feet. Kerrywants one-half of the garden to have roses,and she says that the rose plot will havedimensions of 2 feet by 3 feet. Is she correct?Explain.

[449]

450. Which statement is the converse of "If it is a300 ZX, then it is a car"?

[450]

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

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

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

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

451. If the expression 3 4 62

2− + is evaluated,

what would be done last?

[451]

[A] subtracting [B] squaring

[C] dividing [D] adding

452. Subtract 5 7 62x x− − from 9 3 42x x+ − .

[452]

453. A total of 600 tickets were sold for a concert.Twice as many tickets were sold in advancethan were sold at the door. If the tickets soldin advance cost $25 each and the tickets soldat the door cost $32 each, how much moneywas collected for the concert?

[453]

454. A treasure map shows a treasure hidden in apark near a tree and a statue. The mapindicates that the tree and the statue are 10feet apart. The treasure is buried 7 feet fromthe base of the tree and also 5 feet from thebase of the statue. How many places arepossible locations for the treasure to beburied? Draw a diagram of the treasure map,and indicate with an X each possible locationof the treasure.

[454]


455. In the accompanying diagram, the base of a15-foot ladder rests on the ground 4 feet froma 6-foot fence.

a If the ladder touches the top of the fenceand the side of a building, what angle, to thenearest degree, does the ladder make with theground?b Using the angle found in part a, determinehow far the top of the ladder reaches up theside of the building, to the nearest foot.

[455]

456. What is the converse of the statement "IfAlicia goes to Albany, then Ben goes toBuffalo"?

[456]

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

[B] Alicia goes to Albany if and only if Bengoes to Buffalo.

[C] If Ben goes to Buffalo, then Alicia goesto Albany.

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

457. The student scores on Mrs. Frederick’smathematics test are shown on the stem-and-leaf plot below.

Find the median of these scores.

[457]

458. Given the true statements: "Jason goesshopping or he goes to the movies" and"Jason does not go to the movies." Whichstatement must also be true?

[458]

[A] Jason stays home.

[B] Jason goes shopping.

[C] Jason does not go shopping and he doesnot go to the movies.

[D] Jason does not go shopping.

459. What is the value of x in the equation34

2 54

6x x+ = − ?

[459]

[A] 16 [B] 4 [C] -16 [D] -4

460. The sum of the measures of the interior anglesof an octagon is

[460]

[A] 540° [B] 180°

[C] 1,080° [D] 360°

461. Which letter below has point symmetry, butdoes not have line symmetry?

[461]

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

462. What is a common factor of x2 9− andx x2 5 6− + ?

[462]

[A] x − 3 [B] x − 2

[C] x + 3 [D] x2


463. To measure the length of a hiking trail, aworker uses a device with a 2-foot-diameterwheel that counts the number of revolutionsthe wheel makes. If the device reads 1,100.5revolutions at the end of the trail, how manymiles long is the trail, to the nearest tenth of amile?

[463]

464. If 6 and x have the same mean (average) as 2,4, and 24, what is the value of x?

[464]

[A] 14 [B] 36 [C] 5 [D] 10

465. Which properties best describe the coordinategraph of two distinct parallel lines?

[465]

[A] different slopes and different intercepts

[B] same slopes and same intercepts

[C] same slopes and different intercepts

[D] different slopes and same intercepts

466. In the accompanying diagram, right triangleABC is inscribed in circle O, diameter AB =26, and CB = 10. Find, to the nearest squareunit, the area of the shaded region.

[466]

467. What is the smallest integer greater than 1that is both the square of an integer and thecube of an integer?

[467]

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

468. How many points are equidistant from twoparallel lines and also equidistant from twopoints on one of the lines?

[468]

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

469. Stan was trying to guess Melanie's age. Shetold him her age was an even number and amultiple of three. What could be Melanie'sage?

[469]

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

470. The volume of a rectangular pool is 1,080cubic meters. Its length, width, and depth arein the ratio 10:4:1. Find the number of metersin each of the three dimensions of the pool.

[470]

471. If a and b are integers, which equation isalways true?

[471]

[A] ab

ba

= [B] a b b a+ = +

[C] a b b a+ = +2 2 [D] a b b a− = −

472. Factor completely: 3 272ax a−

[472]


473. On the accompanying set of axes, draw thereflection of ABCD in the y-axis. Label andstate the coordinates of the reflected figure.

[473]

474. If x xx

3 1< < , then x could be equal to

[474]

[A] 15

[B] 1 [C] 65

[D] 5

475. When 72 is expressed in simplest a bfrom, what is the value of a?

[475]

[A] 6 [B] 8 [C] 2 [D] 3

476. A swimmer plans to swim at least 100 lapsduring a 6-day period. During this period, theswimmer will increase the number of lapscompleted each day by one lap. What is theleast number of laps the swimmer mustcomplete on the first day?

[476]

477. Sarah's mathematics grades for one markingperiod were 85, 72, 97, 81, 77, 93, 100, 75,86, 70, 96, and 80.a. Complete the tally sheet and frequencytable below, and construct and label afrequency histogram for Sarah's grades usingthe accompanying grid.

b. Which interval contains the 75th percentile(upper quartile)?

[477]

478. If 2x + 5 = -25 and -3m - 6 = 48, what is theproduct of x and m?

[478]

[A] -270 [B] 270 [C] 3 [D] -33

479. Solve for x: 15 3 3 4 6x x− + =b g

[479]

[A] 1 [B] −12

[C] 13

[D] 3

480. An algebra class of 21 students must send 5students to meet with the principal. Howmany different groups of 5 students could beformed from this class?

[480]


481. Line contains the points (0,4) and (2,0).Show that the point (-25,81) does or does notlie on line .

[481]

482. During a 45-minute lunch period, Albert (A)went running and Bill (B) walked forexercise. Their times and distances are shownin the accompanying graph. How much fasterwas Albert running than Bill was walking, inmiles per hour?

[482]

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

[483]

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

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

[C] I will play baseball if and only if it issunny.

[D] If I do not play baseball, then it is notsunny.

484. When 3 62x x− is divided by 3x, the result is

[484]

[A] x + 2 [B] x − 2[C] − 2x [D] 2x

485. There are 12 people on a basketball team, andthe coach needs to choose 5 to put into agame. How many different possible ways canthe coach choose a team of 5 if each personhas an equal chance of being selected?

[485]

[A] 12 5C [B] 5 12C [C] 12 5P [D] 5 12P

486. A stop sign in the shape of a regular octagonis resting on a brick wall, as shown in theaccompanying diagram.

What is the measure of angle x?

[486]

[A] 45° [B] 120° [C] 60° [D] 135°

487. Solve algebraically for x: 1 16x

x=

+

[487]

488. Keesha wants to tile the floor shown in theaccompanying diagram. If each tile measures1 foot by 1 foot and costs $2.99, what will bethe total cost, including an 8% sales tax, fortiling the floor?

[488]


489. A woman has a ladder that is 13 feet long. Ifshe sets the base of the ladder on level ground5 feet from the side of a house, how many feetabove the ground will the top of the ladder bewhen it rests against the house?

[489]

[A] 11 [B] 12 [C] 8 [D] 9

490. The plan of a parcel of land is represented bytrapezoid ABCD in the accompanyingdiagram. If the area of ∆ABE is 600 squarefeet, find the minimum number of feet offence needed to completely enclose the entireparcel of land, ABCD.

[490]

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

[491]

492. If 2 62x x− + is subtracted from x x2 3 2+ − ,the result is

[492]

[A] x x2 4 8− + [B] x x2 2 8+ −

[C] − + −x x2 2 8 [D] − + −x x2 4 8

493. An arch is built so that it is 6 feet wide at thebase. Its shape can be re presented by aparabola with the equation y x x= − +2 122 ,where y is the height of the arch.a Graph the parabola from x = 0 to x = 6 onthe grid below.

b Determine the maximum height, y, of thearch.

[493]

494. If x a b= −2 2 , then a equals

[494]

[A] b x2

2− [B] x b− 2

2

[C] x b+ 2

2[D] x b+ 2

495. In a town election, candidates A and B wererunning for mayor. There were 30,500 people

eligible to vote, and 34

of them actually

voted. Candidate B received 13

of the votes

cast. How many people voted for candidateB? What percent of the votes cast, to thenearest tenth of a percent, did candidate Areceive?

[495]


496. Which statement is logically equivalent to "Ifthe team has a good pitcher, then the team hasa good season"?

[496]

[A] If the team has a good season, then theteam has a good pitcher.

[B] If the team does not have a good season,then the team does not have a goodpitcher.

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

[D] If the team does not have a good pitcher,then the team does not have a goodseason.

497. In the accompanying diagram, parallel linesAB and CD are intersected by transversalEF at points G and H, respectively,m AGH x∠ = +15 , and m GHD x∠ = 2 .

Which equation can be used to find the valueof x?

[497]

[A] 2x + x + 15 = 90

[B] 2x + x + 15 = 180

[C] 2x(x + 15) = 0 [D] 2x = x + 15

498. Tina wants to sew a piece of fabric into ascarf in the shape of an isosceles triangle, asshown in the accompanying diagram.

What are the values of x and y?

[498]

[A] x = 69 and y = 69

[B] x = 90 and y = 48

[C] x = 96 and y = 42

[D] x = 42 and y = 96

499. The equation P = 2L + 2W is equivalent to

[499]

[A] L P W= − [B] L P W=

+ 22

[C] 22

L PW

= [D] L P W=

− 22

500. What is the slope of line in theaccompanying diagram?

[500]

[A] −32

[B] 32

[C] −23

[D] 23


501. What is the solution set of the equationx x5 2

14+ = ?

[501]

[A] {49} [B] {20} [C] {4} [D] {10}

502. Triangle ABC represents a metal flag on poleAD, as shown in the accompanying diagram.On a windy day the triangle spins around thepole so fast that it looks like a three-dimensional shape.

Which shape would the spinning flag create?

[502]

[A] sphere [B] pyramid

[C] right circular cylinder [D] cone

503. Sean knows the length of the base, b, and thearea, A, of a triangular window in hisbedroom. Which formula could he use to findthe height, h, of this window?

[503]

[A] h A b= −2 [B] h Ab

=2

[C] h Ab

=2 [D] h A b= 2b gb g

504. The expression 8 84 6− ⋅ is equivalent to

[504]

[A] 8 2− [B] 82 [C] 810 [D] 8 24−

505. What is the solution set for the equationx x2 5 6 0− + =

[505]

[A] {2,3} [B] {6,-1}

[C] {-6,1} [D] {-2,-3}

506. Mary and Amy had a total of 20 yards ofmaterial from which to make costumes. Maryused three times more material to make hercostume than Amy used, and 2 yards ofmaterial was not used. How many yards ofmaterials did Amy use for her costume?

[506]

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

[507]

[A] isosceles [B] scalene

[C] obtuse [D] equilateral

508. What was the median high temperature inMiddletown during the 7-day period shown inthe table below?

[508]

[A] 73 [B] 75 [C] 70 [D] 69


509. Which statement is not always true about aparallelogram?

[509]

[A] The diagonals are congruent.

[B] The opposite angles are congruent.

[C] The opposite sides are parallel.

[D] The opposite sides are congruent.

510. If a ≠ 0 and the sum of x and 1a

is 0, then

[510]

[A] x = -a [B] x = 1 - a

[C] x = − 1a

[D] x = a

511. On a science quiz, 20 students received thefollowing scores: 100, 95, 95, 90, 85, 85, 85,80, 80, 80, 80, 75, 75, 75, 70, 70, 65, 65, 60,55. Construct a statistical graph, such as ahistogram or a stem-and-leaf plot, to displaythis data. [Be sure to title the graph and labelall axes or parts used.]If your type of plot requires a grid, show yourwork here.

If no grid is necessary, show your work here.

[511]

512. When − + +2 4 22x x is subtracted fromx x2 6 4+ − , the result is

[512]

[A] 3 2 62x x+ − [B] − − +3 2 62x x

[C] 2 2 62x x− − [D] − + −x x2 10 2

513. At the Phoenix Surfboard Company,$306,000 in profits was made last year. Thisprofit was shared by the four partners in theratio 3:3:5:7. How much more money did thepartner with the largest share make than oneof the partners with the smallest share?

[513]

514. Write the equation for the line shown in theaccompanying graph. Explain your answer.

[514]

515. Which equation represents the locus of points4 units from the origin?

[515]

[A] x = 4 [B] x y2 2 4+ =

[C] x y2 2 16+ = [D] x y+ = 16


516. In the accompanying figure, ACDH andBCEF are rectangles, AH = 2, GH = 3, GF =4, and FE = 5.

What is the area of BCDG?

[516]

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

517. If a > 0, then 9 162 2a a+ equals

[517]

[A] 5a [B] 7a [C] 5 a [D] 7a

518. The owner of a movie theater was countingthe money from 1 day's ticket sales. He knewthat a total of 150 tickets were sold. Adulttickets cost $7.50 each and children's ticketscost $4.75 each. If the total receipts for theday were $891.25, how many of each kind ofticket were sold?

[518]

519. The test scores for 10 students in Ms.Sampson's homeroom were 61, 67, 81, 83, 87,88, 89, 90, 98, and 100. Which frequencytable is accurate for this set of data?

[519]

[A] [B]

[C] [D]

520. The accompanying diagram shows a sectionof the city of Tacoma. High Road, StateStreet, and Main Street are parallel and 5miles apart. Ridge Road is perpendicular tothe three parallel streets. The distancebetween the intersection of Ridge Road andState Street and where the railroad trackscross State Street is 12 miles. What is thedistance between the intersection of RidgeRoad and Main Street and where the railroadtracks cross Main Street?

[520]


521. Expressed as a single fraction, what is1

11 0 1

x xx

++ ≠ −, , ?

[521]

[A] 2 12

xx x

++

[B] 22 1x +

[C] 2 32

xx x

++

[D] 32x

522. A box contains six black balls and four whiteballs. What is the probability of selecting ablack ball at random from the box?

[522]

[A] 110

[B] 610

[C] 46

[D] 64

523. An equation of the line that has a slope of 3and a y-intercept of -2 is

[523]

[A] y = 3x - 2 [B] y = - x

[C] y = -2x + 3 [D] x = 3y - 2

524. The coordinates of point R are (-3,2) and thecoordinates of point T are (4,1). What is thelength of RT ?

[524]

[A] 2 2 [B] 10

[C] 4 3 [D] 5 2

525. The expression 29 C is equivalent to

[525]

[A]!2!9 [B] 29 P [C] 79 C [D] 79 P

526. If 2 4 62x x− + is subtracted from5 8 22x x+ − , the difference is

[526]

[A] 3 4 42x x+ + [B] 3 12 82x x+ −

[C] − + +3 4 42x x [D] − − +3 12 82x x

527. To get from his high school to his home,Jamal travels 5.0 miles east and then 4.0 milesnorth. When Sheila goes to her home fromthe same high school, she travels 8.0 mileseast and 2.0 miles south. What is the measureof the shortest distance, to the nearest tenth ofa mile, between Jamal's home and Sheila'shome? [The use of the accompanying grid isoptional.]

[527]

528. In the accompanying diagram, lines a and bare parallel, and lines c and d are transversals.

Which angle is congruent to angle 8?

[528]

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


529. If the value of dependent variable y increasesas the value of independent variable xincreases, the graph of this relationship couldbe a

[529]

[A] line with a negative slope

[B] vertical line [C] horizontal line

[D] line with a positive slope

530. At the beginning of her mathematics class,Mrs. Reno gives a warm-up problem. Shesays, "I am thinking of a number such that 6less than the product of 7 and this number is85." Which number is she thinking of?

[530]

[A] 637 [B] 84 [C] 1127

[D] 13

531. Julio's wages vary directly as the number ofhours that he works. If his wages for 5 hoursare $29.75, how much will he earn for 30hours?

[531]

532. Given the statement: "If two sides of atriangle are congruent, then the anglesopposite these sides are congruent."

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

What is true about this statement and itsconverse?

[532]

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

[B] Both the statement and its converse aretrue.

[C] Neither the statement nor its converse istrue.

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

533. A rocket car on the Bonneville Salt Flats istraveling at a rate of 640 miles per hour. Howmuch time would it take for the car to travel384 miles at this rate?

[533]

[A] 36 minutes [B] 245 minutes

[C] 1.7 hours [D] 256 minutes

534. Which statement is logically equivalent to "IfI did not eat, then I am hungry"?

[534]

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

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

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

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



[535]

[A] 9 [B] π [C] 0 [D] −13

536. The accompanying graph represents theyearly cost of playing 0 to 5 games of golf atthe Shadybrook Golf Course. What is thetotal cost of joining the club and playing 10games during the year?

[536]

537. Tamika could not remember her scores fromfive mathematics tests. She did rememberthat the mean (average) was exactly 80, themedian was 81, and the mode was 88. If allher scores were integers with 100 the highestscore possible and 0 the lowest score possible,what was the lowest score she could havereceived on any one test?

[537]

538. Mr. Gonzalez owns a triangular plot of landBCD with DB = 25 yards and BC = 16 yards.He wishes to purchase the adjacent plot ofland in the shape of right triangle ABD, asshown in the accompanying diagram, with AD= 15 yards. If the purchase is made, what willbe the total number of square yards in the areaof his plot of land, ∆ACD ?

[538]

539. On June 17, the temperature in New YorkCity ranged from 90° to 99°, while thetemperature in Niagara Falls ranged from 60°to 69°. The difference in the temperatures inthese two cities must be between

[539]

[A] 25° and 35° [B] 20° and 40°

[C] 30° and 40° [D] 20° and 30°

540. The product of 4 2x y and 2 3xy is

[540]

[A] 8 3 4x y [B] 8 3 3x y

[C] 8 2 3x y [D] 8 2 4x y

541. Which expression is an example of theassociative property?

[541]

[A] x y z xy xz( )+ = +

[B] ( ) ( )x y z x y z+ + = + +

[C] x y z z y x+ + = + + [D] x x⋅ =1


542. If the number of molecules in 1 mole of asubstance is 6 02 1023. × , then the number ofmolecules in 100 moles is

[542]

[A] 6 02 1025. × [B] 6 02 1021. ×

[C] 6 02 1022. × [D] 6 02 1024. ×

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

[543]

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

544. Let x and y be numbers such that0 1< < <x y , and let d x y= − . Which graphcould represent the location of d on thenumber line?

[544]

[A]

[B]

[C]

[D]

545. It t = -3, then 3 5 62t t+ + equals

[545]

[A] 18 [B] 6 [C] -6 [D] -36

546. Mr. Santana wants to carpet exactly half ofhis rectangular living room. He knows thatthe perimeter of the room is 96 feet and thatthe length of the room is 6 feet longer than thewidth. How many square feet of carpetingdoes Mr. Santana need?

[546]

547. Which is an equation of the parabola shownin the accompanying diagram?

x

y

–4 –3 –2 –1 1 2 3 4

–4–3–2–1

1234

[547]

[A] y x x= − +2 2 3 [B] y x x= + +2 2 3

[C] y x x= − + +2 2 3 [D] y x x= − − +2 2 3

548. Three brothers have ages that are consecutiveeven integers. The product of the first andthird boys' ages is 20 more than twice thesecond boy's age. Find the age of each of thethree boys.

[548]

549. What is the solution set of the equationx x2 11 28 0+ + = ?

[549]

[A] {-7,-4} [B] {-3,-4}

[C] {3,4} [D] {-7,4}

550. Kyoko's mathematics teacher gave her theaccompanying cards and asked her to arrangethe cards in order from least to greatest. Inwhat order should Kyoko arrange the cards?

[550]


551. In the accompanying diagram ofparallelogram ABCD, diagonals AC and DBintersect at E, AE = 3x - 4, and EC = x + 12.

What is the value of x?

[551]

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

552. The locus of points equidistant from two sidesof an acute scalene triangle is

[552]

[A] the third side [B] an altitude

[C] an angle bisector [D] a median

553. The number 0.14114111411114 . . . is

[553]

[A] rational [B] irrational

[C] whole [D] integral

554. For five algebra examinations, Maria has anaverage of 88. What must she score on thesixth test to bring her average up to exactly90?

[554]

[A] 100 [B] 98 [C] 92 [D] 94

555. Which transformation does not alwaysproduce an image that is congruent to theoriginal figure?

[555]

[A] rotation [B] dilation

[C] translation [D] reflection

556. Six members of a school's varsity tennis teamwill march in a parade. How many differentways can the players be lined up if Angela,the team captain, is always at the front of theline?

[556]

557. What is the value of y in the following systemof equations?

2 3 62 2

x yx y+ =+ = −

[557]

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

558. If the circumference of a circle is 10πinches, what is the area, in square inches, ofthe circle?

[558]

[A] 100π [B] 50π

[C] 10π [D] 25π

559. Five people have volunteered to work on anawards dinner at Madison High School. Howmany different committees of four can beformed from the five people?

[559]

[A] 20 [B] 10 [C] 5 [D] 1

560. If a b c d< <, , and a, b, c, and d are allgreater than 0, which expression is alwaystrue?

[560]

[A] ad

bc

> [B] ac < bd

[C] a + c > b + d [D] a - c + b - d = 0


561. If there are four teams in a league, how manygames will have to be played so that eachteam plays every other team once?

[561]

[A] 8 [B] 3 [C] 16 [D] 6

562. What is the solution of the equation3 5 10 36y y− + = ?

[562]

[A] 4.5 [B] 2 [C] 13 [D] -13

563. A total of $450 is divided into equal shares.If Kate receives four shares, Kevin receivesthree shares, and Anna receives the remainingtwo shares, how much money did Kevinreceive?

[563]

[A] $200 [B] $250

[C] $100 [D] $150

564. The product of 3 5x and 2 4x is

[564]

[A] 6 20x [B] 5 20x [C] 6 9x [D] 5 9x

565. Mr. James wanted to plant a garden thatwould be in the shape of a rectangle. He wasgiven 80 feet of fencing to enclose his garden.He wants the length to be 10 feet more thantwice the width. What are the dimensions, infeet, for a rectangular garden that will useexactly 80 feet of fencing?

[565]

566. There are 357 seniors in Harris High School.The ratio of boys to girls is 7:10. How manyboys are in the senior class?

[566]

[A] 147 [B] 107 [C] 117 [D] 210

567. If 7 2 3 5x a x a+ = + , then x is equivalent to

[567]

[A] 74a [B] 3

10a [C] 3

4a [D] 7

10a

568. Which expression has the smallest value?

[568]

[A] − 10 [B] −165

[C] −π [D] − 302.

569. In the accompanying diagram, a ladderleaning against a building makes an angle of58° with level ground. If the distance fromthe foot of the ladder to the building is 6 feet,find, to the nearest foot, how far up thebuilding the ladder will reach.

[569]

570. Which expression is equivalent to ax

bx

+2

?

[570]

[A] 2a bx+ [B] a b

x+

2

[C] 22a b

x+ [D] a b

x+

3


571. If n + 4 represents an odd integer, the nextlarger odd integer is represented by

[571]

[A] n + 5 [B] n + 2

[C] n + 6 [D] n + 3

572. In a molecule of water, there are two atoms ofhydrogen and one atom of oxygen. Howmany atoms of hydrogen are in 28 moleculesof water?

[572]

[A] 14 [B] 56 [C] 42 [D] 29

573. The sum of 75 and 3 is

[573]

[A] 15 [B] 18 [C] 78 [D] 6 3

574. A student council has seven officers, of whichfive are girls and two are boys. If twoofficers are chosen at random to attend ameeting with the principal, what is theprobability that the first officer chosen is agirl and the second is a boy?

[574]

[A] 714

[B] 713

[C] 27

[D] 1042

575. If a + b is less than c + d, and d + e is lessthan a + b, then e is

[575]

[A] less than d [B] greater than d

[C] equal to c [D] less than c

576. What is the total number of points ofintersection in the graphs of the equationsx y2 2 16+ = and y = 4?

[576]

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

577. Jerry and Jean Jogger start at the same timefrom point A shown on the accompanying setof axes. Jerry jogs at a rate of 5 miles per hourtraveling from point A to point R to point Sand then to point C. Jean jogs directly frompoint A to point C on AC at the rate of 3miles per hour. Which jogger reaches point Cfirst? Explain or show your reasoning.

[577]

578. The plot of land illustrated in theaccompanying diagram has a perimeter of 34yards. Find the length, in yards, of each sideof the figure. Could these measures actuallyrepresent the measures of the sides of atriangle? Explain your answer.

[578]


579. A square dartboard is represented in theaccompanying diagram. The entire dartboardis the first quadrant from x = 0 to 6 and from y= 0 to 6. A triangular region on the dartboardis enclosed by the graphs of the equations y =2, x = 6, and y = x. Find the probability that adart that randomly hits the dartboard will landin the triangular region formed by the threelines.

[579]

580. Line P and line C lie on a coordinate planeand have equal slopes. Neither line crossesthe second or third quadrant. Lines P and Cmust

[580]

[A] be vertical [B] be horizontal

[C] be perpendicular

[D] form an angle of 45°

581. Draw and label a diagram of the path of anairplane climbing at an angle of 11° with theground. Find, to the nearest foot, the grounddistance the airplane has traveled when it hasattained an altitude of 400 feet.

[581]

582. A surveyor needs to determine the distanceacross the pond shown in the accompanyingdiagram. She determines that the distancefrom her position to point P on the southshore of the pond is 175 meters and the anglefrom her position to point X on the northshore is 32°. Determine the distance, PX,across the pond, rounded to the nearest meter.

[582]

583. What is the least common denominator of 12

,

27x

, and 5x

?

[583]

[A] 14 2x [B] 9x [C] 2x [D] 14x

584. When solved graphically, which system ofequations will have exactly one point ofintersection?

[584]

[A]

196.0

1253

−=

+=

xy

xy [B]17

20+=−−=

xyxy

[C]305.0305.0

−=+=

xyxy [D]

2515

+−=+−=

xyxy


585. The accompanying diagram shows a kite thathas been secured to a stake in the ground witha 20-foot string. The kite is located 12 feetfrom the ground, directly over point X. Whatis the distance, in feet, between the stake andpoint X?

[585]

586. A bicyclist leaves Bay Shore traveling at anaverage speed of 12 miles per hour. Threehours later, a car leaves Bay Shore, on thesame route, traveling at an average speed of30 miles per hour. How many hours after thecar leaves Bay Shore will the car catch up tothe cyclist?

[586]

[A] 8 [B] 4 [C] 5 [D] 2

587. The equation ∗ + ◊ =∗ + ∗◊( )∆ ∆ is anexample of the

[587]

[A] commutative law [B] transitive law

[C] distributive law [D] associative law

588. When 3 82x x− is subtracted from 2 32x x+ ,the difference is

[588]

[A] − +x x2 11 [B] x x2 5−

[C] − −x x2 5 [D] − −x x2 11

589. A plot of land is in the shape of rhombusABCD as shown below.

Which can not be the length of diagonal AC?

[589]

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

590. In the accompanying diagram, ABCD is astraight line, and angle E in triangle BEC is aright angle.

What does a° + d° equal?

[590]

[A] 180° [B] 270°[C] 160° [D] 135°

591. Judy needs a mean (average) score of 86 onfour tests to earn a midterm grade of B. If themean of her scores for the first three tests was83, what is the lowest score on a 100-pointscale that she can receive on the fourth test tohave a midterm grade of B?

[591]

592. How many different five-digit numbers canbe formed from the digits 1, 2, 3, 4, and 5 ifeach digit is used only once?

[592]

[A] 24 [B] 120 [C] 60 [D] 20


593. An image of a building in a photograph is 6centimeters wide and 11 centimeters tall. Ifthe image is similar to the actual building andthe actual building is 174 meters wide, howtall is the actual building, in meters?

[593]

594. Using only a compass and a straightedge,construct the perpendicular bisector of ABand label it c. [Leave all construction marks.]

[594]

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

[595]

596. Virginia has a circular rug on her squareliving room floor, as represented in theaccompanying diagram. If her entire livingroom floor measures 100 square feet, what isthe area of the part of the floor covered by therug?

[596]

597. 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 setof axes, plot and label quadrilateral A’B’C’D’,the reflection of quadrilateral ABCD in the y-axis. Determine the area, in square units, ofquadrilateral A’B’C’D’.

[597]

598. Which number is rational?

[598]

[A] 7 [B] π [C] 32

[D] 54


599. Which equation illustrates the associativeproperty of addition?

[599]

[A] x + y = y + x [B] 3 + x = 0

[C] 3(x + 2) = 3x + 6

[D] (3 + x) + y = 3 + (x + y)

600. What is the slope of the linear equation5 10 15y x− = − ?

[600]

[A] -15 [B] 10 [C] -10 [D] 2

601. Shanaya graphed the line represented by theequation y x= − 6.Write an equation for a line that is parallel tothe given line.Write an equation for a line that isperpendicular to the given line.Write an equation for a line that is identical tothe given line but has different coefficients.

[601]

602. If two lines are parallel and the slope of oneof the lines is m, what is the product of theirslopes?

[602]

[A] 2m [B] 0 [C] 1 [D] m2

603. The ratio of Tariq's telephone bill to Pria'stelephone bill was 7:5. Tariq's bill was $14more than Pria's bill. What was Tariq's bill?

[603]

[A] $35 [B] $28 [C] $21 [D] $49

604. Written in simplest factored form, thebinomial 2 502x − can be expressed as

[604]

[A] 2x(x - 50) [B] (x - 5)(x + 5)

[C] 2(x - 5)(x + 5) [D] 2(x- 5)(x - 5)

605. What is the perimeter of an equilateraltriangle whose height is 2 3 ?

[605]

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

606. Ashanti is surveying for a new parking lotshaped like a parallelogram. She knows thatthree of the vertices of parallelogram ABCDare A(0,0), B(5,2), and C(6,5). Find thecoordinates of point D and sketchparallelogram ABCD on the accompanying setof axes. Justify mathematically that the figureyou have drawn is a parallelogram.

[606]

607. Which shape does not have rotationalsymmetry?

[607]

[A] trapezoid [B] circle

[C] square [D] regular pentagon


608. 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, andthe longer side of the box is 5 inches morethan the shorter side. Find the number ofinches in the shorter side of the original sheetof cardboard.

[608]

609. As shown in the accompanying diagram,radio station KMA is increasing its radiolistening radius from 40 miles to 50 miles.How many additional square miles oflistening area, to the nearest tenth, will theradio station gain?

[609]

610. When 3 2 52a a− + is subtracted froma a2 1+ − , the result is

[610]

[A] − + +2 3 62a a [B] 2 3 62a a− +

[C] − + −2 3 62a a [D] 2 3 62a a− −

611. Two parallel roads, Elm Street and OakStreet, are crossed by a third, Walnut Street,as shown in the accompanying diagram. Findthe number of degrees in the acute angleformed by the intersection of Walnut Streetand Elm Street.

[611]

612. The value of 5! is

[612]

[A] 5 [B] 15

[C] 20 [D] 120

613. In a recent poll, 600 people were askedwhether they liked Chinese food. A circlegraph was constructed to show the results.The central angles for two of the three sectorsare shown in the accompanying diagram.How many people had no opinion?

[613]

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

[614]


615. If the measure of an angle is represented by2x, which expression represents the measureof its complement?

[615]

[A] 90 - 2x [B] 88x

[C] 180 - 2x [D] 90 + 2x

616. The accompanying graph shows Marie'sdistance from home (A) to work (F) at varioustimes during her drive.

a Marie left her briefcase at home and had toreturn to get it. State which point representswhen she turned back around to go home andexplain how you arrived at that conclusion.b Marie also had to wait at the railroad tracksfor a train to pass. How long did she wait?

[616]

617. Solve for m: 0.6m + 3 = 2m + 0.2

[617]

618. Paloma has 3 jackets, 6 scarves, and 4 hats.Determine the number of different outfitsconsisting of a jacket, a scarf, and a hat thatPaloma can wear.

[618]

619. Which expression is rational?

[619]

[A] 3 [B] 12

[C] π [D] 14

620. 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 thelength of each side and the measure of eachangle for the quadrilateral you draw.

[620]

621. Find, to the nearest tenth of a foot, the heightof the tree represented in the accompanyingdiagram.

[621]

622. On the accompanying set of axes, graph∆ABC with coordinates A(-1,2), B(0,6), andC(5,4). Then graph ∆A B C' ' ' , the image of∆ABC after a dilation of 2.

[622]


623. Solve the following system of equations:y x xy x= + += +

2 4 15 3

[The use of the grid is optional.]

[623]

624. The accompanying figure shows the graph ofthe equation x = 5.

What is the slope of the line x = 5?

[624]

[A] undefined [B] -5 [C] 5 [D] 0

625. Three roses will be selected for a flower vase.The florist has 1 red rose, 1 white rose, 1yellow rose, 1 orange rose and 1 pink rosefrom which to choose.a How many different three rose selectionscan be formed from the 5 roses?b What is the probability that 3 roses selectedat random will contain 1 red rose, 1 whiterose, and 1 pink rose?c What is the probability that 3 roses selectedat random will not contain an orange rose?

[625]

626. The height of a golf ball hit into the air ismodeled by the equation ,4816 2 tth +−=where h represents the height, in feet, and trepresents the number of seconds that havepassed since the ball was hit. What is theheight of the ball after 2 seconds?

[626]

[A] 16 ft [B] 64 ft [C] 80 ft [D] 32 ft

627. All seven-digit telephone numbers in a townbegin with 245. How many telephonenumbers may be assigned in the town if thelast four digits do not begin or end in a zero?

[627]

628. If the lengths of two sides of a triangle are 4and 10, what could be the length of the thirdside?

[628]

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

629. What is the greatest possible number of pointsof intersection of a triangle and a circle?

[629]

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


630. During a recent winter, the ratio of deer tofoxes was 7 to 3 in one county of New YorkState. If there were 210 foxes in the county,what was the number of deer in the county?

[630]

[A] 90 [B] 280 [C] 147 [D] 490

631. A truck traveling at a constant rate of 45miles per hour leaves Albany. One hour latera car traveling at a constant rate of 60 milesper hour also leaves Albany traveling in thesame direction on the same highway. Howlong will it take for the car to catch up to thetruck, if both vehicles continue in the samedirection on the highway?

[631]

632. In the accompanying diagram, triangle A issimilar to triangle B. Find the value of n.

[632]

633. A car travels 110 miles in 2 hours. At thesame rate of speed, how far will the car travelin h hours?

[633]

[A] h220

[B] h55

[C] 55h [D] 220h

634. Two health clubs offer different membershipplans. The graph below represents the totalcost of belonging to Club A and Club B forone year.

a If the yearly cost includes a membershipfee plus a monthly charge, what is themembership fee for Club A?b (1) What is the number of the month whenthe total cost is the same for both clubs? (2) What is the total cost for Club A whenboth plans are the same?c What is the monthly charge for Club B?

[634]

635. Ashanti and Maria went to the store to buysnacks for their back-to-school party. Theybought bags of chips, pretzels, and nachos.They bought three times as many bags ofpretzels as bags of chips, and two fewer bagsof nachos than bags of pretzels. If xrepresents the number of bags of chips theybought, express, in terms of x, how many bagsof snacks they bought in all.

[635]

636. What is the solution set of the equation3 482x = ?

[636]

[A] {2,8} [B] {4,4}

[C] {-2,-8} [D] {4,-4}


637. John left his home and walked 3 blocks to hisschool, as shown in the accompanying graph.

What is one possible interpretation of thesection of the graph from point B to point C?

[637]

[A] John returned home to get hismathematics homework.

[B] John arrived at school and stayedthroughout the day.

[C] John waited before crossing a busy street.

[D] John reached the top of a hill and beganwalking on level ground.

638. The distance from Earth to the Sun isapproximately 93 million miles. A scientistwould write that number as

[638]

[A] 93 107× [B] 9 3 107. ×

[C] 93 1010× [D] 9 3 106. ×

639. Expressed in factored form, the binomial4 92 2a b− is equivalent to

[639]

[A] (2a + 3b)(2a - 3b)

[B] (2a - 3b)(2a - 3b)

[C] (4a - 3b)(a + 3b) [D] (2a - 9b)(2a + b)

640. Find three consecutive odd integers such thatthe product of the first and the second exceedsthe third by 8.

[640]

641. On the first six tests in her social studiescourse, Jerelyn's scores were 92, 78, 86, 92,95, and 91. Determine the median and themode of her scores. If Jerelyn took a seventhtest and raised the mean of her scores exactly1 point, what was her score on the seventhtest?

[641]

642. What is the sum of 2x

and x2

?

[642]

[A] 1 [B] 42

2+ xx

[C] 42+ xx

[D] 22+ xx

643. Melissa is walking around the outside of abuilding that is in the shape of a regularpolygon. She determines that the measure ofone exterior angle of the building is 60°.How many sides does the building have?

[643]

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

644. What is the total number of points equidistantfrom two intersecting straight roads and also300 feet from the traffic light at the center ofthe intersection?

[644]

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

645. Twenty-five percent of 88 is the same as whatpercent of 22?

[645]

[A] 100% [B] 40%

[C] 12 12

% [D] 50%


646. A picture held by a magnet to a refrigeratorslides to the bottom of the refrigerator, asshown in the accompanying diagram.

This change of position is an example of a

[646]

[A] reflection [B] translation

[C] dilation [D] rotation

647. A girl can ski down a hill five times as fast asshe can climb up the same hill. If she canclimb up the hill and ski down in a total of 9minutes, how many minutes does it take herto climb up the hill?

[647]

[A] 4.5 [B] 1.8 [C] 7.5 [D] 7.2

648. The graph of a quadratic equation is shown inthe accompanying diagram. The scale on theaxes is a unit scale. Write an equation of thisgraph in standard form.

x

y

[648]

649. Which set is closed under division?

[649]

[A] counting numbers [B] {1}

[C] integers [D] whole numbers

650. The senior class at South High Schoolconsists of 250 students. Of these students,130 have brown hair, 160 have brown eyes,and 90 have both brown hair and brown eyes.How many members of the senior class haveneither brown hair nor brown eyes?

[650]

651. In the graph of y x≤ − , which quadrant iscompletely shaded?

[651]

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

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

[652]

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

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

[653]

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

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

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

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


654. An engineer measured the dimensions for arectangular site by using a wooden pole ofunknown length x. The length of therectangular site is 2 pole measures increasedby 3 feet, while the width is 1 pole measuredecreased by 4 feet. Write an algebraicrepresentation, in terms of x, for the perimeterof the site.

[654]

655. 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 by 12

as the image is if it is dilated by

12

, then reflected in the x-axis? Justify your

answer.

[655]

656. There are 461 students and 20 teachers takingbuses on a trip to a museum. Each bus canseat a maximum of 52. What is the leastnumber of buses needed for the trip?

[656]

[A] 9 [B] 10 [C] 11 [D] 8

657. The expression 93 is a number between

[657]

[A] 9 and 10 [B] 46 and 47

[C] 8 and 9 [D] 3 and 9

658. The larger root of the equationx x+ − =4 3 0b gb g is

[658]

[A] -3 [B] 4 [C] 3 [D] -4

659. 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

[659]

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

660. Which inequality is represented in the graphbelow?

[660]

[A] − ≤ ≤4 2x [B] − < ≤4 2x[C] − ≤ <4 2x [D] − < <4 2x


661. Using only 32-cent and 20-cent stamps,Charlie put $3.36 postage on a package hesent to his sister. He used twice as many 32-cent stamps as 20-cent stamps. Determinehow many of each type of stamp he used.

[661]

662. From January 3 to January 7, Buffalorecorded the following daily hightemperatures: 5°, 7°, 6°, 5°, and 7°. Whichstatement about the temperatures is true?

[662]

[A] mean < median [B] median = mode

[C] mean = mode [D] mean = median

663. In the accompanying diagram of ∆BCD ,∆ABC is an equilateral triangle and AD =AB. What is the value of x, in degrees?

[663]

664. Greg is in a car at the top of a roller-coasterride. The distance, d, of the car from theground as the car descends is determined bythe equation d t= −144 16 2 , where t is thenumber of seconds it takes the car to traveldown to each point on the ride. How manyseconds will it take Greg to reach the ground?For an algebraic solution show your workhere.For a graphic solution show your work here.

[664]

665. The expression a b2 2 2+c h is equivalent to

[665]

[A] a a b b4 2 2 44+ + [B] a a b b4 2 2 4+ +

[C] a b4 4+ [D] a a b b4 2 2 42+ +

666. A truck travels 40 miles from point A to pointB in exactly 1 hour. When the truck ishalfway between point A and point B, a carstarts from point A and travels at 50 miles perhour. How many miles has the car traveledwhen the truck reaches point B?

[666]

[A] 60 [B] 40 [C] 25 [D] 50


667. Jorge made the accompanying stem-and-leafplot of the weights, in pounds, of eachmember of the wrestling team he wascoaching.

What is the mode of the weights?

[667]

[A] 152 [B] 168 [C] 150 [D] 145


[668]

[A] 49 [B] 3.0 [C] π [D]83

669. In the accompanying diagram of right triangleABC, AB = 8, BC = 15, AC = 17, andm ABC∠ = 90.

What is tan ?∠C

[669]

[A] 1715

[B] 817

[C] 815

[D] 1517

670. If the temperature in Buffalo is 23°Fahrenheit, what is the temperature in degrees

Celsius? [Use the formula C F= −59

32( ).]

[670]

[A] 5 [B] -5 [C] 45 [D] -45

671. If 2(x + 3) = x + 10, then x equals

[671]

[A] 4 [B] 7 [C] 14 [D] 5

672. The expression 3 3 32 3 4⋅ ⋅ is equivalent to

[672]

[A] 2724 [B] 39 [C] 279 [D] 324

673. How many feet from the base of a house musta 39-foot ladder be placed so that the top ofthe ladder will reach a point on the house 36feet from the ground?

[673]

674. Which letter demonstrates line symmetry butnot point symmetry?

[674]

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

675. Which expression represents an irrationalnumber?

[675]

[A] 0 [B] 2 [C] 12

[D] 0.17

676. The sum of 3 82x x+ + and x2 9− can beexpressed as

[676]

[A] 4 12x x+ − [B] 4 172x x+ −

[C] 3 14x x+ − [D] 4 14x x+ −

677. When − 9 5x is divided by − ≠3 03x x, , thequotient is

[677]

[A] 3 2x [B] 27 8x

[C] − 3 2x [D] − 27 15x


678. A straight line with slope 5 contains thepoints (1,2) and (3,K). Find the value of K.[The use of the accompanying grid isoptional.]

[678]

679. A locker combination system uses three digitsfrom 0 to 9. How many different three-digitcombinations with no digit repeated arepossible?

[679]

[A] 30 [B] 1,000 [C] 720 [D] 504

680. Which statement is logically equivalent to "Ifa triangle is an isosceles triangle, then it hastwo congruent sides"?

[680]

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

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

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

[D] If a triangle is an isosceles triangle, thenit does not have two congruent sides.

681. What is the inverse of the statement “If I donot buy a ticket, then I do not go to theconcert”?

[681]

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

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

682. What is the solution set of the equationx x2 5 24 0− − = ?

[682]

[A] {-3,-8} [B] {3,8}

[C] {-3,8} [D] {3,-8}

683. On the accompanying diagram of ∆ABC , usea compass and a straightedge to construct amedian from A to BC .

[683]

684. One root of the equation 2 15 02x x− − = is

[684]

[A] 52

[B] 32

[C] − 3 [D] 3


685. 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.

[685]

686. Which graph represents the solution set for2 4 8x − ≤ and x + ≥5 7 ?

[686]

[A]

[B]

[C]

[D]

687. On a scale drawing of a new schoolplayground, a triangular area has sides withlengths of 8 centimeters, 15 centimeters, and17 centimeters. If the triangular area locatedon the playground has a perimeter of 120meters, what is the length of its longest side?

[687]

[A] 40 m [B] 45 m

[C] 24 m [D] 51 m

688. If 2m + 2p = 16, p equals

[688]

[A] 9m [B] 16 - m

[C] 8 - m [D] 16 + 2m

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

[689]

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