SAT II MATH PRACTICE.pdf

8/14/2019 SAT II MATH PRACTICE.pdf

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SAT SHEET

(calculators allowed)

33. If 15 15 , thenx x! = ! =

A) -30 B) -15 C) 0 D) 15 E) 30

34. A dozen roses cost $15.60 and the cost of one rose and one lily together cost $4.50. What is the cost of onelily?

A) $1.30 B) $3.20 C) $5.80 D) $11.10 E) $20.10

35. If temperatures at 1 p.m. during a week in August were: 81 , 88 , 97 , 98 , 101 , 103 , and 78 , then the

median temperature was

A) 81 B) 88 C) 97 D) 98 E) 103

36. If points A and B above are two vertices of an equilateral triangle, what is the perimeter of the triangle?A) 12 B) 15 C) 16 D) 22 E) 25

37. If the earth turns 360 longitude in 24 hours, how many minutes does it take for the earth to revolve

through 1 ?

A)1

4minute B) 4 minutes C) 6 minutes D) 15 minutes E) 30 minutes

38. Ifxis an even integer andyis an odd integer, then which of the following must be even?

I. xy II. ( )x x y+ III.2

2

xy !

A) I only B) I and II only C) II and III only D) I and III only E) I, II, and III

39. A set of math exams are numbered in order from 1 to 49. Ms. Jacobsen is going to correct some of thetests. She selects the third paper and every ninth paper thereafter. What is the number of the last paper shecorrects?

A) 45 B) 46 C) 47 D) 48 E) 49


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Note: Figure not drawn to scale

40. What is the value of a+ b?A) 120 B) 150 C) 180 D) 210 E) 240

41. If 35 25x x+ = , thenx=

A) 1 B) 2 C) 3 D) 4 E) 5

42. In triangleABCabove, side ais 100% greater than side band side cis 2 feet longer than side b. What isthe length of side aif the perimeter equals 132 feet?A) 26 feet B) 32.5 feet C) 52 feet D) 65 feet E) 67 feet

43. In a group of 44 students, 26 are boys. If 33 of the students have a drivers license and if 5 girls do nothave a drivers license, how many boys have a drivers license?A) 10 B) 13 C) 15 D) 18 E) 20

44. If a number multiplied by 10 is the same as 10 less than the number, what is the number?

A)10

9! B)

12

11! C) 1! D)

10

11! E)

9

10!

45. The average of three fractions is2

5. If two of the fractions are

1

3and

3

4, what is the value of the missing

fraction?

A)1

12 B)

7

60 C)

2

15 D)

11

12 E)

6

5


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46. If nx= d +x, what isxin terms of nand d?

A)d n

n

+ B) d(n 1) C)

1

d

n! D) d(n+ 1) E)

1

d

n+

47. If the isosceles triangle and the square have the same area, in terms ofs, what is the altitude hof the

triangle?A) s B) 2s C) 2s D) 22s E) 3s

48. If 1 100,j k! ! ! andjand kare integers, what is the greatest possible value ofk j

jk

!

?

A) 0 B)1

2 C)

97

98 D)

99

100 E) 1

49. If circleR, in the figure above, is tangent to sideACand has a circumference of 4! , what is the length of

sideAC?A) 2 2 2+ B) 4 2 C) 3 2 2+ D) 4 2 2+ E) 4 4 2+

50. Ifxy= 6! and 2 221y x= ! , what is the value of 2( )x y! ?

A) 9 B) 15 C) 27 D) 33 E) 39


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51. The price of a dress is mdollars and the price of a coat ispdollars. If the store gives a 25% discount on thedress and a 40% discount on the coat, then the dress and the coat would each cost the same. What is the

ratio ofm

p?

A)1

5 B)

5

8 C)

4

5 D)

5

4 E)

8

5

52. In the cube shown above, if diagonalFGin a face of the cube is 7 2 , andAEequals 3, what is the length

of a diagonal of squareABCD?

A) 5 B) 5 2 C) 7 D) 7 2 E) Cannot be determined from the information given

53. At the farmers market, pears are sold for $1.20 for the first point and $1.00 for each additional pound. Ifthe weight is rounded to the nearest whole pound, which of the following could express the cost of thepears as a function of n, where nis the number of pounds of pears purchased?

A) ( ) 2.2f n n= B) ( ) 1.2f n n= + C) ( ) 1.2f n n= D) ( ) 2.2f n n= + E) ( ) 0.2f n n= +

54. Given: tvaries inversely asp. Ifp is divided by 2, then t isA) decreased by 2 B) increased by 2 C) divided by 2 D) multiplied by 2 E) squared

55. If there is only one solution to this function,y = ax2+ bx + c, wheny= 0, then the graph of the parabolacould be

A) B) C) D) E)

56. Which compound statement is equivalent to -4 5x! < ?

A) The union of {-4! x} and {x < 5} B) The intersection of {-4! x} and {x < 5}C) The union of {x 4}! and {x < 5} D) the intersection of {x! -4} and {x < 4}

E) None of the statements above.


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x f(x)

0 7

1 7

2 7

3 7

57. If the tables above show values for he two functionsf andg, then which of the following statements is true?

A) f(0) =g(0) B) f(1) =g(1) C) f(0) =g(0) 5 D) f(2) =1

3g(2) E) 2f(3) =g(3) + 1

58. T-cells, under certain stimulus, show a growth rate of 25% every two hours. If we begin with 100 T-cells,to the nearest integer, how many T-cells are present after 12 hours?A) 250 B) 300 C) 381 D) 400 E) 1,455

59. Which of the following is a function whose domain is the set of real numbers and whose range is the set ofall non-positive real numbers?

A) y x= B) 2y x= C) y x=! D) 2y x=! E) 2y x=

60. In the figure above, a quarter circle is placed on a square target. If the radius of the quarter circle is thesame as the length of a side of the square, what is the probability that a dart hits the square does not hit thequarter circle?

A)16

! B)

2

3

! C)

4

4

!" D)

4

! E)

2

!

Note: Figure not drawn to scale.

61. IfAB=BC, what is thex-coordinate of point C?

x f(x)

0 -2

1 0

2 0

3 4


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62. If3

7m =

7

3n, then what is the value of

m

n

?

63. If Connie has 11

2cups of flour and a cake recipe calls for

114

cups of flour, then what pecent of her flour

will she use to make the cake?

64. For how many positive integersNis it true that 2N+ 10 < 23?

65. EFGH is a rectangular pool surrounded by a walkway. The uniform width of the walkway is 3. EF = 7andFG= 5. What is the outer perimeter of the walkway?

66. On line segmentABabove, pointsPandRare placed between pointsAandB so thatAP=1

4

AB and

RB=1

3AB PRi is what fraction ofAB?

67. The base of an isosceles triangle is 30% less than one of the equal sides, and the perimeter is 81. How longis the shortest side?

68. In the figure above, the radius OAis 5 and the area of the shaded region is 15! . What is the degree

measure of a?


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69. A Halloween bag has sourballs and peppermint candies. The probability of selecting a peppermint candy

is3

11. If there are exactly 32 sourballs in the bag, how many peppermint candies are in the bag?

70. If the slope of line labove is

1

3 , what is the area of the shaded portion?

71. If 75% of a group of 48 graduates are men and 1/3 of these men are law students, how many men in thisgroup are law students?

A) 4 B) 12 C) 16 D) 32 E) 36

72. DiagonalsACandBD in rectangleABCDin the above figure intersect at pointE. What is the sum of theperimeters of the shaded regions?A) 16 B) 20 C) 22 D) 26 E) 32

73. If b=1

5, what is the value of

5

bdivided by

5

b?

A)1

625 B)

1

25 C) 1 D) 5 E) 25


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74. In the figure above, if the radius of the inscribed circle is ! , what is the area of the square?

A) 22! B) 4! C) 24! D) 8! E) 216!

75. Five out of 10 different positive integers are 10, 20, 30, 40, and 50. The other integers are greater than 70.If the average of the 10 integers is 100, what is the value of the largest possible integer?A) 99 B) 100 C) 150 D) 290 E) 560

76. If 2 9x a! = and 3x b! = , and 0ab ! , then 3x + =

A)a

b B)

9a

b

+ C) a b! D) a b+ E) ab

77. The areas of two circles differ by 36! square inches and their radii differ by 2 inches. Find the length of

the radius, in inches, of the larger circle.A) 6 B) 8 C) 9 D) 10 E)12

Appetizer Entre Dessert

First(5 Points)

Saul Beth

Second(3 points)

Beth

Third(1 Point) Max

78. Saul, Beth, and Max were finalists in a cooking contest. The chart shows a partial display of pointsawarded. If there are no ties, what is the greatest number of points by which Sauls total score couldexceed Maxs total score?A) 8 B) 10 C) 12 D) 14 E) Cannot be determined from the information given

79. If , , ,a b c d is defined for all positive integers as c da b! , what is the value of 2,3,4,2 ?

A) -1 B) 0 C) 2 D) 7 E) 10


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80. If the area of the rectangle is equal to the area of the semicircle and the lengthADof the rectangle is 4,what is the width of the rectangle?

A)4

! B)

2

! C) ! D) 2! E) 4!

81. Which statement is true about the data collected in the scatterplot above?A) There is a positive correlation and the slope of the line of best fit is close to 1.B) There is a positive correlation and the slope of the line of best fit is greater than 2.

C) There is a positive correlation and the slope of the line of best fit is less than1

2

D) There is a negative correlation and the slope of the line of best fit is close to -1.

E) There is a negative correlation and the slope of the line of best fit is less than1

2!

82. If for all positive numbersx, =8 ( 1)

3

x x

! !

, what is the value of ?

A)1

3 B) 1 C) 2 D) 3 E)

123

A = {-2, 1, 3} and B = {3,5,9}

83. Two number,xandy, are to be selected at random from setsAandBabove. Ifxis selected fromAandyisselected fromB, what is the probability that x2+ y!9?

A)1

3 B)

4

9 C)

1

2 D)

5

9 E)

2

3


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84. A liquid nitrogen container, shown above, has a radius of 5 and height of 12. If pointsPand Qlie on thecircumference of the bottom and top of the cylinder, respectively, what is the greatest possible straight-linedistance betweenPand Q?

A) 12 B) 13 C) 14 D) 2 61 E) 22

85. A circular engine part must be made with a diameter of 8 inches and an error tolerance of at most 0.05 inchWhich of the following inequalities best describes the radius,r, of this engine part?

A)4 0.025r! "

B)4 0.10r! "

C)0.05 4r! "

D)0.025r !

E)4 0.05r! "

86. Given the table above, and the function2 1

( )3

xf x

+= , what is the value ofb?

A) 5 B) 6 C) 7 D) 8.5 E) 9.5

x f(x)

1 1

3 a

a + 1 b


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ANSWERS

33. E34. B35. C36. B37. B38. B39. D40. D

41. C42. D43. E44. A45. B46. C47. B

48. D49. D50. D51. C52. B53. E54. D55. D56. B57. E58. C59. D

60. C61. 862. 49/9 or 5.4463. 83.364. 665. 4866. 5/1267. 21

68. 14469. 1270. 21/2 or 10.571. B72. E73. A74. C

75. E76. A77. D78. B79. D80. B81. D82. B83. E84. D85. A86. C

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SAT II MATH PRACTICE.pdf