Satii-virtual-ic02.pdf

1 1 = , then k = 4k - 1 15

1. If

(A) 3 (B) 4 (C) 5 (D) 10 (E) 16

2. If 4 3t = 64 , then t = (A) 1 (B)

4 3

(C) 4 (D)

16 3

(E) 16

3. If x = 3 , then ( x - 8)( x + 3) = (A) 30 (B) 5 (C) -3 (D) -5 (E) -30

4. Chet traveled to Bayport. He took a bus

1 of 5

the way, then walked 2 miles, and then took a train

2 of the way, arriving in Bayport. How 3

many miles did he travel ? (A) 10 (B) 12 (C) 15 (D) 24 (E) 30

5. The distance between the points ( - 7 , 1) and ( - 15 , 1) is (A)

22

(B) 8 (C) 34 (D) 22 (E)

176

6. If

3

x - 7 = - 0.8, then x =

(A) 6.072 (B) 6.488 (C) 6.800 (D) 7.640 (E) 7.894

7. If ∣1 - x∣ = 2x - 11, then which of the following could be the value of x ? (A) -4 (B) -1 (C) 0 (D) 5 (E) 10

8. The volume of container a is one-third that of container b, and the volume of container b is two-thirds that of container c . If volume of a is 180 cubic meters, what is the volume of c in cubic meters ? (A) 60 (B) 135 (C) 270 (D) 405 (E) 810

9. If Figure 1, what is the value of m + n ? (A) 65 (B) 100 (C) 165 (D) 195 (E) 330 Figure 1 10. If a - b = 12 , and a + b = 10 , then

ab = (A) -11 (B) -5 (C) 2 (D) 11 (E) 120

11. In Figure 2, if AB = BD = DC ,

B

then x =

60

〫

(A) 15

〫

(B) 60 (C) 129 (D) 150 (E) 165

12. If an operation Φ is defined for all real numbers x and y by the equation

x Φ y = xy - x, then 3 Φ ( - 3) = (A) -12 (B) -9 (C) 0 (D) 9 (E) 12

x

D

A

Figure 2

C

13. Of all rectangles with a given area, the square has minimum perimeter. What is the minimum perimeter of a rectangle with area 100 ? (A) 10 (B) 25 (C) 40 (D) 50 (E) 100

14. what is the slope of the line given by the equation

y- 7=

(A) -

4 3

(B) -

7 6

(C)

3 4

(D)

6 7

(E)

37 4

3 ( x + 6) ? 4

15. If f ( x) = 2 - x and g( x) = x2 + 3 , then g( f ( 4) ) = (A) -14 (B) -7 (C) 7 (D) 17 (E) 19

16. Each of the 80 employees of a company took a vacation during the months of May through October. The number of employees who took a vacation each month is pictured in the chart above. Approximately what percent of the employees took a vacation in the months of August through October ? (A) 10 % (B) 30 % (C) 32 % (D) 35 % (E) 40 %

17. If 5 < s < 11 and - 2 < t < 7 , which of the following describes all possible values of st ? (A) - 22 < st < 35 (B) - 22 < st < 77 (C) - 10 < st < 0 (D) - 10 < st < 77 (E) 0 < st < 35

2

18. If 2 x ⋅2 4x⋅2 4 = 512 and x > 0 , then x = (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

19. Which of the lines in Figure 3 is the graph of x + y = 3 ? (A) a (B) b (C) c (D) d (E) e Figure 3

20. If a and b are positive integers and r = 8a + 12b, then r must be divisible by which of the following ? (A) 4 (B) 5 (C) 12 (D) 20 (E) 24

21. Most radio stations in the United States are identified by "call letters" -a sequence of four letters of the alphabet in a specific order. If each set of call letters must begin with either K or W , how many different sets of call letters are possible ? (A) 80 (B) 104 (C) 2,704 (D) 35,152 (E) 456,976

22. In Figure 4, a quadrilateral has three of its sides with lengths 6, 7, and 10. If the length n of the four side is also an integer, what is the greatest possible value of n ? (A) 10 (B) 16 (C) 17 (D) 22

Note: Figure not drawn to scale

(E) 23 Figure 4

23. Which of the following lines is perpendicular to the line 4x + 5y = 17 ? (A) 4x + 5y = 10 (B) 4x - 5y = 17 (C) 8x + 10y = 34 (D) 8x - 10y = 3 (E) 10x - 8y = 17

24. In Figure 5, ray OA forms an angle with the positive

x-axis. If tan a

〫 = 1 , how far counterclockwise would

ray OA have to be rotated about point O so that tan a

〫=

〫 30〫 45〫 60〫 70〫

3 ? y

A

(A) 15 (B) (C) (D) (E)

a

〫

O

x

Figure 5

25. At a meeting, everyone shakes hands with every other person exactly once. If there are ten people at the meeting, how many handshakes occur ? (A) 10 (B) 20 (C) 25 (D) 45 (E) 50

△PQR us equilateral and PQ = 6 , what is the area of △PQR ?

26. If

(A) 9 2 (B) 9 3 (C) 18 (D) 18 2 (E) 36

27. LIsa's average(arithmetic mean) grade on three of math tests is 87. What grade would she have to receive on a fourth test in order to make the average of all four test grades equal to 90 ? (A) 87 (B) 90 (C) 93 (D) 96 (E) 99

28. In Figure 6, segments AD and BE intersect at point C . What is the value of

(A)

3 4

(B)

6 7

(C)

7 8

(D)

8 7

(E)

7 6

s t ?

Figure 6

29. If 0

〫≤ θ ≤90〫, then

2

sin θ - 5 + cos 2θ = ? (A) -16 (B) -4 (C) 6 (D) 16 (E) 26

30. In Figure 7, if the circle has a length of r , what is the value of the ratio area of the circumscribed ? area of the inscribed square

(A)

4 2 1

(B)

4 1

(C)

2 2 2

(D)

2 1

(E)

2 1

Figure 7

31. The height of a ball thrown into the air is a function of the time that the ball has been in flight. If h represents the height, in meters, of the ball, and t represents the time, in seconds, that the ball has been in flight, then h ( t) = 28t - 4.9t 2 . Of the following, which is the closest approximation to the to the height, in meters, of the ball after it has been in flight for 2 seconds ? (A) 33.6 (B) 36.4 (C) 40.0 (D) 46.2 (E) 204.4

32. In circle O , chord AC has a length of 6, and is a distance of 4 from point O . what is the length of radius OB ? (A) 5 (B) 5.657 (C) 6 (D) 6.928 (E) 7.211

Figure 8

33. What value of x satisfies 1 - x=

(A) -2 (B) 0 (C) 1 (D)

2

(E)

3

-2

x+ 1 ?

34. The function f is defined as f ( x) = ( 1 - x) 2 for - 3 ≤ x ≤ 3. What is the range of f ? (a) 0 ≤ f ( x) ≤ 1 (b) 0 ≤ f ( x) ≤ 9 (c) 0 ≤ f ( x) ≤ 16 (d) 1 ≤ f ( x) ≤ 9 (e) 1 ≤ f ( x) ≤ 16

35. If i 2 = - 1 and x = 6 + 3i , then x2 = (a) 27 + 9i (b) 36 + 9i (c) 45 + 9i (d) 27 + 36i (e) 45 + 36i

36. In

△RST in Figure 9 is reflected across the

line y = x, what will be the coordinates of the reflection of point R ? (a) ( 5 , 1) (b) ( - 5 , - 1) (c) ( 1 , 5) (d) ( 1 , - 5) (e) ( - 1 , - 5)

Figure 9

37. A delivery person delivers three different sandwiches to three different people without paying attention to who ordered which sandwich. What is the probability that at least one person will get the wrong sandwich ?

(a)

1 6

(b)

1 3

(c)

1 2

(d)

2 3

(e)

5 6

38. Which of the following points is not on the circle defined by x2 + y 2 = 25 (a) ( 2 3 , (b) ( 5 ,

13) 5)

(c) ( - 10 ,

15)

(d) ( 0 , - 5) (e) ( - 3 , 4)

39. If f ( x) = 2x3 + 4x2 - 70x, g( x) = 2x2 + 14x,

x ≠ 0, and x = - 7, then (a) x - 5 (b) (c)

1

x- 5 2x x- 5

(d) 2x2 - 10x (e) 2x3 + 2x2 - 84x

f ( x) = g( x)

40. In Figure 10, if r =

2 s and s = 3t, what is 3

the volume of the rectangular solid in terms of r ?

(a) (b)

r3 2

r3 3

(c)

3r 3 4

(d)

4r 3 3

(e)

3r 3 2

41. At the end of 1998, a certain house was worth $135,000. If the value of the house increases at a rate of 4 percent each year, approximately how much will the house be worth at the end of 2018 ? (a) $140,400 (b) $167,400 (c) $243,000 (d) $280,000 (e) $295,800

42. The points E ( 3 , 0), F ( 0 , 8), G ( 7 , 10) and

H( 7 , 0) are connected in that order to form a quadrilateral with sides EF , FG , GH, and

HE . What is the area of quadrilateral EFGH ? (a) 15.82 (b) 29.82 (c) 40 (d) 51 (e) 70

Figure 10

43. If m is the mean of the numbers a , b, and c , which of the following must be true ? I a + b + c = 3m II. a = ( m - b) + ( m - c ) + m III. m + 1 =

a + b+ c+ 1 3

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

44. If

f ( x) = x2 + 0.25 and if f - 1 is the

inverse function of f , what is f - 1 (1) ? (A) 0.500 (B) 0.563 (C) 0.707 (D) 0.750 (E) 0.866

45. Rectangle WXYZ is inscribed in the circle shown in Figure 11. If the length of side WX is 6 and the length of side XY is 8, what is

X

Y

W

Z

the area of the shaded region ? (A) 30.54 (B) 65.10 (C) 102.80 (D) 153.06 (E) 266.16

Figure 11

46. In the right circular cylinder cone shown in Figure 12, segment AB is a diameter of the base with length 8. If the height of the cone is 9, what is the perimeter of

△APB ?

P

(A) 23.70 (B) 26 (C) 27.70

A

(D) 32.80

B

(E) 36 Figure 12

47. Which of the following has a solution, if k must be a positive integer ?

(A) (B)

1

k 3

k

=

3

k 3

=

(C) 3k = (D) k = (E) k2 =

k 3

k 3

k 3

k

+

4

k 4

+ + + +

k 4

k 4

k 4

k

+

5

k 5

+ + + +

k 5

k 5

k 5

k

48. A sequence S is of the form mn + p, where

n is the number of the term in S , and m and p are constants. If the first four terms of S are 5, 14, and 32, what is the value of the twentieth term of S ? (A) 127 (B) 143 (C) 168 (D) 176 (E) 195

〫 < x < 90〫, then

49. If 0

tan x = sin x⋅ cos x

(A) sin 2x (B) cos 2x (C)

1 sin 2x

(D)

1 cos 2x

(E)

1 tan x

50. If p + q = pr , where p, q and r are positive integers, which of the following must be true ? I. q is a multiple of p II. r is a multiple of p III. r is a multiple of q (A) None (B) I only (C) II only (D) I and II only (E) I and III only