Pra ctic e Test 6: Level 2 381

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MATHEMATICS LEVEL 2

Directions: For each of the following problems, identify the BEST answer of the
choices given. If the exact numerical value is not one of the choices, select the answer
that is closest to this value. Then fill in the corresponding oval on the answer sheet.

1. Which number is NOT in the domain 5. A church bell chimes 8 times at 8:00.
x12 Eight seconds elapse between the
of y 5 ? first chime and the last chime. How
x13
many seconds elapse between the
(A) 2
first and last chimes at 12:00?
(B) 22
(Assume each actual chime takes no
(C) 23
time at all.)
O(D) 3
(E) 0 &
(A) 12
(B) 12.5
2. What trigonometric function(s) is (C) 12.57
(are) positive in the third quadrant? (D) 13
sin x
(A) (E) 11
cos x
(B)
6. Given the figure below, find y.
sin x and cos x
(C)
& tsainn xx and
(D)
(E)
and cot x
csc x

3. If the vertex of a function f(x) is at

(1, 1), where is the vertex of the
function f(x 2 2) 1 1?
(A) (2, 3)
&
(B) (3, 2)
(C) (2, 21)
(D) (21, 0)
(E) (21, 2)
(A) 4
4. You have 7 marbles—2 black, 3 (B) 2
white, and 2 red, but otherwise not
distinguishable. How many different &(C)
(D)
3
6
ways can the 7 marbles be ordered? (E) 8
(A) 5,040
7. If
(B) 84
(C) 140 f 5 {~0,23!,~21,22!,~2,21!} and
(D) 210 g 5 {~21,2!,~22,1!,~23,3!}, then
&
(E) 280 g + f ~21! equals
(A) 21
(B) 1
&
(C)
(D)
2
22
(E) Not defined

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 382 PART IV: Four Pra ctic e Tests
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8. What is the period of y 5 3cos (2x) 1 4? 12. What are the asymptotes of the
hyperbola 4x2 2 9y2 5 36?
(A) 2p
3 (A) y 5 9x and y 5 2 9x
p 3x 23x
(B) (B) y 5 and y 5
2 2 2
(C) 4p (C) y 5 2x and y 5 22x
&
(D) p
(E) 3p &
(D) y 5
2x
3
and y 5
22x
3
9. Solve 2sin x 1 3 5 4 for x in the (E) y 5 4x and y 5 24x
interval (0, 360). (Remember, x is 13. There are six movie stars who pass
measured in degrees.) through towns A and B in a certain
&
(A) 60 1 1
state. Of these, stop at A, stop at
(B) 30 and 150 2 3
(C) 30 1
B, and stop at both A and B. How
(D) 60 and 120 6
(E) 150 many movie stars don’t stop at either
town?
10. Find the volume of the solid below
that is a cylinder with a section cut (A) 0
out of it. (B) 1
&
(C) 2
(D) 3
(E) Cannot be determined from the
2m
information given.

14. In the figure below, s is parallel to

t and v is parallel to w, find the
angle measure of angle 1.

(A) 28p cubed meters

(B) 12 cubed meters
(C) 12p cubed meters
&
(D) 24p cubed meters
56p
(E) cubed meters
3

11. If x 1 2 , 0, then |x 1 2| 5 &

(A) 65
(B) 55
(A) x12 (C) 45
(B) x22 (D) 125
(C) 2x 1 2 (E) 115
&(D)
(E)
2x 2 2
x

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 Pra ctic e Test 6: Level 2 383
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15. If 2x 1 3 is a divisor of 2x3 1 7x2 1 20. What is the exact value of tan
8x 1 c with a remainder of 0, c is
(A) 233
S 3
Arccos ?
4 D
(B) 23 23=7
& 33
(C) (A)
7
3
(D) 2 3=7
2 (B)
(E) 3 & 2 =77

16. If we restrict the domain of the f(x) 5 (C)

3
x2 1 3 to (22, 1), then the range of 3
f(x) is (D)
4
(A) (3, 7) =7
(B) All positive real numbers (E)
3
(C) (3, 4)
(D) (4, 7) 21. Given the graph below, find the
&
(E) (0, 7) amplitude.
17. Two distinct lines can intersect one
time at most and three distinct lines
can intersect three times at most.
What is the greatest number of times
that four distinct lines can intersect?
(A) 3
(B) 4
(C) 5
&
(D) 6 (A) .5
(E) 7 (B) p
p
18. If a square field is completely (C)
enclosed by x feet of fencing, then the 2
area of the field as a function of (D) 1.5
x equals &
(E) 2

(A) x2 22. Solve the equation log2 (x 2 3) 1 log2

x2 (x 2 2) 5 1 for x.
&
(B)
4 (A) 3
(C) 4x2 (B) 2 and 3
x2 (C) 1 and 4
(D)
16 &
(D)
(E)
4
1
(E) 16x2

19. If f(x) 5 x2 1 x, then find the num-

ber(s) so that f(a) 5 6.
(A) 3
(B) 22
(C) 3 and 22
&
(D) 23 and 2
(E) 23

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 384 PART IV: Four Pra ctic e Tests
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23. In a dark room where colors are not 27. Simplify the expression
distinguishable, how many towels tan(2h)cos(2h) in terms of a positive
must a person take from a basket angle h, sin h and cos h.
containing 10 blue towels, 8 black
(A) sin h
towels and 6 green towels—to be
(B) cos h
assured of having two towels that
(C) 2sin h
match in color?
&2cos h
(D)
(A) 1 (E) tan h
(B) 2
(C) 3 28. To draw the graph of the inverse of a
function f(x), one must mirror the
&
(D) 4
(E) 5 graph of f(x) about the
(A) x-axis
24. Find the next number in the se-
(B) y-axis
quence 1, 7, 19, 37, 61, ?, . . .
(C) line y 5 2x

I
(A)
(B)
(C)
85
78
91
&
(D)
(E)
line y 5 x
lines y 5 x and y 5 2x

(D) 95 29. In numbering the pages of a book,

(E) 90 beginning with page 1, 3,457 digits
are required. What is the number of
25. Given the square with two diagonals pages in the book?
in the figure below, there are a
(A) 1,003
maximum of eight total triangles
(B) 3,457
that can be formed. With two squares
(C) 1,141
with diagonals adjoined on one side,
there are a maximum of eighteen &
(D)
(E)
1,140
1,138
total triangles that can be formed.
What is the maximum number of
triangles that can be formed with
three squares with diagonals ad-
30. S DS D
12
x
y
÷ y2
x2
y
simplifies to

joined on one side? (A) y2x

(B) y1x
(C) (y 1 x)21
(D) (y 2 x)21
&
(E) (y 2 x)(y 1 x)21

31. Find c in the figure below.

(A) 26
(B) 29
I
(C)
(D)
28
30
(E) 27

26. The function f(x) 5 x2 is an example

of a(n)
(A) even function.
(B) polynomial. (A) 2.71
(C)
d
(D)
quadratic function.
All of the above &
(B)
(C)
8.00
2.83
(E) Only choices (B) and (C) (D) 5.03
(E) 3.71

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 Pra ctic e Test 6: Level 2 385
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32. Find x in the figure below. (DC i PQ) 36. The axis of symmetry for f(x) 5 x2 2
2x 1 3 is x 5
(A) 2
(B) 1
&
(C) 22
(D) 21
1
(E)
2
(A) 2 37. The figure below shows three of the
(B) 6 faces of a cube. If the six faces of the
&
(C) 4 cube are numbered consecutively,
(D) 8 what are the possible values for the
(E) 10 product of all six faces?
33. Find all the
2
values of x that satisfy
(2x 1 1)x 2 4 5 1.
(A) 62 and 0
6
(B) 22 and 1
(C)
(D)
1 and 2
2 and 22 4
& (E) None of the above 2
34. How many subsets are there from a
set of m elements?
(A) m I. 5,040
&
(B) 2m II. 20,160
(C) m2 III. 720
(D) m! (A) I only
(E) m(m 2 1) (B) II only
(C)
& III only
35. Find the volume of the prism below.
(D) I and II
(E) I and III

38. If axn 2 bx 5 0 and x is nonzero,

then b equals

&
(A) axn 2 1
2n
(B) ax
(C) an
(D) na
(E) axn 1 1

(A)
(B)
380 cubed centimeters
480 cubed centimeters
39. If f(x) 5 2sin 3x and f
find b.
SDp
2
5 b, then

I
(C)
(D)
600 cubed centimeters
720 cubed centimeters (A) 1
(E) 1,200 cubed centimeters (B) 21
(C) 2
(D) 22
I
(E) 0

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 386 PART IV: Four Pra ctic e Tests
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~cos 2x! 1 43. A rectangle has a height of 8 units
40. Simplify sin2x 1 1 and a width of 6 units. A second
2 2
rectangle with a height of 4 units
(A) sin 2x
and a width of 3 units overlaps the
d
(B) 1

SD
first rectangle as shown in the figure
x
(C) sin2 x 1 sin below. What is the difference in area
2

SD
between the two nonoverlapping
x regions of the two rectangles?
(D) sin2 x 1 cos
2
(E) 21

x2 y2
41. If the equation 2 5 1, what
42C C
type of curve is represented if C , 0?
48 [

(A) circle
(B) ellipse
&(C)
(D)
hyperbola
parabola
(E) line
12
42. What is the units’ digit of 330?
(A) 9
D
(B) 3
(A) 36 square units
(C) 7
(B) 12 square units
(D) 1
(E) 2 &(C)
(D)
24
30
square
square
units
units
(E) 18 square units

44. If x22 5 36, then x equals

(A) 66
1
(B) 6
6
&
(C) 66i
(D) 618
i
(E) 6
6

45. A pit filled with balls for kids at an

amusement park is 10 feet long and
2 feet deep at one end. If it is 4 feet
deep at the other end, find the total
distance along the bottom in feet.
(A) 10.77
(B) 10
(C) 4.47
(D) 11
&
(E) 10.20

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