Pra ctic e Test 5: Level 2 361

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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.

S D S D S D
1. If 2 2
x
3
x
5 1 2 , then 1 1
2
x
6
5 5. If =3x 5 3.89, then x 5
(A) 22 (A) 2.25
(B) 0 (B) 5.04
(C) 3.89
2
(C) (D) 6.51
3 (E) 1.73
1
(D) 6. In three angles A, B, and C of a
3
triangle, the measure of angle A
1
(E) 2 exceeds the measure of angle B by
6 15 degrees and is twice the measure
2. (2 2 5i) 1 (4 1 3i) 5 of angle C. The measures of angles
A, B, and C are:
(A) 4i
(B) 4 (A) m∠A 5 68, m∠B 5 63, and
(C) 6 2 2i m∠C 5 49
(D) 6i 2 2 (B) m∠A 5 65, m∠B 5 50, and
(E) 0 m∠C 5 65
(C) m∠A 5 78, m∠B 5 63, and
1 1 1 m∠C 5 39
3. 1 1 5 (D) m∠A 5 39, m∠B 5 78, and
x y z
m∠C 5 63
xy 1 yz 1 xz (E) m∠A 5 63, m∠B 5 39, and
(A) m∠C 5 78
xyz
xy 1 1 7. Two men start walking in opposite
(B)
xyz directions along a straight line at 4
xyz mi/hr and 5 mi/hr, respectively. What
(C) will be the distance between them in
x1y1z
3 x hours?
(D) (A) 9 mi
x1y1z
3 (B) x mi
(E) (C) 9x mi
xyz
(D) 1 mi
b3 • b2 (E) 20x mi
2 3
4. ~a ! 1 5
b24 8. The value of ~25 1 2=24! 1
(A) a5 1b ~1 2 =29! 5
(B) a6 1 b10
(A) 25
(C) a5 1 b10
(B) 23
(D) a6 1 b9
(C) 24 1 i2
(E) a6 • b5
(D) 42i
(E) 24 1 i

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9. What is the present age of John’s son 13. A cylindrical tank has a height of 12
if 2 years ago it was one-third of and a radius of 3. How many cans of
John’s age. Take John’s present age height 4 and radius 2 will be needed
to be x years. to fill the bigger tank fully?

x22 (A) 5
(A) 12 (B) 6
3
(C) 7
x
(B) 12 (D) 8
3 (E) 9
x
(C) 14. The domain of the function y 5
3
x22 x23
is
(D) ~x 2 2!~x 1 4!
3
x (A) x°3
(E) 22 (B) x ° 2 and x Þ 24
3
(C) x≥22
10. If 16.67% of a number is 12, the (D) x≤4
number is (E) 22 , x , 4

(A) 2 15. A box is formed by cutting squares of

(B) 36 side x from all four corners of the
(C) 6 rectangular plate and folding along
(D) 72 the dotted line, as shown below.
1
(E)
6

11. If f(x) 5 x2 2 5x 1 4, then f(x 1 a) 2

f(a) 5
(A) a2 2 5a 1 4
(B) x 2 1 2ax 2 5x
(C) (x2 2 5x 1 4) 2 (a2 2 5a 1 4)
(D) x2 2 5x 1 4 The volume of the box is
(E) 0
(A) (32 2 2x)(20 2 2x)x
12. Two square tiles are placed such that (B) (32 2 x)(20 2 x)2x
they touch each other all along one (C) 640 2 4x2
side. They have areas of 36 sq.in. (D) (32 2 x)(20 2 x)x
each. The length of a wire bounding (E) (32)(20)(2x)
the two tiles will be
16. The graph of the function y 5 x2 1 x
(A) 36 in. 2 12 cuts the x-axis at the points
(B) 18 in.
(C) 72 in. (A) (3, 0) and (24, 0)
(D) 48 in. (B) (0, 0) and (3, 0)
(E) 24 in. (C) (23, 0) and (4, 0)
(D) (0, 0) and (24, 0)
(E) (0, 0) and (12, 0)

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17. By how many degrees does the minute 20. The graph of y 5 f(x) is shown below.
hand of a clock turn in 20 minutes? The graph of y 5 ?f(x)? would be
(A) 90°
(B) 150°
(C) 120°
(D) 180°
(E) 100°

18. In the figure below, the coordinates

of point P are

(A)

(B)

(A) (3.46, 3.46)

(B) (3.46, 2)
(C) (2, 2)
(C)
(D) (2, 3.46)
(E) (3, 1.73)

19. In triangle OAB, OA 5 AB, and the

height of the triangle is 8.

(D)

(E)

The slope of segment OA is

(A) 0.375
(B) 0.5
(C) 2.67
(D) 1
(E) Cannot be determined by the
given information.

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 364 PART IV: Four Pra ctic e Tests
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21. The equation of the line passing 23. What is the circumference of a circle
through the point (0, 22) and passing through all the vertices of
perpendicular to the line 3x 1 5y 5 the right triangle ABC in the figure
15 is below?
(A) 3x 2 5y 5 10
(B) 3x 1 5y 5 210
(C) 5x 1 3y 5 26
(D) 5x 2 3y 5 26
(E) 5x 2 3y 5 6

22. In the figure below, the cube has

sides of length 3 each.

(A) 78.55
(B) 31.42
(C) 10
(D) 100
(E) 24

24. If sin2u 2 cos2u 5 0.5, then sin4u 2

cos4u 5
(A) 0.5
The distance between points A and (B) 1.5
B is (C) 0.25

(A) 3=3
(D) =0.5
(E) 0
(B) 3
(C) 3 1 =3
(D) 9
(E) =3

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25. A man throws a stone up an incline 27. In the parallelogram below, if m∠A 5
of gradient 1 from the base of the 120°, then the measures of angles
incline. The stone follows a path B, C, and D are
given by the equation y2 5 4x. What
are the coordinates of the point at
which the stone hits the incline?
Assume the man to be at the origin
of the coordinate system.

(A) 60°, 120°, and 60°

(B) 120°, 60°, and 60°
(C) 120°, 120°, and 240°
(D) 60°, 60°, and 120°
(E) 180°, 120°, and 180°

28. Consider a point P(2, 3, 4). If we are

allowed to travel only parallel to the
three coordinate axes, what is the
distance we have to cover to get to
point P from the origin?
(A) (4, 0)
(B) (4, 4) (A) =29
(C) (0, 4) (B) 9
(D) (3, 3) (C) 7
(E) (5, 5) (D) 5
(E) 3
26. A triangle is cut into three regions of
equal height by two lines that are 29. What is the area of the shaded
parallel to the base. If the height of region in the figure below?
the triangle is h and the other
dimensions are as shown below, what
is the area of the middle region?

(A) 12.57
(B) 8
(C) 4.57
(A) 0.5h (D) 7.89
(B) 3h (E) 6.32
(C) 18h
(D) 1.5h
(E) 9h

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 366 PART IV: Four Pra ctic e Tests
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30. If an angle u measured counter- 34. Which of the following equations
clockwise from the positive x-axis represents the curve in the figure
terminates in the third quadrant, below?
which of the following is true?
(A) sinu is positive, and cosu is
negative.
(B) sinu is positive, and cosu is 1
(0, )
positive. 2
(C) sinu is negative, and cosu is
positive. π 2π
(D) sinu is negative, and cosu is 3 3
−1
negative. (0, )
2
(E) None of the above.

31. If cscu 5 1.414, then cosu 5 (A) y 5 sinx

x
(A) 0.50 (B) y 5 2sin
3
(B) 0.87
(C) y 5 0.5sin3x
(C) 0.71
(D) 0.33 x
(D) y 5 0.5sin
(E) 0.68 3
(E) y 5 20.5sin3x
32. In the figure below, if cosu 5 0.8 and
the length of segment BC 5 8, what =1 2 sin2u is the same as
is the perimeter of the triangle? 35.
sinu
(A) cosu
(B) secu
(C) tanu
(D) cscu
(E) cotu

36. In triangle ABC below, AB 5 10 and

BC 5 8, while m∠A 5 40°. The
measure of ∠ACB is

(A) 26
(B) 16
(C) 24
(D) 30
(E) 32

33. When the sun is 20° above the

horizon, how long is the shadow that
is cast by a tree 150 feet tall? (A) 50°
(A) 374 feet (B) 53°
(B) 391 feet (C) 60°
(C) 412 feet (D) 48°
(D) 405 feet (E) 65°
(E) 402 feet

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37. If triangles ABC and CDE are 40. If (3.5)x 5 (4.2)y, then 5
similar and other dimensions are as y
(A) 1.15
shown below, what is the length of (B) 1.25
segment AE? (C) 1.35
(D) 1.45
(E) 1.55
p p
41. If arcsin(sin x) 5 , and 0 ≤ x ≤ ,
6 2
then x could be
(A) 0
1
(B)
2
p
(C)
6
p
(D)
3
p
(E)
2

42. The probability that the roll of an

unbiased cubical die produces a 4 or
(A) 18.03 a 6 is
(B) 17.05
(C) 16.86 1
(D) 19.85 (A)
6
(E) 18.28 1
(B)
38. The resale value of a car t years after 3
purchase is given by the function 4
S(t) 5 S0e20.2t, where S0 is the initial (C)
6
price of the car. If the car is pur- 6
chased at $20,000, its resale value (D)
6
after five years will be
10
(A) $6,000 (E)
6
(B) $6,750
(C) $7,000
(D) $7,125
(E) $7,358

39. The mean of fifteen integers is 102.

On adding another integer, the mean
reduces to 100. What is the new
integer added?
(A) 90
(B) 85
(C) 70
(D) 65
(E) 60

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43. In the figure below, the coordinates 47. If the population of a city is increas-
of the center, P, of the circle are ing by 3 percent every year, and the
current population is 300,000, what
was the population five years ago?
(A) 258,783
(B) 250,000
(C) 265,956
(D) 311,569
(E) 303,214

48. If a, b, and x are nonzero real

6x3a5b2
numbers, and if x4a3b5 5 ,
b24
then x 5
(A) (3, 2) (A) 6
(B) (3, 8) (B) 6a8b11
(C) (3, 6) (C) 6a2b
(D) (3, 4) (D) 6ab
(E) (3, 5) (E) a 2b
44. The value of ln e3 is 49. The next three terms in the sequence
(A) 2.718 of the geometric progression 236, 12,
(B) 3.123 4
24, , . . . are
(C) 3 3
(D) 2.93 4 4 4
(E) 3.287 (A) 2 , , 2
9 27 81
45. The seventh term of an arithmetic 4 4 4
progression is 41 and the thirteenth (B) , 2 ,
9 27 81
term is 77. What is the twentieth 1 1 1
term of the progression? (C) 2 , , 2
3 9 27
(A) 117 1 1 1
(B) 118 (D) , 2 ,
3 9 27
(C) 120
1 1
(D) 121 (E) , 0, 2
(E) 119 3 3

46. How many possible five-digit zip 50. What is the domain of the function
codes can be formed from the set of defined by
digits {0, 1, 2 . . . 9} such that no
code begins with a zero?
f~x! 5 H
x2, x,3
2x 1 1, x ≥ 3
(A) 100,000 (A) 0,x,3
(B) 90,000 (B) x,3
(C) 256 (C) x≥3
(D) 128 (D) x≤0
(E) 1,024 (E) All real numbers.

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