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PRACTICE TEST 2

235

PRACTICE TEST 2
MATH LEVEL 2
Tear out this answer sheet and use it to complete the practice test. Determine
the BEST answer for each question. Then, fill in the appropriate oval using
a No. 2 pencil.

1.

21.

41.

2.

22.

42.

3.

23.

43.

4.

24.

44.

5.

25.

45.

6.

26.

46.

7.

27.

47.

8.

28.

48.

9.

29.

49.

10.

30.

50.

11.

31.

12.

32.

13.

33.

14.

34.

15.

35.

16.

36.

17.

37.

18.

38.

19.

39.

20.

40.

PRACTICE TEST 2

237

PRACTICE TEST 2
Time: 60 minutes
Directions: Select the BEST answer for each of the 50 multiple-choice questions. If the exact solution is not one of the
five choices, select the answer that is the best approximation. Then, fill in the appropriate oval on the answer sheet.
Notes:

1. A calculator will be needed to answer some of the questions on the test.

Scientific, programmable, and graphing calculators are permitted. It is up
to you to determine when and when not to use your calculator.
2. Angles on the Level 2 test are measured in degrees and radians. You need
to decide whether your calculator should be set to degree mode or radian
mode for a particular question.
3. Figures are drawn as accurately as possible and are intended to help solve
some of the test problems. If a figure is not drawn to scale, this will be stated in the problem. All figures lie in a plane unless the problem indicates
otherwise.
4. Unless otherwise stated, the domain of a function f is assumed to be the set
of real numbers x for which the value of the function, f (x), is a real number.
5. Reference information that may be useful in answering some of the test
questions can be found below.

Reference Information
Right circular cone with radius r and height h:

Volume =

1 2
r h
3

Right circular cone with circumference of base c

and slant height :

Lateral Area =

Volume =

1
c
2

4 3
r
3

Surface Area = 4r2

Pyramid with base area B and height h:

Volume =

1
Bh
3

238

PRACTICE TEST 2 QUESTIONS

1. If x5 = 84, x =
(A) 0.13
(B) 5.28
(C) 13.45
(D) 819.20
(E) 6,208.37

(A) 0.07
(B) 2,981
(C) 1.13
(D) 1.27
(E) 7.89
m
1
n
= , then
=
3m n
5
m
(A) 2
1
(B)
2
1
(C)
2
(D) 2
3
(E)
5

3. If

4. For all x 0,

1
2
3
+
+
=
x
x2
x3

6
x3
6
(B) 6
x
(A)

( x 2 + x + 1)
x3
2
( x + 2 x + 3)
(D)
x3
2
( x + 5)
(E)
x3
(C)

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

1
6
6i
35
6+i
36
6i
37
6i
36

PRACTICE TEST 2

239

(A)
(B)
(C)
(D)
(E)
7.

USE THIS SPACE AS SCRATCH PAPER

(x 2)(x + 2)2
(x 2)(x + 2)(x + 1)
(x 2)2(x + 2)
(x 2)3
(x 2)(x2 + 2)
50 x 4 y 2 =

20 x 2 y 7

(A) 20 3 (50 3 )x6y9

1

(B) 70 3 x2y3
8

(C) 10x 3 y
(D) 10x2y3

14
3

14

(E) 1,000x 3 y 3
x
x
(A)
(B)
(C)
(D)
(E)

8. If

+2
0 , then which of the following describes x?
5
x 2
2 x < 5
x 2 or x > 5
x>5
x 2 or x 5

9. Which of the following expressions represents the

statement N varies jointly with the square of x and
with y?
(A) N = kx2y
k
(B) N =
y x
(C) N = ky x
(D) N = kx2y2
k
(E) N = 2
x y
10. What is the vertex of the parabola given by f (x) =
x2 6x + 5?
(A) (3, 4)
(B) (3, 4)
(C) (3, 4)
(D) (3, 3)
(E) (4, 4)

240

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

0.01
0.63
0.60
0.75
0.80

12. What are the zeroes of f (x) = 8x3 2x2 3x?

Figure 1

1 3
(A) ,
2 4
3 1
(B) ,
4 2
1 1 3
(C) , ,
2 2 4
3 1
(D) , 0,
2
4
3
1
(E) , 0,
2 4
2
and,
3
independently, the probability that it will also snow
1
the day after tomorrow is . What is the probability
5
that it will snow tomorrow but not the day after
tomorrow?
2
(A)
15
2
(B)
5
3
(C)
4
8
(D)
15
22
(E)
15

14. An operation is defined on any three real numbers by

a b c = a(c b). If 2 1 x = 10, then x =
(A) 6
(B) 4
(C) 5
(D) 6
(E) 4

GO ON TO THE NEXT PAGE

PRACTICE TEST 2

241

15. If ( x 1) 3 = 25 , then x =
(A)
(B)
(C)
(D)
(E)

USE THIS SPACE AS SCRATCH PAPER

8.5
15,625
124
125
126

16. If cos 2 =

3
1
, then
=
2
4
cos sin 2

(A) 1
3
(B)
4
4
(C)
3
(D) 4
(E) 1
17. What does the angle
(A)
(B)
(C)
(D)
(E)

5
equal in degree measure?
12

75
15
150
37.5
52.5

4x2 9
, what value does the function
2x + 3
3
approach as x approaches ?
2

18. If f ( x ) =

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

0.02
0
4.33
6
9

19. If i is a zero of the polynomial p(x), then which of the

following must be a factor of p(x)?
(A) i
(B) x2
(C) x2 + 1
(D) x2 1
(E) x2 2ix + 1

242

PART III / EIGHT PRACTICE TESTS

20. For all x 2, f (x) = (x 2)(2 x)1. Which of the following must be a true statement?

f (1) = f (1)
f (4) = f (0)
1
III. f = f (2)
2

I.
II.

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

I only
III only
I and II only
II and III only
I, II, and III

21. If f (x) = 5x 1 and g( f (3)) = 18, then g(x) could be

which of the following?
(A) x + 2
(B) x + 2
(C) 2x 12
x
+ 14
(D)
4
(E) x + 4
22. Which of the following is a y-intercept of the hypery2
x2

= 1?
bola
9
16
(A) (0, 3)
(B) (0, 4)
(C) (3, 0)
(D) (0, 81)
(E) (0, 9)
z

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

3.46
4.47
6
6.16
11

E (0,2,5)

D (3,0,0)
x
Figure 2

PRACTICE TEST 2

24. A car is purchased for \$24,500. If it decreases in

value at a rate of 7% per year, how much will it be
worth in 5 years?
(A)
(B)
(C)
(D)
(E)

243

\$15,851
\$15,925
\$17,044
\$22,785
\$32,787

25. f (x) = 4x for all real values of x. If p > 1 and q > 1,

then f 1(p) f 1(q) =
(A)
(B)
(C)
(D)
(E)

4p+q
log4 p log4 q
log4 pq
log4 p + log4 q
logp 4 logq 4

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

0.17
0.50
1.05
1.50
2

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

0.66
0.75
0.80
0.88
41.4

28. Five-sixths of the students in class are passing with

a grade of C or better. Three-fourths of the students
in the same class are passing with a grade of B or
better. What fraction of the class is not passing with
a grade of B or better but is passing with a grade of
C or better?
5
(A)
8
1
(B)
12
1
(C)
6
1
(D)
4
1
(E)
15

244

44 = 0?
(A)
(B)
(C)
(D)
(E)

2.2
3
6.6
9
44

30. Which of the following equations has the graph

shown in Figure 3?
(A) y = cos 2x
(B) y = 2cos x
(C) y = 2cos 2x
x
(D) y = 2 cos
2
x
(E) y = cos
2

y
4
2

10

15 5()

2
4

Figure 3

x >3
x2

?
f (x) = 2
11
3
x
x

3
(A)
(B)
(C)
(D)
(E)

y0
3 y 3
y3
y9

32. If vector v = (3, 7) and vector u = (2, 1), then vector u v =

(A) (5, 8)
(B) (1, 6)
(C) (8, 5)
(D) (6, 7)
(E) (5, 8)
33. A cube has edges of length 3. If P and Q are points
on its surface, what is the maximum straight-line distance from P to Q?
(A) 3 2
(B) 3 3
(C) 6
(D) 3 5
(E) 9
34. If a is any positive integer, then which of the following is not a true statement?
(A) 2a + 1 is always an odd integer.
(B)

a is always an imaginary number.

(C)
(D) a3 is always an odd integer.
1
(E) The product of a and
always equals 1.
a

PRACTICE TEST 2

n
1
1
=
+
, then n =
x 2 36
x6 x+6
(A) x
(B) 2x
(C) 2(x + 6)
(D) 2(x 6)
(E) 2

35. If

245

36. If f (x) = x3 and h(x) is obtained by shifting f (x) down

4 units and right 2 units, then h(x) =
(A)
(B)
(C)
(D)
(E)

(x 2)3 + 4
(x + 2)3 4
(x 2)3 4
(x 4)3 2
4 (x 2)3

37. If the lines y1 = (n + 2)x + 10 and y2 = (n 4)x + 2

are perpendicular, then n could equal which of the
following?
(A)
(B)
(C)
(D)
(E)

3.45
3.83
1
0.5
6

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

intersects the x-axis at exactly one point.

intersects the x-axis at exactly two points.
intersects the x-axis at exactly three points.
intersects the x-axis at exactly four points.
does not intersect the x-axis.

39. Which of the following is equivalent to the equation

x2 + 5x + y2 1 = 0 in polar form?
(A) r2 + 5r cos 1 = 0
(B) r = 5r cos + 1
(C) r2 = 5r cos
(D) r2 + 5r sin 1 = 0
(E) r2 = 5r sin
40. If A is a 2 3 matrix, and B is a 3 4 matrix, then the
product of A times 3B is a matrix of which of the following dimensions?
(A) 6 4
(B) 2 3
(C) 2 4
(D) 3 3
(E) 2 12
41. (sec + tan )(sec tan ) =
(A) sec2
(B) 1
(C) tan2 sec2
(D) 1
(E) 2sec2 1

246

42. The linear regression model C = 13.2m + 20.5 relates

the calories burned using a new exercise machine (C)
to the number of minutes a person uses the machine
model must be true?
I.
When a person spends 22 minutes using the
machine, the predicted number of calories burned
is approximately 311.
II. There is relatively no correlation between C
and m.
III. A person burns approximately 13.2 calories each
minute he or she uses the machine.
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III

43. If (x, y) is a point on the graph of f (x), then which of

the following is a point on the graph of f 1(x)?
(A)
(B)
(C)
(D)
(E)

(x, y)
(x, y)
(y, x)
(x, y)
(y, x)

44. The graph of y = 2x + 7 can be expressed as a set of

parametric equations. If x = 1 t, and y = f (t), then
what does f (t) equal?
(A) 2t 7
(B) 2t + 5
(C) 2t + 9
1
(D) t 7
2
(E) 2t + 5
45. If x0 = 5 and x n +1 = x n x n + 4 , then x4 =
(A) 23.4
(B) 65.4
(C) 544.6
(D) 12,709.8
(E) 12,756.4
1

=
343
(A) 3
(B) 18
1
(C)
216
1
(D)
1, 296
(E) 216

PRACTICE TEST 2

247

47. How long is the base of an isosceles triangle if the

other two sides measure 20 cm and each base angle
measures 28?
(A)
(B)
(C)
(D)
(E)

12.7
28.3
30.6
35.3
88.6

48. A committee of 4 people is to be selected from a group

of 8 women and 4 men. Assuming the selection is
made randomly, what is the probability that the committee consists of 2 women and 2 men?
(A)
(B)
(C)
(D)
(E)

56
165
6
495
28
495
28
165
34
495

(A) 2 sin2
(B) 4 sin cos
1
tan
(C)
2
(D) 2 sin cos
1
(E)

b
Figure 4
y

50. If f is a function whose graph is the line segment

shown in Figure 5, then f 1(6.2) =
(A)
(B)
(C)
(D)
(E)

(2,14)

0.44
0.76
0.89
1.11
1.77

Figure 5

S T O P
IF YOU FINISH BEFORE TIME IS CALLED, YOU MAY CHECK YOUR WORK ON THIS TEST ONLY.
DO NOT TURN TO ANY OTHER TEST IN THIS BOOK.
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