Unformatted text preview: MATHEMATICS LEVEL 2 TEST
REFERENCE INFORMATION THE FOLLOWING INFORMATION IS FOR YOUR REFERENCE IN ANSWERING SOME
OF THE QUESTTIONS IN THIS TEST.
Volume of a right circular cone with radius r and height h: V= 12
πr h
3 Lateral Area of a right circular cone with circumference of the base c and slant
height l: S= 1
cl
2 Volume of a sphere with radius r: V= 42
πr
3 Surface Area of a sphere with radius r: S= 4π r 2 Volume of a pyramid with base area B and height h: V= 1
Bh
3 DO NOT DETACH FROM BOOK. studysatonline.net
Level 2 Test 2 1. If 2 − 2x = 6− 6
2x , then 1 1
2x = 1 (A) − 3 (B) 1 (C) 0 (D) 2 2 5 (E) 3 ⎛1 1⎞
+ ⎟=
⎝ y z⎠ 2. x ⎜ (A) (B) (C) (D) (E) x
yz
x
y−z
2x
y−z
xy + xz
yz
1
xy − xz Unauthorized copying or reuse of any part of this page is illegal.
2 studysatonline.net
Level 2 Test
3. Figure 1 shows one cycle of the graph of the
1
function y = sin 2 x for 0 ≤ x ≤ 2π . If the minimum
2
value of the function occurs at point P, then the
coordinates of P are ⎛ 3π π ⎞
,− ⎟
2⎠
⎝4 (A) ⎜ ⎛ 3π 1 ⎞
,− ⎟
2⎠
⎝4 Figure 1 (B) ⎜ ⎛ 3π
⎞
, −π ⎟
2
⎝
⎠ (C) ⎜ ⎛ 3π
⎞
, −1 ⎟
⎝2
⎠ (D) ⎜
(E) (π , 0 ) 4. If P and Q are different points in a plane, the set of all
points (x, y) the sum of whose distances from those
two points P and Q is constant is
(A) The region of two plane on one side of line
(B) The exterior of a square
(C) The region of the plane bounded by a parabola
(D) A circle
(E) An ellipse Unauthorized copying or reuse of any part of this page is illegal.
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Level 2 Test
5. If 4 x =5.2, then x = (A) 0.52
(B) 1.95
(C) 3.97
(D) 6.76
(E) 12.46 6. In Figure 2, r cos θ =
(A) − x
(B) − y
(C) r
Figure 2 (D) x − y
(E) r + x 7. If f ( x ) = x − 2 x and g ( x) =
2 x2 + 1
x2 − 3 , then g ( f (6)) = (A) 0.2
(B) 1.19
(C) 1.25
(D) 3.63
(E) 4.15 Unauthorized copying or reuse of any part of this page is illegal.
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Level 2 Test
8. If a, b, and c are nonzero real numbers and if a 9b 7 c 4 = (A) a −3 , then c =
2 1 (B) 9b3c 2 1 8 4 (C) 4a
(D)
(E) 2 9
6 a b4 3
3 a b2 9. In the triangle in Figure 3, if OA = AB , what is the
slope of segment AB ?
(A) 2 (B) 2
2 (C) − 2 Figure 3 2 (D) − 2
(E) It cannot be determined from the information
given. 10. Where defined, sec(5θ )icos(5θ ) =
(A) 1
(B) 0
(C) –1
(D) 2 csc(4θ )
(E) 2 sec(4θ ) Unauthorized copying or reuse of any part of this page is illegal.
5 studysatonline.net
Level 2 Test
11. The graph of y = f ( x) is shown in Figure 4. Which of
the following could be the graph of y = f ( x) ? (A) (B) Figure 4 (C) (D) (E) Unauthorized copying or reuse of any part of this page is illegal.
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Level 2 Test
12. If 5 and –3 are both zeros of the polynomial P ( x ) ,
then a factor of P ( x ) is
(A) x 2 − 15
(B) x 2 + 2 x − 15
(C) x 2 + 15
(D) x 2 − 2 x − 15
(E) x 2 + 2 x + 15 13. A surveyor is standing 100 feet from the base of a
large tree. The surveyor measures the angle of
elevation to the top of the tree as 71.5 . How tall is
the tree?
(A) 138.15
(B) 197.52
(C) 298.87
(D) 300.14
(E) 312.38 14. If f ( x) = 5 x − 2 and f ( g (2)) = 13 , which of the
following could be g ( x)?
(A) 7 x − 11
(B) 11x + 7
(C) 11x − 7
(D) 11x + 7
(E) 7 x + 11 Unauthorized copying or reuse of any part of this page is illegal.
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Level 2 Test
15. Figure 5 shows a cube with edge of length 5
centimeters. If points A and C are midpoints of the
edges of the cube, What is the perimeter of region
ABCD?
(A) 6.71 cm
(B) 13.42 cm
(C) 22.36 cm
(D) 31.25 cm
(A) 45.00 cm 16. An equation of line Figure 5 in Figure 6 is (A) y = x + 2
(B) y = 2x
(C) y = 2x – 2
(D) y = 2x + 2
(E) y = x – 2
Figure 6 17. The mean score of 11 students in a certain geometry
class was 69. When a new student enrolled, the
mean increased to 71. What was the score of the
new student?
(A) 91
(B) 92
(C) 93
(D) 101
(E) 110 Unauthorized copying or reuse of any part of this page is illegal.
8 studysatonline.net
Level 2 Test
18. If 0 < x < 2π and sin x = 0.866 , what is the value of ⎛ x⎞
cot ⎜ ⎟ ?
⎝2⎠
(A) 1.732
(B) –1.732
(C) –0.577
(D) 1
(E) 1 19. Recently 3,164 students at Woodson High School
and 2,464 students at Fairfax High School took a
math exam. A total of 4,221 students passed. If the
same percentage of the students in each school
passed, how many of the students at Woodson
passed?
(A) 3164
(B) 2373
(C) 5628
(D) 31643
(E) 24641 20. If f : ( x, y ) → ( x − 3 y, y ) for every pair ( x, y ) in the
plane, for what points ( x, y ) is it true that ( x, y ) → ( x, y ) ?
(A) The set of points ( x, y ) such that y = 0
(B) The set of points ( x, y ) such that x = 1
(C) The set of points ( x, y ) such that x = 0
(D) (1, −1) only
(E) (0,0) only Unauthorized copying or reuse of any part of this page is illegal.
9 studysatonline.net
Level 2 Test
21. What number must be added to each of the three
numbers –1, 1, and 5 so that the resulting three
numbers form a geometric sequence?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5 2
22. If f ( x) = ax − bx − c for all real numbers x and if
f (0) = 1 and f (1) = 1 , then a – b = (A) –1
(B) 0
(C) 1
(D) 2
(E) 3 23. If θ is the degree of the largest angle of a triangle
that has sides of 10, 8, and 8, then what is sin θ ?
(A) 0.78
(B) 0.84
(C) 0.98
(D) 1
(E) 1.05 Unauthorized copying or reuse of any part of this page is illegal.
10 studysatonline.net
Level 2 Test 24. What is the domain of f ( x) = − x + 16
5 2 (A) x > 0
(B) x > 4
(C) −4 ≤ x ≤ 4
(D) x < 14
(E) All real numbers 25. If sin x = cot x , which of the following is a possible
radian value of x ?
(A) –1.00
(B) –0.71
(C) 0.71
(D) 0.81
(E) 0.91 26. Figure 7 shows a portion of the graph of y = 5 .
What is the sum of the areas of the three inscribed
rectangles shown?
x (A) 4682
(B) 3,380
(C) 2,912
(D) 1302
(E) 625
Figure 7 Unauthorized copying or reuse of any part of this page is illegal.
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Level 2 Test
−0.116 t 27. Suppose Q(t ) = cie
is the equation for the
amount that exists at any time t after a certain
radioactive element decays, where c equals the initial
amount and t is the elapsed time in years. How long
will it take for the element decays to a level of 30%
of the original amount?
(A) 1
(B) 5
(C) 10
(D) 20
(E) 25 28. Which of the following lines are asymptotes of the
graph of f ( x) = x2 − x
?
x +1 I. x = − 1
II. y = x − 2
III. y = −2
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III 29. If f ( x − 2) = x + 3 for all real numbers x, then f ( x) =
(A) x − 1
(B) x + 1
(C) x + 5
(D) x − 5
(E) 2 x − 1 Unauthorized copying or reuse of any part of this page is illegal.
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Level 2 Test
30. Which of the following can be the coordinates of the
center of a circle tangent to the xaxis and yaxis in
the third quadrant?
(A) (2, 0)
(B) (2, 0)
(C) (0, 2)
(D) (2, 2)
(E) (2, 2) 31. What is the range of the function defined by ⎧2 x , x > 3
⎪
h( x ) = ⎨ 1
?
⎪x5 , x ≤ 3
⎩
1 (A) y > 35
(B) y ≥ 3
1 (C) 3 5 < y < 3
(D) y ≤ 3
1 (E) y > 8 and y ≤ 35 2
32. If 5 x − 6 y + 3 = 0 and 3 y − 2 x = 0 for x ≥ 0 , then 8 x = (A) 12.06
(B) 13.19
(C) 13.54
(D) 14.72
(E) 14.91 Unauthorized copying or reuse of any part of this page is illegal.
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Level 2 Test
−1
33. If f ( x) = ln x for x > 0 , then f ( x) = (A) e x
(B) x 2
(C) x
e (D) e
x (E) ln x 34. If x1 = 1 and xn +1 =3 5 + xn , then x3 = (A) 1.68
(B) 1.72
(C) 1.89
(D) 2.13
(E) 2.65 35. Figure 8 shows a triangle inscribed in a semicircle.
What is the area of the triangle in terms of θ ?
(A) tan(2θ )
(B) 2π
(C) 2 sin θ cos θ
(D) 4 cos θ Figure 8 (E) 4 sin(2θ ) Unauthorized copying or reuse of any part of this page is illegal.
14 studysatonline.net
Level 2 Test
36. A random number generator on a machine selects
five integers from 1 to 20. What is the probability
that all five numbers are less than or equal to 10?
(A) 0.03125
(B) 0.0613
(C) 0.125
(D) 0.167
(E) 0.24 37. If the magnitudes of vectors u and v are 7 and 15,
respectively, then the magnitude of vector (u − v)
could NOT be
(A) 7
(B) 8
(C) 11
(D) 14
(E) 18 a
b
38. If (8.02) = (4.12) , what is the value of a
?
b (A) –0.34
(B) 0.34
(C) 0.48
(D) 0.68
(E) 1.3 Unauthorized copying or reuse of any part of this page is illegal.
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Level 2 Test 39. If arcsin(sin θ ) = − π
2 ≤θ ≤ π
2 , then θ= 3 π (B) − 2 (C) 0 (E) 3 and − π (A) − (D) π π
3 π 2 40. The 4th term of an arithmetic sequence is 20, and
the 13th term is 65. What is the 15th term?
(A) 50
(B) 75
(C) 100
(D) 125
(E) 150 41. Which of the following is the equation of the line
perpendicular to y = 3
x + 4 that passes through the
5 point (3, 13)?
(A) y = − 5
x + 12
3 (B) y = − 5
x −8
3 (C) y = − 3
x+8
5 (D) y = 3
4
x − 14
5
5 (E) y = 3
4
x + 14
5
5 Unauthorized copying or reuse of any part of this page is illegal.
16 studysatonline.net
Level 2 Test
42. For all θ , sin( −2θ ) + cos(θ ) + cos(−θ ) =
(A) 0
(B) 1
(C) 2 sin θ + 2 cos θ
(D) 2 cos θ (1 − sin θ )
(E) 2(sin θ − cos θ ) ⎡( n + 1)!⎤
⎣
⎦=
43.
2
⎡( n − 1)!⎤
⎣
⎦
2 (A) n
(B) n+1
(C) n(n+1)
2
(D) n (n + 1) (E) [n(n + 1)] 2 44. The radius of the base of a right circular cone is 10
and the radius of a parallel cross section is 6. If the
distance between the base and the cross section is
12, what is the height of the cone?
(A) 10
(B) 12
(C) 18
(D) 24
(E) 30 Unauthorized copying or reuse of any part of this page is illegal.
17 studysatonline.net
Level 2 Test 45. For the given statement, “If x = __ , then
a rational number” can be true when x is x is not (A) 0
(B) 1
(C) 2
(D) 4
(E) 9 46. If f ( x) = −( x + 1) horizontally shifts 3 units left and
vertically 2 units up and the resulting graph is g ( x) ,
2 then what is g (−2) ?
(A) 3
(B) –2
(C) –1
(D) 0
(E) 1 47. In how many distinguishable ways can you write the
letters in INTERNET?
(A) 5,040
(B) 7,620
(C) 10,080
(D) 20,160
(E) 40,320 Unauthorized copying or reuse of any part of this page is illegal.
18 studysatonline.net
Level 2 Test
48. Which of the following sets have an element of 0 in
that set?
I.
II.
III. The set of positive rational numbers
The set of positive even integers
The set of natural numbers (A) None
(B) I only
(C) II only
(D) III only
(E) I, II, and III 49. What is the length of the major axis of the ellipse
2
2
whose equation is 90( x − 1) + 60( y + 3) = 1500 ?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 10 50. Under which of the following conditions is ab
positive?
a −b
(A) 0 > b > a
(B) a > 0 > b
(C) a > b > 0
(D) b > a > 0
(E) None of the above Unauthorized copying or reuse of any part of this page is illegal.
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This note was uploaded on 02/27/2010 for the course MATH 20092173 taught by Professor Dr.wrong during the Spring '10 term at École Normale Supérieure.
 Spring '10
 dr.wrong
 Math, Cone

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