SAT Subject Test Practice Test II: Math Level II Time—60 ...
Name
Date
Class
SAT Subject Test Practice Test II: Math Level II
Time--60 minutes, 50 Questions
All questions in the Math Level 1 and Math Level 2 Tests are multiple-choice questions in which you are asked to choose the BEST response from the five choices offered. The directions for the tests are below:
Directions: For each of the following problems, decide which is the BEST of the choices given. If the exact numerical value is not one of the choices, select the choice that best approximates this value. Then fill in the corresponding circle on the answer sheet.
Notes: 1. A scientific or graphing calculator will be necessary for answering some (but not all) of the questions in this test. For each question you will have to decide whether or not you should use a calculator. 2. Level 1: The only angle measure used on this test is degree measure. Make sure your calculator is in the degree mode. Level 2: For some questions in this test you may have to decide whether your calculator should be in the radian mode or the degree mode. 3. Figures that accompany problems in this test are intended to provide information useful in solving the problems. They are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale. All figures lie in a plane unless otherwise indicated. 4. Unless otherwise specified, the domain of any function f is assumed to be the set of all real numbers x for which f (x) is a real number. The range of f is assumed to be the set of all real numbers f (x), where x is in the domain of f. 5. Reference information that may be useful in answering the questions in this test can be found on the page preceding Question 1.
Reference Information. The following information is for your reference in answering some of the questions in this test. Volume of a right circular cone with radius r and height h: V _13pr 2h Volume of a sphere with radius r : V _43pr 3 Surface Area of a sphere with radius r : S 4pr 2 Volume of a pyramid with base area B and height h : V _13Bh
1. What is an equation of the circle whose diameter has endpoints (1, 2) and (5, 6)? (A) (x 3) 2 (y 2) 2 20 (B) (x 3) 2 (y 2) 2 20 (C) (x 3) 2 (y 2) 2 20 (D) (x 3) 2 (y 2) 2 80 (E) (x 3) 2 (y 2) 2 80
USE THIS SPACE FOR SCRATCH WORK.
Copyright ? by Holt McDougal. All rights reserved.
99
Holt McDougal College Entrance Exam
Name
Date
SAT Subject Test Practice Test II: Math Level II continued
Class
2. A frequency distribution for the ages of 50 men in a certain association is given. What is the approximate mean age of the men?
(A) 35.7
(B) 35.9
(C) 36.3
(D) 36.5
(E) 37.1
3. What is the period of f (x) sin(3x)cos(4x)?
(A)
_p_ 3
(B)
_p _ 2
(C)
_2_p_ 3
(D) p
(E) 2p
USE THIS SPACE FOR SCRATCH WORK.
Age Frequency
32
4
35
20
36
11
37
5
38
7
40
3
4. A pyramid and a box share a base and have the same volume. What is the ratio of the height of the pyramid to the height of the box?
(A) 1 : 3
(B) 1 : 3
(C) 1 : 1
(D) 2 : 1
(E) 3 : 1
5. If a loan is compounded continuously at a rate of 5% per year, approximately how many years will it take for the loan amount to triple?
(A) 20
(B) 21
(C) 22
(D) 24
(E) 25
Copyright ? by Holt McDougal. All rights reserved.
100
Holt McDougal College Entrance Exam
Name
Date
SAT Subject Test Practice Test II: Math Level II continued
Class
6. The graph of the polar function r 2u is a(n)
(A) spiral
(B) circle
(C) ellipse
(D) cardioid
(E) lemniscate 7. The area of circle x 2 y 2 6x 4 0 is
(A) 4p
(B) 5p
(C) 6p
(D) 8p
(E) 12p
8.
Evaluate lim x r 2
_xx____22__ .
(A) Does not exist
(B) 2
(C) 1
(D) 1
(E) 2
9. Given the piecewise function
{ } 3x, if x 0
f (x) tan x, if 0 x p , where x is in
x 1, if x p
radians, what are the values of x for which f (x) is discontinuous?
(A)
0
and
_p_ 2
(B) 0, _p2_, and p
(C) 0 and p
(D)
_p_ 2
and
p
(E)
_p2_,
p,
and
_3_p_ 2
USE THIS SPACE FOR SCRATCH WORK.
Copyright ? by Holt McDougal. All rights reserved.
101
Holt McDougal College Entrance Exam
Name
Date
SAT Subject Test Practice Test II: Math Level II continued
Class
10. If (3, y) is a point on the graph of the inverse of f (x) 2x 5 5x 3 6x 10,
then y ?
(A) 626
(B) 3
(C) 1
(D) 3
(E) 626
11. A triangle has sides of length 2, 3, and 4. What is the approximate measure of the smallest angle?
(A) 26
(B) 27
(C) 28
(D) 29
(E) 30
12. The graph of h (x) is a line. If h (1) 3 and h (5) 9, then an equation of h (x) is
(A)
h
(x)
_23_x
_5_ 3
(B)
h (x)
_23_x
_1_ 3
(C)
h (x)
_23_x
_5_ 3
(D)
h
(x)
_32_x
_3_ 2
(E)
h (x)
_32_x
_3_ 2
13. Which of the labeled sections represent (A B) C
(A) I, II, III, IV, V, VI, and VII
(B) I, II, III, IV, V, and VI
(C) II, IV, V, VI, and VII
(D) II, IV, V, and VI
(E) IV, V, and VI
USE THIS SPACE FOR SCRATCH WORK.
A
B
I
II
III
V
IV
VI
VII C
Copyright ? by Holt McDougal. All rights reserved.
102
Holt McDougal College Entrance Exam
Name
Date
Class
SAT Subject Test Practice Test II: Math Level II continued
14.
The
graph
of
g (x)
(_x___2_)_(_x___3_)_(x____4_) (x 2)(x 3)
USE THIS SPACE FOR SCRATCH WORK.
has the following asymptotes.
(A) no horizontal or vertical asymptotes
(B) no horizontal and one vertical asymptote
(C) no horizontal and two vertical asymptotes
(D) one horizontal and one vertical asymptote
(E) one horizontal and two vertical
asymptotes
15.
Evaluate
tan(cos
1
_3_ 8
).
(A)
_3__} 5_5_ 55
(B)
_8__} 5_5_ 55
(C)
__} 5_5_ 8
(D)
__} 5_5_ 3
(E)
__} 7_3_ 3
16.
If
f (x)
x 2
2x
then
f_(_x___h_)___f_(_x_) h
(A) 1
(B) 2x 2
(C) 2x 2 h
(D)
1
_4_x_ h
(E)
2x
2
h
_4_x_ h
17. What is the probability of rolling two regular 6-sided dice and getting a sum of 10 or higher?
(A)
_1__ 10
(B)
_1_ 6
(C)
_7__ 36
(D)
_5__ 18
(E)
_1_ 2
Copyright ? by Holt McDougal. All rights reserved.
103
Holt McDougal College Entrance Exam
Name
Date
SAT Subject Test Practice Test II: Math Level II continued
Class
18. If 9.264y 3.264x, then x (A) 0.35y (B) 0.53y (C) 1.88y (D) 2.84y (E) 3.00y
USE THIS SPACE FOR SCRATCH WORK.
19. A cone shares its base with a cylinder and is inscribed inside the cylinder. If the volume of the cone is 24 cubic units, what is the volume in cubic units of the cylinder?
(A) 8
(B) 24
(C) 48
(D) 72
(E) Cannot be determined 20. Evaluate (2 2i }3) 3.
(A) 64 (B) 8 24}3 (C) 8 24}3 (D) 8 24i }3 (E) 8 24i }3
21. If the points (1, ?2), (1, 6), and (2, 1) all lie on the graph of f (x) ax 2 bx c, then respectively a, b, and c
(A) 3, 4, and 5
(B) 3, 4, and 5
(C) 3, 4, and 5
(D) 3, 4, and 5
(E) 3, 5, and 5
Copyright ? by Holt McDougal. All rights reserved.
104
Holt McDougal College Entrance Exam
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