226 Lesson 8
MATHEMATICS SUBJECT TEST, LEVEL IIC
Directions: For each problem in this test, determine which is the best of the five choices given. Then
darken the corresponding oval space on the answer sheet.
Notes: (1) Figures that accompany problems in this test are drawn as accurately as possible
EXCEPT when accompanied by the words “NOTE: Figure not drawn to scale.”
(2) Unless otherwise indicated, all figures lie in a plane.
(3) Unless otherwise specified, the domain of a function is assumed to be the set of all real
numbers x such that f(x) is a real number.
(4) A calculator is necessary for answering some—but not all—of the questions in this test. In
each case, you must decide whether or not to use a calculator. For some items, you will
need to determine whether the calculator should be in the degree mode or the radian mode.
1. If x and y are positive integers such that x 4. A group of students consisting of 4 seniors, 5
divided by 7 leaves a remainder of 4, and y juniors, and 6 sophomores plans to nominate
divided by 7 leaves a remainder of 3, then what a slate of 3 officers—president, vice–president,
is the remainder when xy is divided by 7? and treasurer—for the student government
(A) 0 election. If the presidential candidate must be
(B) 1 a senior and the vice–presidential candidate
(C) 3 must be a junior, how many different slates
(D) 5 are possible?
(E) 6 (A) 3,375
(B) 840
2. The radius of a sphere with volume 35 is how
(C) 300
much greater than the radius of a sphere with
(D) 260
volume 24?
(E) 120
(A) 0.58
(B) 0.49 5. If f(x) = x2 + bx + 1, and if f(1) = 4, then b =
(C) 0.37 (A) 4
(D) 0.24 (B) 2
(E) 0.12 (C) 1
(D) 0
3. If S is the set of all integers that can be written
(E) –2
in the form n2 + 1, then which of the follow-
ing is a member of S? 6. Points P and Q lie in the coordinate plane.
(A) 8 If the coordinates of P are (5,3) and Q are
(B) 16 (–2, –6), what is the distance between point P
(C) 24 and point Q?
(D) 52 (A) 11.4
(E) 65 (B) 13.2
(C) 15.8
(D) 17.5
(E) 21.2
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, Mathematics Level IC/IIC Subject Tests 227
7. During the last 4 hours of a 400–kilometer trip, 10. How many integers are in the solution set of
a passenger train traveled at an average speed |3x – 2| < 1?
of t kilometers per hour. If the train completed (A) None
the entire trip in 6 hours, at what speed, in ki- (B) One
lometers per hour, did the train travel during (C) Two
the first 2 hours? (D) Three
(E) Infinitely many
(A)
11. If f(x,y) = x2 – xy + y2, for all real numbers,
(B) then which of the following must be true?
(C) 200 + t (A) f(x,y) = f(x,–y)
(D) 200 – 2t (B) f(x,y) = f(–x,y)
(E) 2t – 100 (C) f(x,y) = f(–x, –y)
(D) f(x,y) = f(x,1/y)
(E) f(x,y) = f(x, –1/y)
12. If , for what value of x is
f(x) undefined?
(A) –4
(B) –2
(C) 0
8. In the above figure, if AC is a diameter of the (D) 2
circle, B is a point on the circle, and sin θ = 1/2, (E) 4
then sin φ =
13. An angle measure of 45° is equivalent to an
angle measure of
(A)
1
(A) radians
(B) 4
1
(B) radians
(C) π
π
(C) radians
4
(D)
π
(D) radians
2
(E) (E) π radians
9. If an equilateral triangle is rotated 360° around π
one of its altitudes, the resulting solid is a 14. If cos x = 0.2586 and 0 < x < , what is the
2
(A) cone value of x?
(B) cube (A) 8.254
(C) cylinder (B) 1.309
(D) sphere (C) 0.999
(E) right prism (D) 0.688
(E) 0.005
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ARCO ■ SAT II Subject Tests www.petersons.com/arco
MATHEMATICS SUBJECT TEST, LEVEL IIC
Directions: For each problem in this test, determine which is the best of the five choices given. Then
darken the corresponding oval space on the answer sheet.
Notes: (1) Figures that accompany problems in this test are drawn as accurately as possible
EXCEPT when accompanied by the words “NOTE: Figure not drawn to scale.”
(2) Unless otherwise indicated, all figures lie in a plane.
(3) Unless otherwise specified, the domain of a function is assumed to be the set of all real
numbers x such that f(x) is a real number.
(4) A calculator is necessary for answering some—but not all—of the questions in this test. In
each case, you must decide whether or not to use a calculator. For some items, you will
need to determine whether the calculator should be in the degree mode or the radian mode.
1. If x and y are positive integers such that x 4. A group of students consisting of 4 seniors, 5
divided by 7 leaves a remainder of 4, and y juniors, and 6 sophomores plans to nominate
divided by 7 leaves a remainder of 3, then what a slate of 3 officers—president, vice–president,
is the remainder when xy is divided by 7? and treasurer—for the student government
(A) 0 election. If the presidential candidate must be
(B) 1 a senior and the vice–presidential candidate
(C) 3 must be a junior, how many different slates
(D) 5 are possible?
(E) 6 (A) 3,375
(B) 840
2. The radius of a sphere with volume 35 is how
(C) 300
much greater than the radius of a sphere with
(D) 260
volume 24?
(E) 120
(A) 0.58
(B) 0.49 5. If f(x) = x2 + bx + 1, and if f(1) = 4, then b =
(C) 0.37 (A) 4
(D) 0.24 (B) 2
(E) 0.12 (C) 1
(D) 0
3. If S is the set of all integers that can be written
(E) –2
in the form n2 + 1, then which of the follow-
ing is a member of S? 6. Points P and Q lie in the coordinate plane.
(A) 8 If the coordinates of P are (5,3) and Q are
(B) 16 (–2, –6), what is the distance between point P
(C) 24 and point Q?
(D) 52 (A) 11.4
(E) 65 (B) 13.2
(C) 15.8
(D) 17.5
(E) 21.2
www.petersons.com/arco ARCO ■ SAT II Subject Tests
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SAT Downloads:
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SAT official guide tests download:
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SAT online course tests download:
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SAT subject tests download:
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PSAT real tests download:
http://www.cracksat.net/psat/download/
1000+ College Admission Essay Samples:
http://www.cracksat.net/college-admission/essays/
, Mathematics Level IC/IIC Subject Tests 227
7. During the last 4 hours of a 400–kilometer trip, 10. How many integers are in the solution set of
a passenger train traveled at an average speed |3x – 2| < 1?
of t kilometers per hour. If the train completed (A) None
the entire trip in 6 hours, at what speed, in ki- (B) One
lometers per hour, did the train travel during (C) Two
the first 2 hours? (D) Three
(E) Infinitely many
(A)
11. If f(x,y) = x2 – xy + y2, for all real numbers,
(B) then which of the following must be true?
(C) 200 + t (A) f(x,y) = f(x,–y)
(D) 200 – 2t (B) f(x,y) = f(–x,y)
(E) 2t – 100 (C) f(x,y) = f(–x, –y)
(D) f(x,y) = f(x,1/y)
(E) f(x,y) = f(x, –1/y)
12. If , for what value of x is
f(x) undefined?
(A) –4
(B) –2
(C) 0
8. In the above figure, if AC is a diameter of the (D) 2
circle, B is a point on the circle, and sin θ = 1/2, (E) 4
then sin φ =
13. An angle measure of 45° is equivalent to an
angle measure of
(A)
1
(A) radians
(B) 4
1
(B) radians
(C) π
π
(C) radians
4
(D)
π
(D) radians
2
(E) (E) π radians
9. If an equilateral triangle is rotated 360° around π
one of its altitudes, the resulting solid is a 14. If cos x = 0.2586 and 0 < x < , what is the
2
(A) cone value of x?
(B) cube (A) 8.254
(C) cylinder (B) 1.309
(D) sphere (C) 0.999
(E) right prism (D) 0.688
(E) 0.005
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ARCO ■ SAT II Subject Tests www.petersons.com/arco
