Lesson 8226 www.petersons.com/arcoARCO ■ SAT II Subject Tests
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 divided by 7 leaves a remainder of 4, and y divided by 7 leaves a remainder of 3, then what is the remainder when xy is divided by 7?(A)0 (B)1 (C)3 (D)5 (E)6 2.The radius of a sphere with volume 35 is how much greater than the radius of a sphere with volume 24?
(A)0.58
(B)0.49
(C)0.37
(D)0.24
(E)0.12
3.If S is the set of all integers that can be written in the form n 2
- 1, then which of the follow-
ing is a member of S?(A)8 (B)16 (C)24 (D)52 (E)65 4.A group of students consisting of 4 seniors, 5 juniors, and 6 sophomores plans to nominate a slate of 3 officers—president, vice–president, and treasurer—for the student government election. If the presidential candidate must be a senior and the vice–presidential candidate must be a junior, how many different slates are possible?
(A)3,375
(B)840
(C)300
(D)260
(E)120
5.If f(x) = x 2
- bx + 1, and if f(1) = 4, then b =
(A)4 (B)2 (C)1 (D)0
(E)–2
6.Points P and Q lie in the coordinate plane.If the coordinates of P are (5,3) and Q are (–2, –6), what is the distance between point P and point Q?
(A)11.4
(B)13.2
(C)15.8
(D)17.5
(E)21.2 1 / 3
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Mathematics Level IC/IIC Subject Tests227 ARCO ■ SAT II Subject Testswww.petersons.com/arco 7.During the last 4 hours of a 400–kilometer trip, a passenger train traveled at an average speed of t kilometers per hour. If the train completed the entire trip in 6 hours, at what speed, in ki- lometers per hour, did the train travel during the first 2 hours?(A) (B) (C)200 + t (D)200 – 2t (E)2t – 100 8.In the above figure, if AC is a diameter of the circle, B is a point on the circle, and sin θ = 1/2, then sin φ = (A) (B) (C) (D) (E) 9.If an equilateral triangle is rotated 360° around one of its altitudes, the resulting solid is a (A)cone (B)cube (C)cylinder (D)sphere (E)right prism 10.How many integers are in the solution set of |3x – 2| < 1?(A)None (B)One (C)Two (D)Three (E)Infinitely many 11.If f(x,y) = x 2 – xy + y 2 , for all real numbers, then which of the following must be true?(A)f(x,y) = f(x,–y) (B)f(x,y) = f(–x,y) (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 (D)2 (E)4 13.An angle measure of 45° is equivalent to an angle measure of (A)
1 4 radians (B)
1 π radians (C)
π 4 radians (D)
π 2 radians (E)π radians 14.If cos x = 0.2586 and 0 < x <
π 2 , what is the value of x?
(A)8.254
(B)1.309
(C)0.999
(D)0.688
(E)0.005
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