7. The olynomial P (x) =x, 9x 4 +9x, 4x +4x, 4 can be written in the form P (x) =(x, ) n Q(x), where n is a ositive integer and Q(x) is not divisible

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1 . Which of the following intervals contains all of the real zeros of the function g(t) =t, t + t? (a) (,; ) (b) ( ; ) (c) (,; ) (d) (; ) (e) (,; ) 4 4. The exression ((a), + b), is equivalent to which of the following exressions? (a) +ab a (b) ab + b (c) a +ab (d) b ab + (e) a b. Find the sum of the solutions of the equation x = x,,. (a) 4 (b), (c) 0 (d) (e) 4. Simlify the exression +i + i + i + + i 6, where i =,. (a) 0 (b) (c), (d) i (e),i. If log b x + log x b =,b>, and x 6= then x equals what value? (a) b (b) b + (c) (d) b (e) b 6. Find the area (in square inches) of a circle inscribed in a rhombus whose erimeter is 00 inches and whose longer diagonal is 40 inches. (a) 44 (b) 44 (c) (d) (e)

2 7. The olynomial P (x) =x, 9x 4 +9x, 4x +4x, 4 can be written in the form P (x) =(x, ) n Q(x), where n is a ositive integer and Q(x) is not divisible by x,. What is n? (a) 4 (b) (c) (d) (e) 8. Given that (x) =6x + ax,, nd the value of a so that (, 8 )=( )=0. (a),4 (b),8 (c) 484 (d) 00 (e),90 9. Determine the number of distinct solutions of the equation 4 x, 68x + 89 = 0. (a) 0 (b) (c) (d) 4 (e) 0. The continued fraction + x + x+7 can be exressed as x + ax + b. Find a + b + c + d. x + cx + d (a) 8 (b) (c) 0 (d) 8 (e) 9. How many subsets of f,,, 4,, 6, 7, 8, 9, 0 g contain at least one odd integer? (a) (b) 00 (c) 04 (d) 99 (e). Find the value for x such that 4 = log x 6. (a) (b) 4 (c) (d), (e) 6

3 . Find the radius of the circle with center (; 4) that is tangent to the line x + y, 4=0. (a) (b) (c) (d) (e) 7 4. Provided that c 6= 0, dene [a; b; c] to mean a + b. What is the value of c [[8; 4; ]; [48; 0; ]; [00; 00; 7]]? (a) 6 (b) 4 (c) (d) 0 (e) 8. Ann, Bob, Carl and Doc are all thinking of the same natural number. Ann says it consists of two digits. Bob says it is a divisor of 0. Carl says it is not 0. Doc says it is divisible by. Given that exactly three of them are telling the truth, which of them is not? (a) Doc (b) Ann (c) Bob (d) Carl (e) cannot be determined 6. Find the sum of the solutions of jx, j +=jx +j. (a),9 (b), (c), (d), (e) 7. (*) Referring to the gure below, if S denotes the sum of the angles A,B,C,D, and E (measured in radians), then what can be said about the value of S? (a) S < (b) S = (c) S = (d) S = (e) S > A B C E D

4 8. What is the area of the largest triangle that can be inscribed within a circle of radius r, given that one of the triangle's sides must coincide with a diameter of the circle? (a) r (b) r (c) r (d) r (e) r 9. Suose that a -inch slice is to be removed from a cube. If taking a slice arallel to a face leaves 648 cubic inches, what is the side length (in inches) of the cube? (a) 900 (b) 898 (c) (d) 0 (e) 9 0. If a jet lane ies at an altitude of miles above the earth's equator and circles the globe once, how much farther (in miles) than the circumference of the equator does it y? (a) 4 (b) 0 (c) 4 (d) (e) 8. Calculate the fth root of ( ). (a) (b) (,) (c) (4 ) (d) (4 ) (e) ( ). (*) Let V denote the set of natural numbers, n, such that n is the sum of the squares of three consecutive ositive integers. Which of the following is true? (a) All elements of V are even. (b) No element of V is divisible by. (c) All elements of V are odd. (d) No element of V is divisible by. (e) No element of V is divisible by. 4

5 . Find the circumference of a circle circumscribed about a square having side length 8. (a) 8 (b) 8 (c) (d) The following ath from P to Q consists of vertical and horizontal straight line segments having lengths as shown. If s is the diagonal distance from P to Q, nd s. (a) 4 (b) (c) (d) (e) 4 P s 6 Q 8. If f(x) = x + x +, comute f() + f() + f() : (a) (b) 7, (c) 7+ (d) 7+ (e) A ackage of six light bulbs contains two defective bulbs. If three bulbs are to be selected at random for use, nd the robability that none of the three are defective. (a)! 6! (b)! 6! (c)!! 6! (d) 4! 6! (e) 4!! 6!

6 7. Suose B and C are oints on straight line segment AD (ictured below), with the roerty that AB = BC = CD. What ercent of AC is AD? (a) % (b) 0% (c) % (d) 0% (e) 66 %.... A B C D 8. If 60% of x is 40% of y, and y is 0% of z, then x is what ercent of z? (a) 0% (b) 0% (c) 0% (d) 0% (e) 7% 9. Comute +i! 00. (a) +i (b),+i (c),, i (d), (e), i 0. Referring to the gure below, determine the measure of q in degrees. (a) 0 (b) 48: (c) 8:6 (d) 0: (e) 49:7 4 q q 6

7 . The area of a right triangle is 0 square inches. The ratio of its legs is :. Find the number of inches in the hyotenuse of this triangle. (a) 9 (b) 8 (c) 4 9 (d) 9 (e) 9. A college graduate goes to work for x dollars er week. After several months the comany gives all emloyees a 0% ay cut. A few months later the comany gives all emloyees a 0% raise. What is the college graduate's new weekly salary? (a) 0:96x (b) 0:8x (c) x (d) :0x (e) :x. In the sequence of numbers,,,-,... each term after the rst two terms is equal to the term receding it minus the term receding that one. Determine the sum of the rst one hundred terms of the sequence. (a) 4 (b) (c) (d) (e), 4. Find the sum of the digits of the number (0 n +9 +), where n is a ositive integer. (a) n (b) (c) n (d) 4 (e) n +n+. Let a 0 =and b 0 =. For all n, let a n =a n, +b n,, and b n = a n,, b n,. What is the remainder when a is divided by 4? (a) (b) (c) (d) 0 7

8 6. What is the smallest rime number dividing the sum ? (a) (b) (c) (d) Let A denote the set of integers between and 000 which are divisible by. Let B denote the set of integers between and 000 which are divisible by 8. How many elements are in the set A [ B? (a) 8 (b) 7 (c) 0 (d) 6 (e) 8. Suose that f(x + y) =f(x) f(y) for all real numbers x and y. If f() = 8, what is f( )? (a) 4 (b) 8 (c) (d) 8 (e) 9. (*) Find the solution set for the inequality +x + x + x + ::: + x (a) fx : x,g (b) fx : x,g (c) fx : x 0g (d) fx :, x 0g 40. An equilateral triangle with a erimeter of inches is inscribed in a circle. What is the diameter of the circle (in inches)? (a) (b) (c) + 6 (d) (e) 8

9 4. Find the area (in square centimeters) of a circular sector having a 0 central angle and a 6 cm radius. (a) (b) 9 (c) 6 (d) 4. A ositive integer N with three digits in its base ten reresentation is chosen at random. If each three digit number has an equal chance of being selected, determine the robability that log N is an integer. (a) 0 (b) 899 (c) (d) 40 (e) An assembly oeration for a comuter circuit board consists of four distinct oerations, which can be erformed in any order. One of the oerations involves soldering a wire to a microchi. If all ossible assembly orderings are equally likely, what is the robability that the soldering oeration comes rst or second? (a) (b) 4 (c) 6 (d) 8 (e) 44. (*) In the gure below ABCD is a square and CMN is an equilateral triangle. If the area of ABCD is one square inch, nd the area of CMN in square inches. (a), = (b) =4 (c), (d) = (e) 4, D C M A N B 9

10 4. Assume a and b are nonzero real numbers. What is the maximum of the function f(x) =a sin x + b cos x? (a) ja + bj (b) maxfjaj; jbjg (c) a + b (d) jaj + jbj (e) (jaj + jbj) 46. (*) For each natural number n, let s n =, +, 4+, 6+::: +(,) n, n. What can be said about the value of s s 000? (a) negative (b) (c) (d) 0 (e) greater than 47. Find the smallest ositive integer m such that the grah of y = mx intersects the grah of y = 4 x (a) 4 (b) 8 (c) (d) (e) The lengths of two sides of a triangle are 7 and 0. Between what two numbers does the length of the third side lie? (a) and 7 (b) 0 and (c) 7 and 70 (d) 7 and The rst three terms of a geometric sequence are x, 4, x, 7 and 0x + 4 for some value of x. What is the fourth term of the sequence? (a)or (b),7 (c),90 (d), or, (e) 0 or 6 0

11 0. Find a formula, in the variable x, for the distance between an arbitrary oint (x,y) on the arabola y = x and the oint (7; 7). (a) x, 7 (b) x 4, x, 4x +98 (c) x 4 +x +4x +98 (d) x 4 + x, 98 (e) x + x, 4

SAT Subject Test Practice Test II: Math Level I Time 60 minutes, 50 Questions

SAT Subject Test Practice Test II: Math Level I Time 60 minutes, 50 Questions All questions in the Math Level 1 and Math Level Tests are multiple-choice questions in which you are asked to choose the BEST