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์‹ค์ „ 19 1 1. For what values of x is the expression 3ํ ตํฑฅ2 โˆ’3 ํ ตํฑฅโˆ’1 undefined? (A) โ€“1 only (B) 0 only (C) 1 only (D) โ€“3 and 3 (E) โ€“1 and 1 2. In the xy -plane, if y = mx + 7 and y = kx โ€“ 7 are equations of parallel lines, which of the following must be true? (A) m = k (B) m = โ€“k (C) m = โ€“1 ํ ตํฑ˜ (D) m + k = โ€“1 (E) m โ€“ k = โ€“1 3. The net for a rectangular solid is shown in the figure above. When the solid is formed, what is its volume? (A) 32 (B) 96 (C) 144 (D) 152 (E) 192

์‹ค์ „ 19 2 If p is a prime number, then 2p + 1 is a prime number. 4. Which of the following prime numbers could be a value of p that yields a COUNTEREXAMPLE to the statement above? (A) 19 (B) 11 (C) 5 (D) 3 (E) 2 5. If the parabola in the figure above is translated 3 units to the right, which of the following could represent the equation of this translated parabola? (A) � = (�โˆ’ 3)2+ 2 (B) � = (�+ 3)2+ 2 (C) � = (�โˆ’ 3)2โˆ’ 2 (D) � = (�+ 3)2โˆ’ 2 (E) � = (�โˆ’ 3)2+ 5 6. The graph of the linear function f has slope โ€“3. If the graph of f passes through the point (2, 6), which of the following could be an expression for �(�)? (A) โ€“3x (B) โ€“3x + 12 (C) โ€“3x + 20 (D) 3x (E) 3x โ€“ 16

์‹ค์ „ 19 3 7. What is the range of the function whose graph is shown above ? (A) The set of all real numbers less than or equal to 2 (B) The set of all real numbers greater than or equal to โ€“2 (C) The set of all real numbers greater than or equal to 2 (D) The set of all real numbers between 1 and 3 (E) The set of all real numbers 8. In the figure above, x = 58 and BD = 4. What is the length of �� ? (A) 2.50 (B) 4.72 (C) 6.40 (D) 7.55 (E) 8

์‹ค์ „ 19 4 9. If | x| = | y|, which of the following must be true? (A) โˆš� = โˆš� (B) x = y (C) x = โ€“y (D) �2 = �2 (E) �3 = �3 10. A certain radioactive substance decomposes at a rate such that the amount of mass remaining at the end of each day is 1 2 the amount left at the end of the previous day. If the mass at the beginning of the first day is M0, which of the following could express the mass remaining at the end of t days? (A) 2Mot (B) 2(M0)t (C) 2ํ ตํฑ€0 ํ ตํฑก (D) ํ ตํฑ€0ํ ตํฑก 2 (E) ํ ตํฑ€0 2ํ ตํฑก 11. I f sin x = 0.90 and 0 < x < ํ ตํผ‹ 2, then cos ํ ตํฑฅ 2 = (A) 0.22 (B) 0.45 (C) 0.56 (D) 0.85 (E) 0.97 12. If f(x) = 10 x and x > 0, for what value of x is f(x) = 11.2? (A) 0.89 (B) 0.95 (C) 1.05 (D) 1.07 (E) 1.12

์‹ค์ „ 19 5 13. If y = 1 (2ํ ตํฑฅโˆ’3)2 , what value does y approach as x approaches 3 2 ? (A) โ€“ 1 36 (B) 0 (C) 1 36 (D) 1 (E) The value of y increases without bound 14. For (1 โ€“ cos x)(1 + cos x) = 0.64, what is the value of sin 2x? (A) 0.36 (B) 0.41 (C) 0.60 (D) 0.64 (E) 0.80 15. In the xy -plane, the points (0,4), (4,0), (8,4), and (4,8) are vertices of a square. If the x and y coordinates of each vertex are doubled, a new square is formed. The area of the new square is how many times the area of the original square ? (A) 8 (B) 4 (C) 2 (D) 1 2 (E) 1 4

์‹ค์ „ 19 6 16. If y = 4 x โ€“ 12, what is the value of y when it is twice the value of x? (A) 4 (B) 6 (C) 12 (D) 24 (E) 30 17. In the xy -plane, the endpoints of �� have coordinates ( โ€“1,0) and (0,1). If O is the origin and M is the midpoint of �� , what is the slope of ํ ตํฑ‚ํ ตํฑ€ ? (A) โ€“2 (B) โ€“1 (C) โ€“1 2 (D) 1 2 (E) 1 Score Frequency 10 3 15 4 20 7 25 2 30 8 Total 24 18. What is the mean of the scores in the frequency distribution shown above? (A) 20 (B) 20.42 (C) 21.67 (D) 22.92 (E) 30

์‹ค์ „ 19 7 76= 10 r + s 19. I n the equation above, if r and s are positive integers and s is less than 10, what is the value of s? (A) 1 (B) 2 (C) 3 (D) 7 (E) 9 20. If ํ ตํฑกํ ตํฑŽ� 2� = 1.0913, which of the following could cot x equal? (A) โ€“1.0447 (B) 0.3022 (C) 0.9573 (D) 1.0447 (E) 1.4461 21. Let f, g, and h be linear functions satisfying f(g(x)) = h(x) for all x. If f(x) = x + 1 and h(x ) = 2 x โ€“ 1, then g(x) = (A) 2x + 1 (B) 2x โ€“ 2 (C) x โ€“ 1 (D) x + 1 (E) x + 2 22. If b and c are real numbers, what is the greatest possible number of real solutions of x = �2 + bx + c? (A) None (B) One (C) Two (D) Three (E) Infinitely many

์‹ค์ „ 19 8 23. The graph of �2โˆ’ 6�+ �2+ 4�โˆ’ 12 = 0 in the xy -plane is a circle with radius 5, centered at (A) (โ€“9, 4) (B) (โ€“3, โ€“2) (C) (โ€“3, 2) (D) (3, โ€“2) (E) (9, โ€“4) 24. A sphere and a cone each have the same radius and volume. If the volume of the sphere is 1,000 cubic centimeters, what is the height of the cone? (A) 4.0cm (B) 5.4cm (C) 8.3cm (D) 15.8cm (E) 24.8cm 25. Let f be a polynomial function such that the graph of y = f(x) contains the points ( โ€“2, โ€“2), (โ€“1, 4), and (2, 1). Which of the following must be true about the zeros of f? (A) f has a zero between x = โ€“2 and x = โ€“1 (B) f has a zero between x = โ€“1 and x = 2 (C) f has no zeros (D) f has exactly one zero (E) f has exactly two zeros (6 โ–ณ 4) โจ (5 โ–ณ 3) = 2 1 2 26. In the equation above, โจ and โ–ณ represent two distinct operations shown from the set {+, โ€“, ร—, รท}. What is the value of (6 โจ 2) โ–ณ 4? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

์‹ค์ „ 19 9 27. If m and n are integers between โ€“4 and 4, inclusive, then for how many ordered pairs ( m, n) does 2� = 4�? (A) Five (B) Four (C) Three (D) One (E) None 28. If f is defined for all numbers x by f(x) = 1 โ€“ �2, for which of the following values of x does f(x) = ํ ตํฑ“(ํ ตํฑฅ) 3 ? (A) 0 (B) 1 (C) 2 (D) 3 (E) 6 29. The depth of the water D, in feet, at the end of a fishing pier is related to the numbers of hours h after midnight by D(h) = 8.5 โ€“ 4.2 cos ( ํ ตํผ‹ 6(โ„Žโˆ’ 3)) How much does the depth change f rom its lowest point to its highest point? (A) 4.2 ft (B) 4.3 ft (C) 8.4 ft (D) 8.5 ft (E) 12.7 ft

์‹ค์ „ 19 10 30. What is the probability that the sum of two numbers, chosen at random with replacement from the integers from 1 to 10 inclusive, is equal to 7? (A) 0.01 (B) 0.06 (C) 0.1 (D) 0.5 (E) 0.9 31. If ��� 2x = โ€“ 1.7, what is the value of x? (A) โ€“ 3.40 (B) โ€“ 0.85 (C) 0.31 (D) 2.89 (E) 3.25 32. Which of the following gives only values of x for which 1 2�3+ 2�2โ€“2 > 0? (A) โ€“1.2 < x < โ€“1.0 (B) โ€“3.7 < x < 1.0 (C) x < โ€“3.7 and x > 1.0 (D) x < โ€“3.7 and โ€“1.2 < x < 1.0 (E) โ€“3.7 < x < โ€“1.2 and x > 1.0 33. The rate R of decomposition, in moles per liter second, of a certain chemical is given by the formula R = �� �, where C is the chemicalโ€™s concentration, in moles per liter, and k and m are constants. If R = 1.0 when C = 0.2 and R = 16.0 when C = 0.8, what is the v alue of m? (A) 2 (B) 4 (C) 8 (D) 16 (E) 32

์‹ค์ „ 19 11 34. The figure above shows a portion of the graph of a function f, where f(x) = 2sin(2 x). One of the vertices of โ–ณABC is a maximum point of the graph of f, and the other two vertices are consecutive x- intercept s of this graph. What is the area of โ–ณABC? (A) ํ ตํผ‹ 2 (B) ํ ตํผ‹ (C) 2 ํ ตํผ‹ (D) 3 ํ ตํผ‹ (E) 4 ํ ตํผ‹ 35. A piece of paper is 0.03 inch thick. Each time the paper is folded in half, the thickness is doubled. Someone claims that the paper can be folded in half 12 times. If this were true, how thick, to the nearest foot , would the folded paper be? (A) 1,475 ft (B) 1,229 ft (C) 123 ft (D) 10 ft (E) 5 ft

์‹ค์ „ 19 12 �(�)= { |�| � , for � โ‰  0 0 , for � = 0 36. For function f defined above, what is the value of f(4.5) โ€“ f(โ€“4.5)? (A) โ€“1 (B) 0 (C) 1 (D) 2 (E) 9 1.1, 1.1, 1.3, 1.3 37. T he weights, in pounds, of four books are shown above. The standard deviation of those weights is 0.1 pound. Each book is packaged into a separate shipping box. Each empty box weighs 2 pounds. What is the standard deviation of the weights of the four packages? (A) 0.1 pound (B) 0.2 pound (C) 2.0 pounds (D) 2.1 pounds (E) 8.1 pounds

์‹ค์ „ 19 13 38. The graph in the figure above could be a portion of the graph of which of the following pairs of parametric equations? (A) x = t y = t 2 + 1 (B) x = t y = t 2 โ€“ 1 (C) x = t 2 โ€“ 1 y = t (D) x = โ€“t2 + 1 y = t (E) x = โ€“t2 โ€“ 1 y = t 39. If x, y, and z are consecutive positive integers, the product xyz must be divisible by which of the following numbers? I. 2 II. 3 III. 4 (A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III

์‹ค์ „ 19 14 40. In the figure above, what is the length of ํ ตํฑ…ํ ตํฑ‡ ฬ…ฬ…ฬ…ฬ…ฬ…in terms of ํ ตํผƒ? (A) sin ํ ตํผƒ โ€“ cos ํ ตํผƒ (B) tan ํ ตํผƒ โ€“ 1 (C) 1 โ€“ sin ํ ตํผƒ (D) 1 โ€“ cos ํ ตํผƒ (E) 2 sin ํ ตํผƒcos ํ ตํผƒ 41. The graph of the function f, given by f(x) = a(x + b)(x + c)(x + d) , where a, b, c, and d are constants, is shown in the figure above. Which of the following could be true ? (A) a = 0 , b โ‰  c , b โ‰  d , and c โ‰  d (B) a < 0 , b = c , and c โ‰  d (C) a < 0 , and b = c = d (D) a > 0 , b = c, and c โ‰  d (E) a > 0 , and b = c = d

์‹ค์ „ 19 15 42. Which of the following equations has exactly two distinct real roots? (A) (�2+ 8)(�2 + 4) = 0 (B) (�3โˆ’ 8)(�2 + 5) = 0 (C) (�2โˆ’ 1)(�2 + 1) = 0 (D) (�4โˆ’ 1)(� + 2) = 0 (E) (�2โˆ’ 4)(�2 โ€“ 9) = 0 43. In the figure above, r and s are vectors of magnitude 4 a nd 8, respectively. If the ang le between the two vectors is 50ยบ, what is the magnitude of vector r + s? (A) 5.5 (B) 6.2 (C) 8.9 (D) 11.0 (E) 12.0 44. A person invest s $3,500 at 5.2 percent annual interest compounded quarterly. How much will this investment be worth at the end of 1 year? (A) $3,545.50 (B) $3,682.00 (C) $3,685.57 (D) $4,286.77 (E) $5,706.65

์‹ค์ „ 19 16 45. Which of the following functions is the same as its inverse function? I. f(x) = 1 ํ ตํฑฅ II. g(x) = 1 ํ ตํฑฅ + 1 III. h(x) = 1 ํ ตํฑฅโˆ’1 + 1 (A) I only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III 46. What is the period of the function f, where f(x) = |cos (1 2�)|+ 3? (A) ํ ตํผ‹ 2 (B) ํ ตํผ‹ (C) 3ํ ตํผ‹ 2 (D) 2ํ ตํผ‹ (E) 4ํ ตํผ‹ 47. In the xyz - coordinate system, what is an equation of the set of all points in space equidistant from points A(1, 1, 3) and B(1, 2, 3) (A) x = 1 (B) y = 1 2 (C) y = 1 (D) y = 3 2 (E) z = 3

์‹ค์ „ 19 17 48. A laboratory receives 16 samples from an experiment. A group of 4 of these samples is selected for testing. One sample from this group of 4 is then selected for a special second t est. In how many different ways could the samples for this two -stage testing procedure be selected? (A) 24 (B) 64 (C) 1,820 (D) 7,28 0 (E) 3,312,400 49. The probability that an incoming phone call is long -distance is 1 3, and that it is local is 2 3. If two incoming phone calls are independent events, what is the probability that one will be local and the other long -distance? (A) 2 9 (B) 4 9 (C) 1 2 (D) 5 9 (E) 1 50. I f x = arcta n y, then โˆš1+ �2 = (A) |sin x| (B) |cos x| (C) |sec x| (D) |cot x| (E) |csc x|

์‹ค์ „ 19 18

์‹ค์ „ 19 19 1. C 2. A 3. B 4. A 5. A 6. B 7. A 8. C 9. D 10. E 11. D 12. C 13. E 14. D 15. B 16. C 17. B 18. C 19. E 20. C 21. B 22. C 23. D 24. C 25. A 26. C 27. A 28. B 29. C 30. B 31. C 32. E 33. A 34. A 35. D 36. D 37. A 38. E 39. C 40. D 41. D 42. C 43. D 44. C 45. C 46. D 47. D 48. D 49. B 50. C