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실전 6 1 1. What is the greatest common divisor of the three integers 144, 216, and 360? (A) 12 (B) 18 (C) 24 (D) 36 (E) 72 2. If the graph of the parabola y=ax 2+bx+c opens up, which of the following must be true? (A) a > 0 (B) c > 0 (C) a > c (D) b2 – 4ac > 0 (E) b2 – 4ac < 0 3. What is the fifth term of the geometric sequence whose first three terms are 486, 162, and 54? (A) 2 (B) 3 (C) 4.5 (D) 6 (E) 9 4. In ∆��� , x= 55. What is the value of h? (A) 5.74 (B) 8.19 (C) 12.21 (D) 14.28 (E) 17.43 5. If 4 x + 8 = √94 , then ( x+ 2) 2? (A) 1.70 (B) 2.42 (C) 5.88 (D) 9.70 (E) 23.50 A B C 10 h x

실전 6 2 6. If x> 0, and y< 0 then xy + y can be which of the following? I. Greater than 0 II. Equal to 0 III. Less than 0 (A) I only (B) II only (C) III only (D) I and II only (E) I, II, III 7. The figure is the graph of which of the following? (A) y = |x–2| –1 (B) y = |x–1| –2 (C) y = |x–1| +2 (D) y = |x+ 1| –2 (E) y = |x+ 2| –1 8. If f(x) = sin x, g(x) = cos x and h(x)= f(x)–g(x), what is the value of h(𝜋 5)? (A) –0.476 (B) –0.221 (C) 0 (D) 0.221 (E) 0.476 9. In the xy -plane the graph of y = 2x and x = x 2– 10 x + 19 intersect at the point ( r, s). W hat is the value of r? (A) 5.000 (B) 3.754 (C) 3.696 (D) 1.886 (E) 1.877 –2 –1 – –1 – 1 (–2,–1)

실전 6 3 10. When a service call by Johnson’s repair shop takes more than one hour, the labor cost for the service call is modeled by f(t)=55+20[2( t–1)]. Where f(t) is the labor cost S and t is the number of hours it takes for the repair, what is the labor cost for a service call that takes 2.75 hours? (A) 115 (B) 125 (C) 135 (D) 145 (E) 175 11. If f(x)= x2+1 and g(x)= 2 x–5, then f(g(2 x))=? (A) 8x2 –3 (B) 4x2 –20 x +26 (C) 16 x2 –40x+ 25 (D) 16 x2 –40x+ 26 (E) 64 x2 –80x+ 101 12. If the point ( –1 2, 1) is on the graph of f(x)= a(x–3) 2+50 in the xy -plane, what is the value of a? (A) –12.625 (B) –4 (C) 4 (D) 4.16 (E) 14 13. If x ≠ 0, then 𝑥2–𝑟 𝑥2 (A) 1 𝑥2 (B) 1 𝑥𝑟 (C) 1 𝑥(𝑟–2) (D) 𝑥2 𝑥𝑟 (E) �4–𝑟

실전 6 4 14. Which of the following is an equation of the line that contains the point ( –1,4) and is perpendicular to the line y = –3 2�+ 1? (A) y = 2 3�+ 1 (B) y = 2 3(�–1)–4 (C) y = 3 2(�+ 1)+ 4 (D) y = 2 3(�+ 1)–4 (E) y = 2 3(�+ 1)+ 4 15. Data set B is formed by adding 5 to each of the numbers in data A. Which of the following statistics is the same for data sets A and B? (A) Maximum (B) Mean (C) Median (D) Mode (E) Standard Deviation Refer to the following for Problems 16, 17: bt = 3 bn = b n–1 +2n–1, for n> 1 16. What are the first five terms? (A) 3,4,7,12,19 (B) 3,6,9,12,15 (C) 3,6,11,18,27 (D) 6,9,12,15,18 (E) 3,6,11,20,26 17. Which of the followings is the n the term, bn of the sequence? (A) 3n (B) 3( n+1) (C) 3n (D) n2+ 2 (E) n3+2

실전 6 5 18. All of the following are equal to each other except (A) log 10100 (B) log 610 (C) log 24 (D) –log 31 9 (E) –log 2 1 4 19. Which of the following functions has all real numbers for its domain? (A) f(x)= √� (B) f(x)= 1 𝑥2 (C) f(x)= 𝑥4 5 (D) f(x)= |𝑥| 𝑥–1 (E) f(x)= 𝑥2–4 𝑥+2 20. In the xyz coordinate system, how many lines may be drawn perpendicular to a given line at a given point on the line? (A) 1 (B) 2 (C) 3 (D) 4 (E) Infinitely Many 21. The graph shown has equation y= 2sin x. If this graph is shifted 𝜋 2 units to the right, which of the following could be the equation fo the shifted graph? (A) y= 2sin x+ 𝜋 2 (B) y= 2sin x–𝜋 2 (C) y= πsin x (D) y= 2sin( x+ 𝜋 2) (E) y= 2sin( x–𝜋 2) – –2 – 2

실전 6 6 22. Which of the following inequalities must be true for all real numbers x? I. x2 –2x >0 II. x2 –2x +1>0 III. x2 –2x+2 >0 (A) None (B) II only (C) III only (D) I and II only (E) II and III only 23. If 2 6� is an integer, which of the following must be an integer? (A) 𝑛 12 (B) 𝑛 4 (C) 𝑛 2 (D) 2𝑛 5 (E) 2𝑛 3 24. A line segment is 10 units in length with one end point on the y-axis at the point (0,6). If the segment makes one complete rotation about the point (0,6), which of the following intervals represents all values of x for which the segment intersects the x- axis? (A) [–8,8] (B) [–8,0] (C) [–6,6] (D) [0,8] (E) There is no such interval

실전 6 7 25. A set of 12 numbers has an arithmetic mean of 20. If the numbers 10 and 14 are removed from the set, what is the arithmetic mean of the 10 numbers remaining in the set? (A) 18 (B) 20 (C) 21.6 (D) 22 (E) 22.6 26. In the figure, a cable 40ft long is attached to a vertical pole. To the nearest foot, how far from the base of the pole is the cable attached to the ground? (A) 26 (B) 31 (C) 32 (D) 38 (E) 48 27. A function is defined by the table above. For which of the following values of x does f(f(x))=6? (A) 0 (B) 2 (C) 3 (D) 5 (E) 6 x f(x) 0 4 1 5 2 3 3 6 4 2 5 1 6 0 28. In a plane, what is the set (locus) of all points equidistance from two intersecting lines in the plane? (A) A line (B) Two perpendicular lines (C) Two parallel lines (D) Four points (E) None of these 40ft 50º

실전 6 8 29. Thirty cards are numbered from 1 to 30, inclusive. If one card is drawn at random, what is the probability that the number on the card will be divisible by either 3 or 5? (A) 1 15 (B) 1 5 (C) 1 3 (D) 7 15 (E) 8 15 30. �(�)= (�+ 3)(�–1) and �(�)= 1 𝑥+4. What are all values of x for which g(f(x)) is undefined? (A) {–1} (B) {1} (C) {–3,1} (D) {–1,3} (E) {–4,–3,1} 31. If a circle with center ( r, g) in the second quadrant is tangent to the x and y axes, then, in terms of y, what does r equal? (A) g (B) 1 𝑔 (C) –g (D) 1–g (E) √�2− 1 32. If � = 140 , what is the measure of ∠� to the nearest degree? (A) 29 (B) 30 (C) 37 (D) 49 (E) 59 A B y 15 20

실전 6 9 33. �(3�+ 2)= � for all �, then �(�)= (A) 3�− 2 (B) 3� (C) � (D) 𝑥−3 2 (E) 𝑥−2 3 34. 𝑃(−3,−5), what is the measure of angle 𝜃? (A) 121 º (B) 211 º (C) 217 º (D) 233 º (E) 239 º 35. If the frequency of the periodic function is defined as reciprocal of the period, what is the frequency of �(�)= 4sin (2�− 1)? (A) 1 2𝜋 (B) 1 𝜋 (C) 1 2 (D) π (E) 2π 36. The volume of a certain right circular cylinder is 16. A larger circular cylinder has radius 25% greater and height 50% greater than the radius and height respectively, of the smaller cylinder. What is the volume of the larger cylinder? (A) 20 (B) 24 (C) 25 (D) 30 (E) 37.5 P – –5 x –3 𝜃

실전 6 10 37. If �(�)= 𝑥2+𝑥−6 𝑥−2 , what number does �(�) approach as � approaches 2? (A) 0 (B) 1 (C) 3 (D) 5 (E) �(�) increases without limit 38. An operation ∎ is defined on the real number � and � by the equation �∎� = |�|− �2. Which of the following is true for all real numbers � and �? (A) �∎� = �∎� (B) �∎� = (−�)∎� (C) If �∎� = 0, then y= 0 (D) If �∎� = 0, then y=–x (E) If �∎� = 1, then y=0 39. If � and � are functions defined by �(�,�,�)= (�,�,�),�(�,�,�)= (�,�,�) then �(�(�,�,�)) (A) (�,�,�) (B) (�,�,�) (C) (�,�,�) (D) (�,�,�) (E) (�,�,�) 40. The equation 𝑎� = 𝑎+ 2� has a solution for all values of a except (A) 𝑎 = –2 (B) 𝑎 = –1 (C) 𝑎 = 0 (D) 𝑎 = 1 (E) 𝑎 = 2 41. A function f is defined and continuous on the set of real numbers. If �(2)=–3,�(4)= 6 and if �(�)= 0 for exactly one number �, then � could be (A) –2 (B) –1 (C) 0 (D) 3 (E) 5

실전 6 11 42. How far apart are the cities? (A) 1.32km (B) 1.70km (C) 2.40km (D) 4.91km (E) 5.82km 43. The equation 4�3− 3�2− 1= 0 has how many non -real roots? (A) None (B) One (C) Two (D) Three (E) More than three 44. John leaves home of noon driving at 50 miles per hour for t hours. His wife Ann leaves home an hour later driving at 60 miles per hour on the same straight road in the same direction. Which of the following represents the distance between them t hours after noon for t ≥ 1? (A) |10 t–60| (B) |10 t–50| (C) |10 t–10| (D) |10 t+10| (E) |10 t+60| 45. Which of the following expressions are equal to 1 for all real values of � such that 0< � < 𝜋 2? I. sin 2�•csc 2� II. 2sin �•cos � III. √sin 2�+ cos 2� (A) I only (B) II only (C) III only (D) I and III only (E) I, II, III 39º 27º City A City B 8km

실전 6 12 46. A certain population of bacteria grows 10% larger each day. The population 100 days from now will be how many times the size of the population today? (A) 10 (B) 110 (C) 1100 (D) 1378 (E) 13781 47. Which of the following is the set of all real numbers � for which there are points on the graph of � = √−�2 in the �� plane? (A) The empty set (B) The set containing only zero (C) The set of all positive real numbers (D) The set of all negative numbers (E) The set of all real numbers 48. In the frequency distribution, the mean of the distribution is equal to one of the values, � =? (A) 0 (B) 2 (C) 3 (D) 4 (E) 5 Value Frequency 0 1 2 3 3 2 4 X 5 1 49. Which of the following intervals contains all of the values of � for which �2< 4? (A) (–4,1) (B) (–3,3) (C) (–1,4) (D) (0,2) (E) (0,5)

실전 6 13 50. In a biology class, three multiple -choice tests were given, on given test. Each question was worth the same number of points. The table above lists the number of questions answered correctly and the total number of points received by each of three stude nts. How many points were awarded for each question on test 2? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 Student name Numbers of question answered correctly Total points Test 1 Test 2 Test 3 Sue 34 15 9 177 Juan 33 19 7 172 Latoya 35 17 10 189



실전 6 14 1. e 36. e 2. a 37. d 3. d 38. b 4. b 39. a 5. c 40. e 6. c 41. d 7. e 42. e 8. b 43. c 9. d 44. a 10. b 45. d 11. d 46. e 12. b 47. b 13. b 48. c? 14. e 49. d 15. e 50. b 16. c 17. d 18. b 19. c,e 20. e 21. e 22. c 23. e 24. a 25. c 26. a 27. b 28. b 29. e 30. a 31. c 32. a 33. e 34. e 35. b