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실전 5 1 1. xm x–2m = (A) xm (B) 1 �𝑚 (C) 1 �−𝑚 (D) x–3m (E) 𝑥−2𝑚2 2. All of the following numbers satisfy the inequality (2 x + 1)( x – 5) < 0 EXCEPT (A) -1 (B) 0 (C) 1 (D) 2 (E) 3 3. For all real numbers m, the equation y = mx + 3 represents which of the following in the xy -plane? (A) Lines whose x-intercept is 3 (B) Lines whose y-intercept is 3 (C) Lines whose slope is 3 (D) Vertical lines through (3,0) (E) Horizontal lines through (0,3) 4. If 2 a = 4b = 64, what is the value of a + b? (A) 3 (B) 8 (C) 9 (D) 18 (E) 48 5. What is the domain of the function f defined by f (x) = �2 �2+1? (A) –1 < x ≤ 1 (B) 0 ≤ x < 1 (C) x ≥ 0 (D) All real numbers except –1 (E) All real numbers

실전 5 2 6. If y = 2 x3 + x2, what is the value of | y| when x = –2? (A) –20 (B) 8 (C) 12 (D) 20 (E) 60 7. If f (x) = ( x – 3)2, what is the greatest value of x for which f (x) = 5? (A) –0.76 (B) 0.76 (C) 3.74 (D) 4.00 (E) 5.24 8. The stem -and -leaf plot shows the mathematics scores on a national test for a group of juniors at Pacific High School. What is the median score for this group? (A) 45 (B) 49.7 (C) 50.5 (D) 56 (E) 58 2 6 3 2 7 4 5 5 5 6 8 8 6 1 3 6 2 | 6 represents 26. 9. If f (x) = 2 x + 1 and g (x) = 1 �− 2, for what value of x is g (f (x)) equal to 0? (A) –1 (B) − 1 4 (C) 1 4 (D) 1 2 (E) 2 3

실전 5 3 10. Let a be a nonzero constant. If 2 x2 – 4 = a, then x2 – 2 = (A) 1 2 (B) 𝑎 2 (C) 2 𝑎 (D) 2 (E) 2a 11. The table shows the profit made by a new company. Of the following functions, which best models the relationship between the company’s profit and the number of months in business? (A) P(x) = 2 x – 1 (B) P(x) = 5x – 2 (C) P(x) = x2 (D) P(x) = 2x2 – 1 (E) P(x) = x3 x Number of months in business 0 1 2 3 4 5 P(x) Profit (in thousands of dollars) 0 1 4.2 9.1 15.8 25.3 12. If yn = 1 – (–1)n, where n = 1,2,3,…, which of the following statements is true? (A) For all n, y n = 0 only. (B) For all n, y n = 0 or yn = 2. (C) For all n, y n = or yn = 1. (D) For n ≥ 1,000, yn > 0. (E) For n ≥ 1,000, yn < 0.

실전 5 4 13. Which of the following is N OT a graph of y as a function of x? o x y (C) o x y (D) o x y (A) o x y (B) (E) o x y

실전 5 5 14. The figure shows the xy -plane. If f (x) = cx + 3 and g (x) = dx + 1 for 0 < c < d, which of the following is true about the graphs of f and g? (A) The graphs intersect in quadrant I. (B) The graphs intersect in quadrant II. (C) The graphs intersect in quadrant III. (D) The graphs intersect in quadrant IV. (E) The graphs do not intersect. 15. Eight cars, each of a different color (red, blue, black, gray, white, green, tan, gold), travel one behind the other to a campground. The red car must lead and the green car must be last. How many different orderings of the cars are there? (A) 6! (B) 8! (C) 2•6! (D) 2• 8! (E) 8! 2 16. If ln( x) = 1.58, then ln(2 x) = (A) 1.15 (B) 2.27 (C) 2.49 (D) 3.16 (E) 3.58 17. An insect population is growing in such a way that the number in each generation is approximately 1.5 times that of the previous generation. If there are 100 insects in the first generation, approximately how many insects will there be in the fourth gene ration? (A) 338 (B) 475 (C) 506 (D) 813 (E) 1,319 o x y I II III IV

실전 5 6 18. Which of the following are true? I. If x ≠ 2, then x2 + 4 ≠ 8. II. If x2 + 4 ≠ 8, then x ≠ 2. III. If x2 + 4 = 8, then x = 2. (A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III 19. In parallelogram ABCD , AB = 8 and AD = 13. If x = 42, what is the value of h? (A) 5.35 (B) 5.95 (C) 7.20 (D) 8.70 (E) 9.66 20. If f (1) = –3, f (3) = 2, and for all real numbers x, f (x) = ax + b, then ( a, b) = (A) (5 2,11 2) (B) (5 2,− 11 2) (C) (5 2,− 13 2) (D) (− 5 2,11 2) (E) (− 5 2,− 13 2) A B C D x° h Note: figure not drawn to scale.

실전 5 7 21. Which value of x in the interval – 𝜋 2 < x < 𝜋 2 satisfies the equation cos x = sec x? (A) − 𝜋 3 (B) − 𝜋 4 (C) 0 (D) 𝜋 4 (E) 𝜋 3 22. The function g is defined by g (x) = 3sin (2 x + 1) – 1. What is the range of g? (A) – 4 ≤ g (x) ≤ 2 (B) – 2 ≤ g (x) ≤ 4 (C) – 1 ≤ g (x) ≤ 3 (D) − 1 2 ≤ g (x) ≤ 0 (E) 2 ≤ g (x) ≤ 3 23. In the first quadrant of the xy -plane, the point of intersection of the graphs of the line y = x and the ellipse �2 16 + �2 25 = 1 is which of the following? (A) (3.12, 3.12) (B) (4.47, 4.47) (C) (4.50, 4.50) (D) (6.67, 6.67) (E) (9.76, 9.76)

실전 5 8 24. The probability of randomly drawing a piece of red candy from a bag containing only red and purple candies is 2 3. Which of the following could be the number of red and the number of purple candies in the bag? (A) 10 red, 20 purple (B) 20 red, 10 purple (C) 20 red, 30 purple (D) 20 red, 50 purple (E) 30 red, 20 purple 25. The table defines the function f, which has domain {0,1,2,3,4}. What is the value of f (f (3))? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 x f (x) 0 3 1 0 2 1 3 4 4 2 26. Func tions f and g are defined for all real numbers. The function f has zeros at –2, 3, and 7; a nd the function g has zeros at –3, –1, 4, and 7. How many distinct zeros does the product function f • g have? (A) Three (B) Four (C) Six (D) Seven (E) Twelve 27. In the fi gure, the diameter of the base of the right circular cone is 8. What is the volume of the cone? (A) 153.6 (B) 167.6 (C) 351.9 (D) 402.1 (E) 670.2 10

실전 5 9 28. In the xy -plane, what is the distance between the points whose coordinates are (2 √3,4√5) and ( –√3, 7√5)? (A) 3.45 (B) 4.24 (C) 6.93 (D) 8.00 (E) 8.49 29. An isosceles triangle has a base of length 25 centimeters and a vertex angle (the angle opposite the base) of 50º. What is the perimeter of the triangle? (A) 42.3cm (B) 57.9 cm (C) 67.3cm (D) 84.2cm (E) 101.0cm 30. A taxi charges a base fee of $1.25 plus $0.75 for each mile (or part thereof). Which of the following would represent the taxi fare for a trip of length x miles? (Let ⌈𝑥⌉ represent the least integer that is greater than or equal to x.) (A) $2.00 ⌈𝑥⌉ (B) $1.25+$0.75 ⌈𝑥⌉ (C) $0.75+$1.25 ⌈𝑥⌉ (D) $1.25+$0.75 ⌈𝑥+ 1⌉ (E) $0.75+$1.25 ⌈𝑥+ 1⌉ 31. If f (x, y) = �2+�2 �2−�2, then f (x, –y) = (A) –1 (B) 1 (C) �2−�2 �2+�2 (D) �2+�2 �2−�2 (E) �2+�2 �2−�2

실전 5 10 32. Twenty -seven identical cubes are arranged to form a larger cube. The diagonal of each face of each of the 27 identical cubes measures 1.415 centimeters. What is the volume of the larger cube? (A) 1.002cm 3 (B) 2.833cm 3 (C) 9.018cm 3 (D) 27.045cm 3 (E) 76.495cm 3 t, 8, 5, 4, 12, 8 33. In the list above, t is an integer. For the list, if the mean is equal to the median and the range is les than 10, what is the value of t? (A) 2 (B) 6.5 (C) 8 (D) 11 (E) 14 34. Which of the following are polar coordin ates of a point on the graph of r = cos 𝜃? (A) (1,𝜋 2) (B) (0.5,𝜋 3) (C) (1,𝜋) (D) (0.5,2𝜋 3) (E) (1,𝜋 4)

실전 5 11 35. The prime factorization of a positive integer n is p3. Which of the following is true? I. n cannot be even. II. n has only one positive prime factor. III. n has exactly three distinct factors. (A) I only (B) II only (C) III only (D) II and III only (E) I, II, and III 36. In the xy -plane, the asymptotes of a hyperbola are the lines y = x + 5 and y = – x – 5. What are the coordinates of the center of the hyperbola? (A) (0, 0) (B) (–5, 0) (C) (0, –5) (D) (0, 5) (E) (5, 0) 37. The table shows a student’s record of performance on five tests. On which test did the student rank the highest in relation to the other students in class? (assume that the test scores on each test are normally distributes.) (A) Test 1 (B) Test 2 (C) Test 3 (D) Test 4 (E) Test5 Test Number Student’s Score Class Mean Class Standard Deviation 1 85 76 3 2 87 89 7 3 94 88 4 4 88 80 6 5 82 72 5 38. When a positive integer n is divided by 4, the remainder is 3. Which of the following could equal n for some integer t? (A) 4t + 2 (B) 4t (C) 4t – 1 (D) 4t – 2 (E) 4t – 3

실전 5 12 39. In the figure, O is the center of the circle with radius 1, and line CD is tangent to the circle at A. If the measure of ∠AOC is 30º and the length of �� is 3. What is the length of �� ? (A) 2.53 (B) 2.62 (C) 2.93 (D) 3.14 (E) 3.20 40. Let f (x)= ex + x + k. I f f (x) < 0 when x = 1.27 and f (x) > 0 when x = 1.28, which of the following could be a value of k? (A) – 4.70 (B) – 4.75 (C) – 4.80 (D) – 4.85 (E) – 4.90 41. In the graphs, Graph I shows a portion of the graph of f (𝜃) =A[sin( B𝜃+C)]+ D, where A, B, C, and D are constants. Graph II could result from changing which of the constants in f (𝜃)? (A) A only (B) B only (C) C only (D) D only (E) A and D C A B D O 4 2 0 π 2π f(𝜃) 𝜃 Graph I 4 2 0 π 2π f(𝜃) 𝜃 Graph I I

실전 5 13 42. The number of birds on each of islands X and Y remains constant from year to year; however, the birds migrate between islands. After one year, 20 percent of the birds on X have migrated to Y, and 15 percent of the birds on Y have migrated to X. I f the total number of birds is 14,000, how many birds are on island X? (A) 2,800 (B) 6,000 (C) 6,788 (D) 7,212 (E) 8,000 43. If z = 1 – i, which of the points in the figure above is the graphical representation of z2? (A) A (B) B (C) C (D) D (E) E 44. What is the total surface are a of a right circular cylindric al solid if the diameter of its base is 2 r and its height is 2 r? (A) 2πr + 2r (B) πr 2 + 2r (C) 8πr 2 (D) 6πr 2 (E) 2πr 2 45. If the terminal s ide of an angle 𝜃, in standard position, lies in quadrant IV of the xy -plane above, which of the following must be true? (A) csc 𝜃 < 0 and sec 𝜃 > 0 (B) csc 𝜃 < 0 and sec 𝜃 < 0 (C) csc 𝜃 < 0 and tan 𝜃 > 0 (D) csc 𝜃 > 0 and sec 𝜃 < 0 (E) csc 𝜃 > 0 and tan 𝜃 < 0 E C D 1 x y 0 0 i A B o x y I II III IV

실전 5 14 46. A ball is tossed into the air, and the height of the ball above the ground at different times is recorded in the table above. A quadratic regression equation is obtained for these data, with height expressed as a function of time. According to the regress ion equation, what is the maximum height of the ball? (A) 18.8ft (B) 20.5 ft (C) 22.2 ft (D) 22.4ft (E) 30.9ft Time (seconds) 0 0.5 1.5 2 Height (feet) 5 17 20.5 11.9 47. In right triangle ABC , the measure of ∠A is 90º, AB = 3, and BC = x. I f sin C=k, then, in terms of k, AC = (A) √9𝑘2− 9 (B) √9− (3 𝑘) 2 (C) √9− (𝑘 3) 2 (D) √(𝑘 3) 2 − 9 (E) √(3 𝑘) 2 − 9 48. If f(x)= {𝑥 when 0≤ 𝑥 < 1 𝑓(𝑥− 1) when 𝑥 ≥ 1, what is the value of f(4,7)? (A) 4.7 (B) 3.7 (C) 0.7 (D) 0.3 (E) -0.3 49. How many noncongruent triangles ABC exist such that the measure of ∠A is 42 º, AB = 6, and BC = 4? (A) None (B) One (C) Two (D) Three (E) An infinite number

실전 5 15 50. A magazine article described the growth of a computer network as exponential. The article sated that in 10 years, the number of use rs of the network had risen from 1 million to 20 million. Assuming that this article was correct, in how many years would the number of users increase from 20 mil lion to 200 million? (A) 20 (B) 18 (C) 15 (D) 10 (E) 8



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