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[PDF] SAT Mathematics Level 2 Practice Test 05 with Answer Keys.pdf | Plain Text

실전 7 1 1. What is the greatest common divisor of the three integers 36 , 72 , and 90 ? (A) 27 (B) 18 (C) 12 (D) 9 (E) 6 2. If �(�)= ��2+ �� + � is concave downward, which of the following must be true? (A) � < 0 (B) � > 0 (C) �2− 4�� > 0 (D) �< 0 (E) �2− 4�� < 0 3. Given that the set of data 486, 162, 54,… is geometric sequence, what is the sixth term? (A) 6 (B) 2 (C) 2 3 (D) 2 9 (E) 2 27 4. In the figure below, the length of h is (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 5. If �(�)= 𝑥+1 𝑥2−𝑥−30, vertical asymptote(s) of �(�) is(are) (A) � = 10 ,−3 (B) � = 6 (C) � = −5,6 (D) � = 5 (E) � = −6,5 8 h 61º

실전 7 2 6. If �(�)= 2cos � and �(�)= �4− 2, then the value of �(�(𝜋 6))=? (A) 27 (B) 18 (C) 12 (D) 9 (E) 7 8. If � = �� + � and � = �� + � are perpendicular, which one of the following is true? (A) �� = −1 (B) � = �,� ≠ � (C) � = �,� = � (D) � ≠ � (E) �� = �� 9. In the figure, if tan � = 3, what is the area of triangle? (A) 72 (B) 84 (C) 96 (D) 108 (E) 120 10. If t is the time passed since consumer buys a product and �(𝑡)= −𝑡2+ 3𝑡+ 4 is the satisfaction of a consumer. When does the satisfaction of a consumer reach zero? (A) in one hour (B) in two hour (C) in three hours (D) in four hours (E) in five hours A 8

실전 7 3 11. If |�|+ |�|≤ 1, which of the following can be (�,�)? (A) (− 1 3,1 2) (B) (3 2,5 3) (C) (2,1 2) (D) (− 3 2,−1) (E) (− 5 2,1) 12. If � = 2�− 5, which one of the following has the same x- intercept? (A) � = 4�− 6 (B) � = 1 2�+ 10 (C) � = 1 3�− 10 3 (D) � = − 2 3�+ 5 (E) � = − 2 3�+ 5 3 13. In a used car market, 50% of the cars are black and 12% of them have two doors. When a customer buys a car, the probability that he selects a black with two doors is (A) 3 50 (B) 3 20 (C) 1 15 (D) 1 10 (E) 1 3

실전 7 4 14. The graph of the curve represented by {� = 𝑡 � = √𝑡 is ( t ≥ 0) (A) a portion of circle (B) line (C) a portion of ellipse (D) a portion of hyperbola (E) a portion of parabola 15. lim𝑥→0 sin 2𝑥 𝑥 = (A) ∞ (B) –∞ (C) 0 (D) 1 (E) 2 16. Given the set of data 1, 1, 2, 4, 5, 6, 9, which two numbers should be added to make its mode and mean equal? (A) (2,4) (B) (3,5) (C) (4,4) (D) (5,6) (E) (7,7) 17. If �(�)= �(�− 2)2+ 15 and �(1)= 2, then � =? (A) 13 (B) –13 (C) 10 (D) –10 (E) 7 18. Which one of the following is different from the others? (A) log 525 (B) log 24 (C) log 510 (D) log 13 1 9 (E) log 12 1 4

실전 7 5 19. Which o ne of the following has domain of all real numbers? (A) � = √� (B) � = 2𝑥+1 𝑥−2 (C) � = |�− 3| (D) � = ln � (E) � = |log �| 20. If 3(𝑥−15)2 = 1,then � =? (A) 0 (B) 1 (C) 1 3 (D) 1 5 (E) 2 21. When a group of bees constructs a hive, it doubles in size every year. If the area is 1 square at first, how long does it take to become 100,000 square? (A) 16.61 (B) 12.21 (C) 10.31 (D) 8.65 (E) 6.72 22. Which of the following is always true for all real numbers? I. �2− 2�− 3> 0 II. �2− 4�+ 4> 0 III. �2− �+ 5 > 0 (A) I (B) II (C) III (D) I, II (E) I, II, III

실전 7 6 23. If 4 9𝑛 is a positive integer, which one of the following is also a positive integer? (A) 2 3𝑛 (B) 3 4𝑛 (C) 2 5𝑛 (D) 1 2𝑛 (E) 2 7𝑛 24. If x is an acute angle and cos (𝜋 2− 2�)= 1 2, then x =? (A) 𝜋 12 (B) 5 12 𝜋 (C) 𝜋 12 ,5 12 𝜋 (D) 𝜋 12 ,7 12 𝜋 (E) 5 12 𝜋,7 12 𝜋 25. The arithmetic mean of ten numbers is 25. If 7, 9, and 12 are excluded from the ten numbers, the arithmetic mean of the seven numbers is (A) 31.71 (B) 27.12 (C) 21.45 (D) 18.72 (E) 11.35 26. Which of the following is the solution of |�3− 3|< 7? (A) −2< � < 3.16 (B) −1.59 < � < 2.15 (C) � > 2.15 or � < −1.59 (D) � > 2 or � > 3.16

실전 7 7 (E) � < 3.16 or � > −1.59 27. If x and f(x) are given in the table below and f(f(x))=10, then x = ? (A) 3 (B) 5 (C) 7 (D) 8 (E) 10 x f(x) 3 10 5 2 7 3 8 12 10 1 28. If �2+ �2= 15 and �� = 3.75 , then (�+ �)2=? (A) 11.5 (B) 13.5 (C) 18.5 (D) 20.5 (E) 22.5 29. There are �(�),|�(�)| and they have no solutions in common. Which one of the following must be true? (A) �(�)= −�(−�) (B) If x1 < x2, then f(x1)> f(x2) (C) �(�)= �(−�) (D) �(�)< 0 for all real numbers (E) �(�)> 0 for all real numbers 30. In the figure below, the length of �� is? (A) 7.18 (B) 9.55 (C) 10.50 (D) 17.36 (E) 25.37 31. If a a1 = 1, a2 =3, and an = 2𝑎𝑛−1+3 𝑎𝑛−2 , then a5 = ? (A) 9 (B) 7 (C) 5 3 (D) 13 6 A C B 30º 13.5 40º

실전 7 8 (E) 17 9 32. If (�− 1)(�− 3)(�+ 3)(�+ 5)< 0, the range of its roots is included by (A) −5< � < −2 (B) −4< � < −2 (C) −3< � < 1 (D) 0< � ≤ 1 (E) 2≤ � < 4 33. When 367 is divided by primer number n, the remainder is 10. When 45 is divided by n, the remainder is? (A) 3 (B) 5 (C) 7 (D) 9 (E) 11 34. Which one of the following satisfies f=f–1? (A) � = log � (B) � = �𝑥 (C) � = −� (D) � = 2𝑥+3 𝑥+1 (E) � = |�| 35. If � = 2cos (4�− 1)+ 2, which line of the following has the same frequency? (A) � = tan (2�− 1) (B) � = 4cos 2�+ 1 (C) � = 4sin 8� (D) � = 1 2sin (2�+ 1)− 1 (E) � = 2sin 2�+ 2

실전 7 9 36. There is a cylinder. If its radius is decreased by 50% and the height is increased by 60% compared to its initial state, the volume of the cylinder… (A) increased by 40% (B) decreased by 40% (C) increased by 60% (D) decreased by 60% (E) did not change

실전 7 10 37. If the figure below represents � = �(�), which of the following represents �(�)= −�(�− 2)? y x x y (C) x y (D) x y (A) x y (B) (E) x y

실전 7 11 38. In the figure below, 𝜃 =? (A) 110.31º (B) 123.69º (C) 133.62º (D) 142.32º (E) 151.35º 39. If �(�)= (�,�,�)= (�,�,�) and �(�,�,�)= (−�,−�,0), then �(�(3,2,1))= (A) (–3,–1,0) (B) (–3,0, –1) (C) (–1,–3,0) (D) (0, –1,–3) (E) (–1,0, –3) 40. In the expression �� = �− 3�, which of the following cannot be the value of �? (A) 0 (B) –1 (C) –3 (D) 1 (E) 3 41. What is the probability of correcting at least four questions among 5 -true -or -false questions? (A) 3 16 (B) 3 8 (C) 3 4 (D) 1 2 (E) 1 42. In the figure, the area of rectangles is (A) 3.67 (B) 4.97 (C) 5.31 (D) 7.74 (E) 8.65 x y 𝜃 (-2,3)

실전 7 12 43. Which of the following has the same root when you replace x with –x? (A) 2�2+ 2�− 1= 0 (B) 2�3− 3� = 0 (C) �4+ �2− 2� = 0 (D) �4− 3�2+ �+ 1= 0 (E) 2�3− 3�2+ 1 = 0 44. There are seven people in total. If a group is made up of either 3 or 4 people. How many different groups can be made up? (A) 30 (B) 50 (C) 70 (D) 80 (E) 110 45. Edward leaves home t hours before noon driving at 50 miles per hour for t hours. His wife Ann leaves home an hour later driving at 40 miles per hour on the same straight road in the same direction. Which of the following represents the distance between them at noon? (A) |10 t–10| (B) |10 t+40| (C) |10 t+10| (D) |10 t+50| (E) |10 t–50| 46. What is the maximum value of (1− sin �)(2− cos 3�)? (A) 3.19 (B) 4.78 (C) 5.12 (D) 5.64 (E) 6.21 4 x y 5 3 2 1 y= ln x

실전 7 13 47. Which of the following can be produced when distant planes meet? I. line II. point III. ray (A) I (B) I,II (C) I,III (D) II, III (E) I,II,III 48. If 7 3≤ � ≤ 22 5, the probability of � ≥ 4 is? (A) 0.12 (B) 0.19 (C) 0.23 (D) 0.31 (E) 0.37 49. In the figure below, the airplane flies 11 feet above the ground. The angle between ongoing direction and city A, B is 43º, 17º respectively. What is the distance from city A to B? (A) 15.32 (B) 17.75 (C) 19.02 (D) 20.71 (E) 24.18 50. If 0< 𝜃 < 𝜋 2 and cos 𝜃 = 2𝑡, then sin 𝜃 2= (A) √1+2𝑡 2 (B) √1−2𝑡 2 (C) 1− 4𝑡2 (D) 8𝑡2− 1 (E) √1−2𝑡 1+2𝑡 43 º 17 º City A City B 11



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