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# 20 1 1. There is a computer that takes 58 seconds to save 2 mega bytes . How long will it take to save 420 mega bytes to 1.44 megabyte floppy disk? (A) 472 (B) 679 (C) 1,480 (D) 7,362 (E) 12,180 2. When x = 3, which of the following is the greatest value? (A) 2 −7 (B) 3 +1 (C) 2 −1 (D) 1 (E) +1 −2 3. When ( x – 2)3 = 10, what is the value of x? (A) 2.82 (B) 3.34 (C) 4.15 (D) 5.17 (E) 6.47 4. From 3 k + 1, k is an integer and 3 k + 1 is a prime number. Which of the following is the counterexample of k? (A) 2 (B) 4 (C) 6 (D) 8 (E) 10
# 20 2 5. If f(g(x)) = 4 x + 1 and g(x) = 2 x – 1, then f(x) = (A) 8− 3 (B) 8− 4 (C) 1 2− 1 (D) 2+ 3 (E) 2+ 1 6. What is the sum of arithmetic sequence 2+6+10+14+18+22? (A) 36 (B) 48 (C) 52 (D) 64 (E) 72 7. The relation between the height and the length of the radius of a pine tree in a certain region is like the following. When the height of this pine tree is h and the length of a radius is l, h = 25(1.50) k, l = k2(h – 52). When k = 1.87, what is l, the length of the radius of this pine tree? (A) 12 (B) 15 (C) 17 (D) 22 (E) 29 8. x is a real number in ( x – 2)(x2 + 4) = 0. Then, what is the value of ( x – 1)( x2 + 4) ? (A) 1 (B) 2 (C) 4 (D) 8 (E) 16
# 20 3 9. How many positive three -digit integers are not divisible 3 ? (A) 214 (B) 300 (C) 548 (D) 600 (E) 782 10. �()= (−1)(+1)(+2) (−1) . Which of the following is true? (A) f(x) is discontinuous at x = –2 (B) f(x) is discontinuous at x = –1 (C) f(x) is discontinuous at x = 1 (D) f(x) is discontinuous at x = 0 (E) f(x) is continuous for all real numbers 11. 1 + 1 3 = 1 12. Then what is the value of k? (A) 1 (B) 2 (C) 6 (D) 12 (E) 16
# 20 4 12. In the figure below, what is ? (A) 195.04º (B) 207.73º (C) 210.96º (D) 221.37º (E) 239.04º 13. How many positive four digit even integers can be made by using digits 0, 1, 2, 3 once? (A) 6 (B) 10 (C) 12 (D) 24 (E) 48 14. What is the center point of the circle equation, (x – 1)2 + ( y – 3) 2 = 25? (A) (1, 3) (B) (3, 1) (C) (–1, –3) (D) (–3, –1) (E) (1, –3)
# 20 5 15. When x is all real numbers, what is the domain of √9−2 −1? (A) x ≠ 1 (B) |x| ≦ 3 (C) |x| ≦ 3, x ≠ 1 (D) x ≧ 1 (E) |x| ≧ 3, x ≠ 1 16. If x approaches 2 infinitely, what is the value of 2−3+2 −2 (A) ∞ (B) 0 (C) 1 (D) 2 (E) None of these 17. In a 320 -mile trip, a car was driving at 100 mile per hour until certain time t. After t hour, if the car traveled the rest of the trip at 80 mile per hour, what is the equation that represents total trip time? (A) 16 t (B) �−16 4 (C) 16−� 4 (D) �−1 4 (E) 8
# 20 6 18. ()! (+1)! = (A) n (B) 1 −1 (C) +1 (D) 1 (E) 1 +1 19. ax 2 + bx + c = 3 has exactly two roots. Which of the following must be true? (A) a ≠ 0 (B) b > 3 (C) a + b + c > 0 (D) a > b (E) c > 0 20. y = f(x) is shown on the graph below. Which of the following is true if y = ax 3 + bx 2 + cx + d? (A) f(x) have three real roots. (B) a > 0 and f(x) has one real root and two imaginary roots. (C) a < 0 and f(x) has three real roots. (D) a < 0 and f(x) has one real root and two imaginary roots (E) a > 0 and b = c = d
# 20 7 21. What is the midpoint between (1, 2, 3) and (3, 4, 3)? (A) (3, 1, 2) (B) (2, 2, 3) (C) (1, 2, 2) (D) (0, 1, 2) (E) (2, 3, 3) 22. There are 100 consecutive odd integers. Which of the following must be true? I. Range is always even. II. Mean and median is the same. III. Median is the same with standard deviation. (A) I (B) II (C) I and II (D) I and III (E) II and III 23. When ln x = 0, what is the value of �? (A) –2.71 (B) –1 (C) 0 (D) 1 (E) 2.71 24. What is the magnitude of a vector whose initial point is (1, 2) and the terminal point is ( –2, –2)? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5
# 20 8 25. If f(x) = { || (≠ 0) 1 (= 0) , what is the value of f(1.5) – f(–1.5)? (A) –2 (B) 0 (C) 2 (D) 3 (E) 9 26. When f(x) = [] , [] is the greatest integer less than or equal to x, what is the value of (f ∘ f)(√3)? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 27. (s, t ) is on f(x) = √22+ 3. Which of the following points is on y = f(x) ? (A) (–s, –t) (B) (s, –t) (C) (t, s ) (D) (–s, t ) (E) (–t, –s) 28. For f(x) = 2 + bx + 4, a and b are all real numbers. If f(x) intersects with x axis at 1 and 4, what is the value of a? (A) – 1 (B) – 1 2 (C) 1 2 (D) 1 (E) 2
# 20 9 29. y = sin3 x is moved to the left by 1 units and up by 2 units. Which of the following is true? (A) y – 2 = sin (3( –x + 1)) (B) y – 2 = sin (3( x + 1)) (C) y – 2 = sin (3( x – 1)) (D) y + 2 = sin (3( x – 1)) (E) y + 2 = sin (3( x + 1)) 30. What is the range of f(x) = 4 – 3x + 1? (A) f(x) ≧ 1.06 (B) f(x) ≧ 0 (C) f(x) ≧ – 1.03 (D) f(x) ≧ 1 (E) All real numbers 31. ‘n’ friends were to pay $240 for the dinner. However, at the last moment four of friends couldn’t participate. Therefore, each of the rest of the members need to pay $80 more for the dinner. How much is the final cost of the dinner per person? (A) $40 (B) $80 (C) $100 (D) $120 (E) $200
# 20 10 32. In the figure above, which of the following is true? I. �→ = �→ II. �→ = �→ III. |�|→ =|�|→ (A) I (B) II (C) III (D) I and II (E) I and III 33. The re are three seats at the front row of the classroom. Jim, Jane, and Pam are trying to sit at the front. What is the probability that Jane and Pam will sit next to each other? (A) 2 3 (B) 1 6 (C) 1 2 (D) 1 3 (E) 1 4
# 20 11 34. cos = 0.21 and is the radian. Which of the following is NOT ? (A) 1.359 (B) – 1.359 (C) 1.359 + 2 (D) – 1.359 – 2 (E) – 1.359 + 35. Three different points A, B, and C lie on a line in that order. If A(2, 3), B(4, 6), and AB : BC = 2 : 1, what is the coordinate of point C? (A) (5, 7.5) (B) (7.5, 5) (C) (8, 12) (D) (12, 8) (E) (5, 8) 36. In the figure above , (�∘�)()= 4. What is the value of x? (A) –8 (B) –6 (C) 0 (D) 12 (E) 24
# 20 12 37. A writer is paid $475 every month and $0.25 per a poem additionally. If the writer gave n poems to the publisher, 40% of the total money that he earned can be expressed as _____. (A) 0.2(�+ 0.2)+ 475 (B) 0.4(�+ 0.2)+ 475 (C) 0.4(0.25 �+ 475 ) (D) 0.4 × 0.25 �+ 475 (E) 0.2(�+ 475 ) 38. When cos(cos x) = 0.57, what is cos x? (A) 0.570 (B) 0.842 (C) 0.893 (D) 0.964 (E) 1.000 39. Minute hand of a certain clock is twice the length of its hour hand. If the length of the hour hand is 4cm and the hour hand and minute hand are each pointing at 3 and 1, when the end of the minute hand is connected to the end of hour hand by the chord, what is the length of the chord? (A) 2 (B) 2√3 (C) 4√2 (D) 4√3 (E) 6
# 20 13 40. Box A and box B both contain black balls and yellow balls. F or box A, probability of getting black is 2 7 and 3 5 for box B. What is the probability of getting yellow ball from both boxes A and B? (A) 1 5 (B) 2 7 (C) 5 7 (D) 6 35 (E) 2 5 41. In the figure above, x = 5 and y = 12. What is the volume of this solid figure? (A) sin (B) 150sin (C) 25� 2 (D) 12sin (E) 300sin 42. If =–∙−1 and 1= 1+ , then what is 14 ? (A) –1+ (B) –1− (C) 1− (D) 1+ (E)
# 20 14 43. The volume of a cylinder is 10. The other cylinder’s radius is 30% larger than that of the other cylinder and its height 30% longer. What is the volume of the other cylinder? (A) 15.55 (B) 17.62 (C) 19.35 (D) 21.97 (E) 23.57 44. There are 10 -capped bottles on the table. The weight of 10 bottles is equal, and the weight of the caps is also equal. If all 10 caps of the bottles are removed, which of the following is not true? (A) Mean is decreased (B) Median is decreased (C) Mode is decreased (D) Standard deviation is decreased (E) Range is not changed 45. The mean of the annual salaries of the five workers at company A is 43,275 and the median of the salaries is 48,300. The annual salaries of the ten workers at company B are each 45,000. Which one of the following statements is true? (A) The mode and the median of B company are different (B) The mean salary of the company A workers who earn less than 48,300 is always higher than the mean of the annual salaries of the ten company B workers. (C) As a median gets larger, a mean always gets smaller. (D) The annual salary of the company A workers who get the lowest salary is equal to the mean of the annual salaries of the ten company B workers. (E) The highest annual salary of the company A workers is higher than the mean of the annual salaries of the ten compa ny B workers.
# 20 15 46. For �� �� = 0.7 and �� �� = 2, what is the value of �� ��� ? (A) 1.3 (B) 1.4 (C) 1.8 (D) 2.1 (E) 2.7 47. How many intersection points do f(x) and g(x) have when f(x) = ln x and g(x ) = x – 100? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 48. Which of the following is true? I. �� 2− 1= �� 2 II. �� 2 = 1− 2�� 2 III. �� 2+ 2�� 2 = 1 (A) None (B) I (C) II (D) I and II (E) II and III 49. 11 + 510 is a perfect square integer. Which of the following could be the value of x? (A) 2 (B) 3 (C) 10 (D) 11 (E) 15
# 20 16 50. ln (1+ �� 2) = (A) –2ln|csc x| (B) 2ln|cot x| (C) ln|sin 2x| (D) ln|sec x| (E) –2ln |cos x|
# 20 17 1. E 2. E 3. C 4. D 5. D 6. E 7. B 8. D 9. D 10. C 11. E 12. C 13. B 14. A 15. C 16. C 17. C 18. E 19. A 20. B 21. E 22. C 23. E 24. E 25. C 26. B 27. D 28. D 29. B 30. C 31. D 32. E 33. A 34. E 35. A 36. E 37. C 38. D 39. D 40. B 41. B 42. C 43. D 44. D 45. E 46. E 47. C 48. C 49. D 50. E