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실전 4 1 1. If y=f (x) passes through the point (0,0), which point does y=f (x–2)+3 pass through? (A) (3,2) (B) (–2,3) (C) (2,3) (D) (2, –3) (E) (–2,–3) 2. If f(x) = [ x] and ([ x] is the greatest integer less than or equal to x), then what is the value of f(f(–1 3))? (A) –2 (B) –1 (C) 0 (D) 1 (E) 2 3. If (�)= { || ,� ≠ 0 1,� = 0 , what is the value of f(4.5) – f(–4.5)? (A) –2 (B) 0 (C) 2 (D) 4 (E) 9 4. If s and t are two roots of x2 – 7x + 2 = 0, the quadratic equation whose roots are s+ 1 and t+ 1 is equal to (A) x2+9 x+10=0 (B) x2–10 x+9=0 (C) x2+9 x–10=0 (D) x2+10 x+9=0 (E) x2–9x+10=0 5. What is the length of the major axis of an ellipse whose equation is 16 x2+32 x+25y 2–384=0 (A) 6 (B) 7 (C) 8 (D) 9 (E) 10

실전 4 2 6. What is the ma gnitude of vector �→ with initial point (0,1) and terminal point (3, –3)? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 7. Vector �→ has initial point (1, –2) and terminal point (2, 1). Vector �→ has initial point (3,4) and terminal point ( –5,7). What is 2�→ +3 �→ ? (A) (–22,15) (B) (22, –15) (C) (15, –22) (D) (–15,22) (E) (–22, –15) 8. Find all values that satisfy the determinant equation for |� 5 � �|=4 9. If w is the complex number shown in the figure below, which of the following points could be –iw ? (A) A (B) B (C) C (D) D (E) E 10. Find the vertex, focus and the directrix 10 -1. ( y–1)2 = 8( x+2) 10 -1. ( x–3)2 = 2( y+1) 11. The angle for the �⃗ and �⃗ is 50º. The magnitude for these vectors �⃗ and �⃗ are 5 and 8 respectively, what is the magnitude of �⃗ – �⃗? x y D A C E B i W 50 0 �⃗ �⃗

실전 4 3 12. Given the three vectors, �⃗, �⃗⃗, �⃗ in the figure, which of the following expressions denotes the vector operation shown? (A) �⃗ + �⃗⃗ = �⃗ (B) �⃗ + �⃗ = �⃗⃗ (C) �⃗ + �⃗⃗ = �⃗ (D) �⃗⃗ – �⃗ = �⃗ (E) –�⃗⃗ – �⃗ = �⃗ 13. What is the inverse matrix of [1 2 1 3]? 14. If the asymptotes do not exist in the expression 3+6 +, what is the value of k? 15. Which of the following line is (are) asymptotes of the graph of f(x) = 10(2−4) (22−2)? I. y= 5 II. x=± 2 III. x=± 1 (A) I only (B) II only (C) III only (D) I and II only (E) I and III only 16. If the graph shown is the graph of y=f (x), when y=f (x), what is the value of zero of 1 ()? 17. Which of the following is equivalent to the equation x2+y 2–2y+ 3=0 in its polar form? (A) r2 –rsin +3=0 (B) r2 –2rsin +3=0 (C) r2 –2cos +3=0 (D) –r2 –rsin =0 (E) r2 +3=0 �⃗ �⃗⃗ �⃗ x y 3

실전 4 4 18. A point has polar coordinate (1, 3). The same point cannot be represented by (A) (–1, 7 3) (B) (1, 7 3) (C) (1, –5 3) (D) (–1, 4 3) (E) (–1, 10 3 ) 19. Which of the following has the point on the polar curve r=2cos(2 )? (A) (2, 2) (B) (1, 4) (C) (1, 6) (D) (√2, 6) (E) (–1, 3 4) 20. If the second term of an arithmetic sequence is 7, and the 6 th term is 23, then what is the 90 th term? (A) 127 (B) 180 (C) 243 (D) 327 (E) 359 21. Some number “ a” is added to the number 1, 13, 61 to create the first three terms of a geometric sequence, what is the value of “ a”? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

실전 4 5 22. A committee of people is to be selected from a group of 5 men and 4 women. Assuming that the selection is made randomly, what is the probability that the committee consists of 3 men and 2 women? (A) 10 21 (B) 5 21 (C) 1 7 (D) 1 5 (E) 4 15 23. A jar contains 7 black, 5 red, 8 green balls. Every time a ball is removed from the jar, it is not replaced. What is the probability that the second ball is red if the first ball chosen is red? (A) 1 4 (B) 7 20 (C) 2 5 (D) 1 19 (E) 4 19 24. What is the probability of getting three odd numbers when choosing three numbers among {1,2,3,4,5,6,7} at random? (A) 4 17 (B) 4 35 (C) 3 70 (D) 4 45 (E) 1 5

실전 4 6 25. There are three seats at the front row of the class room. Jim, Jane, and Pam are trying to sit at the front. What is the probability that Jane and Pam will sit right next to each other? (A) 2 3 (B) 1 6 (C) 1 2 (D) 1 3 (E) 1 4 26. In a used car market, 50% of the cars are white, and 30% of them have two doors, what is the probability of choosing a white car with two doors? (A) 0.10 (B) 0.12 (C) 0.15 (D) 0.2 (E) 0.25 27. In a recent survey, it was reported that 75% of the population of a c ertain state lived within 10 miles of its largest city and that 40% of those who lived within 10 miles of the largest city lived is single -family house. If a resident of this state is selected at ran dom, what is the probability that he lives in a single -family house within 10 miles of the largest city? (A) 0.10 (B) 0.15 (C) 0.30 (D) 0.35 (E) 0.53

실전 4 7 28. In a certain experiment there is a 0.23 probability that any thermometer used is in error by more than 1 error. If 3 thermometers are used, what is the probability that all of them are in error by more than one error? (A) 0.0062 (B) 0.027 (C) 0.21 (D) 0.012 (E) 0.18 29. What is the probability of either getting 3 or 4 correct answers among 5 true -or-false questions? (A) 0.12 (B) 0.53 (C) 0.72 (D) 0.33 (E) 0.47 30. If 4 3 ≤ x≤ 27 8, then what is the probability of x≥ 2? (A) 0.37 (B) 0.52 (C) 0.67 (D) 0.75 (E) 0.87 31. If –1≤ x ≤1 and –1≤ y ≤1, what is the probability that the distance from the origin is less then 1? (A) 2 (B) 4 (C) 5 (D) 6 (E) 8

실전 4 8 32. The probability of Andy answering correctly is 0.6 and the probability of Jim getting the answer correct is 0.4. What is the probability of at least one of them getting the answer correctly? (A) 0.76 (B) 0.70 (C) 0.24 (D) 0.48 (E) 0.52 33. Box A and box B both contain red balls and blue balls. From the box A, the probability of getting red is 3 8 and 2 3 from the box B. W hat is the probability of getting a blue ball from both of the boxes A and B? (A) 1 4 (B) 5 21 (C) 5 24 (D) 5 48 (E) 5 63 34. When we randomly select two members from {1,5,10,100}, what is the probability that the sum of these two selected numbers is bigger than 100? (A) 0.3 (B) 0.4 (C) 0.5 (D) 0.6 (E) 0.7 35. We choose a number 1 to 10 twice. We replace the selected number for the next selection. Find the probability that these two selected numbers is equal to 7. (A) 0.01 (B) 0.06 (C) 0.07 (D) 0.08 (E) 0.09

실전 4 9 36. The diagram represents 5 points on a segment. How many segments can we make by connecting with the end point? (A) 6 (B) 8 (C) 10 (D) 12 (E) 16 37. In how many ways can 9 people be divided into two groups, one with 5 people and the other with 4 people? (A) 72 (B) 92 (C) 126 (D) 252 (E) 504 38. If x – 1 is a factor of x3 + 3x2 – kx + 5 then k is? (A) 3 (B) 5 (C) 7 (D) 9.6 (E) 11 39. A taxi charge $1.2 for the first 3 miles and $0.7 for each additional mile. If a customer rides in this taxi for 1 5 miles which of the following represents the price that a customer needs to pay? (A) $5.4 (B) $12 (C) $14.1 (D) $16.5 (E) $28.5

실전 4 10 40. The mean of the ages of 15 girls is A and the mean of the ages of 20 boys is B. What is the total Average of all the ages combined? (A) 15A+20B (B) 35(A+B) (C) � 15 + � 20 (D) 20A+15B (E) 15�+20� 35 41. A club has ten members, and the number of the members is tripled in 54 minutes. At this rate, what will be the number of the members in 3.6 hours? (A) 810 (B) 930 (C) 1020 (D) 1150 (E) 1240 42. The price of houses was $17850 in 1950 and it doubled in 2000. At what rate did the price increase each year from 1950 to 2000? (A) 1.0% (B) 1.4% (C) 1.7% (D) 2.1% (E) 2.5% 43. An initial amount of radioactive material is M p. However, every year the initial amount halves. Obtain an expression for the amount of radioactive material left after t years? (A) M 02t (B) M0 2 (C) M0 22 (D) 2 M0 (E) teM0

실전 4 11 44. What is the ratio of the volume for two spheres with radius r and 2r? (A) 1:8 (B) 1:4 (C) 1:2 (D) 1:1 (E) 1:10 45. The diagram shown represents that AB and CD is parallel and the length of AB is 2.5. What is the area of the trapezoid ABCD? (A) 6.13 (B) 7.23 (C) 8.13 (D) 8.83 (E) 9.02 46. In the figure, what is the area of trapezoid? y= log K (A) 135 (B) 170 (C) 235 (D) 270 (E) 300 47. The distance between the origin and a post (x,y) is 3, what is the distance between the origin and a point (2 x, 2 y)? (A) 4 (B) 5 (C) 6 (D) 8 (E) 12 48. If n! must be divided into 9, then what is the condition required for n? (A) n>2 (B) n≥3 (C) n is a multiple of 3 (D) n is a prime number (E) n≥9 A D C x y B y = 4–x2 0 x y 10 100 y = log K

실전 4 12 49. Given that 7 6=10r+s, and that S is a smaller integer than 10. What is the value of S? (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 50. In the distribution below, ABC is a prime number and C is a multiple of 3. What is the possible value of A+B+C? 2, ABC, 233, 326… (A) 2 (B) 3 (C) 5 (D) 6 (E) 9

실전 4 13 1. c 36. c 2. b 37. c 3. c 38. d 4. e 39. b 5. e 40. e 6. b 41. a 7. a 42. b 8. –0.7016 5.7016 43. b 9. a 44. a 10. 10 -1. ( –2,1) (0,1) x= –4 10 -2. (3, –1) (3, –1 2) � = –3 2 45. 7.92 11. 6.13 46. a 12. c 47. c 13. [3 –2 –1 1 ] 48. e 14. 2 49. e 15. e 50. c 16. 3 17. b 18. a 19. c 20. e 21. c 22. a 23. d 24. b 25. a 26. c 27. c 28. d 29. e 30. c 31. b 32. a 33. c 34. 1 2c 35. a?