[PDF] SAT Mathematics Level 2 Practice Test 07.pdf | Plain Text

실전 9 1 1. If �(𝑡)= 3𝑡2− 8𝑡+ 1, then �(3)− �(2)= (A) 7 (B) 4 (C) –3 (D) –4 (E) –7 5, 8, 9, 10, t 2. For what value of t is the average (arithmetic mean) of the five numbers above equal to 7? (A) –4 (B) –1 (C) 3 (D) 4 (E) 7 3. In the xy -plane, which of the following is an equation for the line that contains the point (2, –3) and has an x-intercept of 5? (A) � = −4�+ 5 (B) � = �− 5 (C) � = 2�− 7 (D) � = 3�− 9 (E) � = 5�− 3 4. When 𝑛 = 5, which of the following is greatest? (A) 6 𝑛 (B) 6 𝑛+1 (C) 6 𝑛−1 (D) 𝑛 6 (E) 𝑛+2 6 5. If |�− 2|= 9, which of the following could equal |�+ 3|? (A) 4 (B) 7 (C) 8 (D) 10 (E) 11

실전 9 2 6. In the coordinate plane, if the distance between the point (�,�) and the origin is 3, what is the distance between the point (2�,2�) and the origin? (A) 3 2 (B) 3 (C) 6 (D) 6√2 (E) 9 7. What is the radius of a sphere whose volume is 75.8 cubic centimeters? (A) 1.0cm (B) 2.6cm (C) 3.2 cm (D) 3.8cm (E) 5.6cm 8. If 2� = � and �= � 4, then � �= (A) 8 (B) 4 (C) 2 (D) 1 4 (E) 1 8 9. For which of the following functions is �(2)= �(4)? (A) �(�)= 2� (B) �(�)= �2 (C) �(�)= (�+ 3)2 (D) �(�)= (�− 3)2 (E) �(�)= |�− 4| 10. If 0º < 𝜃 < 90º and sin 2𝜃+cos 2𝜃 sin 𝜃 = 1.61 , what is the measure of 𝜃? (A) 31.8º (B) 37.6º (C) 38.4º (D) 51.6º (E) 58.2º

실전 9 3 {1, 5, 10, 100} 11. If two distinct numbers are chosen at random from the set above, what is the probability that their sum will be greater than 100? (A) 0.17 (B) 0.33 (C) 0.50 (D) 0.67 (E) 0.83 12. A store sets the price of an item as the cost of the item plus a percent markup. If the store’s cost for a certain item is $120 and the store sets the price of the item at $174, what is the percent markup? (A) 31% (B) 45% (C) 54% (D) 69% (E) 145% 13. In the xy -plane, two lines, l and n, are perpendicular. If the equation of line l is � = −4�+ �, which of the following could be the equation of line n? (A) � = −4�− � (B) � = −4�− 1 � (C) � = − � 4+ � (D) � = � 4+ � (E) � = 4�+ � 14. If �(�)= ln � and �(�)= 2�+ 1, then �(�(√2))= (A) 1.32 (B) 1.34 (C) 1.69 (D) 1.73 (E) 2.04

실전 9 4 15. Two ordered pairs of integers (�,�) and (�,�), where �� ≠ 0, are defined to be equivalent if and only if �� = �� . Which of the following is equivalent to (4,3)? (A) (–3,–4) (B) (8, –6) (C) (9,7) (D) (12,9) (E) (16,9) 16. If a and b are nonzero real numbers, which of the following equations is NOT equivalent to any of the other four? (A) −�= (−�)2 (B) −� = �2 (C) � = −(−�)2 (D) � = −�2 (E) � = (−�)2 17. A water balloon is dropped from a window 40 feet above ground level. The balloon’s height ℎ(𝑡)= −16 2+ 40 . How many seconds after the water balloon is dropped will it be 20 feet above ground level? (A) 0.89 (B) 1.12 (C) 1.25 (D) 1.58 (E) 2.00 18. The temperature in degrees Fahrenheit F is related to the temperature in degrees Celsius C by the formula � = 9 5� + 32 . At which of the following temperatures is the equivalent Fahrenheit temperature one half of the Celsius temperature? (A) –40ºC (B) –24.6º C (C) –12.3ºC (D) 32ºC (E) 160ºC

실전 9 5 19. What is the second term of the geometric sequence with common ratio -3 and third term 18? (A) 15 (B) 6 (C) 5 (D) –6 (E) –54 20. If �(�)= �2− 1, which of the following are true? I. �(�)= �(−�) for all x. II. �(�)= −�(�) for all x. III. �(0)> �(−1) (A) I only (B) III only (C) I, and II only (D) II and III only (E) I, II, and III 21. Vince is standing 100 feet from the base of a palm tree, as shown in the figure above. He measures the angle of elevation from the top of his head to the center of the top of the tree to be 26º. If Vince is 6 feet tall, how tall is the palm tree? (A) 48.8ft (B) 49.8ft (C) 54.8ft (D) 95.9ft (E) 211.0ft 22. In the xy -plane, what is the shortest distance between the curve �2 4 + �2 9 = 1 and the line � = 15 ? (A) 6 (B) 12 (C) 13 (D) 17 (E) 18

실전 9 6 23. The 2 bases of prism P are pentagons. If P has 5 rectangular faces, how many edges does P have? (A) Five (B) Seven (C) Ten (D) Twelve (E) Fifteen 24. If �(�(�))= � and �(�)= 1 �, then �(�)= (A) 1 �2 (B) 1 � (C) � (D) �2 (E) −� 25. The first row in the figure above contains 1 small triangle. In the second row of the figure, there are 3 small triangles. If the pattern is continued as shown, with 2 triangles being added to each new row, how many triangles will be in row 101? (A) 103 (B) 201 (C) 203 (D) 251 (E) 10,201 If n is a number such that both n–2 and n+2 are primer numbers, then n is a prime number. 26. Which of the following integers is a counter - example to the statement above? (A) 15 (B) 17 (C) 19 (D) 23 (E) 25

실전 9 7 27. If log 1.05 � = 10 , then � = (A) 1.00 (B) 1.05 (C) 1.63 (D) 8.96 (E) 11.22 28. For what value of k does the graph of the function f, given by �(�)= 3�+6 �+𝑘, NOT have a vertical asymptote? (A) –3 (B) –2 (C) 0 (D) 2 (E) 3 29. The graphs of the functions f and g for –� ≤ � ≤ � are shown. Which of the following is true for all x in this interval? (A) �(�)≥ 0 (B) �(�)≥ 0 (C) �(�)− �(�)≥ 0 (D) 2�(�)− �(�)≥ 0 (E) �(�)− �(�)≥ 0 30. Which of the following is equal to 1 for 0< � < 𝜋 2? (A) sin �cos � (B) sin � cos � (C) sec �csc � (D) tan � cot � (E) tan �cot �

실전 9 8 31. The graph of � = �(�) is shown in the figure above. Which of the following could be the graph of � = �−1(�)? 0 y x o x y (C) o x y (D) o x y (A) o x y (B) (E) o x y

실전 9 9 32. In 2004 there were approximately 293 million people living in the United States. The population was increasing by approximately 0.92 percent per year. If the population continues to increase at the same rate, approximately how many million people will be living in the United States in 2014? (A) 127 (B) 296 (C) 321 (D) 333 (E) 706 33. Which of the following stat ements is true for all x and y greater than zero? (A) log �+ log �= log (�+ �) (B) log (2�+ 2�)= log (�+ �)+ log (�+ �) (C) log �− log �= log � log � (D) log �− log �= log (� �) (E) (log �)2= 2log � 34. What is the period of the function f given by �(�)= |tan (2�)|? (A) 4π (B) 2π (C) π (D) 𝜋 2 (E) 𝜋 4 35. A painter wishes to paint the ceiling and walls of rectangular storage room that is 18 feet long by 15 feet wide by 8 feet high. How many square feet must be painted? (A) 528 (B) 534 (C) 798 (D) 1,068 (E) 2,160

실전 9 10 36. For which of the following values of x in the interval [0,2π] is �(�)= 2 3sin �+2 undefined? (A) 0.73 (B) 2.30 (C) 2.41 (D) 2.74 (E) 3.87 37. The arithmetic mean for each of the following distributions is 10. Which distribution has the smallest standard deviation? (A) 8, 9, 9, 10, 11, 13 (B) 0, 9, 10, 10, 11, 20 (C) 8, 9, 10, 10, 11, 12 (D) 8, 10, 10, 10, 10, 12 (E) 5, 10, 10, 10, 10, 15 38. Which of the following statements are true about the relationship between �2 and 2�? I. �2= 2�for some � > 2. II. �2> 2� for some � > 2. III. �2< 2� for some � > 2. (A) II only (B) III only (C) I and II only (D) I and III only (E) I, II, and III 39. In ∆��� shown above, sin 𝜃 = (A) –0.866 (B) –0.5 (C) 0.5 (D) 0.707 (E) 0.866 40. In the figure, Graph I is the graph of � = �(�) for −2≤ � ≤ 2. Which of the following is an equation for Graph II? (A) � = −�(�) (B) � = �(−�) (C) � = −�(−�) (D) � = −�(|�|) (E) � = �(−|�|) Y X Z 𝜃 3 4 √37 0 y � Graph I 0 y � Graph I I

실전 9 11 41. If �2− �2= 72 and �− � = 6, then �+ � = (A) –12 (B) –6 (C) –3 (D) 3 (E) 12 42. At My Video, the regular price for a previously viewed video is d dol lars. The store is having a clearance sale with all previously viewed videos 40 percent off the regular price. If du ring this sale, Roger bought n previously viewed videos for x dollars before tax, which of the following must be true? (A) 𝑛 = �− 0.6� (B) 𝑛 = �− 0.4� (C) 𝑛 = 0.6�� (D) 𝑛 = � 0.4� (E) 𝑛 = � 0.6� 43. If 𝜋 2< � < 𝜋 and sin � = 0.3, what is cos �? (A) 0.9553 (B) 0.9539 (C) 0.3 (D) –0.866 (E) –0.9539

실전 9 12 44. Which of the following graphical metho ds yields the solutions to the equation �(�)= �(�)? I. Graphing � = �(�) and � = �(�) and finding the x-values of the points of intersection II. Graphing � = �(�) and � = �(�) and finding the y-values of the points of intersection III. Graphing ℎ(�)= �(�)− �(�) and finding the zeros of h (A) I only (B) II only (C) III only (D) I and II (E) I and III 45. When a company first introduced a new type of cell phone, it initially sold 400 such phones. After 5 weeks, a total 850 such phones were sold. After 10 weeks, a total of 1,520 such phones were sold. If an exponential regre ssion is used to model the sales of the new type of cell phone, what is the predicted minimum numb er of weeks it would take to sel l a total of 10,000 such phones? (A) 21 (B) 24 (C) 28 (D) 86 (E) 107 46. In the figure above, ∆��� is similar to ∆��� , and the ratio of �� to �� is 3 to 2. If �� = 9, what is the length of side �� ? (A) 4 (B) 4.7 (C) 6 (D) 7.1 (E) 7.6 D E F C 58 ° A B C 58 ° 42 ° 42 °

실전 9 13 47. Two juniors and three seniors will be chosen to form the Booster Committee. They will be selected from a pool of six juniors and eight seniors. How many different five -person combinations are possible in forming this committee? (A) 77 (B) 366 (C) 840 (D) 2,002 (E) 10,080 48. For which of the following functions is �(�+ 3)= �(�)•�(3) for all values of x in the domain of the function? (A) �(�)= � (B) �(�)= �� (C) �(�)= log � (D) �(�)= sin � (E) �(�)= tan � 49. The scores of a test taken by each member of a class are whole numbe rs represented in the boxplot above. What percent of the class scored between 70 and 90, inclusive, on this test? (A) 20% (B) 40% (C) 50% (D) 75% (E) 90% 50. A sequence { an} of complex numbers has the property that an} = ian–1 for all n. If the 10 th term of the sequence is –2+ i, what is the 99 th term of the sequence? (A) 1+2 i (B) –1+2 i (C) –1–2i (D) 2–i (E) –2–i 50 60 70 80 90 100 65 69.5 83 90.5 93



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