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# 25 1. If π₯ + π₯ + π₯ = π₯ 2 , what are the possible values of x? (A) 0 only (B) 3 only (C) 0 and 3 only (D) β3 and 3 only (E) β3, 0, and 3 2. If 52π₯+1 = 96, then x = (A) 0.1417 (B) 0.4795 (C) 0.9180 (D) 1.2833 (E) 2.3360 3. Which of the following is an equation of a line that has an x-intercept of 2? 1 (A) π¦ = 2 π₯ β 1 (B) π¦ = π₯ + 2 (C) π¦ = 2π₯ β 2 (D) π¦ = 2π₯ (E) π¦ = 2π₯ + 1 4. There were b boy and g girls in a classroom. After 10 girls left the room, the number of boys was twice the number of girls. Which of the following equations represents the relationship between b and g? (A) π = (B) π (C) π (D) π (E) π πβ20 2 πβ10 = 2 = 2(π β 10) = 2π β 10 = 2π 1 # 25 5. If π₯ = β2 + β2, then (π₯ 2 β2)2= (A) 16 (B) 8 (C) 4 (D) 2 (E) 1 6. The radius of a machine shaft is specified to be 0.75 inch, but errors up to and including 0.001 inch are allowed. The allowable values for the radius r of the shaft can be described by which of the following? (A) r β€ 0.751 (B) 0.749 β€ r β€ 0.75 (C) 0.741 β€ r β€ 0.751 (D) 0.749 β€ r β€ 0.751 (E) 0.74 β€ r β€ 0.75 7.If π(π₯) = π₯ 3 β7 π₯ , what is the product of f(3) and f(4)? (A) 0.5 (B) 11.9 (C) 20.9 (D) 48 (E) 95 8. In the figure above, how many line segments are there whose endpoints are any two of the five labeled points? (A) 4 (B) 5 (C) 10 (D) 15 (E) 25 2 # 25 9. If 4π₯ β 8 = 2(2π₯ β π) for all x, then c = (A) β4 (B) β2 (C) 2 (D) 4 (E) 8 10. If a > 0 and (π3 )2 = 123.1, then a = (A) 0.8 (B) 1.0 (C) 1.7 (D) 2.2 (E) 2.6 11. What is the least positive even integer n for which 3n β 1 is NOT a prime? (A) 8 (B) 10 (C) 12 (D) 14 (E) 20 12. If π(π₯) = π₯ 3 β π₯ β π and if f(0) = β3, then k = (A) β30 (B) β24 (C) β3 (D) 0 (E) 3 1, 3, 4.6, 6.5, 9.2, 7.4, 6, 11.4 13. What number must be added to the list above so that the mean of the new list is 6.5? (A) 6.1 (B) 6.5 (C) 6.7 (D) 7.9 (E) 9.4 3 # 25 14. If π(π₯) = π₯ 2 + 1 and π(π₯) = π₯ 3 + 1, then π(π(π₯)) = (A) π₯ 6 + 1 (B) π₯ 6 + 2π₯ 3 + 2 (C) π₯ 6 + 3π₯ 4 + 3π₯ 2 + 2 (D) π₯ 5 + π₯ 3 + π₯ 2 + 1 (E) π₯ 3 + π₯ 2 + 2 1 15. A salesperson earns $275 per week plus 5 2 percent commission on the dollar amount of all products that she sells. To the nearest dollar, how much must her product sales total for her to earn $500 per week? (A) $4,091 (B) $4,263 (C) $8,816 (D) $9,366 (E) $14,091 16. The cube shown above has edges of length 7. What is the perimeter of triangle ACF? (A) 26.8 (B) 29.7 (C) 33.8 (D) 42.4 (E) 49.0 4 # 25 17. If π₯ > 0, what does π₯ π₯ approach as x approaches 0? (A) 0 (B) 0.5 (C) 0.8 (D) 1 (E) e 18. In β³ π΄π΅πΆ, the measure of β A is 50º, and the measure of β C is 30º. If AB = 10.2, what is the length of side BC? (A) 6.7 (B) 7.6 (C) 15.6 (D) 17.0 (E) 20.1 19. Line segment AB shown above is extended beyond point B to a point C (not shown). If AB:BC = 1:2, what are the coordinates of point C? (A) (6,8) (B) (6,9) (C) (8,12) (D) (8,18) (E) (12,18) 5 # 25 20. If ππ = π(π + 1)(π + 2), which of the following statements must be true for all positive integers n? I. ππ is divisible by 2 II. ππ is divisible by 3 III. ππ is divisible by 4 (A) I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III 21. If π¦ = ππ₯ + 3 and π¦ = ππ₯ β 1 are equations of perpendicular lines, then mp = (A) β1 (B) 0 (C) 1 (D) π2 (E) π2 22. In the xy-plane, the point (0,0) is on the graph of π¦ = π(π₯). Which of the following points must be on the graph of π¦ = π(π₯ β 2) + 3 ? (A) (2, β3) (B) (2, 2) (C) (2, 3) (D) (β2, β3) (E) (β2, 3) 23. If 2 + 3i is a zero of a polynomial function with real coefficients, which of the following must be another zero of the function? (A) 3 β 2i (B) 2 β 3i (C) β2 + 3i (D) β2 β 3i (E) It cannot be determined from the information given. 6 # 25 24. If x is an integer greater than 2, which of the following CANNOT be an integer? π₯ (A) π₯β1 (B) (C) (D) (E) π₯ 2 +5π₯+6 π₯ π₯ 2 β1 5 π₯ 2 +1 π₯+2 π₯3 π₯β2 25. On a test, 5 true-false questions are asked. If a person taking the test knows nothing about the material and guesses randomly at the answers, what is the probability that this person will answer all 5 correctly? (A) (B) (C) (D) (E) 1 20 1 25 1 32 1 50 1 120 26. In the xy-plane, what is the perimeter of an equilateral triangle with one vertex at (0, 3) and a second at (4, 0)? (A) 9 (B) 12 (C) 15 (D) 21 (E) It cannot be determined from the information given 7 # 25 27. Triangle OPR in the figure above is revolved about the x-axis. What is the volume of the solid generated? (A) 3.0 (B) 6.0 (C) 12.6 (D) 18.8 (E) 56.5 π‘ 28. If π(π‘) = 2 cos π‘ and π(π‘) = sin 2, what is the slope of the line joining (0, π(0)) and (π, π(π))? 2 (A) β π 1 (B) β π (C) 0 1 (D) π (E) 2 π 29. In the xy-plane, the points (2, 2) and (β2, β2) are symmetric with respect to which of the following? I. II. III. The origin The x-axis The line y = βx (A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III 8 # 25 30. The scores for each of 5 people in a contest were 125, 125, 126, 128, and 131. For these 5 scores, which of the following is true? (A) Mode < median < mean (B) Mode < mean < median (C) Median < mode < mean (D) Median < mean < mode (E) Mean < median < mode 31. Which of the following degree measures is approximately equal to a radian measure of 1.5? (A) 0.026º (B) 0.052º (C) 21.5º (D) 43.0º (E) 85.9º 32. If 0 < x < y and a < 0, which of the following inequalities are true? I. II. III. ax < ay 1 π¦ π π₯ 1 <π₯ π <π¦ (A) I only (B) II only (C) I and II only (D) II and III only (E) I, II, and III 9 # 25 33. Which of the following is the equation of the circle graphed in the figure above? (A) (π₯ β 1)2 + (π¦ + 2)2 (B) (π₯ + 1)2 β (π¦ β 2)2 (C) (π₯ + 1)2 + (π¦ + 2)2 (D) (π₯ + 1)2 + (π¦ β 2)2 (E) (π₯ + 1)2 + (π¦ β 2)2 =4 =2 =4 =2 =4 1 34. If f(x) = sin x and g(x) has a period that is 2 that of f(x), which of the following could be g(x)? 1 (A) 2 sin π₯ (B) sin 2π₯ π₯ (C) sin 2 (D) 2sin π₯ 1 (E) sin(π₯ + 2) 10 # 25 35. The graph of f is shown above. If π(π₯) = 1 , for π(π₯) which of the following values of x in [β10, 10] could π(π₯) = 0? (A) β10 (B) 0 (C) 2 (D) 3 (E) 5 π 36. If sinπ = x 2 and 0 < π < 2 , then sin(2π) = (A) 2π₯ 2 (B) 2π₯ 2 β1 β π₯ 4 (C) π₯ 2 β1 β π₯ 4 1 (D) 2 4 (E) π₯ β1βπ₯ 1 2π₯ 2 β1βπ₯ 4 11 # 25 37. If f is a function whose graph is shown above, which of the following is the graph of the inverse of f? (A) (B) (C) (D) (E) 12 # 25 38. If the domain of a function f is {1,2}, which of the following CANNOT be the range of f? (A) {1} (B) {3} (C) {1,2} (D) {3,4} (E) {1,2,3} 39. In the figure above, ππ΄ and ππ΅ are radii of the unit circle with the center O. Which of the following represents the length of chord AB? (A) 2sin π (B) sin (2π) (C) cos (2π) (D) 2cos (2π) (E) 2 40. In a contest, each of n judges assigns a wholenumber score between 1 and 10, inclusive, to a performer. The performerβs final score is the arithmetic mean of the n ratings. If two performers have final scores of exactly 5.4 and 6.0, respectively, what is the least possible number of judges? (A) 3 (B) 5 (C) 6 (D) 10 (E) 15 13 # 25 41. If ππ = 1.05ππβ1 and π1 = 100, what is π10 ? (A) 148 (B) 155 (C) 163 (D) 1,103 (E) 1,258 42. What is the y-intercept of the line defined by the parametric equations π₯(π‘) = β3π‘ + 7 and π¦(π‘) = 2π‘ β 5? (A) β5 7 (B) β 5 1 (C) β 2 1 (D) β 3 (E) 7 43. If a > 1 and b < 0, then |π|β|ππ| |π|β1 = (A) β1 (B) 1 (C) βb (D) b π(π+1) (E) πβ1 44. A car travels from point X to point Y at 60 miles per hour (mph), and then back to point X along the same route at 40 mph. Which of the following is true of the carβs round trip? (A) The distance traveled at 60 mph is greater than the distance traveled at 40 mph. (B) The car travels the same amount of time at 60 mph as at 40 mph. (C) The car travels a longer time at 60 mph than at 40 mph. (D) The average speed of the car is 50 mph. (E) The average speed of the car is less than 50 mph. 14 # 25 45. What is the value of ln x when ln x = π βπ₯ ? (A) 0 (B) 0.27 (C) 0.37 (D) 1.00 (E) 2.72 46. If n is an integer greater than 4, then 1 1 1 1 1 1 + (1 β ) + ( β ) + β― + ( β )= 2 2 3 πβ1 π (A) 1 β 1 π 1 (B) 1 + π 1 (C) 2 + π 1 (D) 2 β π 1 (E) 2 + (πβ1)π 2 3 47. If the slope of line β is 5 and the slope of line m is 5, what is the degree measure of the smaller angle formed at the intersection of β and m? (A) 9.16º (B) 11.31º (C) 13.29º (D) 21.80º (E) 30.96º π(π₯+1) 48. If π(π₯) = π(3) β π(1) = 2 and π(2) = 4, then (A) 0 (B) 2 (C) 4 (D) 6 (E) 8 15 # 25 If t < 3x, then 0 < y < 4 49. If the above statement is true and y = 5, which of the following statements must be true? (A) t < 3x (B) t β€ 3x (C) t = 3x (D) t > 3x (E) t β₯ 3x 50. A laser operator is aiming a laser at the center of a circular disk in space. The disk has a radius of 50 feet and is situated 225 miles directly above the surface of the Earth where the laser is located. If the operator makes a 0.05º error in aiming the laser, by how many feet will the laser beam miss the edge of the disk? (5,280 feet = 1 mile) (A) 937 (B) 987 (C) 1,012 (D) 1,037 (E) The laser beam will not miss the disk. 16 # 25 1. C 2. C 3. A 4. C 5. D 6. D 7. E 8. C 9. D 10.D 11.C 12.E 13.E 14.B 15.A 16.B 17.D 18.C 19.C 20.C 21.A 22.C 23.B 24.A 25.C 26.C 27.D 28.B 29.D 30.A 31.E 32.D 33.E 34.B 35.D 36.B 37.D 38.E 39.A 40.B 41.B 42.D 43.D 44.D 45.B 46.D 47.A 48.D 49.E 50.B 17