1969, 1973, 1985, 1993, 1997, 1998 AP Multiple Choice Sections, AB and BC, Solutions (620)

All rights reserved available at

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( x) dx + 14 g ( x) dx + 28 g ( x) dx + 7 g ( x) dx + 14 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 148 1998 AP Calculus BC: Section I, Part B 83. The Taylor series for ln x , centered at x = 1 , is ∞ ∑ ( −1) n +1 ( x − 1)n . Let n n =1 f be the function given by the sum of the first three nonzero terms of this series. The maximum value of ln x − f ( x) for 0.3 ≤ x ≤ 1.7 is (A) 0.030 (B) (C) 0.039 84. What are all values of x for which the series ∞ ∑ ( x + 2 )n n n =1 (A) −3 < x < −1 (B) −3 ≤ x < −1 (D) 0.145 2 f ( x) 5 7 (E) 0.529 (E) −1 ≤ x ≤ 1 converges? (C) −3 ≤ x ≤ −1 (D) x 0.153 −1 ≤ x < 1 8 10 30 40 20 85. The function f is continuous on the closed interval [ 2,8] and has values that are given in the table above. Using the subintervals [ 2,5] , [5, 7 ] , and [ 7,8] , what is the trapezoidal approximation of 8 ∫ 2 f ( x) dx ? (A) 110 (B) 130 (C) 160 (D) 190 (E) 210 86. The base of a solid is a region in the first quadrant bounded by the x-axis, the y-axis, and the line x + 2 y = 8 , as shown in the figure above. If cross sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid? (A) 12.566 (B) 14.661 (C) 16.755 (D) 67.021 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (E) 134.041 149 1998 AP Calculus BC: Section I, Part B 87. Which of the following is an equation of the line tangent to the graph of f ( x) = x 4 + 2 x 2 at the point where f ′( x) = 1? (A) (B) (C) (D) (E) y = 8x − 5 y = x+7 y = x + 0.763 y = x − 0.122 y = x − 2.146 88. Let g ( x) = ∫ x a f (t ) dt , where a ≤ x ≤ b. The figure above shows the graph of g on [ a, b ] . Which of the following could be the graph of f on [ a, b ] ? AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 150 1998 AP Calculus BC: Section I, Part B 89. The graph of the function represented by the Maclaurin series ( −1) x + … intersects the graph of y = x3 at x = x 2 x3 1− x + − +…+ n! 2! 3! n (A) 0.773 (B) n 0.865 (C) 0.929 (D) 1.000 (E) 1.857 90. A particle starts from rest at the point ( 2, 0 ) and moves along the x-axis with a constant positive acceleration for time t ≥ 0 . Which of the following could be the graph of the distance s (t ) of the particle from the origin as a function of time t ? AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 151 1998 AP Calculus BC: Section I, Part B t (sec) 0 2 4 6 a (t ) (ft/sec 2 ) 5 2 8 3 91. The data for the acceleration a (t ) of a car from 0 to 6 seconds are given in the table above. If the velocity at t = 0 is 11 feet per second, the approximate value of the velocity at t = 6 , computed using a left-hand Riemann sum with three subintervals of equal length, is (A) 26 ft/sec (B) 30 ft/sec (C) 37 ft/sec (D) 39 ft/sec (E) 41 ft/sec 92. Let f be the function given by f ( x) = x 2 − 2 x + 3 . The tangent line to the graph of f at x = 2 is used to approximate values of f ( x) . Which of the following is the greatest value of x for which the error resulting from this tangent line approximation is less than 0.5 ? (A) 2.4 (B) 2.5 (C) 2.6 (D) AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 2.7 (E) 2.8 152 1969 Answer Key 1969 BC 1969 AB 1. B 2. C 3. B 4. D 5. E 6. B 7. D 8. B 9. C 10. E 11. B 12. A 13. C 14. E 15. B 16. B 17. B 18. E 19. C 20. A 21. B 22. E 23. C 24. C 25. A 26. C 27. C 28. C 29. A 30. E 31. C 32. B 33. A 34. D 35. A 36. B 37. D 38. C 39. D 40. E 41. D 42. D 43. D 44. C 45. D 1. C 2. E 3. B 4. D 5. E 6. B 7. D 8. C 9. D 10. A 11. B 12. E 13. C 14. D 15. B 16. B 17. B 18. E 19. C 20. A 21. B 22. E 23. D AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 24. C 25. A 26. C 27. C 28. D 29. C 30. D 31. C 32. B 33. A 34. D 35. A 36. B 37. D 38. A 39. D 40. E 41. D 42. B 43. E 44. E 45. E 153 1973 Answer Key 1973 BC 1973 AB 1. E 2. E 3. B 4. A 5. A 6. D 7. B 8. B 9. A 10. C 11. B 12. C 13. D 14. D 15. C 16. C 17. C 18. D 19. D 20. D 21. B 22. B 23. C 24. B 25. B 26. E 27. E 28. C 29. C 30. B 31. D 32. D 33. A 34. C 35. C 36. A 37. A 38. B 39. B 40. E 41. D 42. D 43. E 44. B 45. C 1. A 2. D 3. A 4. C 5. B 6. D 7. D 8. B 9. A 10. A 11. E 12. D 13. D 14. A 15. C 16. A 17. C 18. D 19. D 20. E 21. B 22. C 23. C AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 24. A 25. B 26. D 27. E 28. C 29. A 30. B 31. E 32. C 33. A 34. C 35. C 36. E 37. E 38. B 39. D 40. C 41. D 42. D 43. E 44. A 45. E 154 1985 An...
View Full Document

This note was uploaded on 12/29/2010 for the course MATH 214 taught by Professor Smith during the Fall '10 term at Oregon Tech.

Ask a homework question - tutors are online