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

Dx 6 b this is the derivative of f x 8 x8 at x 1 2 7

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Unformatted text preview: swer Key 1985 BC 1985 AB 1. D 2. E 3. A 4. C 5. D 6. C 7. E 8. B 9. D 10. D 11. B 12. C 13. A 14. D 15. C 16. B 17. C 18. C 19. B 20. A 21. B 22. A 23. B 24. D 25. E 26. E 27. D 28. C 29. D 30. B 31. C 32. D 33. B 34. A 35. D 36. B 37. D 38. C 39. E 40. D 41. E 42. C 43. B 44. A 45. A 1. D 2. A 3. B 4. D 5. D 6. E 7. A 8. C 9. B 10. A 11. A 12. A 13. B 14. C 15. C 16. C 17. B 18. C 19. D 20. C 21. B 22. A 23. C AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 24. D 25. C 26. E 27. E 28. E 29. D 30. B 31. D 32. E 33. C 34. A 35. B 36. E 37. A 38. C 39. A 40. A 41. C 42. E 43. E 44. A 45. D 155 1988 Answer Key 1988 BC 1988 AB 1. C 2. D 3. A 4. E 5. A 6. D 7. D 8. B 9. E 10. C 11. A 12. B 13. A 14. D 15. B 16. C 17. D 18. E 19. B 20. C 21. C 22. C 23. B 24. C 25. B 26. E 27. E 28. C 29. B 30. A 31. C 32. A 33. A 34. D 35. B 36. C 37. D 38. E 39. E 40. B 41. A 42. C 43. B 44. C 45. D 1. A 2. D 3. B 4. E 5. C 6. C 7. A 8. A 9. D 10. D 11. A 12. B 13. B 14. A 15. E 16. A 17. D 18. E 19. B 20. E 21. D 22. E 23. E AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 24. D 25. D 26. C 27. B 28. E 29. B 30. C 31. C 32. E 33. E 34. C 35. A 36. E or D 37. D 38. C 39. C 40. E 41. B 42. A 43. A 44. A 45. B 156 1993 Answer Key 1993 BC 1993 AB 1. C 2. B 3. D 4. A 5. A 6. D 7. B 8. E 9. E 10. D 11. C 12. B 13. A 14. A 15. D 16. B 17. E 18. D 19. E 20. B 21. C 22. E 23. C 24. A 25. C 26. D 27. C 28. B 29. C 30. C 31. E 32. A 33. B 34. D 35. E 36. D 37. C 38. A 39. D 40. C 41. D 42. B 43. B 44. C 45. B 1. A 2. C 3. E 4. B 5. D 6. A 7. A 8. B 9. D 10. E 11. E 12. E 13. C 14. B 15. D 16. A 17. A 18. B 19. B 20. E 21. A 22. B 23. D AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 24. C 25. D 26. B 27. C 28. A 29. E 30. C 31. A 32. B 33. A 34. E 35. A 36. E 37. B 38. C 39. C 40. C 41. C 42. E 43. A 44. E 45. D 157 1997 Answer Key 1997 BC 1997 AB 1. C 2. A 3. C 4. D 5. E 6. C 7. D 8. C 9. B 10. E 11. E 12. B 13. A 14. C 15. B 16. D 17. A 18. C 19. D 20. E 21. E 22. D 23. A 24. B 25. A 76. E 77. D 78. D 79. C 80. A 81. A 82. B 83. C 84. C 85. C 86. A 87. B 88. E 89. B 90. D 1. C 2. E 3. A 4. C 5. C 6. A 7. C 8. E 9. A 10. B 11. C 12. A 13. B 14. C 15. D 16. B 17. B 18. C 19. D 20. E AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 21. A 22. C 23. E 24. D 25. A 76. D 77. E 78. A 79. D 80. B 81. D 82. B 83. E 84. C 85. D 86. A 87. B 88. C 89. D 90. B 158 1998 Answer Key 1998 BC 1998 AB 1. D 2. B 3. C 4. B 5. E 6. A 7. E 8. E 9. D 10. D 11. A 12. E 13. B 14. C 15. D 16. E 17. D 18. B 19. C 20. A 21. B 22. C 23. A 24. D 25. D 26. A 27. A 28. E 76. A 77. C 78. B 79. A 80. B 81. D 82. E 83. B 84. A 85. C 86. C 87. D 88. C 89. B 90. D 91. E 92. D 1. C 2. A 3. D 4. A 5. A 6. E 7. E 8. B 9. D 10. E 11. A 12. E 13. B 14. E 15. B 16. C 17. D 18. B 19. D 20. E 21. C 22. A 23. E AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 24. C 25. C 26. E 27. D 28. C 76. D 77. E 78. B 79. A 80. B 81. B 82. B 83. C 84. B 85. C 86. C 87. D 88. C 89. A 90. A 91. E 92. D 159 1969 Calculus AB Solutions 1. B Sine is the only odd function listed. sin(− x) = − sin( x) . 2. C ln t < 0 for 0 < t < 1 ⇒ ln ( x − 2 ) < 0 for 2 < x < 3 . 3. B Need to have lim f ( x) = f (2) = k . x →2 k = lim x →2 2x + 5 − x + 7 2x + 5 − x + 7 2x + 5 + x + 7 = lim ⋅ x→2 x−2 x−2 2x + 5 + x + 7 2x + 5 − ( x + 7) 1 1 1 ⋅ = lim = x →2 x−2 2 x + 5 + x + 7 x→2 2 x + 5 + x + 7 6 = lim 8 dx = 2 1+ x 1+ x 8 = 2 ( 3 − 1) = 4 4. D ∫0 5. E Using implicit differentiation, 6 x + 2 xy′ + 2 y + 2 y ⋅ y′ = 0 . Therefore y′ = 0 −2 y − 6 x . 2x + 2 y When x = 1 , 3 + 2 y + y 2 = 2 ⇒ 0 = y 2 + 2 y + 1 = ( y + 1) 2 ⇒ y = −1 dy Therefore 2 x + 2 y = 0 and so is not defined at x = 1 . dx 6. B This is the derivative of f ( x) = 8 x8 at x = 1 2 7 1 ⎛1⎞ ⎛1⎞ f ′ ⎜ ⎟ = 64 ⎜ ⎟ = 2 ⎝2⎠ ⎝2⎠ k k , we need 0 = f ′(−2) = 1 − and so k = 4. Since f ′′(−2) < 0 for k = 4, f x 4 does have a relative maximum at x = −2 . With f ( x) = x + 7. D 8. B p ( x) = q ( x)( x − 1) + 12 for some polynomial q ( x) and so 12 = p (1) = (1 + 2 )(1 + k ) ⇒ k = 3 9. C A = π r2, So, 2 dA dr dA dr and from the given information in the problem = 2π r ⋅ =2 . dt dt dt dt dr dr 1 = 2π r ⋅ ⇒ r = dt dt π AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 160 1969 Calculus AB Solutions 10. E x = e y ⇒ y = ln x 11. B ⎛ x2 ⎞ 1⎞ ⎛ Let L be the distan...
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