Princeton Exam 1-1MPCstsemester[2]dec12-1-4 PDF

AP Exam Review Multiple Choice- Non Calculator Part 1. If f(x) = , then f’(8) = (a) 10 (b) (c) 40 (d) 80 (e) 2. is (a) 0...

AP Exam Review Multiple Choice- Non Calculator Part 1. If f(x) = , then f’(8) = (a) 10 (b) (c) 40 (d) 80 (e) 2. is (a) 0 (b) (c) (d) (e) 3. If f(x) = then f’(x) is (a) 1 (b) (c) (d) (e) 4. If the function f is continuous for all real numbers and if f(x) = when x , then f(4) = (a) 1 (b) (c) -1 (d) 0 (e) undefined 5. If , then (a) (b) (c) (d) (e) 6. If f(x) = sec x + csc x, then f’(x) = (a) 0 (b) (c) (d) (e) 7. An equation of the line normal to the graph of y = at (2, 4) is (a) (b) (c) (d) (e) 8. If f(x) = , then f” = (a) -2 (b) 0 (c) 1 (d) 2 (e) 9. If f(x) = and g(x) = 3x, then g(f(2)) = (a) -3 (b) (c) 3 (d) 5 (e) 10. The slope of the line tangent to the graph of at (2, 1) is (a) (b) (c) (d) 12 (e) -7 11. If f(x) = , for all real numbers x, which of the following must be true? I. f(x) is continuous everywhere II. f(x) is differentiable everywhere. III. f(x) has a local minimum at x = 2. (a) I only (b) I and II only (c) II and III only (d) I and III only (e) I, II, and III 12. For what value of x does the function f(x) = have a local minimum? (a) 10 (b) 4 (c) 3 (d) -4 (e) -10 13. (a) 2 (b) (c) (d) 0 (e) undefined 14. If f(x) = then f’ (a) (b) (c) (d) (e) 0 15. (a) (b) (c) (d) 0 (e) 16. If g(x) = find g’ (4). (A) -72 (B) -32 (C) -24 (D) 24 (E) 32 17. The domain of the function f(x) = is (A) x < -2 or x > 2 (B) or (C) -2 < x < 2 (D) (E) 18. is (A) 0 (B) 10 (C) -10 (D) 5 (E) The limit does not exist 19. Evaluate (A) (B) (C) 40 (D) 160 (E) The limit does not exist 20. Find k so that f(x) = is continuous for all x. (A) All real values of k make f(x) continuous for all x. (B) 0 (C) 16 (D) 8 (E) There is no real value of k that makes f(x) continuous for all x. 21. If f(x) = , find f ‘(x). (A) (B) (C) (D) (E) 22. An equation of the line tangent to y = at x = 3is (A) y + 45 = 66(x + 3) (B) y – 45 = 66(x – 3) (C) y = 66x (D) y = 66(x – 3) (E) y – 45 = 23. Find a positive value c, for x, that satisfies then conclusion of the Mean Value Theorem for Derivatives for f(x) = on the interval [2, 5]. (A) 1 (B) (C) (D) (E) 24. Given f (x) = 2x2 -7x -10, find the absolute maximum of f (x), on [-1, 3]. (A) -1 (B) 7/4 (C)-13 (D) (E) 0 25. Find if x3y + xy3 = -10. (A)(3x2 + 3xy2 ) (B)-(3x2 + 3xy2) (C) (D) - (E) 26. Find the equation of the tangent line to 9x2 + 16y2 = 52 through (2, -1). (A) -9x + 8y - 26 = 0 (B) 9x - 8y - 26 = 0 (C) 9x - 8y - 106 = 0 (D) 8x+9y -17 = 0 (E) 9x+16y -2 = 0 27. A particle’s position is given by s = t3 – 6 t2 + 9t. What is its acceleration at time t = 4? (A) 0 (B) 9 (C) -9 (D) -12 (E) 12 28. If f (x) = 3 , then f’ (x) = (A) (B) (C) (D) (E) 29. If f (x) = sin2x, find f’’’ (x). (A) – sin2x (B) 2cos2x (C) cos 2x (D) – 4 sin 2x (E) – sin 2x 30. Find the slope of the normal line to y = x + cos xy at (0, 1). (A) 1 (B) -1 (C) 0 (D) 2 (E) Undefined 31. = (A) -8 (B) -2 (C) 2 (D) 8 (E) The limit does not exist 32. If y = , find at x = 1 (A) -52 (B) -28 (C) -13 (D) 13 (E) 52 33. The graph of y = had an inflection point (or points) at (A) x = 0 only (B) x = 3 only (C) x = 0, 3 (D) x = -3 only (E) x = 0, -3 34. Find the value(s) of of at y = 1 (A) only (B) only (C) only (D) (E) CALCULATOR PART 35. A 20 foot ladder slides down a wall at 5ft/sec. At what speed is the bottom sliding out when the top is 10 feet from the floor? (A) 0.346 (B) 2.887 (C) 0.224 (D) 5.774 (E) 4.472 36. If f(x) is continuous and differentiable and f(x) = , then b = (A) 0.5 (B) 0 (C) 2 (D 37. Boats A and B leave the same place at the same time. Boat A heads due North at 12km/hr. Boat B due East at 18km/hr. After 2.5 hours, how fast is the distance between the boats increasing (in km/hr)? (a) 21.63 (b) 31.20 (c) 75.00 (d) 9.84 (e) 54.08 38. The graph of y = has a local minimum at (a) (0.46, 2.87) (b) (0.46, 0) (c) (2.87, -4.06) (d) (4.06, 2.87) (e) (1.66, -0.59) 39. Use differentials to approximate the change in the volume of a sphere when the radius is increasing from 10 to 10.02cm? (a) 4213.973 (b) 1261.669 (c) 1256.637 (d) 25.233 (e) 25.133 40. If the function f(x) is continuous and differentiable = then a = (a) 0 (b) 1 (c) -14 (d) -24 (e) 26 41. Two particles leave the origin at the same time and move along the y-axis with their respective positions determined by the functions and for. For how many values of t do the particles have the same acceleration? (a) 0 (b) 1 (c) 2 (d) 3 (e) 4 Answer key 1. b 2. d 3. c 4. a 5. e 6. e 7. e 8. a 9. c 10. a 11. a 12. a 13. d 14. a 15. b 16. b 17. d 18. b 19. a 20. d 21. d 22. b 23. e 24. a 25. d 26. b 27. e 28. e 29. d 30. b 31. d 32. a 33. b 34. d 35. b 36. d 37. a 38. c 39. e 40. c 41. d