Ontario Secondary School Diploma (OSSD) · Mathematics (Grades 11 and 12)

Trigonometry, Sequences, Calculus and Data

66 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 66 questions

  1. What is the exact value of cos 60 degrees?
  2. In triangle ABC, A = 40 degrees, B = 70 degrees and a = 8. What is b, to one decimal?
  3. Two sides of a triangle are 7 and 9 with a 60 degree angle between them. How long is the third side, to one decimal?
  4. Convert 150 degrees to radians.
  5. What is the period of y = 3 sin(4x)?
  6. Solve 2 sin x = sqrt(3) for 0 <= x < 2pi.
  7. If sin(theta) = 3/5 and theta lies in quadrant II, what is cos(theta)?
  8. An arithmetic sequence has t1 = 5 and d = 3. What is the sum of the first 20 terms?
  9. A geometric sequence has t1 = 3 and r = 2. What is t8?
  10. What is the sum of the infinite series 12 + 6 + 3 + 1.5 + ...?
  11. What is the derivative of f(x) = 4x^3 - 5x + 2?
  12. What is the derivative of f(x) = x^2(3x - 1)?
  13. What is the slope of the tangent to y = x^2 - 4x at x = 3?
  14. A farmer has 100 m of fence for a rectangular pen against a barn wall (no fence on the wall side). What is the largest area?
  15. What is the derivative of (2x + 1)^5?
  16. A bag holds 5 red and 3 blue marbles. Two are drawn without replacement. What is the probability both are red?
  17. In how many ways can a committee of 3 be chosen from 8 people?
  18. What is the population standard deviation of 4, 6, 8, 10, 12?
  19. For a normal distribution, about what proportion of data lies within one standard deviation of the mean?
  20. A particle moves with s(t) = t^2 + 3t metres. What is its velocity at t = 4 s?
  21. A 6 m ladder leans against a wall at 70 degrees to the ground. How high up the wall does it reach?
  22. What is the magnitude of the vector (8, 15)?
  23. What is the dot product of the vectors (-2, 3) and (4, -2)?
  24. What is the dot product of the vectors (3, 4) and (4, -2)?
  25. In how many ways can 2 students be chosen from a group of 7 to represent the class?
  26. Convert 60° to radians.
  27. In how many ways can 2 students be chosen from a group of 8 to represent the class?
  28. What is the magnitude of the vector (6, 8)?
  29. What is the slope of the tangent to y = 4x^4 at x = 1?
  30. What is the slope of the tangent to y = 5x^3 at x = 2?
  31. $10000 is invested at compound interest of 20% per year. What is the amount after 2 years?
  32. What is the slope of the tangent to y = 4x^5 at x = 1?
  33. Five numbers have a mean of 17. When one of them, 25, is removed, what is the mean of the remaining four?
  34. What is the population standard deviation of the data 4, 6, 6, 8?
  35. Five numbers have a mean of 12. When one of them, 20, is removed, what is the mean of the remaining four?
  36. Pipe A fills a tank in 20 hours and pipe B fills it in 5 hours. Working together, how many hours do they need?
  37. What is the sum of the infinite series 10 + 5/2 + 5/8 + ... in which each term is 1/4 of the previous one?
  38. What is the population standard deviation of the data 6, 8, 8, 10?
  39. A fair die is rolled 3 times. What is the probability of getting at least one six?
  40. A price of $2000 rises by 20% and then falls by 20%. What is the final price?
  41. $4000 is invested at compound interest of 5% per year. What is the amount after 2 years?
  42. Pipe A fills a tank in 6 hours and pipe B fills it in 3 hours. Working together, how many hours do they need?
  43. A triangle has sides 5 cm, 8 cm and 7 cm. What is the angle between the sides of 5 cm and 8 cm?
  44. What is the magnitude of the vector (7, 24)?
  45. What is the dot product of the vectors (5, 0) and (1, 5)?
  46. What is the exact value of cos 30°?
  47. What is the exact value of sin 30°?
  48. What is the magnitude of the vector (3, 4)?
  49. What is the magnitude of the vector (5, 12)?
  50. Convert 135° to radians.
  51. Convert 90° to radians.
  52. $2500 is invested at compound interest of 10% per year. What is the amount after 2 years?
  53. What is the slope of the tangent to y = 5x^2 at x = -1?
  54. In a triangle, angle A = 30°, angle B = 90° and the side opposite A is 6 cm. What is the length of the side opposite B?
  55. Pipe A fills a tank in 30 hours and pipe B fills it in 20 hours. Working together, how many hours do they need?
  56. A price of $1200 rises by 10% and then falls by 10%. What is the final price?
  57. A fair die is rolled 4 times. What is the probability of getting at least one six?
  58. A colony of 1000 bacteria doubles every 4 hours. How many bacteria are there after 16 hours?
  59. If f(x) = x^1(x + 4), what is f'(2)?
  60. What is the minimum value of f(x) = x^2 - 4x - 21?
  61. What is the sum of the infinite series 3 + 3/2 + 3/4 + ... in which each term is 1/2 of the previous one?
  62. In a class, 24 students play football, 15 play volleyball and 8 play both. 3 play neither. How many students are in the class?
  63. Five numbers have a mean of 13. When one of them, 25, is removed, what is the mean of the remaining four?
  64. What is the sum of the infinite series 12 + 4 + 4/3 + ... in which each term is 1/3 of the previous one?
  65. A colony of 200 bacteria doubles every 4 hours. How many bacteria are there after 8 hours?
  66. If f(x) = x^1(x + 4), what is f'(1)?

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