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CAPE Applied Mathematics Unit 1 · 2010 · Paper 2

63 questions and parts from this paper. Open one to see it in full, then practise it on Quelpr and get it marked against the mark scheme.

Practise this paper
  1. 1(a)(i)2 marksState the letters of TWO variables which are qualitative.
  2. 1(a)(ii)2 marksState the letters of TWO variables which are quantitative.
  3. 1(a)(iii)1 markState the letter of ONE discrete variable.
  4. 1(a)(iv)1 markState the letter of ONE continuous variable.
  5. 1(b)(i)1 markState the value of a parameter.
  6. 1(b)(ii)1 markState the value of a statistic.
  7. 1(c)(i)1 markIndicate whether a group of 50 persons selected to test a new milk drink refers to a population or a sample.
  8. 1(c)(ii)1 markIndicate whether the total number of cars sold by a car dealership in the last year refers to a population or a sample.
  9. 1(d)(i)1 markSelect a sample of 10 classes out of 14, and then take a sample of 5 students from each class.
  10. 1(d)(ii)1 markTake a random sample of students from each class proportionate to the number of students in the school.
  11. 1(d)(iii)1 markUse the school roll and choose every 25th name on the school roll.
  12. 1(d)(iv)1 markStand at the school gate and choose the first 50 students that come into the school.
  13. 1(d)(v)1 markPut the names of all students in a box and randomly select 50 names from the box.
  14. 1(e)(i)2 marksState the boundaries of the third class.
  15. 1(e)(ii)2 marksCalculate the width of the fifth class.
  16. 1(e)(iii)2 marksCalculate the frequency density of the second class.
  17. 1(e)(iv)3 marksEstimate the number of children who took more than 60 minutes to complete the assignment.
  18. 1(e)(v)1 markState a disadvantage of presenting data in this grouped frequency table format.
  19. 2(a)(i)4 marksIllustrate these data in a stem-and-leaf diagram.
  20. 2(a)(ii)1 markState ONE advantage of using the stem-and-leaf diagram to display data.
  21. 2(b)(i)2 marksDetermine the median age of the students in the class.
  22. 2(b)(ii)1 markDetermine the modal age of the students.
  23. 2(c)4 marksCalculate the mean age of the students.
  24. 2(d)2 marksState ONE disadvantage of using the mean to report the average age of the class.
  25. 2(e)4 marksCalculate the 8% trimmed mean for the data.
  26. 2(f)(i)2 marksDetermine the upper and lower quartiles of the ages.
  27. 2(f)(ii)3 marksDetermine the semi-interquartile range of the ages.
  28. 2(g)2 marksDescribe the shape of the distribution of the ages.
  29. 3(a)(i)2 marksDetermine P(A ∩ B).
  30. 3(a)(ii)2 marksDetermine P(A | B).
  31. 3(a)(iii)2 marksDetermine P(A' ∩ B').
  32. 3(b)(i)2 marksCalculate the probability that the student is a jazz dancer.
  33. 3(b)(ii)3 marksCalculate the probability that the student practises BOTH jazz and hip-hop.
  34. 3(b)(iii)3 marksTwo students are chosen at random from the dance school. What is the probability that they are BOTH hip-hop dancers?
  35. 3(c)(i)2 marksCalculate the probability that the next THREE patrons all choose chicken patties.
  36. 3(c)(ii)3 marksCalculate the probability that the next THREE patrons all choose the same type of patty.
  37. 3(c)(iii)3 marksCalculate the probability that the next THREE patrons all choose different types of patties.
  38. 3(c)(iv)3 marksCalculate the probability that the next THREE patrons all choose chicken patties, given that they all have the same type of patty.
  39. 4(a)(i)2 marksHow many days in September is it expected to rain?
  40. 4(a)(ii)4 marksWhat is the probability that it will rain on exactly 3 days in the next 7 days?
  41. 4(a)(iii)2 marksWhat is the probability that it will rain on the fourth, fifth, and sixth of September?
  42. 4(b)(i)3 marksShow that n = 15.
  43. 4(b)(ii)2 marksHence calculate E(Y).
  44. 4(b)(iii)3 marksCalculate P(Y = 10).
  45. 4(c)(i)2 marksState TWO conditions that should exist for the normal distribution to be used as an approximation for the binomial distribution.
  46. 4(c)(ii)7 marksThe probability that a pen is faulty is 0.06. In a box of 100 pens, what is the probability that at MOST 5 pens will be faulty?
  47. 5(a)2 marksState the distribution of X̄ giving its parameters.
  48. 5(b)(i)4 marksCalculate the value of X̄.
  49. 5(b)(ii)4 marksCalculate the number of observations taken, n.
  50. 5(c)2 marksIf 20 independent samples, EACH of size n, are drawn from a distribution and the 90% confidence interval is calculated for EACH, how many of these intervals will NOT contain the population mean μ?
  51. 5(d)(i)a)3 marksCalculate an unbiased estimate of the population mean.
  52. 5(d)(i)b)5 marksCalculate an unbiased estimate of the population standard deviation.
  53. 5(d)(ii)5 marksConstruct a 94% confidence interval for the mean amount of money spent by the students at the bookstore.
  54. 6(a)(i)2 marksState clearly the null and alternative hypotheses.
  55. 6(a)(ii)a)2 marksCalculate, to the nearest whole number, the expected number of textbooks with hard back covers.
  56. 6(a)(ii)b)2 marksCalculate, to the nearest whole number, the expected number of novels with paper back covers.
  57. 6(a)(iii)2 marksIdentify the rejection region for this test.
  58. 6(a)(iv)2 marksThe calculated χ² value is 9.2649. State clearly the conclusion of this test.
  59. 6(b)(i)1 markState the assumption that must be made under which a t-test is valid.
  60. 6(b)(ii)3 marksState clearly the null and alternative hypotheses for the test.
  61. 6(b)(iii)3 marksIdentify the critical region for this test.
  62. 6(b)(iv)5 marksCalculate the test statistic to be used in this test.
  63. 6(b)(v)3 marksState clearly the conclusion for this test, giving a reason for your answer.

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