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CAPE Applied Mathematics Unit 1 · 2015 · Paper 2

64 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)1 markState whether the types of pastry sold at a restaurant is quantitative or qualitative.
  2. 1(a)(ii)1 markState whether the weight of a red snapper sold at a fish market is quantitative or qualitative.
  3. 1(a)(iii)1 markState whether the number of seats available at a concert hall is discrete or continuous.
  4. 1(a)(iv)1 markState whether the height of pea trees at six weeks old is discrete or continuous.
  5. 1(a)(v)1 markState whether the number of kilowatt-hours of electricity used by a household in the last month is discrete or continuous.
  6. 1(b)(i)2 marksDistinguish between a 'census' and a 'sample survey'.
  7. 1(b)(ii)2 marksState TWO reasons why taking a sample may be necessary.
  8. 1(b)(iii)a)2 marksState, with a reason, whether the following situation is a sample survey or a census: Every week a store calls 15 of the 40 persons who made purchases at the store during the week to find out whether they were satisfied…
  9. 1(b)(iii)b)2 marksState, with a reason, whether the following situation is a sample survey or a census: The management of High Street Appliance Store called all of the 5 persons who bought stoves last week to find out if they were…
  10. 1(c)(i)1 markThe types of cars entering a particular car park between 9:00 a.m. and 11:00 a.m.
  11. 1(c)(ii)1 markThe types of cellphones owned by persons.
  12. 1(c)(iii)1 markThe types of radio programmes that persons listen to.
  13. 1(d)(i)3 marksUsing the stratified random sampling method, calculate the number of masons in a sample of 25 employees.
  14. 1(d)(ii)1 markState ONE advantage of using the stratified random method for collecting this sample.
  15. 1(d)(iii)a)1 markState ONE reason why this is not a suitable question.
  16. 1(d)(iii)b)4 marksRewrite the question in a more suitable manner.
  17. 2(a)(i)1 markState ONE disadvantage of displaying data in groups.
  18. 2(a)(ii)2 marksDetermine the size of the third class.
  19. 2(a)(iii)3 marksUsing the graph paper provided, draw a histogram to show this distribution of daily profit.
  20. 2(a)(iv)3 marksUse the histogram drawn in (a)(iii) to estimate the mode of the distribution.
  21. 2(a)(v)5 marksCalculate an estimate of the mean profit made by the vendor over the 90-day period.
  22. 2(a)(vi)4 marksCalculate an estimate of the standard deviation of the profit made by the vendor over the 90-day period.
  23. 2(b)(i)3 marksDetermine the total number of students in the sample.
  24. 2(b)(ii)2 marksDetermine the size of the angle that represents the sector of bicycles.
  25. 2(b)(iii)2 marksCalculate the number of students who walk to school.
  26. 3(a)(i)a)2 marksCalculate the probability that a randomly chosen patron buys both French fries and macaroni cheese.
  27. 3(a)(i)b)2 marksCalculate the probability that a randomly chosen patron buys French fries only.
  28. 3(a)(ii)3 marksDraw a FULLY labelled Venn diagram to show the cafeteria patron information.
  29. 3(a)(iii)1 markState the probability that a patron buys neither French fries nor macaroni cheese.
  30. 3(b)(i)2 marksWhat is the probability that a person chosen at random from the sample is a female?
  31. 3(b)(ii)2 marksWhat is the probability that a person chosen at random prefers Pepsi-Cola?
  32. 3(b)(iii)2 marksWhat is the probability that a person chosen at random likes Ginger ale and is a male?
  33. 3(b)(iv)3 marksWhat is the probability that a person chosen at random prefers Coco-Cola given that the person is a female?
  34. 3(c)(i)3 marksList ALL the possible selections of flavours that could be made.
  35. 3(c)(ii)2 marksGiven that the first toffee selected was coffee flavoured, find the probability that the second toffee selected will also be coffee flavoured.
  36. 3(c)(iii)3 marksCalculate the probability that EXACTLY two of the three toffees selected will be vanilla flavoured.
  37. 4(a)(i)3 marksPrepare a probability distribution table to show this information, giving values to 3 decimal places.
  38. 4(a)(ii)3 marksCalculate P(2 <= X <= 4).
  39. 4(a)(iii)3 marksCalculate the expected number of errors per page.
  40. 4(b)(i)3 marksName the distribution of Y, and state its parameters.
  41. 4(b)(ii)a)3 marksCalculate the probability that at any moment EXACTLY 4 lines will be engaged.
  42. 4(b)(ii)b)3 marksCalculate the probability that at any moment AT LEAST 1 line will be engaged.
  43. 4(c)7 marksDetermine the percentage of students who will get a Grade A.
  44. 5(a)(i)2 marksCalculate the width of the interval.
  45. 5(a)(ii)2 marksCalculate the mean of the sample.
  46. 5(a)(iii)3 marksCalculate the standard deviation of the value of the sales invoice.
  47. 5(b)(i)3 marksState the approximate distribution modelled by X̄, giving its parameters.
  48. 5(b)(ii)5 marksCalculate P(X̄ < 28).
  49. 5(c)(i)2 marksState null and alternative hypotheses, using statistical symbols to test whether the mean mass has changed.
  50. 5(c)(ii)3 marksDetermine the critical region(s) of the test conducted at the 4% significance level.
  51. 5(c)(iii)3 marksCalculate the value of the test statistic used in this test.
  52. 5(c)(iv)2 marksClearly state the conclusion of the test.
  53. 6(a)(i)1 markIdentify the independent variable between: The income of a family, and The monthly rent paid.
  54. 6(a)(ii)1 markIdentify the independent variable between: The advertising expense of a company, and The sales of a company.
  55. 6(a)(iii)1 markIdentify the independent variable between: The damage done to a certain home after a hurricane, and The amount of money spent in repairs to a certain home after a hurricane.
  56. 6(b)(i)3 marksUse graph paper to plot these values in a scatter diagram.
  57. 6(b)(ii)3 marksCalculate the mean age of the operators and the mean number of days required for training, to the NEAREST whole number.
  58. 6(b)(iii)1 markPlot the point (x̄, ȳ) on the scatter diagram.
  59. 6(b)(iv)3 marksDraw the regression line of y on x given by y = -0.05 + 0.27x on the same graph as the scatter diagram.
  60. 6(b)(v)2 marksUse the regression line to estimate the number of days required to train a new operator aged 22 years, to the NEAREST whole number.
  61. 6(c)(i)2 marksState appropriate null and alternate hypotheses for this chi-squared test.
  62. 6(c)(ii)3 marksDetermine the critical value of the test at the 5% level of significance.
  63. 6(c)(iii)3 marksCalculate the expected number of students who attended School B and received a Grade II.
  64. 6(c)(iv)2 marksGiven the calculated chi-squared test value is 9.1625, clearly state the conclusion that may be drawn.

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