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CAPE Applied Mathematics Unit 1 · 2016 · Paper 2

54 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 the population of interest.
  2. 1(a)(ii)1 markState the sampling method used to collect the data.
  3. 1(a)(iii)1 markState the variable which is qualitative.
  4. 1(a)(iv)1 markState the variable which is continuous.
  5. 1(a)(v)1 markState the variable which is discrete.
  6. 1(b)(i)2 marksCalculate the angle of the sector representing persons who love potato.
  7. 1(b)(ii)3 marksIf 10 persons love yam, determine the total number of persons living in the home to the nearest whole number.
  8. 1(b)(iii)3 marksCalculate the number of persons who love cassava to the nearest whole number.
  9. 1(c)(i)1 markState a disadvantage of displaying this data in groups as shown.
  10. 1(c)(ii)8 marksOn the grid provided on page 7, draw a clearly labelled histogram displaying the information in the table, using a scale of 1 cm = 5 years and 2 cm = 5 persons.
  11. 1(c)(iii)3 marksUse the histogram to estimate the mode of the ages.
  12. 2(a)(i)1 markState which ONE of the mean, median and mode may be determined from qualitative data.
  13. 2(a)(ii)1 markState which ONE of the mean, median and mode is affected by extreme values.
  14. 2(a)(iii)1 markState which ONE of the mean, median and mode may have the largest value for a given set of data.
  15. 2(b)(i)1 markState which ONE of the range, interquartile range and variance is influenced most by extreme values.
  16. 2(b)(ii)1 markState which ONE of the range, interquartile range and variance may be obtained by squaring the standard deviation.
  17. 2(b)(iii)1 markState which ONE of the range, interquartile range and variance is the middle 50% of the distribution.
  18. 2(c)(i)3 marksCalculate estimates for the mean.
  19. 2(c)(ii)3 marksCalculate the estimates for the standard deviation of the data.
  20. 2(c)(iii)5 marksAnother data value, x = 29, was added to the values. Calculate values for the mean and the standard deviation of the 37 values.
  21. 2(d)(i)2 marksDetermine the median number of marbles per packet.
  22. 2(d)(ii)1 markDetermine the mode of the distribution.
  23. 2(d)(iii)4 marksCalculate the mean number of marbles per packet.
  24. 2(d)(iv)1 markDescribe the shape of the distribution.
  25. 3(a)(i)3 marksCalculate the values of x, y and z.
  26. 3(a)(ii)3 marksCalculate the probability that the drug is effective.
  27. 3(a)(iii)3 marksGiven that the drug was effective, what is the probability that a person using the drug is a man?
  28. 3(b)(i)2 marksCalculate the probability that a person selected at random pays for his/her item with cash.
  29. 3(b)(ii)2 marksCalculate the probability that a person selected at random makes a purchase that costs between 50 and 200.
  30. 3(b)(iii)2 marksCalculate the probability that a person selected at random makes a purchase over $200 and pays with a debit card.
  31. 3(b)(iv)2 marksCalculate the probability that a person selected at random uses a credit card, given that the purchase was under $50.
  32. 3(c)(i)2 marksCalculate P(R ∪ S).
  33. 3(c)(ii)2 marksDetermine P(R|S).
  34. 3(c)(iii)2 marksState, with reason, whether R and S are mutually exclusive.
  35. 3(c)(iv)2 marksState, with reason, whether R and S are independent.
  36. 4(a)(i)2 marksState, with reason, whether or not the given table represents a valid probability distribution.
  37. 4(a)(ii)2 marksState, with reason, whether or not the given table represents a valid probability distribution.
  38. 4(a)(iii)2 marksState, with reason, whether or not the given table represents a valid probability distribution.
  39. 4(b)(i)2 marksShow that k = 1/7.
  40. 4(b)(ii)3 marksDetermine P(4 ≤ X ≤ 6).
  41. 4(c)(i)6 marksCalculate Var(X).
  42. 4(c)(ii)2 marksConstruct a cumulative distribution table for the random variable X.
  43. 4(c)(iii)1 markEvaluate P(X ≥ 4).
  44. 4(d)(i)2 marksIf 80 persons are introduced to the product, determine the number of persons who are expected to buy the product.
  45. 4(d)(ii)3 marksFrom a random sample of 15 persons who were introduced to the product, calculate the probability that exactly 9 will buy the product.
  46. 5(a)(i)2 marksCalculate unbiased estimates for the population mean, µ.
  47. 5(a)(ii)3 marksCalculate unbiased estimates for the standard deviation, σ, of the length of time between planting and germination.
  48. 5(a)(iii)3 marksConstruct a 94% confidence interval for the mean length of time it takes for this type of pepper seed to germinate.
  49. 5(a)(iv)2 marksSixty random samples of 49 pepper seeds are taken and a 95% confidence interval for µ is found for each sample. Determine the appropriate number of intervals that will contain the population mean, µ.
  50. 5(b)5 marksThe mean of 150 observations of X, where X ~ Bin(135, 0.36) is X̄. Use the central limit theorem to state the distribution that is modelled by X̄, giving the values of its parameters.
  51. 5(c)(i)3 marksState, in symbols, appropriate null and alternative hypotheses for the test.
  52. 5(c)(ii)3 marksDetermine the critical region(s) for the test.
  53. 5(c)(iii)2 marksCalculate the value of the test statistic.
  54. 5(c)(iv)2 marksState your conclusions, giving reasons.

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