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CAPE Applied Mathematics Unit 1 · 2017 · Paper 2

40 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)5 marksMatch the phrases or statements in Column A to the phrases in Column B by writing the number from Column A in Column C.
  2. 1(b)3 marksState THREE reasons why it may be necessary to take a sample when carrying out research.
  3. 1(c)2 marksDetermine whether EACH of the following refers to a sample or to a population: • A group of 25 persons selected to test a new drug • The total number of books sold at the book sale
  4. 1(d)3 marksState which of the following represents discrete data and which represents continuous data: • Number of persons in a household • Speed of a car in kilometres per hour • Student enrolment in a college in the last year
  5. 1(e)(i)5 marksUsing a stratified random sample, calculate the number of workers from EACH group that will be in the sample.
  6. 1(e)(ii)2 marksWhat is the advantage of using stratified random sampling to select persons rather than simple random sampling?
  7. 1(f)5 marksState the sampling method to be used in EACH of the approaches to select a sample of 50 students from a school with a roll of 420 students distributed over 14 classes: • Select a sample of 10 classes out of the 14…
  8. 2(a)(i)4 marksUsing groups of 10 and starting at 20, construct a stem-and-leaf diagram to show the data.
  9. 2(a)(ii)6 marksUse the stem-and-leaf diagram to determine the mode, median, interquartile range, and the number of students who got 60 marks or more.
  10. 2(b)(i)1 markState ONE disadvantage of displaying the data in this form.
  11. 2(b)(ii)1 markState the boundaries of the SECOND class.
  12. 2(b)(iii)2 marksCalculate the frequency density of the FIFTH class.
  13. 2(b)(iv)11 marksShowing your method clearly, determine the mean number of days that the employees were late, the standard deviation, the median class, and the median number of days employees were late.
  14. 3(a)(i)3 marksCalculate P(N).
  15. 3(a)(ii)4 marksState, with reason, whether M and N are independent, and whether M and N are mutually exclusive.
  16. 3(b)(i)4 marksIn the space provided, draw a clearly labelled tree diagram to show this information.
  17. 3(b)(ii)3 marksCalculate the probability that an item, selected at random, is defective.
  18. 3(b)(iii)3 marksGiven that an item selected at random is defective, calculate the probability that it is an item for export. Give your answer correct to three significant figures.
  19. 3(c)(i)2 marksDetermine the value of p.
  20. 3(c)(ii)6 marksCalculate E(X) and Var(X).
  21. 4(a)6 marksCalculate the probability that the person plays badminton, BOTH badminton and tennis, and only one of the sports.
  22. 4(b)5 marksThe mass, X, of packages of a certain type of breakfast cereal follows a normal distribution with a mean of 60 g and a standard deviation of 5 g. Calculate the probability that a package chosen at random has a mass of…
  23. 4(c)(i)4 marksState FOUR assumptions that are made in applying a binomial model to this experiment.
  24. 4(c)(ii)1 markState a binomial distribution that will model this experiment.
  25. 4(c)(iii)2 marksWhat is the probability that exactly 4 seedlings will NOT survive transplantation?
  26. 4(c)(iv)7 marksFive hundred seedlings are sent to KG's Gardens. Determine the mean and the variance of the number of seedlings that will NOT survive transplantation, and find the probability that less than 55 seedlings will NOT…
  27. 5(a)4 marksA random sample of 55 sweets was found to have a mean mass of 0.93 g and a standard deviation of 0.10 g. Determine an approximate 99% confidence interval for the mean mass of the sweets.
  28. 5(b)4 marksA certain supermarket found that the price codes on some packages were not clear. In a random sample of 80 packages, 18 had price codes that were not clear. Construct a 97% confidence interval for the proportion of…
  29. 5(c)6 marksA random variable X follows a normal distribution with mean, μ, and an unknown variance, σ². A random sample of 150 observations of X gave ∑x = 1600 and ∑x² = 18 040. Calculate unbiased estimates for the mean and…
  30. 5(d)2 marksForty random samples of 5 soap bars are taken and a 90% confidence interval for the mean mass, μ, is calculated for EACH sample. Find the expected number of intervals that do NOT contain μ.
  31. 5(e)(i)4 marksState the distribution of X̄, giving its parameters.
  32. 5(e)(ii)5 marksCalculate P(X̄ > 4.75).
  33. 6(a)(i)3 marksState clearly the null and alternate hypotheses.
  34. 6(a)(ii)4 marksIdentify the critical region(s) of the test statistic.
  35. 6(a)(iii)4 marksCalculate the value of the test statistic.
  36. 6(a)(iv)3 marksState clearly a valid conclusion of the test, giving a reason for your answer.
  37. 6(b)(i)2 marksState clearly the null and alternative hypotheses.
  38. 6(b)(ii)3 marksCalculate, to the nearest whole number, the expected number of males that have no opinion.
  39. 6(b)(iii)3 marksIdentify the rejection region of the test.
  40. 6(b)(iv)3 marksThe calculated chi-square value of the test is 9.8249. State clearly the conclusion for this test, giving a reason for your answer.

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