Quelpr

CAPE Applied Mathematics Unit 1 · 2011 · Paper 2

51 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)3 marksIndicate, using the letters A, B, C, D and E, which variables are Quantitative.
  2. 1(a)(ii)2 marksIndicate, using the letters A, B, C, D and E, which variables are Qualitative.
  3. 1(a)(iii)2 marksIndicate, using the letters A, B, C, D and E, which variables are Discrete.
  4. 1(a)(iv)1 markIndicate, using the letters A, B, C, D and E, which variables are Continuous.
  5. 1(a)(v)2 marksIndicate, using the letters A, B, C, D and E, which variables Cannot be represented by a histogram.
  6. 1(b)(i)5 marksName EACH of the sampling methods G, H, I, J and K based on the given descriptions.
  7. 1(b)(ii)2 marksCalculate the value of n in sampling method H.
  8. 1(b)(iii)2 marksGiven that 120 of the 300 cans of paint are blue, determine the number of blue cans of paint in the sample selected using method J.
  9. 1(b)(iv)4 marksGive TWO differences between sampling methods G and J.
  10. 1(c)2 marksDistinguish between a 'parameter' and a 'statistic'.
  11. 2(a)(i)2 marksDetermine the median waiting time for the distribution.
  12. 2(a)(ii)3 marksCalculate the interquartile range for the distribution.
  13. 2(a)(iii)3 marksDetermine the number of persons who waited 20 minutes or more at the clinic.
  14. 2(b)(i)a)3 marksUsing groups such as 0 – 4, 5 – 9, ..., 25 – 29 and 30 – 34, draw a stem and leaf diagram.
  15. 2(b)(i)b)2 marksState the mode(s).
  16. 2(b)(i)c)2 marksCalculate the median.
  17. 2(b)(i)d)3 marksDetermine the interquartile range.
  18. 2(b)(i)e)3 marksFind the 8% trimmed mean.
  19. 2(b)(i)f)2 marksState the shape of the distribution.
  20. 2(b)(ii)2 marksWhich of the following measures of a distribution are affected by outliers: a) Mode, b) Mean, c) Median, d) Range?
  21. 3(a)(i)2 marksCalculate the probability that the number of matches won is EXACTLY two.
  22. 3(a)(ii)3 marksCalculate the probability that the number of matches won is at LEAST four.
  23. 3(b)2 marksDetermine the mean number of matches won.
  24. 3(c)7 marksIf 95 matches are selected at random, use a suitable approximation to calculate the probability that between 14 and 21 (inclusive) of the matches are won.
  25. 3(d)(i)4 marksConstruct the probability distribution table.
  26. 3(d)(ii)2 marksHence, determine P(X > 3).
  27. 3(d)(iii)5 marksCalculate E(X) and Var(X).
  28. 4(a)(i)2 marksFind P(A ∩ B).
  29. 4(a)(ii)3 marksFind P(A ∪ B).
  30. 4(a)(iii)3 marksFind P(B|A).
  31. 4(a)(iv)3 marksFind P(A' ∩ B).
  32. 4(a)(v)2 marksState, with a reason, whether the events A and B are independent.
  33. 4(b)(i)5 marksDraw a tree diagram to illustrate this information showing the probability on EACH branch.
  34. 4(b)(ii)a)3 marksCalculate the probability that a student chosen at random will arrive late.
  35. 4(b)(ii)b)4 marksCalculate the probability that a student chosen at random will travel by bus given that the student is not late.
  36. 5(a)4 marksOn the answer sheet provided, draw a scatter diagram of the data in the table.
  37. 5(b)(i)1 markCalculate x̄, the mean of x.
  38. 5(b)(ii)1 markCalculate ȳ, the mean of y.
  39. 5(b)(iii)2 marksPlot the point (x̄, ȳ) on the scatter diagram.
  40. 5(c)7 marksCalculate the equation of the regression line of y on x and draw this line on the scatter diagram.
  41. 5(d)5 marksCalculate the product-moment correlation coefficient r, and interpret the value obtained relative to the scatter diagram.
  42. 5(e)3 marksUse your regression line to estimate the actual age of a person whose age was predicted as 45 years.
  43. 5(f)2 marksComment on the reliability of the value obtained in Part (e).
  44. 6(a)3 marksState the approximate distribution of X̄ giving its parameters.
  45. 6(b)3 marksGiven that the critical value for χ² is 9.488, use your tables to determine the degrees of freedom and the significance level.
  46. 6(c)(i)2 marksFormulate null and alternate hypotheses for this test.
  47. 6(c)(ii)5 marksCalculate the expected frequencies, E, when the null hypothesis is true.
  48. 6(c)(iii)a)2 marksDetermine the number of degrees of freedom.
  49. 6(c)(iii)b)2 marksDetermine the critical region.
  50. 6(c)(iii)c)5 marksCalculate the test statistic.
  51. 6(c)(iv)3 marksState clearly, with reason, your conclusion of the test.

More CAPE Applied Mathematics Unit 1 papers