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CAPE Applied Mathematics Unit 1 · 2022 · Paper 2

56 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 markThe height of students in a class
  2. 1(a)(ii)1 markThe number of laptop computers owned by households in a community
  3. 1(b)(i)1 markThe buses owned by Excel Express transport company
  4. 1(b)(ii)1 markThe students sent to represent a school at track meet
  5. 1(c)(i)1 markThe 700 persons who attended a reggae concert on the weekend were asked to name their favourite artiste.
  6. 1(c)(ii)1 mark700 of the persons who attended a mass gathering in the city were asked to name their preferred political party.
  7. 1(d)(i)2 marksIf the homeowner paid $60 for electricity, determine the total amount of money paid for bills.
  8. 1(d)(ii)2 marksCalculate the amount of money paid for the telephone bill.
  9. 1(e)(i)5 marksDraw a histogram on the grid provided to illustrate the information in the frequency table.
  10. 1(e)(ii)3 marksEstimate the mode of the marks. You must show lines on the histogram drawn in (e)(i).
  11. 1(e)(iii)2 marksOn the histogram drawn in (e)(i), draw a frequency polygon.
  12. 1(e)(iv)1 markBy observing the frequency polygon, determine the shape of the distribution.
  13. 1(e)(v)2 marksState whether the students performed better in the Mathematics examination or the English examination. Give ONE reason related to the skewness of the data presented in BOTH histograms to support your answer.
  14. 1(e)(vi)2 marksA student earned the following marks for 5 class activities in Mathematics: 40, 30, 40, 70, 60. Determine how many marks the student needs to earn for the 6th class activity in order to raise the student's average to 50.
  15. 2(a)(i)4 marksComplete the cumulative frequency row in the table provided.
  16. 2(a)(ii)5 marksOn the grid provided on page 9, draw the cumulative frequency curve to represent the information in the table.
  17. 2(a)(iii)2 marksDetermine the number of candidates who failed the exam if the pass mark was 60. You must show lines on the cumulative frequency curve drawn in (a)(ii).
  18. 2(a)(iv)3 marksDetermine the minimum mark required to score a grade A if 10 candidates earned A's in the examination. You must show lines on the cumulative frequency curve drawn in (a)(ii).
  19. 2(a)(v)3 marksCalculate the mean score.
  20. 2(b)(i)1 markDetermine the median score.
  21. 2(b)(ii)1 markDetermine how many students scored more than 60.
  22. 2(b)(iii)3 marksCalculate the interquartile range.
  23. 2(b)(iv)3 marksConstruct a box-and-whisker diagram to represent the data in the stem-and-leaf plot.
  24. 3(a)(i)2 marksIf an individual is selected at random, find the probability of selecting a person who has primary education.
  25. 3(a)(ii)2 marksFind the probability of selecting a woman, given that she has tertiary education.
  26. 3(a)(iii)2 marksFind the probability of selecting a person with secondary education, given that the person is a male.
  27. 3(a)(iv)4 marksDetermine if secondary education is independent of gender.
  28. 3(b)3 marksA company manufactures three brands of vehicles, A, B and C. The percentage of customers that purchases each of these vehicles is 35%, 50% and 15% respectively. Given that a customer meets in an accident, the…
  29. 3(c)(i)3 marksCalculate the value of k.
  30. 3(c)(ii)3 marksSketch the graph of f(x).
  31. 3(c)(iii)2 marksDetermine the upper quartile.
  32. 3(c)(iv)4 marksDetermine P(1/2 <= X <= 2).
  33. 4(a)(i)3 marksDetermine the probability of getting at LEAST nine of the intended numbers when ten independent calls are made.
  34. 4(a)(ii)2 marksCalculate the mean number of intended numbers and the variance when ten independent calls are made.
  35. 4(a)(iii)6 marksUse a suitable approximation to find the probability of FAILING to get the intended number on at least 10 but NOT more than 20 of the calls.
  36. 4(b)(i)4 marksIf it was found that 0.19% of the computers on a particular occasion had a repair time that was less than 24 hours, show that sigma = 5.5 (to one decimal place).
  37. 4(b)(ii)3 marksFind the probability that the repair time is MORE than 35 hours.
  38. 4(b)(iii)3 marksCompuFix wishes to state in its advertisements that at LEAST 98% of all computers will be repaired in less than a certain number of hours. Determine the SMALLEST integer that could truthfully be used in the…
  39. 4(b)(iv)4 marksIf a repair time is exceptionally long, CompuFix pays compensation to the customer: US$250 if the repair time is between 50 and 55 hours. Determine the expected amount of compensation.
  40. 5(a)(i)1 markState ONE reason why the population proportion, p, cannot be stated as 35%, although the sample size is large.
  41. 5(a)(ii)2 marksDetermine if the required conditions for the construction of a confidence interval for p are satisfied.
  42. 5(a)(iii)3 marksIdentify the sampling distribution of p-hat. You must state the specific parameters of the sampling distribution.
  43. 5(a)(iv)4 marksConstruct a two-sided 90% confidence interval for p.
  44. 5(a)(v)2 marksInterpret the obtained confidence interval in the context of the problem.
  45. 5(a)(vi)a4 marksTest the null hypothesis H_0 : p = 0.40 against the alternative H_1 : p > 0.40 at the significance level of alpha = 0.05: Calculate the test statistics.
  46. 5(a)(vi)b1 markDetermine the critical value.
  47. 5(a)(vi)c1 markDetermine the critical region.
  48. 5(a)(vi)d2 marksState a valid conclusion for the test. Give ONE reason for the conclusion stated.
  49. 5(b)5 marksA scientist collected a random sample of 100 measurements from a normal population with a mean of 500 and a standard deviation of 80. Determine the probability that the scientist will get a sample mean within the values…
  50. 6(a)4 marksCalculate the gradient of the regression line y on x.
  51. 6(b)4 marksCalculate the intercept of the regression line.
  52. 6(c)2 marksInterpret the value of the gradient in the context of the data.
  53. 6(d)2 marksUsing the obtained regression equation (y = a + bx), determine the score of an athlete who trained 64 hours for the competition.
  54. 6(e)3 marksCalculate the correlation coefficient.
  55. 6(f)3 marksInterpret the value of the correlation coefficient calculated in (e).
  56. 6(g)7 marksOn the grid provided on page 27, plot a scatter diagram to represent the information in the table. Draw the regression line on the same grid.

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