CAPE Applied Mathematics Unit 1 · 2008 · Paper 2

45 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.

1. 1(a)6 marksDraw a stem-and-leaf diagram to display the data.
2. 1(b)(i)2 marksDetermine the median of the data.
3. 1(b)(ii)4 marksDetermine the interquartile range of the data.
4. 1(b)(iii)2 marksDetermine the mean of the data.
5. 1(b)(iv)4 marksDetermine the 10% trimmed mean of the data.
6. 1(c)(i)5 marksUsing a scale of 1 cm to represent 5 cars, construct a box-and-whisker plot for this distribution.
7. 1(c)(ii)2 marksHence describe the shape of the distribution.
8. 2(a)(i)4 marksName each of the sampling methods A, B, C, and D described in the question.
9. 2(a)(ii)3 marksGiven that 112 of the 240 cars are white, calculate how many white cars are in the sample selected according to method A.
10. 2(a)(iii)2 marksState two different variables, other than colour, by which the cars could be grouped in sampling method A.
11. 2(a)(iv)2 marksCalculate the value of k in sampling method B.
12. 2(a)(v)2 marksExplain one disadvantage of sampling method C.
13. 2(b)(i)2 marksDistinguish between a population and a sample.
14. 2(b)(ii)2 marksDistinguish between a census and a sample survey.
15. 2(b)(iii)3 marksDistinguish between a parameter and a statistic.
16. 2(c)3 marksJustifying the use of the sample survey in the given example, briefly describe one example where a sample survey is carried out, as opposed to a census.
17. 2(d)(i)1 markState the value of a parameter from the data given.
18. 2(d)(ii)1 markState the value of a statistic from the data given.
19. 3(a)(i)3 marksFind the probability that a randomly selected person does NOT prefer radio station A.
20. 3(a)(ii)3 marksFind the probability that a randomly selected person is a female OR prefers radio station B.
21. 3(a)(iii)3 marksFind the probability that a randomly selected person is a male AND prefers radio station C.
22. 3(a)(iv)4 marksFind the probability that a randomly selected person prefers station D, given that the person is a male.
23. 3(b)(i)2 marksCalculate the probability that the first person selected is a female.
24. 3(b)(ii)5 marksCalculate the probability that each person selected is of a different sex.
25. 3(b)(iii)5 marksCalculate the probability that both persons selected prefer the same radio station.
26. 4(a)5 marksShow that the probability of a randomly selected bottle containing more than 99.8 ml of pepper sauce is approximately 0.516.
27. 4(b)6 marksEighty-one per cent of the bottles contain less than k ml of pepper sauce. Calculate the value of k.
28. 4(c)(i)7 marksCalculate the probability that at least 1 of these 7 bottles contains more than 99.8 ml of pepper sauce.
29. 4(c)(ii)7 marksDetermine the expected number of these 7 bottles that contain more than 101 ml of pepper sauce.
30. 5(a)6 marksOmitting the continuity correction, calculate an approximate 97% confidence interval for p.
31. 5(b)(i)4 marksUsing symbols only, state appropriate null and alternative hypotheses.
32. 5(b)(ii)2 marksJustify the use of a normal distribution approximation in this large-sample test of a binomial proportion.
33. 5(b)(iii)4 marksState the critical region(s) for this test.
34. 5(b)(iv)6 marksUsing an appropriate continuity correction, calculate the test statistic.
35. 5(b)(v)3 marksSupporting your answer with a reasoned argument, state the conclusion that may be drawn from the hypothesis test.
36. 6(a)4 marksOn the answer sheet provided, plot a scatter diagram for the data.
37. 6(b)(i)2 marksCalculate the product-moment correlation coefficient, r, for these data.
38. 6(b)(ii)2 marksInterpret the value obtained for r.
39. 6(c)(i)3 marksCalculate (\bar{x}, \bar{y}), where \bar{x} is the mean of x and \bar{y} is the mean of y.
40. 6(c)(ii)1 markPlot the coordinates (\bar{x}, \bar{y}) on the scatter diagram.
41. 6(d)(i)5 marksDerive the equation of the regression line y on x in the form y = a + bx.
42. 6(d)(ii)2 marksPlot this regression line on the scatter diagram.
43. 6(e)2 marksUse your regression line y on x to estimate the height of an adult whose mass is 60 kg.
44. 6(f)2 marksThe regression line y on x is used to estimate the height of an adult whose mass is 82 kg. Giving a reason for your answer, state whether such an estimate would be reliable.
45. 6(g)2 marksGiving a reason for your answer, state which one of the regression lines, y on x OR x on y, should be used to estimate the mass of an adult whose height is 156 cm.